ANALYSIS OF WILDLIFE ABUNDANCE ESTIMATION METHODS USING...
Transcript of ANALYSIS OF WILDLIFE ABUNDANCE ESTIMATION METHODS USING...
ANALYSIS OF WILDLIFE ABUNDANCE ESTIMATION METHODS USING REAL AND SIMULATED DATA
By
SAIF Z. NOMANI
A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
2007
1
© 2007 Saif Z. Nomani
2
To my sister, Samia Nomani
3
ACKNOWLEDGMENTS
I thank my advisors M. Oli, R. Carthy, and J. Nichols for their guidance and support. I
thank A. Ozgul, J. Hostetler, K. Aaltonen, A. Singh, I. Ismail, and A. Jaffery for insightful
comments on this study and for assistance with statistical analysis of results. Special thanks go to
L. Thomas, S. Buckland, N. Adams, H. Sultan, M. Christman, and M. Sitharam for assistance
with the simulation program; and to K. Miller, E. Lang, E. Cantwell, J. Martin and M. Voight for
data collection. Thanks go to S. Coates and the Ordway-Swisher Biological Station, University
of Florida for use of the study area and for habitat information. I thank my parents, C. Williams,
and my friends from New Jersey for their support and encouragement. The Department of
Wildlife Ecology and Conservation at the University of Florida and U.S. Army Corps of
Engineers-Construction Engineering Research Laboratory (ACOE-CERL) provided funding for
this study. Funding and logistical support was also provided by the Florida Cooperative Fish &
Wildlife Research Unit at the University of Florida.
4
TABLE OF CONTENTS page
ACKNOWLEDGMENTS ...............................................................................................................4
LIST OF TABLES...........................................................................................................................7
LIST OF FIGURES .........................................................................................................................8
ABSTRACT.....................................................................................................................................9
CHAPTER
1 INTRODUCTION ..................................................................................................................11
2 COMPARISON OF METHODS FOR ESTIMATING ABUNDANCE OF GOPHER TORTOISES...........................................................................................................................13
Introduction.............................................................................................................................13 Methods ..................................................................................................................................15
Study Area .......................................................................................................................15 Line Transect Method......................................................................................................16
Pilot study.................................................................................................................16 Data collection..........................................................................................................16 Data analysis ............................................................................................................17
Total Count, Sample Count, and Double Observer Methods..........................................18 Data collection..........................................................................................................18 Data analysis ............................................................................................................19
Burrow Occupancy Rates ................................................................................................20 Data collection..........................................................................................................20 Data analysis ............................................................................................................21
Costs ................................................................................................................................22 Results.....................................................................................................................................22
Line Transect ...................................................................................................................22 Total Count, Sample Count, and Double Observer .........................................................23 Burrow Occupancy Rates ................................................................................................24 Abundance of Gopher Tortoises......................................................................................24 Costs ................................................................................................................................24
Discussion...............................................................................................................................25 Comparison of Abundance Estimation Methods.............................................................25 Burrow Occupancy..........................................................................................................27 Costs of Implementation..................................................................................................28
Conclusion ..............................................................................................................................29
5
3 ACCURACY OF ESTIMATES OF ABUNDANCE BASED ON THE LINE TRANSECT METHOD: INFLUENCE OF SPATIAL DISTRIBUTION OF OBJECTS, AND LENGTH, LAYOUT, AND NUMBER OF TRANSECTS .........................................36
Introduction.............................................................................................................................36 Methods ..................................................................................................................................38
Simulation Inputs.............................................................................................................38 Spatial Distribution and Density of Objects ....................................................................38 Layout Pattern of Line Transects ....................................................................................39 Total Length of Line Transects .......................................................................................40 Number of Transects .......................................................................................................40 Data Collection and Analysis ..........................................................................................41
Results.....................................................................................................................................42 Overall Results ................................................................................................................42 Clumped Distribution ......................................................................................................43
Effects of object density ...........................................................................................43 Effects of object density and transect length............................................................44 Effects of object density and transect layout............................................................44 Effects of object density and transect number .........................................................44 Effects of object density, and transect length, layout, and number..........................45
Random Distribution .......................................................................................................45 Effects of object density ...........................................................................................45 Effects of object density and transect length............................................................46 Effects of object density and transect layout............................................................46 Effects of object density and transect number .........................................................46 Effects of object density, and transect length, layout, and number..........................47
Uniform Distribution .......................................................................................................47 Effects of object density ...........................................................................................47 Effects of object density and transect length............................................................48 Effects of object density and transect layout............................................................48 Effects of object density and transect number .........................................................48 Effects of object density, and transect length, layout, and number..........................49
Discussion...............................................................................................................................49 Conclusion ..............................................................................................................................53
4 CONCLUSION.......................................................................................................................73
APPENDIX
OVERALL RESULTS ...........................................................................................................76
LIST OF REFERENCES...............................................................................................................81
BIOGRAPHICAL SKETCH .........................................................................................................87
6
LIST OF TABLES
Table page 1-1 Comparison of models fitted to line transect data .............................................................31
1-2 Overall summary of estimates of abundance of gopher tortoise burrows for each abundance estimation method in two strata (G5 and C3/C7), Ordway-Swisher Biological Station, Florida .................................................................................................32
1-3 Estimated number of gopher tortoises in stratum C3/C7, Ordway-Swisher Biological Station, Florida...................................................................................................................33
2-1 Density estimates by object spatial distribution and density .............................................55
A-1 Simulation study results.....................................................................................................76
7
LIST OF FIGURES
Figure page 1-1 Map of Ordway-Swisher Biological Station in north-central Florida, USA, depicting
stratum G5 and stratum C3/C7, and locations of line transects and plots .........................34
1-2 Effects of proportion of plots sampled using sample count method on estimates of abundance in two strata (G5 and C3/C7), Ordway-Swisher Biological Station in north-central Florida ..........................................................................................................35
2-1 Examples of simulated spatial distributions of objects with a density of 2 objects ha-1....56
2-2 Transect layout patterns with objects simulated in a random spatial distribution with a density of 2 objects ha-1, and a transect density of 10 m ha-1..........................................58
2-3 Effect of transect length on accuracy of estimates of density for a given object spatial distribution and object densities ranging from 2 objects ha-1 to 10 objects ha-1................61
2-4 Effect of transect length on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha-1 to 10 objects ha-1................63
2-5 Effect of transect layout on accuracy of estimates of density for a given object spatial distribution and object densities ranging from 2 objects ha-1 to 10 objects ha-1................65
2-6 Effect of transect layout on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha-1 to 10 objects ha-1................67
2-7 Effect of transect number on accuracy of estimates of density for a given object spatial distribution and object densities ranging from 2 objects ha-1 to 10 objects ha-1 ....69
2-8 Effect of transect number on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha-1 to 10 objects ha-1................71
8
Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
ANALYSIS OF WILDLIFE ABUNDANCE ESTIMATION METHODS USING REAL AND SIMULATED DATA
By
Saif Z. Nomani
August 2007
Chair: Madan K. Oli Cochair: Raymond R. Carthy Major: Wildlife Ecology and Conservation
For most wildlife species, multiple abundance estimation methods are available and the
choice of a method should depend on cost and efficacy. I field-tested the cost and efficacy of line
transect, total count, sample count, and double observer methods for estimating abundance of
gopher tortoise (Gopherus polyphemus) burrows in two habitats that differed in vegetation
density (sparse and dense) at the Ordway-Swisher Biological Station in north-central Florida.
In the dense vegetation stratum, the density of burrows estimated using the line transect
method (8.58 ± 0.94 burrows ha-1) was lower than that obtained from total count method (11.33
burrows ha-1). In the sparse vegetation stratum, the estimated burrow density using the line
transect method (11.32 ± 1.19 burrows ha-1) was closer to the burrow density using the total
count method (13.00 burrows ha-1). The density of burrows estimated using the double observer
method was identical to that obtained from the total count method in dense vegetation stratum,
but slightly greater than that obtained from the total count method in sparse vegetation stratum.
The density of burrows estimated using the sample count method varied widely depending on the
proportion of sample plots sampled in both strata. The cost of sampling as well as estimates of
burrow density varied with habitat type. The line transect method was the least costly of the
9
methods. Using burrow cameras and patch occupancy modeling approach, I also estimated the
probability of burrow occupancy by gopher tortoises (active: 0.50 ± 0.09; inactive: 0.04 ± 0.04),
and used these values to estimate abundance of gopher tortoises. Using estimates of burrow
abundance based on the line transect method, the density of gopher tortoises was 2.75 ± 0.29 ha-
1 in the sparse vegetation stratum.
I then conducted a simulation study to investigate how the spatial distribution and density
of objects, and the total length, layout, and number of transects influence the accuracy of
estimates of abundance obtained from the line transect method. Using MATLAB I generated
objects in different spatial distributions (clumped, random, uniform) with different object
densities in a simulated study area. I varied the length, layout and number of transects used.
The line transect method worked best for a random distribution of objects; root mean
squared error between the estimated density and the true density was 8.5% of the true density.
For all spatial distributions of objects, increasing transect length increased the accuracy of
estimates of abundance. For a clumped distribution, transect layout and transect number did not
seem to significantly influence accuracy of estimates of abundance. For a random distribution,
transect number did not seem to significantly influence accuracy of estimates of abundance. For
a uniform distribution, when transect layout was random, transect number and transect length did
not seem to significantly influence accuracy of estimates of abundance. For a clumped
distribution I recommend using a higher transect length. For a random distribution I recommend
using a systematic transect layout as this provided slightly greater accuracy. For a uniform
distribution I recommend using a random transect layout as this provided substantially greater
accuracy.
10
CHAPTER 1 INTRODUCTION
Estimates of abundance are essential for monitoring the population status and recovery
progress of threatened and endangered species (Seber 1982, Williams et al. 2002). For most
wildlife species, multiple abundance estimation methods are available, including line transect,
mark-recapture, and double observer (Krebs 1999, Seber 1982, Williams et al. 2002) and the
choice of a method should depend on cost and efficacy. Using the gopher tortoise (Gopherus
polyphemus) as a test species, I compared the cost and efficacy of different abundance estimation
methods.
The gopher tortoise is a species of conservation concern in the southeastern US. Gopher
tortoises spend much of their time in the shelter of self-constructed underground burrows
(Wilson et al. 1994), and direct observation of tortoises is difficult; consequently researchers
typically estimate abundance of burrows, and frequently use it as an index of tortoise abundance
(Cox et al. 1987, Smith et al. 2005, McCoy et al. 2006).
However, it is not easy to estimate abundance of animals (Seber 1982). Two key issues
involved in abundance estimation are detectability and spatial sampling (Royle and Nichols
2002, Williams et al. 2002). Most sampling methods do not result in the detection of all animals
present in a study area so one must estimate detectability (the probability of observing an animal
or object if it is present). Similarly, a sampling method often cannot be applied to the entire study
area due to time and resource limitations, and typically a fraction of the area is sampled.
Abundance can then be estimated considering detectability and spatial sampling simultaneously.
These issues apply to the estimation of gopher tortoise abundance as well. An additional
problem involved in the estimation of gopher tortoise abundance is that not every burrow is
occupied by tortoises. Thus, an important issue relevant to gopher tortoise abundance estimation
11
is the burrow occupancy rate (probability that a burrow is occupied by a gopher tortoise)
(Diemer 1992). Estimates of abundance of gopher tortoises are then obtained by applying burrow
occupancy rates to estimates of burrow abundance.
Methods of estimating abundance of gopher tortoise burrows vary with respect to efficacy
and cost, and given the pivotal role of gopher tortoises in ecosystems where they are found, it is
essential to use rigorous methods for estimating and monitoring gopher tortoise abundance. I
conducted a field study to investigate the cost and efficacy of line transect, total count, sample
count, and double observer methods for estimating gopher tortoise burrow abundance, and to
estimate the probability of burrow occupancy by gopher tortoises using burrow cameras and the
patch occupancy modeling approach in the Ordway-Swisher Biological Station, Florida.
I determined that the line transect method is an effective method for estimating abundance
of gopher tortoise burrows, however, accuracy of estimates of abundance obtained from the line
transect method may vary depending on the spatial distribution and density of objects, and the
length, layout, and number of line transects. The spatial distribution and density of objects
cannot be changed, however it is possible to design a study by varying the length, layout, and
number of transects in order to maximize accuracy of estimates of abundance for a given spatial
distribution and density of objects.
I used a simulation-based approach in MATLAB (Mathworks 2006) to determine the
influence of length, layout and number of transects on accuracy of estimates of abundance for
different object spatial distributions and density levels.
12
CHAPTER 2 COMPARISON OF METHODS FOR ESTIMATING ABUNDANCE OF GOPHER
TORTOISES
Introduction
One of the most relevant questions in wildlife management is: how many are there?
Indeed, estimates of abundance are a prerequisite for listing or delisting of a species, and for
monitoring recovery progress (Seber 1982, Cassey and Mcardle 1999, Williams et al. 2002).
Furthermore, estimates of abundance are needed for understanding density-dependent
relationships, for parameterizing and evaluating population models, and for formulating or
evaluating management programs (Williams et al. 2002).
The gopher tortoise (Gopherus polyphemus) is a species of conservation concern in the
southeastern US. It is federally listed as a threatened species in the western portion of its range
(western Alabama, Mississippi, and Louisiana) (Lohoefener and Lohmeier 1984, Federal
Register 1987). In Florida, gopher tortoise populations have been declining for some time
(Auffenberg and Franz 1982, Schwartz and Karl 2005), and the species has recently been
approved for reclassification to Threatened pending approval of a species management plan
(FFWCC 2006). Several state and federal agencies in the gopher tortoise range are charged with
monitoring their status and population trends which require reliable estimates of abundance.
Estimating abundance of gopher tortoises is a two step process: estimation of burrow
abundance and estimation of burrow occupancy rates. Gopher tortoises spend much of their time
in the shelter of self-constructed underground burrows (Wilson et al. 1994), and direct
observation of tortoises is difficult. These burrows are relatively easy to see due to their half-
moon shape and large mound of sand (commonly referred to as the apron) at the burrow
entrance. Because gopher tortoises are rarely seen outside their burrows, researchers typically
estimate abundance of burrows, and frequently use it as an index of tortoise abundance (Cox et
13
al. 1987, Smith et al. 2005, McCoy et al. 2006). The most commonly used methods for
estimating the abundance of gopher tortoise burrows include line transect, total count, and
sample count methods (Doonan 1986, Mann 1993, Epperson 1997, Doonan and Epperson 2001).
A second issue involved in the estimation of gopher tortoise abundance is that not every
burrow is occupied by tortoises; there are typically more burrows than gopher tortoises and the
number of burrows does not always correspond to the number of tortoises (McRae et al. 1981,
Diemer 1992, Smith et al. 1997, Eubanks et al. 2003, McCoy et al. 2006). Thus, an important
issue relevant to gopher tortoise abundance estimation is the burrow occupancy rate (probability
that a burrow is occupied by a gopher tortoise) (Diemer 1992). The estimates of abundance of
gopher tortoises are then obtained by applying burrow occupancy rates to estimates of burrow
abundance. Auffenberg and Franz (1982) reported that 61.4% of all burrows (active and inactive)
were occupied in their study. Some studies have used this or other similar values (e.g., Ashton
and Ashton (in press)) as a “correction factor” to convert the burrow abundance into an estimate
of tortoise abundance (Kushlan and Mazotti 1984, Doonan 1986, Doonan and Epperson 2001,
FFWCC 2006, Gregory et al. 2006). Burrow occupancy rates vary over time and space, and
unreliable estimates of occupancy rates can lead to erroneous estimates of gopher tortoise
abundance (Burke and Cox 1988, Breininger et al. 1991, McCoy and Mushinsky 1992, Moler
and Berish 2001).
The methods of estimating abundance of gopher tortoise burrows vary with respect to
efficacy and cost, and rigorous field tests of these methods are needed to evaluate the efficacy
relative to costs. Moreover, recent advances in the patch occupancy modeling framework
(Mackenzie et al. 2002, Mackenzie et al. 2006) offer the possibility of statistically rigorous
estimates of burrow occupancy rates which were not possible previously.
14
My objectives were to 1) investigate the cost and efficacy of line transect, total count,
sample count, and double observer methods for estimating gopher tortoise burrow abundance,
and 2) estimate the probability of burrow occupancy by gopher tortoises using burrow cameras
and the patch occupancy modeling approach in the Ordway-Swisher Biological Station, Florida.
I then combined estimates of burrow abundance with estimates of the probability of burrow
occupancy to estimate abundance of gopher tortoises.
Methods
Study Area
This study was conducted in the Ordway-Swisher Biological Station
(http://www.ordway.ufl.edu) located in Putnam County, Florida (29°41' N and 82° W) (Figure
1-1) in the fall of 2005. The Biological Station encompasses approximately 4000 ha, and offers
over 1600 ha of potential gopher tortoise habitat with old fields, pine plantations, and sand hill
habitats of several burn frequency categories.
I selected a portion of the Ordway-Swisher Biological Station and stratified it into two
strata (G5, and C3/C7) based on habitat maps, burn history and visual observation. Stratum G5,
comprising of management unit G5, covered an area of approximately 110.3 ha, and was last
burned in 2003 (two years before this study was conducted). Stratum C3/C7, comprising of
management units C3 and C7, covered an area of approximately 116.5 ha, and was last burned in
Feb 2005 (same year as this study). Due to the recent burn, stratum C3/C7 was more open with
less dense vegetation than stratum G5 (R. R. Carthy, unpublished data). The study was
conducted in two strata to investigate whether the probability of burrow detection, burrow
abundance, and cost of the methods differed between the sandhill habitats with relatively high
versus low vegetation density (Buckland et al. 2001).
15
16
Line Transect Method
TPilot study
I conducted a pilot study in the Ordway-Swisher Biological Station to estimate the
transect length needed for robust estimates of burrow abundance using methods described in
Buckland et al. (2001). I estimated that, to achieve a coefficient of variation of ≤15% I needed to
sample approximately 8 km of total transects in each stratum.
Data collection
I placed 8 km of transects in each stratum systematically at predetermined distances. I
allowed sufficient spacing (30 to 60 m) between transects to ensure that burrows would not be
double-counted, while providing an adequate sample size for statistically robust results
(Buckland et al. 2001). I oriented transects so that they did not run parallel to roads or other
linear topographical features (Buckland et al. 2001, Williams et al. 2002) because they can affect
the distribution of gopher tortoises. I placed flags and recorded GPS coordinates at the origin and
end of all transects.
A team of observers, consisting of an observer and an assistant, walked along each transect
line. The observer (Observer 1) identified all burrows detected and the assistant then measured
the perpendicular distance from the transect line to the burrow (Buckland et al. 2001, Williams et
al. 2002). Perpendicular distance was measured from the transect line to either the burrow's
mouth or the beginning of the burrow apron, whichever was closest to the transect line. The
assistant also recorded the GPS coordinates for the burrow, measured the burrow width 50 cm
inside the burrow, and classified each burrow according to width as juvenile (<14 cm wide), sub-
adult (14 to 23 cm wide), and adult (>23 cm) (Alford 1980, Smith 1992). The observer classified
each burrow into one of two burrow status categories: active and inactive. Active burrows had
burrow aprons and entrances with little or no debris, and had evidence of tortoise occupation.
Inactive burrows, on the other hand, had debris and leaf litter on the apron, at the mouth, and in
the burrow tunnel. In some cases burrow mouths were degraded so that they did not have the
classic, half-moon tortoise shape.
The assistant did not participate in detecting burrows but simply collected and recorded
data for burrows detected by the lead observer. All detected burrows were temporarily marked
with a numbered tag so as to avoid double counting of burrows. Tags were hidden from view of
the second observer, but were placed in a consistent location at burrows so they were easily
located by the second observer's assistant upon close examination of the burrows detected by the
second observer.
Once the first team completed sampling transects I used a second team to collect data in
stratum G5 using the same protocol. These data were used to test for inter-observer variability in
detection probability and estimates of burrow abundance.
One critical assumption of line transect sampling is that all objects located on the line
transect are seen and recorded (Buckland et al. 2001, Williams et al. 2002). Gopher tortoise
burrows are conspicuous, and are associated with mounds that are hard to miss from a close
distance (Lohoefener 1990, Doonan and Epperson 2001). I am, therefore, confident that all
tortoise burrows that were directly on the line were detected.
Data analysis
I used Program DISTANCE (Thomas et al. 2003) to analyze the line transect data to
estimate the abundance of gopher tortoise burrows. The program provides a flexible framework
for parameterization and comparison of alternative models (Buckland et al. 2001). I ran several
different parametric models, each consisting of a key function and a series adjustment term
(Buckland et al. 2001), using Program DISTANCE. I used Akaike's Information Criterion
17
( AIC ) values for model comparison and selected the model with the lowest AIC (Burnham and
Anderson 2002). I excluded 5% of the observations (furthest from the line) from the analysis to
remove possible outliers Buckland et al. (2001).
Of the parametric models discussed above, I selected the most parsimonious model that
allowed covariates and tested for the effect of the width of the burrow entrance (in cm) on the
detection probability for Observer 1 in both strata. I then compared the AIC values for models
with and without burrow width as a covariate to determine the effect of the burrow width on
estimates of detection probability and density. Using the same procedure, I used observer as a
covariate to test for the inter-observer variability in detection probability in stratum G5. Data for
the two observers were pooled together to test for inter-observer variability, and the resulting
AIC value was compared to the sum of the AIC values obtained from the separate analyses of
data collected by the two observers without observer as a covariate (Buckland et al. 2001).
Total Count, Sample Count, and Double Observer Methods
Data collection
I conducted a total count of burrows after line transect data had been collected. I selected
six 1-ha plots in each stratum. I overlaid these plots over portions of each stratum where line
transect data were collected. The four corners of the plots were flagged and their coordinates
were determined using a GPS unit. I further subdivided the plots into ten 20x50 m subplots. Each
plot was comprehensively searched for burrows by two observers so detectability could be
estimated (Nichols et al. 2000, Williams et al. 2002). Initially, I used three observers; however,
the third observer consistently failed to detect any additional burrows so I continued with two
observers. The observers recorded all pertinent information for detected burrows. Sample count
was the total count in a sample of plots.
18
I implemented the dependent double observer method following Nichols et al. (2000) and
Williams et al. (2002). Each of the 20x50 m subplots was comprehensively searched for burrows
by two dependent observers (primary observer and secondary observer, where the secondary
observer is aware of the burrows detected by the primary observer). The primary observer
surveyed the plots, and flagged and called out burrows detected to the secondary observer. The
secondary observer recorded the information and proceeded to survey the plots to detect
additional burrows (Nichols et al. 2000). At the completion of sampling of each subplot, the data
were comprised of burrows detected by the primary observer, and burrows missed by the
primary observer but detected by the secondary observer. Observers alternated roles on
consecutive subplots, as recommended by Nichols et al. (2000).
I conducted the total count, sample count and double observer methods on the same six
1-ha plots and the field methods for the three methods were identical. I used the data collected
for the total count method for the sample count calculations by selecting a subset of plots where
total counts were conducted. This has been described in detail in the next section.
Data analysis
The estimated abundance of burrows using total count was the total number of burrows
detected by both observers. Estimates of cost and abundance obtained from the sample count
method can vary depending on the proportion of total area sampled, spatial distribution of
burrows and the choice of the sample plots. Thus, I evaluated the effects of selecting different
proportions of plots on the estimate of burrow abundance by utilizing data collected for the total
count method. I selected all possible combinations of 3, 4, and 5 out of the 6 plots; each of these
plots was thoroughly surveyed by two observers as described previously. The number of burrows
19
20
in the sampled plots was then extrapolated to obtain an estimate of the number of burrows to the
entire 6-ha area sampled. Sampling a 100% of the plots (6 out of 6) is the total count.
I used Program DOBSERV (Hines 2000) to analyze the double observer data. The overall
detectability was estimated as (Nichols et al. 2000):
( )12 21 22 11ˆ 1p x x x x= − (1-1) Where p̂ = estimate of overall detectability of both observers, 11x = number of burrows detected by observer 1 in a primary role, 21x = number of burrows detected by observer 2 in a primary role, 12x = number of additional burrows detected by observer 1 in a secondary role, and
22x = number of additional burrows detected by observer 2 in a secondary role. This estimate of overall detectability ( p̂ ) was used to obtain the estimate for the
population size for the sampling area ( N̂ ) by dividing the total number of burrows detected by
all observers ( ..x ) by p̂ (Nichols et al. 2000). The standard error ( ˆ( )SE N ) and the 95%
confidence interval for N̂ were estimated using Program DOBSERV.
I divided N̂ obtained from each method by the area of the study site sampled to estimate
the burrow density ( D̂ ) (burrows haP
-1P). I multiplied D̂ by the area of the stratum to obtain an
estimate of burrow abundance in each stratum.
Burrow Occupancy Rates
Data collection
To estimate the probability that a burrow is occupied by a gopher tortoise (burrow
occupancy rate) I conducted burrow occupancy surveys in management unit C3 of stratum
C3/C7 (Figure 1-1). I examined a sub-sample of burrows from C3 that were marked during the
total counts with a burrow camera on three consecutive days (beginning either in the morning or
early afternoon) to determine occupancy status. This sub-sample contained both active and
inactive burrows. I used the Econo GeoVision, Jr. camera system designed by Marks Products,
Inc. (Williamsville, Virginia) for use in borehole and water well systems. I sanitized the
21
equipment with diluted Nolvasan® after examining each burrow, to minimize the risk of disease
transmission. I classified the burrows as “empty” if the operator was certain that she/he had
reached the end of the burrow and no gopher tortoise was present. Burrows were considered
“occupied” only if the operator could identify a gopher tortoise with absolute certainty. Burrow
occupancy was considered "undetermined" if the operator could not maneuver the camera to the
end of the burrow due to burrow architecture (e.g., dramatic turns or tunnel size) or debris (e.g.,
leaf litter and/or sand). Burrows with undetermined occupancy status were not used in analysis
of occupancy rates.
Data analysis
Occupancy data were collected using a burrow camera and a statistically robust occupancy
modeling approach (Mackenzie et al. 2002) implemented in Program MARK (White and
Burnham 1999) to estimate detection probability and burrow occupancy rate. Occupancy survey
was conducted as described previously. A burrow was considered occupied by a tortoise (coded
1) if the observer was certain that a tortoise was present; it was considered unoccupied (coded 0)
if the observer was certain the burrow was not occupied. Using these occupancy data collected
over 3 sampling occasions, I fitted the patch occupancy model (Mackenzie et al. 2002). I used
AIC to select the most parsimonious model. Using the most parsimonious model identified, I
tested for the effect of the width of the burrow entrance (in cm) on the detection probability and
the occupancy rate by modeling the logit of each rate as a linear function of burrow width. If the
95% confidence interval for the slope parameter (β ) did not include 0, the relationship was
considered statistically significant (Williams et al. 2002).
22
Costs
I recorded the time taken for data collection for each method in person-hours. The amount
of time needed for analysis of data varied widely among individuals depending on mathematical
background, computer skills, and learning curves, and thus are not reported. The costs of
equipment required for analysis may also vary tremendously and thus are not reported.
Results
Line Transect
A total of 28 line transects was placed in stratum G5 with a total length of 8025 m.
Observer 1 detected 163 burrows and Observer 2 detected 150 burrows. For Observer 1, the
model with the lowest AIC was Uniform Cosine (Table 1-1). Based on this model, the estimated
burrow density (± SE ) was 8.58 ± 0.94 burrows ha P
-1P ( cv =11.0%). For Observer 2, the model
with the lowest AIC was also Uniform Cosine (Table 1-1). Based on this model, the estimated
burrow density was 8.49 ± 0.98 burrows ha P
-1P ( cv =11.5%) (Table 1-2).
A total of 16 line transects was placed in stratum C3/C7 with a total length of 8003 m. The
first observer (Observer 1) detected 262 burrows. For Observer 1, the models with the lowest
AIC were Hazard Rate Cosine and Hazard Rate Simple Polynomial (Table 1-1). The results for
these two models were identical, so I selected the Hazard Rate Cosine model. Based on this
model, the estimated burrow density was 11.32 ± 1.19 burrows ha P
-1P ( cv =10.5%) (Table 1-2). I
did not analyze the line transect data for Observer 2 for stratum C3/C7 because Observer 2 did
not collect data independently of Observer 1.
In stratum G5, I evaluated the effect of burrow width on detection probability for Observer
1 using the Half Normal Cosine model. The difference between the probability of detecting
smaller burrows and the probability of detecting larger burrows was not substantial ( AIC for
model with burrow width as a covariate: 475.86; AIC for model without burrow width as a
23
covariate: 477.87). Consequently, estimates of burrow density were very similar (with burrow
width as a covariate: 8.99 ± 1.06 burrows ha P
-1P; without burrow width as a covariate:
8.58 ± 0.94 burrows haP
-1P). In stratum C3/C7, I evaluated the effect of burrow width on detection
probability for Observer 1 using the Hazard Rate Cosine model. Although the burrow width
seemed to influence detection probability ( AIC for model with burrow width as covariate:
867.97; AIC for model without burrow width as covariate: 957.48), the difference in the
estimate of burrow density was not substantial (with burrow width as covariate: 11.26 ± 0.84
burrows haP
-1P; without burrow width as covariate: 11.32 ± 1.19 burrows haP
-1P).
Additionally, in stratum G5, I evaluated inter-observer variability in detection probability
using pooled data collected by the two independent observers and the Half Normal Cosine
model. There seemed to be no difference in detection probability between the two observers
( AIC for model with pooled observations: 1871.19; sum of AIC values for models analyzed
separately for Observer 1 and Observer 2: 1871.21), and the difference in the estimate of burrow
density was not substantial (model with pooled observations: 8.55 ± 0.71 burrows ha P
-1P; model
analyzed separately for Observer 1: 8.68 ± 0.97 burrows haP
-1P; model analyzed separately for
Observer 2: 8.41 ± 1.01 burrows haP
-1P).
Total Count, Sample Count, and Double Observer
In stratum G5, the total number of burrows in the 6-ha (six 1-ha plots) sampled was 68
(Table 1-2). In stratum C3/C7, the total number of burrows in the 6-ha (six 1-ha plots) sampled
was 78 (Table 1-2). The extrapolated abundance of burrows based on the sample count method
varied widely in both strata based on the proportion of sample plots used (Figures. 1-2A and
1-2B, Table 1-2). In stratum G5, when 50%, 66%, and 83% of the plots were sampled, the
extrapolated number of burrows in the sampling area ranged from 48 to 88, 54 to 81, and 60 to
74 burrows, respectively. In stratum C3/C7, when 50%, 66%, and 83% of the plots were
24
sampled, the extrapolated number of burrows in the sampling area ranged from 64 to 92, 69 to
87, and 73 to 83 burrows, respectively.
In stratum G5, the overall detectability ( p̂ ) estimated using the double observer method
was 1.0, and ..x and N̂ were 68. Because p̂ was 1.000, ˆ( )SE N or 95% confidence interval
could not be estimated (Table 1-2).
In stratum C3/C7, p̂ estimated using the double observer method was 0.997 ± 0.003, ..x
was 78, and N̂ was 78.23 ± 0.53 (Table 1-2).
Burrow Occupancy Rates
The most parsimonious model indicated that the detection probability (probability of
observing a gopher tortoise if it was in the burrow) was 0.92 ± 0.04 and did not differ between
burrows classified as active or inactive. However, the occupancy rates were significantly
different between the two groups (active: 0.50 ± 0.09; inactive: 0.04 ± 0.04). There was no
evidence that width of the burrow entrance influenced the occupancy rate or the detection
probability.
Abundance of Gopher Tortoises
Using the occupancy rates for active and inactive burrows, and based on the proportion of
active and inactive burrows I estimated the abundance of gopher tortoises in stratum C3/C7. The
estimated abundance varied from 223.68 – 329.70 tortoises in stratum C3/C7 (total area: 116.5
ha), depending on the method used, and in the case of sample count, depending on the proportion
of plots sampled (Table 1-3).
Costs
The cost of sampling varied from 0.52 – 2.38 person-hours ha P
-1 Pin stratum G5, and from
0.46 – 2.08 person-hours haP
-1 Pin stratum C3/C7, depending on the methods used, and in the case
of sample count, depending on the proportion of plots sampled (Table 1-2). I did not analyze cost
of line transect data collected by Observer 2. Observer 2 did not lie out transects or measure and
record information for burrows that had already been detected by Observer 1. Costs of
implementing the double observer method were identical to the cost for the total count method.
The cost of sampling burrows with a burrow camera to determine occupancy status was
0.16 person-hours per burrow camera observation. A total of 168 burrow camera observations
were performed (three observations for each of the 56 burrows scoped) requiring a total time of
26.88 person-hours.
Discussion
Comparison of Abundance Estimation Methods
To monitor the population status, and for appropriate recovery efforts for gopher tortoises,
reliable estimates of abundance are needed. Methods that are currently used to estimate the
abundance of gopher tortoises vary with respect to statistical rigor, efficacy, and cost. Given the
pivotal role of gopher tortoises in ecosystems where they are found (Eisenberg 1983, Wahlquist
1991), it is essential to use rigorous yet cost effective methods for estimating and monitoring
tortoise abundance.
I field-tested the efficacy and cost of line transect, total count, sample count, and double
observer methods for estimating abundance of gopher tortoise burrows. In the dense vegetation
stratum (G5), the estimated burrow density using the line transect method for both observers
(8.58 and 8.49 burrows ha-1, respectively) was nearly 3 burrows ha-1 less than burrow density of
11.33 burrows ha-1 obtained from total count method. Estimates based on total count method did
not fall within the 95% confidence intervals of those obtained from line transect method (Table
1-2). In the sparse vegetation stratum (C3/C7), the estimated burrow density estimated using the
line transect method (11.32 burrows ha-1) was closer to the burrow density obtained from the
25
26
total count method (13.00 burrows ha P
-1P). The total count fell within the 95% confidence interval
for estimates obtained from the line transect method (Table 1-2).
Mann (1993) compared estimates of tortoise burrow abundance obtained from line
transect and total count methods, and found that line transect method overestimated burrow
abundance by as much as 49% in 13 sites and 32% on seven sites. Results from similar studies
suggest a tendency for line transects to overestimate abundance when compared to total counts
(Doonan 1986, Epperson 1997, Doonan and Epperson 2001). I used ≥2 observers to thoroughly
search the sampling area, and ensured that detection probability was 1.0. I also had a large
sample size for a reasonable coefficient of variation. My results do not agree with findings that
the line transect method tends to overestimate burrow numbers. In fact, estimates of burrow
abundance obtained from the line transect method were lower than those obtained from total
count in stratum G5; they did not differ significantly in stratum C3/C7 (Table 1-2). These results
suggest that the estimated burrow abundance obtained from the line transect method are not
consistently greater or smaller than those obtained from the total count method. Therefore, the
line transect method likely captured a greater amount of spatial variability in distribution and
abundance burrows in the study area.
Consistent with previous studies (McCoy and Mushinsky 1995, Epperson 1997, Marques
et al. 2001, McCoy and Mushinsky 2005), my estimates of burrow density varied with habitat
type and burn frequency. Density estimates obtained from all methods were higher in stratum
C3/C7 which had comparatively sparse vegetation and a higher burn frequency. The higher
density of burrows and tortoises in stratum C3/C7 likely indicates that this stratum offered a
better habitat for the tortoises.
27
Burrow Occupancy
My estimates of burrow occupancy rates (active: 0.50 ± 0.09; inactive: 0.04 ± 0.04) were
substantially lower than Auffenberg and Franz’s ‘correction factor’ of 61.4 % for active and
inactive burrows (Auffenberg and Franz 1982). Some studies have used this or a similar
correction factor (e.g., Ashton and Ashton (in press)) for converting estimates of burrow
abundance to tortoise abundance (Kushlan and Mazotti 1984, Doonan 1986, Doonan and
Epperson 2001, FFWCC 2006, Gregory et al. 2006). However, this approach ignores the spatial,
temporal or habitat-specific variation in occupancy rate and can cause estimates of gopher
tortoise abundance to be unreliable (Burke and Cox 1988, Breininger et al. 1991, McCoy and
Mushinsky 1992, Moler and Berish 2001). Moreover, my study is the first to apply the patch
occupancy modeling approach (Mackenzie et al. 2002) to estimate and model burrow occupancy
rates. When appropriate data are available, this approach also provides framework for testing
relevant biological hypotheses.
Because of time and resource limitations, I conducted burrow occupancy surveys only in
management unit C3 of stratum C3/C7, and I did not have empirical estimates of burrow
occupancy rates for stratum G5. Assuming that the burrow occupancy rate was the same in both
strata (C3/C7 and G5), estimates of tortoise abundance in stratum G5 (total area 110.3 ha) varied
from 148.68 - 230.45 tortoises depending on the method used, and in the case of sample count,
depending on the proportion of plots sampled. Based on the line transect method, the estimated
density of gopher tortoises was 2.06 ± 0.23 ha P
-1 Pin stratum G5.
Occupancy rates may vary among habitats due to the ecological needs of gopher tortoises,
and habitat-specific estimates of occupancy rates should be used whenever possible. Estimates of
occupancy rates may also be influenced by the season, time of the day when data are collected,
and time interval between successive samples; these factors should be considered whenever
possible. Additionally, there is the possibility of the same tortoise occupying more than one
burrow during the burrow occupancy surveys, resulting in an overestimation of the occupancy
rate. These potential problems can be minimized by appropriate sampling design. Nonetheless, I
found that patch occupancy models (Mackenzie et al. 2002, Royle and Nichols 2002, Mackenzie
et al. 2006) offer statistically robust approach to estimating burrow occupancy rates and should
be considered in future studies.
Costs of Implementation
The total count and sample count methods were relatively straightforward to implement,
and required no sophisticated software for data analyses. However, these methods are costly,
particularly when a substantial proportion of the sites need to be sampled. Moreover, these
methods do not offer rigorous estimates of precision or meaningful approaches to obtaining
statistical inferences. The double observer method partially addressed some of these concerns by
providing estimates of precision (when detectability is less than 1.0), but is costly to implement.
Using the sample count method, the range of extrapolated estimates for burrow density became
narrower as the sampling proportion increased (Figures 1-2A and 1-2B). However, there was a
cost tradeoff in that more time was needed to collect the data (Table 1-2).
The line transect method was the least costly of the methods, and I was able to sample a
larger effective area with the same effort. The method is considered statistically rigorous and
robust, provides statistical measures of precision, and provides a framework for statistical
inferences (Buckland et al. 2001, Krzysik 2002, Williams et al. 2002). However, the low cost of
sampling in the field may be somewhat offset by increased costs of study design and data
analysis, as a good understanding of underlying theory, sampling protocol and working
knowledge of Program DISTANCE is needed for effective implementation of this method.
28
Costs of data collection differed between the two strata in the study site. The sparse
vegetation stratum (C3/C7) had a lower relative cost of sampling for all the abundance
estimation methods than dense vegetation stratum. In my study, sample counts and total counts
were substantially more costly than line transects in both strata. Detection time may be
substantially less in sparse vegetation (Lohoefener and Lohmeier 1984, Burke and Cox 1988,
Diemer 1992), and prescribed burns prior to sampling may further reduce cost of sampling
(Smith 1992, Mann 1993, Moler and Berish 2001).
Conclusion
Among other factors, the selection of an abundance estimation method should consider the
habitat type of the study area, and available time and resources (Ellis and Bernard 2005). With a
stratified sampling design, and an adequate sample size, the line transect method is perhaps the
most efficient method for estimating gopher tortoise burrow abundance because: 1) it is less
costly than total and sample count methods, 2) it is more likely to capture a wider range of
spatial variation in the distribution and abundance of burrows, 3) it offers statistically robust
estimates of measures of precision, and 4) provides a flexible framework for evaluating effects of
covariates on estimates of abundance.
If one wishes to implement the total (or sample) count method, I recommend using
multiple observers in order to obtain estimates of detectability. I note, however, that the total (or
sample count) method does not provide an estimate of variance, nor does it provide a framework
for statistical test of hypothesis. The double observer approach is reasonable if one wishes to
implement a count-based method, but is unsure that detectability is equal to 1.0.
I recommend that burrow cameras (or similar technologies) should be employed, along
with a patch occupancy modeling approach for data analysis, to estimate burrow occupancy rates
and to test hypothesis regarding the occupancy rate or detection probability. If a study is
29
conducted in >1 habitat types, I recommend obtaining habitat-specific estimates of occupancy
rates. Finally, I suggest that gopher tortoise monitoring programs should simultaneously consider
burrow abundance and burrow occupancy rates. This is because changes in gopher tortoise
abundance may be reflected in changes in one or both of these parameters (i.e., burrow
abundance and burrow occupancy rate), and changes in one may not be interpreted as an
indicator of changes in tortoise abundance.
30
31
Table 1-1. Comparison of models fitted to line transect data Observer 1 Observer 2 Stratum Model AIC∆ Parameters AIC∆ ParametersG5 Uniform CosineP
aP 0 1 0.00 1
Half Normal Cosine 0.13 1 0.93 1 Half Normal Hermite 0.13 1 0.93 1 Uniform Simple Polynomial 1.46 2 0.98 2 Hazard Rate Cosine 2.22 2 2.31 2 Hazard Rate Simple Polynomial 2.22 2 2.31 2 C3/C7 Hazard Rate Cosine P
aP 0 2 - -
Hazard Rate Simple Polynomial 0 2 - - Uniform Cosine 0.98 2 - - Half Normal Cosine 1.32 2 - - Half Normal Hermite 3.14 1 - - Uniform Simple Polynomial 3.59 3 - - Note: For each model the AIC∆ values and the number of parameters are presented.
AIC∆ is the difference in the AIC (Akaike’s Information Criterion) values between each model and the model with the lowest AIC value. P
a PMost parsimonious model
Table 1-2. Overall summary of estimates of abundance of gopher tortoise burrows for each abundance estimation method in two strata (G5 and C3/C7), Ordway-Swisher Biological Station, Florida
ˆMethod D ˆ ( )N tot Cost
G5 Line transecta
Obs 1 8.58 (6.87 - 10.73) 946.40 0.52 Obs 2 8.49 (6.73 - 10.71) 936.25 - Sample count 50%b 8.00 - 14.66c 882.21 - 1616.66c 1.19 66%b 9.00 - 13.50c 992.49 - 1488.74c 1.57 83%b 10.00 - 12.40c 1102.77 – 1367.43c 1.98 100%b 11.33 1249.44 2.38 Double observer 11.33 1249.44 2.38 C3/C7 Line transecta,d
Obs 1 11.32 (9.19 - 13.94) 1318.31 0.46 Sample count 50%b 10.67 - 15.33c 1246.21 – 1781.97c 1.04 66%b 11.50 - 14.50c 1339.39 – 1688.79c 1.38 83%b 12.20 - 13.80c
1420.92 – 1607.27c 1.73
Total count (100%b) 13.00 1514.09 2.08 Double observer
ˆ13.04 1518.75 2.08
Note: D is the estimated burrow density (with 95% confidence interval) in burrows ha-1, and ) is the estimated number of burrows in the stratum. “Cost” are presented in terms of time (person-hours) needed to sample 1 ha.
ˆ (N tota Results are based on the most
parsimonious model (Table 1-1). b Proportion of plots sampled. c Range of estimates d I did not analyze line transect data for Observer 2 for stratum C3/C7 because Observer 2 did not collect data independently of Observer 1.
32
Table 1-3. Estimated number of gopher tortoises in stratum C3/C7, Ordway-Swisher Biological Station, Florida Burrow abundance Gopher tortoise abundance Method
ˆBN (Active)
ˆBN (Inactive)
ˆ ˆGTN (Active) GTN (Inactive) ˆ ( )GTN tot
C3/C7a,b
Line transect Obs1 582.62 735.69 291.31 29.43 320.74 Sample count 50% 447.36 - 639.68 798.85 - 1142.92 223.68 - 319.84 31.95 - 45.72 255.63 - 365.56 66% 480.81 - 606.23 858.58 - 1082.56 240.40 - 303.12 34.34 - 43.30 274.74 - 346.42 83% 510.07 - 576.97 910.84 - 1030.30 255.04 - 288.49 36.43 - 41.21 291.47 - 329.70 Total count 100% 543.52 970.57 271.76 38.82 310.58 Double observer
ˆ 545.19 973.56 272.60 38.94 311.54
Note: (Active) and (Inactive) are the estimates for the total number of active and inactive burrows in the stratum, ˆ (Active) and ˆ (Inactive) are the estimated numbers of gopher tortoises in active and inactive burrows,
respectively, and )t is the estimated total number of gopher tortoises in all burrows in the stratum.
BN ˆBNGTN GTN
ˆ (GTN to a Burrow occupancy surveys were conducted only in management unit C3 (estimated burrow occupancy rates were 0.50 for active burrows and 0.04 for inactive burrows), therefore I estimated gopher tortoise abundance for stratum C3/C7 only. b For stratum C3/C7, the proportion of active and inactive burrows detected using the line transect method for Observer 1 was 0.44 and 0.56, respectively. The proportion of active and inactive burrows detected using the total count methods was 0.36 and 0.64, respectively.
33
Figure 1-1. Map of Ordway-Swisher Biological Station in north-central Florida, USA, showing stratum G5 and stratum C3/C7, and locations of line transects and plots.
34
Proportion Sampled
50% 66% 83% 100%
No.
of B
urro
ws
40
50
60
70
80
90A)
Proportion Sampled
50% 66% 83% 100%
No.
of B
urro
ws
60
65
70
75
80
85
90
95B)
Figure 1-2. Effects of proportion of plots sampled using sample count method on estimates of
abundance in two strata (G5 and C3/C7), Ordway-Swisher Biological Station in north-central Florida. Extrapolated range of total number of burrows are plotted against the proportion of plots sampled. A) In stratum G5. B) In stratum C3/C7.
35
CHAPTER 3 ACCURACY OF ESTIMATES OF ABUNDANCE BASED ON THE LINE TRANSECT METHOD: INFLUENCE OF SPATIAL DISTRIBUTION OF OBJECTS, AND LENGTH,
LAYOUT, AND NUMBER OF TRANSECTS
Introduction
Estimates of abundance are necessary for monitoring population status and for assessing
the impacts of management actions. Obtaining these estimates is notoriously difficult (Seber
1982). Several methods have been developed to estimate abundance, including line transect,
mark-recapture, and double observer (Krebs 1999, Seber 1982, Williams et al. 2002).
Line transect is a distance-based method and is statistically robust for estimating
abundance (Buckland et al. 2001, Krzysik 2002, Williams et al. 2002). Implementation of the
line transect method involves laying out transects either randomly or systematically at
predetermined distances, walking along the line transects detecting objects, and recording
sighting angles and sighting distances, or perpendicular distances of objects to the line. If
assumptions are met, the line transect method is efficient, cost-effective and provides rigorous
estimates of abundance. Consequently, this method has been used to estimate abundance for
many species of birds (Jarvinen and Vaisanen 1975, Hanowski et al. 1990), terrestrial and marine
mammals (Jefferson 1996, Plumptre 2000, Ruette et al. 2003, Calambokidis and Barlow 2004),
reptiles (Lewis et al. 1985, Krzysik 2002), amphibians (Lewis et al. 1985, Donnelly and Guyer
1994), and plants (Abrahamson 1984, Gentry and Emmons 1987). Additionally, line transect
method has been used to estimate abundance of many inanimate objects including nests
(Hashimoto 1995), dung (Marques et al. 2001, Ellis and Bernard 2005), and burrows
(Lohoefener 1990, Swann et al. 2002) as an index of animal abundance (Borchers et al. 1998,
Buckland et al. 2001).
36
The accuracy of estimates of abundance obtained from the line transect method may vary
depending upon the spatial distribution and density of objects, and the length, layout, and
number of line transects. Researchers cannot change the spatial distribution and density of
objects, but it is possible to design a study by varying the length, layout, and number of transects
in order to maximize accuracy and precision of estimates of abundance for a given spatial
distribution and density of objects.
My objectives were to address the following questions: 1) Which spatial distribution
pattern of objects is the line transect method most appropriate for? 2) For a given spatial
distribution, does the line transect method depend on object density? 3) For a given spatial
distribution and density of objects, how can one optimize the study design by varying total
transect length, transect layout pattern, and number of transects in order to maximize accuracy of
estimates of abundance?
Given the large number of factors involved and due to limitations of time and resources,
questions such as these can only be addressed effectively using simulations. Thus I used a
simulation-based approach to achieve my objectives.
The methodology and results in this study could be applied to a number of objects or
organisms, including invertebrates, plants, and nests (Buckland et al. 2000), provided some of
the basic assumptions of line transect abundance estimation (Burnham et al. 1980, Buckland et
al. 2001) are not violated.
I hypothesized that: 1) Estimates of abundance obtained from the line transect method
would be more accurate when objects were randomly or uniformly distributed in space; 2) For a
given spatial distribution pattern, precision of estimates of abundance would increase with
increasing object density; 3) increasing transect length would increase the accuracy of estimates
37
of abundance for all spatial distribution patterns and density levels; 3) for a clumped distribution
of objects, a random transect layout and several short transects would provide more accurate
estimates of abundance because such a study design would provide greater spatial coverage; 4)
for a uniform distribution of objects, a random transect layout would provide more accurate
estimates of abundance; and 5) for a random distribution of objects, transect layout and transect
number would not have a substantial effect on the accuracy of estimates of abundance.
Methods
Simulation Inputs
I considered three spatial distributions of objects: clumped, random and uniform. Within
each spatial distribution I used three levels of object densities: low (2 objects ha-1), medium (6
objects ha-1), and high (10 objects ha-1). For each combination of spatial distribution and density
level, I used a) three transect lengths: 10 m ha-1, 20 m ha-1, and 30 m ha-1, d) two types of
transect layout patters: random transect layout and systematic transect layout, e) and two levels
of total number of transects: few long and several short transects. There were a total of 216
unique combinations of input variables.
Spatial Distribution and Density of Objects
Using MATLAB I designed an 800 ha study area and simulated locations of objects within
the study area using the following spatial distributions: uniform grid (hereafter, uniform),
uniform random (hereafter, random), and clumped (Krebs 1999). For a uniform distribution, I
evenly spaced the objects throughout the study area (Zollner and Lima 1999) (Figure 2-1C). For
a random distribution, each object was distributed independently of all other objects (Figure
2-1B). I implemented this by generating the x and coordinates for the object using a uniform
random distribution throughout the study area (Zollner and Lima 1999). For a clumped
distribution, objects were aggregated in groups or patches (Figure 2-1A). To implement this I
y
38
39
randomly distributed parent objects throughout the study area, and using a random Gaussian
distribution with the parent object as the mean, and variance v (ranging from 2 to 5) depending
upon the density of objects, I generated “offspring” around each parents object (Zollner and
Lima 1999, Conradt et al. 2003). The number of parent objects was selected randomly from a
range of 25 to 50. I divided the total population size by the number of parent objects to determine
the number of “offspring” around each parent. Offspring that fell outside the borders of the study
area were deleted and the overall object density was readjusted.
To evaluate the effect of object density on estimates of abundance obtained from the line
transect method I varied the object densities from 2 objects haP
-1P to 10 objects haP
-1P in increments
of 4 objects ha P
-1 Pfor each spatial distribution.
Layout Pattern of Line Transects
I laid out line transects in two different patterns: systematic and random. For a systematic
transect layout (Figures 2-2C and 2-2D), x and y coordinates and the angle θ for the first
transect were predetermined. The coordinates were chosen to ensure that all line transects would
fall inside the study area. I used 0, 45 and 90 degrees for θ in order to provide an adequate
representation of systematic transect layouts. Subsequent transects were then placed at 90 m
intervals so as to prevent double-counting of objects from two adjacent transects. For a random
transect layout (Figures 2-2A and 2-2B) several different sets of transects were laid out
throughout the study area. The x and y coordinates and the angle θ for the first transect of
each transect set was chosen at random. Subsequent transects were then placed at 90 m intervals
parallel to the first transect. I ensured that all transect sets were located inside the study area and
did not overlap each other.
Total Length of Line Transects
The total transect length was determined using transect density in m ha-1. For instance, a
transect density of 10 m ha-1 would result in a total transect length of 8000 m in an 800 ha study
area. I used transect densities ranging from 10m ha-1 to 30m ha-1 in increments of 10m ha-1. The
lengths of all transects were equal within each simulation run. Based on the transect density used
I chose the total number of transect sets in the study area as well as the number of transects in
each set.
Number of Transects
The number of transect sets and the number of transects in each set varied with transect
density and were chosen to meet either of two conditions: a few long transects, or several short
transects in each transect set (Figures 2-2A, 2-2B, 2-2C, and 2-2D).
For a random transect layout with few long transects (Figure 2-2A) the number of transect
sets for a transect density of 10 m ha-1 was 2, and for transect densities of 20 m ha-1 and 30 m
ha-1 the number of transect sets was a randomly chosen number between 3 or 4. The number of
transects in each transect set was a randomly chosen number between 4 and 6. For a systematic
transect layout with few long transects (Figure 2-2C) the number of transect sets was 1 for all
transect densities. The number of transects for a transect density of 10 m ha-1 was 7, and for
transect densities of 20 m ha-1 and 30 m ha-1 the number of transects was a randomly chosen
number between 8 and 14.
For a random transect layout with several short transects (Figure 2-2B) the number of
transect sets for a transect density of 10 m ha-1 was 3, and for transect densities of 20 m ha-1 and
30 m ha-1 the number of transect sets was a randomly chosen number between 4 or 5. The
number of transects in each transect set was a randomly chosen number between 7 and 10. For a
systematic transect layout with several short transects (Figure 2-2D) the number of transect sets
40
41
was 1 for all transect densities. The number of transects for a transect density of 10 m haP
-1P was
10, and for transect densities of 20 m ha P
-1P and 30 m ha P
-1P the number of transect was a randomly
chosen number between 11 and 19.
Data Collection and Analysis
I set the transect strip width ( w ) at 30 m. This was the width of the area searched on each
side of the line transect; objects beyond 30 m were not considered. I used the half normal
detection function to determine whether objects within 30 m were detected. The half normal
detection function is often a good choice as a key function in line transect sampling (Buckland et
al. 2001). This took the form
2 2( ) exp( / 2 )g x x σ= − (2-1) Where ( )g x = probability of detecting an object at perpendicular distance x from the line, and σ = scale parameter, which I estimated following Brown and Cowling (1998)
1 22 (2 )wσ π −= (2-2) For each object within the strip width I generated a uniform random number between 0 and
1. If the random number was greater than or equal to the detection probability obtained from the
half normal detection function, the object was marked as detected. If the random number was
less than the detection probability, the object was considered undetected. I measured the
perpendicular distance of every object detected within the transect strip width of 30 m. I called
Program DISTANCE (Thomas et al. 2003) from within MATLAB to analyze the data using a
half normal cosine detection function to estimate the density of objects as:
ˆ (0)ˆ2
nfDL
= (2-3)
Where D̂ = estimate of density, n = number of objects detected, L = total transect length, ˆ (0)f = estimated probability distribution function at the line and was determined as
0
1ˆ (0)( )
wfg x dx
=
∫. (2-4)
42
I also calculated the number of objects detected as a percentage of the total number of
objects in the study area. I ran 100 simulations for each combination of spatial distribution of
objects and density of objects, and the layout, density and number of transects. The total number
of simulation runs was 21,600 for 216 different combinations of input variables. I then compared
the estimated density obtained from the line transect method ( D̂ ) with the actual ‘true’ density
( TD ) for each combination of spatial distribution, transect layout pattern, transect density, and
number of transects. To measure accuracy of estimates of abundance I calculated the root mean
squared error between D̂ and TD (RMSE) following Williams et al. (2002).
2
1
1 ˆ( )1
n
i Ti
RMSE D Dn =
= −− ∑ (2-5)
Where n = number of samples I also calculated RMSE as a percentage of TD (RMSE%).
To measure bias of the estimates I calculated the mean of the difference between D̂ and
TD as a percentage of TD (Bias%). Precision of estimates was quantified as the coefficient of
variation of D̂ (CV( D̂ )). I also calculated the percentage of times the 95% CI of estimates of
density computed by Program DISTANCE contained TD . I performed all statistical analyses
using SAS® software (SAS Institute, 2004).
Results
Overall Results
Detailed results are provided in the Appendix (Table A-1). The estimated scale parameter
(σ ) for all simulation runs was 0.24. Ignoring all factors (spatial distribution and density of
objects, and length, layout, and number of transects) RMSE% was 26.8%, Bias% was 3.9%,
CV( D̂ ) was 60.4%, and the 95% CI of D̂ contained TD 83.2% of the time, 11.3% of the time it
was underestimated (below the lower limit of CI), and 5.5% of the time it was overestimated
(above upper limit of CI) (Table 2-1). Accuracy, as well as bias and precision, of estimates of
density varied among spatial distribution patterns and densities of objects depending upon the
length, layout, and number of transects (Table 2-1).
The Bias% across all three spatial distributions (clumped, random and uniform) was less
than 10%. RMSE% ranged from 8.5% to 36.4%, and CV( D̂ ) ranged from 55.0% to 63.4%
depending upon the spatial distribution of objects (Table 2-1). The probability of detecting an
object in the strip of area (2wL p̂ ) was 79.5%, 79.4%, and 83.8% for clumped, random, and
uniform distributions respectively and did not vary substantially within spatial distributions.
Clumped Distribution
Ignoring all other factors, RMSE% was 36.4%, Bias% was 6.1%, CV ˆ( )D was 63.4%, and
95% CI of D̂ contained 67.9% of the time, 20.0% of the time it was underestimated, and
12.1% of the time it was overestimated (Table 2-1). The number of objects detected as a
percentage of the total number of objects simulated was 4.9%, 9.9% and 14.8% when using a
transect density of 10 m ha
TD
-1, 20 m ha-1, and 30 m ha-1 respectively.
Effects of object density
Estimates of density were less biased when object density was the highest. Bias% ranged
from 9.6% when object density was 2 objects ha-1 to 5.6% when object density was 10 objects
ha-1. RMSE% ranged from 37.3% when object density was 2 objects ha-1 to 31.9% when object
density was 10 objects ha-1, with no clear trend. CV ˆ( )D ranged from 33.0% when object density
was 2 objects ha-1 to 30.1% when object density was 10 objects ha-1, with no clear trend (Table
2-1). Surprisingly, the percentage of times 95% CI of D̂ contained was only 64.3% to 72.6%
depending upon object density, with no clear trend (Table 2-1). The percentage of times it was
TD
43
underestimated ranged from 18.5% to 21.5%, and the percentage of times it was overestimated
ranged from 8.8% to 13.3% (Table 2-1).
Effects of object density and transect length
Accuracy of estimates of density increased with increasing transect density for all object
densities with RMSE% ranging from 22.7% to 49.7% depending upon object density and
transect density (Figure 2-3A). When object density was low, Bias% decreased from 13.7% to
6.4% with increasing transect density, however, when object density was medium or high, Bias%
ranged from 5.3% to 6.8%, with no clear trend (Table A-1). Precision ranged from 21.2% to
42.1% depending upon object density and transect density (Table A-1). For all object densities,
the percentage of times 95% CI of D̂ contained increased with increasing transect density.
The range of values was 59.4% to 76.5% (Figure 2-4A) depending upon object density and
transect density.
TD
Effects of object density and transect layout
RMSE% ranged from 28.1% to 40.4% depending upon object density and transect layout,
with no clear trend (Figure 2-5A). For all object densities the bias of estimates of density was
less for a systematic transect layout, however precision was lower. Bias% ranged from 5.0% to
17.6%, and CV ˆ( )D ranged from 25.7% to 33.4% (Table A-1) depending upon object density and
transect layout. The percentage of times 95% CI of D̂ contained ranged from 61.3% to
73.7% with no clear trend (Figure 2-6A).
TD
Effects of object density and transect number
RMSE% ranged from 31.5% to 37.5% depending upon object density and transect layout,
with no clear trend (Figure 2-7A). For all object densities the bias of estimates of density when
using few long transects was less than when using several short transects, however, the precision
44
was lower. Bias% ranged from 4.9% to 11.0%, and CV ˆ( )D ranged from 29.4% to 33.6% (Table
A-1) depending upon object density and transect number. The percentage of times 95% CI of D̂
contained ranged from 63.0% to 73.1% and there was no clear trend (Figure 2-8A). TD
Effects of object density, and transect length, layout, and number
Taking into account all factors for a clumped object distribution, the lowest RMSE% was
17.8% for an object density of 6 objects ha-1, a transect density of 30 m ha-1, a random transect
layout, and few long transects. Bias% was 2.8%, CV ˆ( )D was 17.5%, and 95% CI of D̂
contained 78.0% of the time. TD
Random Distribution
Ignoring all other factors, RMSE% was 8.5%, Bias% was 0.7%, CV ˆ( )D was 55%, and the
95% CI of D̂ contained 94.0% of the time, 3.6% of the time it was underestimated, and
2.4% of the time it was overestimated (Table 2-1). The number of objects detected as a
percentage of the total number of objects simulated was 4.7%, 9.5% and 14.2% when using a
transect density of 10 m ha
TD
-1, 20 m ha-1, and 30 m ha-1 respectively.
Effects of object density
Accuracy of estimates of density increased with increasing object density. RMSE%
decreased from 14.3% when object density was 2 objects ha-1 to 6.6% when object density was
10 objects ha-1 (Table 2-1). Precision of estimates of density increased with increasing object
density. CV ˆ( )D decreased from 14.1% when object density was 2 objects ha-1 to 6.5% when
object density was 10 objects ha-1 (Table 2-1). Bias% ranged from 0.5% to 1.7% depending upon
object density with no clear trend (Table 2-1). The percentage of times 95% CI of D̂ contained
ranged from 93.5% to 94.4% with no clear trend (Table 2-1). The percentage of times it was TD
45
underestimated ranged from 3.0% to 4.1%, and the percentage of times it was overestimated
ranged from 2.1% to 2.7% (Table 2-1).
Effects of object density and transect length
Accuracy of estimates of density increased with increasing transect density for all object
densities. RMSE% ranged from 5.0% to 17.7% depending upon object density and transect
density (Figure 2-3B). Bias% ranged from 0.2% to 1.9% depending upon object density and
transect density with no clear trend (Table A-1). Precision of estimates of density increased with
increasing transect density with CV ˆ( )D ranging from 4.9% to 17.5% depending upon object
density and transect density (Table A-1). The percentage of times 95% CI of D̂ contained
ranged from 93.1% to 95.1% with no clear trend (Figure 2-4B).
TD
Effects of object density and transect layout
Accuracy of estimates of density was slightly higher when using a systematic transect
layout for all object densities. RMSE% ranged from 6.5% to 14.5% depending upon object
density and transect layout (Figure 2-5B). Bias% ranged from 0.3% to 1.6% depending upon
object density and transect layout with no clear trend (Table A-1). Precision of estimates of
density was slightly higher when using a systematic transect layout for all object densities.
CV ˆ( )D ranged from 6.5% to 14.2% depending upon object density and transect layout (Table
A-1). The percentage of times 95% CI of D̂ contained ranged from 93.2% to 94.8% with no
clear trend (Figure 2-6B).
TD
Effects of object density and transect number
For all object densities there was no clear trend in the effect of transect number on
accuracy of estimates of density. RMSE% ranged from 6.5% to 14.6% (Figure 2-7B), Bias%
ranged from 0.3% to 2.0%, and CV ˆ( )D ranged from 6.4% to 14.2% depending upon object
46
density and transect number (Table A-1). The percentage of times 95% CI of D̂ contained D
ranged from 93.1% to 94.8% with no clear trend (Figure 2-8B).
Effects of object density, and transect length, layout, and num
T
ber
lowes SE% was 4.8%
for
Taking into account all factors for a random object distribution, the t RM
an object density of 10 objects ha-1, a transect density of 30 m ha-1, a systematic transect
layout, and several short transects. Bias% was 0.4%, CV ˆ( )D was 4.8%, and 95% CI of D̂
contained TD 94.7% of the time.
Uniform Distribution
For a uniform distribution, ignoring all other factors, RMSE% was 28.1%, Bias% was
5.0%, CV ˆ( )D was 62.1%, and 95% CI of D̂ contained TD 87.5% of the time, 10.4% of the t
it was underestimated, and 2.1% of the tim it was overestimated (Table 2-1). For a uniform
distribution the number of objects detected as a percentage of the total number of objects
simulated was 4.7%, 9.5%, and 14.1% when using a transect density of 10 m ha
ime
e
-1, and
-1
y
end in the effect of object density on accuracy of estimates of density.
RMS
-1, 20 m ha
30 m ha respectively.
Effects of object densit
There was no clear tr
E% ranged from 8.8% to 28.4%, Bias% ranged from 3.7% to 10.1%, and CV ˆ( )D ranged
from 8.3% to 24.6% depending upon object density (Table 2-1). The percentage of es 95% C
of ˆ
tim I
D contained TD ranged from 88.0% to 92.8% with no clear trend (Table 2-1). The
per ntage of tim it was underestimated ranged from 4.0% to 15.3%, and the percenta
times if was overestimated ranged from 0.3% to 3.3% (Table 2-1).
ce es ge of
47
Effects of object density and transect length
estimates of density increased with increasing
transe
%
n
f
When object density was low, accuracy of
ct density, however for medium or high object densities, there was no clear trend in the
effect of object density on accuracy of estimates of density. RMSE% ranged from 7.2% to 47.8
depending upon object density and transect density (Figure 2-3C). Bias% ranged from 1.0% to
24.7% depending upon object density and transect density with no clear trend (Table A-1). Whe
object density was low, precision of estimates of density increased with increasing transect
density, however for medium or high object densities, there was no clear trend in the effect o
object density on the precision of estimates of density. CV ˆ( )D ranged from 5.4% to 32.7%
depending upon object density and transect density (Table A-1). The percentage of times 95%
of ˆ
CI
D contained TD ranged from 62.0% to 98.6% with no clear trend (Figure 2-4C).
Effects of object density and transect layout
For all object densities the accuracy of estimates of density was significantly higher when
using a random transect layout. RMSE% ranged from 4.9% to 32.6% (Figure 2-5C), Bias%
ranged from 0.1% to 13.5%, CV ˆ( )D ranged from 4.9% to 27.0% (Table A-1), and the
percentage of times 95% CI of D̂ contained TD ranged from 77.2% to 99.3% dependin
object density and transect layout (Figure 2-6C).
Effects of object density and transect number
g upon
ates of density was higher when using several
short
cision
For all object densities the accuracy of estim
transects with RMSE% ranging from 8.5% to 28.8% depending upon object density and
transect number (Figure 2-7C). Bias% ranged from 3.3% to 12.2% depending upon object
density and transect number with no clear trend (Table A-1). For all object densities the pre
of estimates of density was higher when using several short transects with CV(D) ranging from
48
8.1% to 25.4% depending upon object density and transect number (Table A-1). The percentage
of times 95% CI of D̂ contained TD ranged from 79.8% to 93.3% and was slightly higher when
using several short transects (Figure 2-8C).
Effects of object density, and transect length, layout, and number
lowest RMSE% was
2.6
Taking into account all factors for a uniform object distribution, the
% for an object density of 6 objects ha-1, a transect density of 30 m ha-1, a random transect
layout, and several short transects. Bias% was 0.2%, CV ˆ( )D was 2.6%, and 95% CI of D̂
contained TD 100.0% of the time.
Discussion
Accuracy of estimates of abundance this method may vary with respect to
spatia
er of
ary
, and number of
transe l
) For a
influence accuracy of density estimates?
obtained from
l distribution and density of objects, but it is typically not possible to alter the spatial
distribution or density study objects. However, it might be possible to improve accuracy of
estimates of density through study design, for example, by altering layout, length, and numb
transects. This, however, requires an understanding of how layout, length, and number of
transects influence accuracy of estimates of densities, and of how these influences might v
depending upon the spatial distribution pattern and density of study objects.
I conducted a simulation study to determine the effect of length, layout
cts on estimates of density and the precision of these estimates for different object spatia
distributions and densities. Specifically, I asked the following questions: (1) How does accuracy
and of estimates of abundance obtained from the line transect method vary across spatial
distribution patterns? (2) How might these patterns be influenced by density of objects? (3
given spatial distribution and density level, how does the layout, length, and number of transects
49
Overall, density estimated using the line transect method was within 3.9% of the true
density, but it varied substantially depending upon spatial distribution pattern of objects (Table
2-1). this
y
ightly
ensity
n of objects was clumped. Bias of estimates of density increased
with i
ere
ias,
The line transect method was most accurate when objects were distributed randomly; in
case root mean squared error (RMSE) between estimated density and true density was 8.5% of
the true density (Table 2-1). Consequently, this method may be most appropriate for objects or
organisms that exhibit a random distribution pattern. In contrast, the line transect method was
least accurate when object were distributed in a clumped pattern; in this case the root mean
squared error (RMSE) between estimated density and true density was 36.4% of the true densit
(Table 2-1). The spatial distribution of objects did not seem to substantially influence the
precision of estimates of density (Table 2-1). The percentage of times 95% CI of estimated
density contained true density was highest for a random distribution of objects (94.0%), sl
less for a uniform distribution of objects (87.5%), and lowest for a clumped distribution of
objects (67.9%) (Table 2-1).
There was no clear trend for the effect of object density on accuracy of estimates of d
when the pattern of distributio
ncreasing object density, but there was no clear trend for precision of estimates of density.
When objects were distributed randomly, accuracy of estimates of density increased with
increasing object density. Precision of estimates of density increased with increasing object
density; however, there was no clear trend in bias of estimates of density. When objects w
distributed uniformly, there was no clear trend for the effect of object density on accuracy, b
or precision of estimates of density. The percentage of times 95% CI of estimated density
contained the true density did not seem to be affected by object density for any object
distribution.
50
The results of my study were consistent with most of my hypotheses. The line tra
method worked well for a random
nsect
distribution of objects (RMSE% was 8.5% of the true
densi
density;
effect
y was
ed
rovide a basis for adequate variance
estim al
ty). However, accuracy of estimates of density was less than desired for a uniform
distribution of objects (RMSE% was 28.1% of the true density) (Table 2-1). For a random
distribution of objects, precision of estimates of density increased with increasing object
however, when object distribution was clumped or uniform, there was no clear trend in the
of object density on precision of estimates of density. Consistent with my hypothesis, accuracy
of estimates of density increased with an increasing transect length for random and clumped
distributions. However, for a uniform distribution of objects with medium and high object
density, there was no clear trend in the effect of transect length on accuracy of estimates of
density (Figures 2-3A, 2-3B, and 2-3C). Consistent with my hypothesis, for a clumped
distribution of objects, a random transect layout worked better than when using a systematic
transect layout when object density was medium and high, however, when object densit
low, a systematic transect layout provided slightly greater accuracy (Figure 2-5A). Transect
number did not seem to have a substantial effect on accuracy of estimates of density for all
object densities (Figure 2-7A). Consistent with my hypothesis, a random transect layout work
very well when objects were distributed uniformly (Figure 2-5C), and when objects were
distributed randomly, transect layout and transect number did not have a substantial effect on the
accuracy of estimates of density (Figures 2-5B and 2-7B).
Buckland et al. (2001) note the importance of replication of transects and stress that a
minimum of 10 to 20 replicate lines should be surveyed to p
ation. In my study, the average number of transects simulated for each of the three spati
distributions (clumped, random, and uniform) was approximately 11 and 18 when using few long
51
transects and several short transects respectively. Additionally, Buckland et al. (2001) note that a
systematic placement of lines provides better spatial coverage and has superior precision to lines
that are randomly and independently distributed. In my study, transect layout did not seem to
affect the spatial coverage of transects, and the number of objects detected as a percentage of the
total number of objects simulated ranged from 9 to 10% for both random and systematic transe
layouts for all spatial distributions. However, transect layout did have an influence on the
precision of estimates of abundance. For a clumped distribution, a random transect layout
provided greater precision than using a systematic transect layout for all object densities. F
random distribution, using a systematic transect layout provided slightly greater precision f
object densities. For a uniform distribution, using a random transect layout provided substantiall
greater precision for all object densities (Table A-1).
Williams et al. (2002) note that systematic positioning of transects is acceptable if the
animal or object locations are random, else random tra
ct
or a
or all
y
nsect placement is necessary to ensure
accur
ties
e
,
found that transect lengths did not
ate statistical inferences. My results were consistent with this observation. I found that
when objects followed a random distribution, results from the line transect method using a
systematic transect layout and a random transect layout were very similar for all object densi
(Figures 2-5B and 2-6B, and Table A-1). However, for uniformly distributed objects, the lin
transect method worked better when using a random transect layout than a systematic transect
layout (Figures 2-5C and 2-6C, and Table A-1). When objects followed a clumped distribution
results from the line transect method using a systematic transect layout and a random transect
layout were similar (Figures 2-5A and 2-6A, and Table A-1).
Fowler (1986) conducted a study to assess the effect of transect length on estimates of
density and precision for species of coral reef fish. The study
52
signif
y
d
f
icantly affect estimates of density; however, precision was variable with the smallest
transect length providing the least precise estimates of density. In my study, for a clumped
distribution, accuracy of estimates of density (Figure 2-3A), precision of estimates of densit
(Table A-1), and 95% CI coverage of TD (Figure 2-4A) increased with increasing transect
density for all object densities. For a random distribution, accuracy of estimates of density
(Figures 2-3B), and precision of estima of density (Table A-1) increased with increasing
transect density for all object densities. However increasing transect density did not seem to
significantly influence the 95% CI coverage of TD for any object density (Figure 2-4B). For a
uniform distribution with low and object density, increasing the transect density increased the
accuracy and precision of estimates of density (F ure 2-3C and Table A-1). However, there
seemed to be a contradictory effect on estimates of density when object density was medium an
high (Figures 2-3C and 2-4C). One reason for this could be the relatively poor performance o
the line transect method for a uniform distribution with an object density of 10 objects ha-1, a
transect density of 20 m ha-1, and a systematic transect layout (RMSE% = 55.1%, Bias% =
32.7%, CV ˆ( )
tes
ig
D = 33.3%, and 95% CI coverage of TD = 50.7%).
Conclusion
For objects that are distributed in a clumped distribution, there was no clear trend in the
effect of object density on accuracy of esti dance. Bias of estimates of density
decre
f
mates of abun
ased as object density was increased; however, there was no clear trend in the effect of
object density on precision of estimates of abundance. The percentage of times the 95% CI o
estimated density contained true density was very low for a clumped distribution of objects
which is troubling because most organisms occur in clumped distributions. There was no
significant effect of transect layout on estimates of abundance. I recommend using a higher
53
transect length as this increased the accuracy of estimates of density, and the 95% CI cove
true density. The number of transects did not have a significant effect on accuracy of estimat
abundance.
For objects that are distributed in a random distribution, accuracy of estimates of
abundance in
rage of
es of
creased with increasing object density. I recommend using a systematic transect
layou dom
ial.
of
or all object densities, I recommend using a random transect layout as
this p
t
cts.
t as accuracy of estimates of abundance was slightly greater than when using a ran
transect layout. I also recommend using a higher transect length as accuracy of estimates of
abundance increased with increasing transect density; however, this increase was not substant
The number of transects (few long, or several short) did not significantly affect the accuracy
estimates of abundance.
For objects distributed in uniform distribution, the line transect method worked best for a
medium object density. F
rovided significantly greater accuracy than when using a systematic transect layout. When
using a random transect layout, total transect length increased the accuracy of estimates of
abundance and I recommend using a higher transect length. I also recommend using several shor
transects as accuracy of estimates of abundance was higher than when using few long transe
54
Table 2-1. Density estimates by object spatial distribution and density
Input TD D̂ 95% CI( D̂ ) RMSE% CV( D̂ ) Bias% 95% DCI Under Over
Overall 5.94 6.17 6.12 – 6.22 26.8% 60.4% 3.9% 83.2% 11.3% 5.5%
Clumped
5.79 6.14 5.72 – 5.86 36.4% 63.4% 6.1% 67.9% 20.0% 12.1%
2 objects ha-1 1.97 2.13 2.13 – 2.19 37.3% 33.0% 9.6% 72.6% 18.5% 8.8%
6 objects ha-1 5.75 6.08 6.01 – 6.16 31.6% 29.7% 5.8% 64.3% 21.5% 14.2%
10 objects ha-1 9.65 10.19 10.07 – 10.32 31.9% 30.1% 5.6% 66.9% 19.8% 13.3%
Random 6.00 6.04 5.92 – 6.08 8.5% 55.0% 0.7% 94.0% 3.6% 2.4%
2 objects ha-1 2.00 2.03 2.02 – 2.04 14.3% 14.1% 1.5% 93.5% 4.1% 2.4%
6 objects ha-1 6.00 6.03 6.01 – 6.05 8.4% 8.4% 0.5% 94.3% 3.0% 2.7%
10 objects ha-1 10.00 10.07 10.05 – 10.10 6.6% 6.5% 0.7% 94.4% 3.5% 2.1%
Uniform 6.02 6.32 5.94 – 6.09 28.1% 62.1% 5.0% 87.5% 10.4% 2.1%
2 objects ha-1 2.00 2.20 2.19 – 2.22 21.5% 17.2% 10.1% 88.0% 11.8% 0.3%
6 objects ha-1 6.04 5.81 5.80 – 5.83 8.8% 8.3% 3.7% 92.8% 4.0% 3.3%
10 objects ha-1 10.01 10.94 10.83 – 11.05 28.4% 24.6% 9.2% 81.9% 15.3% 2.8%
Note: is the true object density, TD D̂ is the estimated object density, 95% CI( D̂ ) is the 95% confidence interval of D̂ , RMSE% is the root mean squared error between D̂ and as a percentage of , CV( ˆ
TD TD D ) is the coefficient of variation of D̂ , Bias% is the mean difference between D̂ and TD as a percentage of TD , 95% DCI is the percentage of times that the 95% CI computed by Program DISTANCE for D̂ contained , ‘Under’ is the percentage of times that was below the lower limit of TD TD 95% DCI , and ‘Over’ is the percentage of times that D was above the upper limit of 95%T DCI .
55
0 5 10 15 20 250
5
10
15
20
25
A)
0 5 10 15 20 250
5
10
15
20
25
B)
Figure 2-1. Examples of simulated spatial distributions of objects with a density of 2 objects ha-1. A) For a clumped distribution. B) For a random distribution. C) For a uniform distribution.
56
0 5 10 15 20 250
5
10
15
20
25
C)
Figure 2-1. Continued
57
0 5 10 15 20 250
5
10
15
20
25
A)
Figure 2-2. Transect layout patterns with objects simulated in a random spatial distribution with a density of 2 objects ha , and a transect density of 10 m ha-1 -1. For the systematic layouts the starting x and y coordinates for the first transect line were chosen as 10 and 10 respectively to ensure that all transects fell inside the study area. A) Random transect layout with ‘few long transects’. B) Random transect layout with ‘several short transects’. C) Systematic transect layout with ‘few long transects’. D) Systematic transect layout with ‘several short transects’.
58
0 5 10 15 20 250
5
10
15
20
25
B)
0 5 10 15 20 250
5
10
15
20
25
C)
Figure 2-2. Continued
59
0 5 10 15 20 250
5
10
15
20
25
D)
Figure 2-2. Continued
60
A)
0
10
20
30
40
50
60
10 m ha-1
20 m ha-1
30 m ha-1
Object density (Objects ha-1)2 6 10
Transect Density
RM
SE%
Figure 2-3. Effect of transect length on accuracy of estimates of density for a given object spatial
distribution and object densities ranging from 2 objects ha to 10 objects ha-1 -1. The root mean squared error between estimated object density ( D̂ ) and true object density ( ) as a percentage of (RMSE%) is plotted against transect density (m haTD TD -1) for different object densities. A) In a clumped distribution. B) In a random distribution. C) In a uniform distribution.
61
0
2
4
6
8
10
12
14
16
18
20
10 m ha-1
20 m ha-1
30 m ha-1
Object density (Objects ha-1)2 6 10
Transect Density
RM
SE%
B)
0
10
20
30
40
50
60
10 m ha-1
20 m ha-1
30 m ha-1
Object density (Objects ha-1)2 6 10
Transect Density
RM
SE%
C)
Figure 2-3. Continued
62
95%
CI o
f den
sity
est
imat
e
0
20
40
60
80
100
10 m ha-1
20 m ha-1
30 m ha-1
Object density (Objects ha-1)2 6 10
Transect density
A)
Figure 2-4. Effect of transect length on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha to 10 objects ha-1 -1. The percentage of times that the 95% CI computed by Program DISTANCE for each density estimate ( D̂ ) contained true object density ( ) is plotted against transect density (m ha
TD-1) for different object densities. A) In a clumped distribution. B) In a
random distribution. C) In a uniform distribution.
63
95%
CI o
f den
sity
est
imat
e
0
20
40
60
80
100
10 m ha-1
20 m ha-1
30 m ha-1
Object density (Objects ha-1)2 6 10
Transect density
B)95
% C
I of d
ensi
ty e
stim
ate
0
20
40
60
80
100
120
10 m ha-1
20 m ha-1
30 m ha-1
Object density (Objects ha-1)2 6 10
Transect density
C)
Figure 2-4. Continued
64
0
10
20
30
40
50
RandomSystematic
Object density (Objects ha-1)2 6 10
Transect layout
RM
SE%
A)
Figure 2-5. Effect of transect layout on accuracy of estimates of density for a given object spatial
distribution and object densities ranging from 2 objects ha to 10 objects ha-1 -1. The root mean squared error between estimated object density ( D̂ ) and true object density ( ) as a percentage of (RMSE%) is plotted against transect layout (random, and systematic) for different object densities. A) In a clumped distribution. B) In a random distribution. C) In a uniform distribution.
TD TD
65
0
2
4
6
8
10
12
14
16
RandomSystematic
Object density (Objects ha-1)2 6 10
Transect layout
RM
SE%
B)
0
5
10
15
20
25
30
35
RandomSystematic
Object density (Objects ha-1)2 6 10
Transect layout
RM
SE%
C)
Figure 2-5. Continued
66
95%
CI o
f den
sity
est
imat
e
0
20
40
60
80
RandomSystematic
Object density (Objects ha-1)2 6 10
Transect layout
A)
Figure 2-6. Effect of transect layout on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha to 10 objects ha-1 -1. The percentage of times that the 95% CI computed by Program DISTANCE for each density estimate ( D̂ ) contained true object density ( ) is plotted against transect density (m ha
TD-1) for different object densities. A) In a clumped distribution. B) In a
random distribution. C) In a uniform distribution.
67
95%
CI
of d
ensi
ty e
stim
ate
0
20
40
60
80
100
RandomSystematic
Object density (Objects ha-1)2 6 10
Transect layout
B)
95%
CI
of d
ensi
ty e
stim
ate
0
20
40
60
80
100
120
RandomSystematic
Object density (Objects ha-1)2 6 10
Transect layout
C)
Figure 2-6. Continued
68
0
10
20
30
40
Few longSeveral short
Object density (Objects ha-1)2 6 10
Transect number
RM
SE%
A)
Figure 2-7. Effect of transect number on accuracy of estimates of density for a given object spatial distribution and object densities ranging from 2 objects ha to 10 objects ha-1 -1. The root mean squared error between estimated object density ( D̂ ) and true object density ( ) as a percentage of (RMSE%) is plotted against transect layout (random, and systematic) for different object densities. A) In a clumped distribution. B) In a random distribution. C) In a uniform distribution.
TD TD
69
0
2
4
6
8
10
12
14
16
Few longSeveral short
Object density (Objects ha-1)2 6 10
Transect number
RM
SE%
B)
0
5
10
15
20
25
30
35
Few longSeveral short
Object density (Objects ha-1)2 6 10
Transect number
RM
SE%
C)
Figure 2-7. Continued
70
Dis
tanc
e 95
% C
I
0
20
40
60
80
FewlongSeveralshort
Object density (Objects ha-1)2 6 10
Transect number
A)
Figure 2-8. Effect of transect number on 95% CI of estimated density for a given object spatial distribution and object densities ranging from 2 objects ha to 10 objects ha-1 -1. The percentage of times that the 95% CI computed by Program DISTANCE for each density estimate ( D̂ ) contained true object density ( ) is plotted against transect density (m ha
TD-1) for different object densities. A) In a clumped distribution. B) In a
random distribution. C) In a uniform distribution.
71
95%
CI o
f den
sity
est
imat
e
0
20
40
60
80
100
FewlongSeveralshort
Object density (Objects ha-1)
2 6 10
Transect number
B)
95%
CI o
f den
sity
est
imat
e
0
20
40
60
80
100
FewlongSeveralshort
Object density (Objects ha-1)2 6 10
Transect number
C)
Figure 2-8. Continued
72
CHAPTER 4 CONCLUSION
The overall goal of my research was to analyze abundance estimation methods using real
and simulated data. I field-tested the efficacy and cost-effectiveness of line transect, total count,
sample count, and double observer methods for estimating gopher tortoise burrow abundance. I
applied these methods to estimate burrow abundance in two strata in the Ordway Swisher
Biological Station, Florida. Additionally, I also addressed the issue of gopher tortoise burrow
occupancy, and used estimates of burrow abundance and occupancy rates to estimate abundance
of gopher tortoises. I then further analyzed the line transect method using a simulation-based
approach in MATLAB.
The results of my field study indicated that habitat type of the study area, and available
time and resources should be taken into consideration when selecting an abundance estimation
method. The line transect method is perhaps the most efficient method for estimating gopher
tortoise burrow abundance because it is less costly than total and sample count methods, and it is
more likely to capture a wider range of spatial variation in the distribution and abundance of
burrows, while providing statistically robust estimates of precision. However, a good
understanding of the method as well as some understanding of underlying theory and working
knowledge of Program DISTANCE is needed for effective implementation of this method.
If one wishes to implement the total count or sample count method, I recommend using
multiple observers in order to obtain estimates of detectability. The total count and sample count
methods are relatively straightforward to implement, and require no sophisticated software for
data analyses. However, these methods are costly, particularly when a substantial proportion of
the sites needed to be sampled. Moreover, these methods do not offer rigorous estimates of
73
74
precision. The double observer method partially addressed some of these concerns by providing
estimates of precision (when detectability is less than one), but is costly to implement.
My estimates of burrow occupancy rates (active: 0.50 ± 0.09; inactive: 0.04 ± 0.04) were
substantially lower than Auffenberg and Franz’s ‘correction factor’ of 61.4% (Auffenberg and
Franz 1982). Some studies have used this or a similar correction factor (e.g., Ashton and Ashton
(in press)) for converting estimates of burrow abundance to tortoise abundance (Kushlan and
Mazotti 1984, Doonan 1986, Doonan and Epperson 2001, FFWCC 2006, Gregory et al. 2006).
However, this approach ignores the spatial, temporal or habitat-specific variation in occupancy
rate and can cause estimates of gopher tortoise abundance to be unreliable (Burke and Cox 1988,
Breininger et al. 1991, McCoy and Mushinsky 1992, Moler and Berish 2001). I recommend that
burrow cameras (or similar technologies) should be used, along with a patch occupancy
modeling approach for data analysis, to estimate habitat-specific burrow occupancy rates.
The results of the simulation study provided valuable information about the influence of
length, layout and number of transects on the accuracy of estimates of abundance for different
spatial distribution patterns and density levels of objects. The accuracy of estimates of abundance
obtained from the line transect method varied substantially depending upon spatial distribution
pattern of objects. The line transect method was most accurate when objects were distributed
randomly. Consequently, this method may be most appropriate for objects or organisms that
exhibit a random distribution pattern. In contrast, the line transect method was least accurate
when object were distributed in a clumped pattern, which is troubling because most organisms
occur in clumped distributions. Increasing transect length had a positive effect on the accuracy of
estimates of abundance for random and clumped spatial distributions of objects, and I
recommend that researchers use, at a minimum, a transect length that will provide 60 to 80
observations as recommended by Buckland et al. (2001). For a clumped distribution of objects,
the positive effect of an increasing transect length on accuracy of estimates of abundance was
greater, as this likely captured the greater spatial variation in distribution of objects, and I
recommend that researchers try to maximize the total transect length when determining study
design.
Transect layout pattern had a significant effect for a uniform distributions of objects; in
this case, accuracy and precision of estimates of abundance were substantially higher, and bias
was lower when using a random transect layout. Furthermore, when using a random transect
layout, increasing transect length increased the accuracy of estimates of abundance. For a
random distribution of objects, using a systematic transect layout provided slightly greater
accuracy than when using a random transect layout. For a clumped distribution, there was no
significant effect of transect layout on estimates of abundance.
The number of transect used did not significantly affect the accuracy of estimates of
abundance when the object distribution pattern was random or clumped. However, for a uniform
distribution of objects, accuracy of estimates of abundance was higher when using several short
transects than when using few long transects.
75
APPENDIX OVERALL RESULTS
76
Table A-1. Simulation study results Dist ODens TDens TL TNum TD D̂ 95% CI( D̂ ) RMSE RMSE% CV( D̂ ) Bias% 95% DCI Sim Runs - - - - - 5.94 6.17 6.12 – 6.22 1.59 26.8% 60.4% 3.9% 83.2% 21600
clumped
- - - - 5.79
6.14
5.72 – 5.86
2.11
36.4%
63.4%
6.1%
67.9%
7200
random
- - - - 6.00
6.04
5.92 – 6.08
0.51
8.5%
55.0%
0.7%
94.0%
7200
uniform
- - - - 6.02
6.32
5.94 – 6.09
1.69
28.1%
62.1%
5.0%
87.5%
7200
clumped
2 - - - 1.97
2.16
2.13 – 2.19
0.73
37.3%
33.0%
9.6%
72.6%
2400
clumped
6 - - - 5.75
6.08
6.01 – 6.16
1.82
31.6%
29.7%
5.8%
64.3%
2400
clumped
10 - - - 9.65
10.19
10.07 – 10.32
3.08
31.9%
30.1%
5.6%
66.9%
2400
random
2 - - - 2.00
2.03
2.02 – 2.04
0.29
14.3%
14.1%
1.5%
93.5%
2400
random
6 - - - 6.00
6.03
6.01 – 6.05
0.51
8.4%
8.4%
0.5%
94.3%
2400
random
10 - - - 10.00
10.07
10.05 – 10.10
0.66
6.6%
6.5%
0.7%
94.4%
2400
uniform
2 - - - 2.00
2.20
2.19 – 2.22
0.43
21.5%
17.2%
10.1%
88.0%
2400
uniform 6 - - - 6.04 5.81 5.80 – 5.83 0.53 8.8% 8.3% 3.7% 92.8% 2400Note: Dist is the spatial distribution of objects, ODens is the density of objects in objects ha-1, TDens is the transect density in m ha-1, TL is the transect layout (‘r’ is random, and ‘s’ is systematic), TNum is the transect number (‘f’ is few long, and ‘s’ is several short), TD is the true object density in objects ha-1, D̂ is the estimated object density in objects ha-1, 95% CI( D̂ ) is the 95% confidence interval of D̂ , RMSE is the root mean squared error between D̂ and TD , RMSE% is RMSE as a percentage of TD , CV( D̂ ) is the coefficient of variation of D̂ , Bias% is the mean of the difference between D̂ and TD as a percentage of TD , 95% DCI is the percentage of times that the 95% CI computed by Program DISTANCE for D̂ covered TD , and ‘Sim runs’ indicates the total number of simulation runs upon which the associated results are based.
77
Table A-1. Continued Dist ODens TDens TL TNum TD D̂ 95% CI( D̂ ) RMSE RMSE% CV( D̂ ) Bias% 95% DCI Sim Runs uniform
10
- - - 10.01
10.94
10.83 – 11.05
2.85
28.4%
24.6%
9.2%
81.9%
2400
clumped
- 10 - - 5.79
6.17
6.00 – 6.34
2.70
46.6%
68.1%
8.4%
64.0%
2400
clumped
- 20 - - 5.79
6.17
6.01 – 6.32
1.92
33.2%
62.2%
6.9%
68.4%
2400
clumped
- 30 - - 5.79
6.09
5.95 – 6.24
1.55
26.7%
59.4%
5.5%
71.4%
2400
random
- 10 - - 6.00
6.05
5.92 – 6.19
0.65
10.8%
55.5%
0.9%
93.9%
2400
random
- 20 - - 6.00
6.03
5.90 – 6.17
0.46
7.7%
54.9%
0.8%
93.8%
2400
random
- 30 - - 6.00
6.04
5.91 – 6.17
0.37
6.2%
54.6%
1.0%
94.4%
2400
uniform
- 10 - - 6.02
5.97
5.84 – 6.10
0.61
10.1%
53.5%
2.0%
95.5%
2400
uniform
- 20 - - 6.02
6.87
6.68 – 7.07
2.79
46.4%
71.2%
10.7%
77.8%
2400
uniform
- 30 - - 6.02
6.11
5.98 – 6.25
0.64
10.6%
55.7%
3.0%
89.3%
2400
clumped
- - r - 5.79
6.27
6.09 – 6.44
1.90
32.8%
60.3%
10.4%
72.8%
1800
clumped
- - s - 5.76
6.10
6.00 – 6.21
2.18
37.6%
64.4%
5.8%
66.3%
5400
random
- - r - 6.00
6.04
5.88 – 6.19
0.53
8.8%
55.0%
0.9%
93.8%
1800
random
- - s - 6.00
6.05
5.96 – 6.11
0.50
8.4%
55.0%
0.9%
94.1%
5400
uniform
- - r - 6.01
6.02
5.88 – 6.19
0.48
8.0%
55.3%
0.1%
97.9%
1800
uniform
- - s - 6.02
6.41
6.30 – 6.52
1.93
32.1%
63.9%
6.9%
84.1%
5400
clumped - - - f 5.79 6.11 5.98 – 6.21 2.11 36.4% 63.5% 6.1% 68.2% 3600
78
Table A-1. Continued Dist ODens TDens TL TNum TD D̂ 95% CI( D̂ ) RMSE RMSE% CV( D̂ ) Bias% 95% DCI Sim Runs clumped - - - s 5.79 6.18 6.06 – 6.31 2.11 36.5% 63.2% 7.7% 67.7% 3600
random
- - - f 6.00
6.05
5.94 – 6.16
0.52
8.6%
55.1%
0.8%
94.1%
3600
random
- - - s 6.00
6.04
5.93 – 6.15
0.50
8.3%
54.8%
1.0%
94.0%
3600
uniform
- - - f 6.02
6.30
6.17 – 6.42
1.72
28.5%
61.8%
5.5%
86.1%
3600
uniform
- - - s 6.02
6.34
6.21 – 6.47
1.67
27.7%
62.4%
4.9%
88.9%
3600
clumped 2 10 - - 1.97 2.24 2.17 – 2.30 0.98 49.7% 42.1% 13.7% 68.4% 800clumped 2 20 - - 1.97 2.14 2.09 – 2.18 0.65 33.1% 29.5% 8.8% 73.0% 800clumped
2 30 - - 1.97
2.09
2.06 – 2.13
0.49
24.7%
22.8%
6.3%
76.5%
800
clumped 6 10 - - 5.75 6.12 5.96 – 6.28 2.35 40.9% 38.2% 6.3% 59.4% 800clumped 6 20 - - 5.75 6.05 5.94 – 6.17 1.65 28.7% 27.1% 5.2% 64.8% 800clumped
6 30 - - 5.75
6.08
5.99 – 6.17
1.30
22.7%
21.2%
5.6%
68.8%
800
clumped 10 10 - - 9.64 10.16 9.89 – 10.43 3.92 40.6% 38.5% 5.3% 64.4% 800clumped 10 20 - - 9.66 10.31 10.12 – 10.51 2.82 29.2% 26.9% 6.7% 67.5% 800clumped
10 30 - - 9.66
10.11
9.95 – 10.27
2.29
23.8%
22.6%
4.6%
68.9%
800
random 2 10 - - 2.00 2.02 2.00 – 2.05 0.35 17.7% 17.5% 1.2% 93.4% 800random 2 20 - - 2.00 2.03 2.01 – 2.05 0.27 13.4% 13.1% 1.5% 93.1% 800random
2 30 - - 2.00
2.04
2.02 – 2.05
0.22
11.2%
10.8%
1.9%
93.9%
800
random 6 10 - - 6.00 6.04 6.00 – 6.09 0.65 10.8%
10.7%
0.7% 94.6% 800random 6 20 - - 6.00 6.01 5.98 – 6.05 0.47 7.8% 7.8% 0.2% 93.3% 800random
6 30 - - 6.00
6.03
6.00 – 6.05
0.35
5.9%
5.9%
0.4%
95.0%
800
random 10 10 - - 10.00 10.09 10.04 – 10.15 0.84 8.4% 8.3% 0.9% 93.8% 800random 10 20 - - 10.00 10.06 10.02 – 10.10 0.60 6.0% 5.9% 0.6% 95.1% 800random
10 30 - - 10.00
10.06
10.03 – 10.10
0.50
5.0%
4.9%
0.6%
94.3%
800
79
Table A-1. Continued Dist ODens TDens TL TNum TD D̂ 95% CI( D̂ ) RMSE RMSE% CV( D̂ ) Bias% 95% DCI Sim Runs uniform 2 10 - - 2.00 2.23 2.20 – 2.26 0.46 23.0% 17.9% 11.5% 91.5% 800 uniform 2
20 - - 2.00 2.18 2.15 – 2.20 0.42 21.1% 17.7% 8.7% 86.1% 800uniform
2 30 - - 2.00
2.20
2.18 – 2.23
0.40
20.1%
15.8%
10.2%
86.3%
800
uniform 6 10 - - 6.04 5.76 5.73 – 5.79 0.54 8.9% 8.0% 4.6% 98.6% 800uniform 6 20 - - 6.04 5.95 5.91 – 5.99 0.61 10.0%
10.1%
1.5% 85.3% 800
uniform
6 30 - - 6.04
5.73
5.71 – 5.76
0.44
7.2%
5.4%
5.0%
94.4%
800
uniform 10 10 - - 10.01 9.92 9.86 – 9.97 0.78 7.8% 7.8% 1.0% 96.4% 800uniform 10 20 - - 10.01 12.49 12.77 – 12.21 4.78 47.8% 32.7% 24.7% 62.0% 800uniform
10 30 - - 10.01
10.41
10.35 – 10.47
0.93
9.3%
8.1%
3.9%
87.4%
800
clumped 2 - r - 1.97 2.31 2.26 – 2.37 0.79 40.4% 31.0% 17.6% 71.3% 600clumped
2 - s - 1.97
2.10
2.07 – 2.14
0.71
36.3%
33.4%
6.9%
73.1%
1800
clumped 6 - r - 5.75 6.10 5.97 – 6.23 1.62 28.1% 26.0% 6.0% 73.3% 600clumped
6 - s - 5.75
6.08
5.99 – 6.16
1.88
32.8%
30.9%
5.6%
61.3%
1800
clumped 10 - r - 9.66 10.39 10.17 – 10.60 2.75 28.5% 25.7% 7.6% 73.7% 600clumped
10 - s - 9.65
10.13
9.98 – 10.28
3.19
33.0%
31.4%
4.9%
64.7%
1800
random 2 - r - 2.00 2.03 2.01 – 2.06 0.29 14.5% 14.2% 1.7% 93.7% 600random
2 - s - 2.00
2.03
2.02 – 2.04
0.29
14.3%
14.0%
1.5%
93.4%
1800
random 6 - r - 6.00 6.02 5.97 – 6.06 0.54 9.0% 8.9% 0.3% 94.5% 600random
6 - s - 6.00
6.03
6.01 – 6.05
0.49
8.2%
8.2%
0.5%
94.2%
1800
random 10 - r - 10.00 10.07 10.01 – 10.12 0.68 6.8% 6.7% 0.7% 93.2% 600random
10 - s - 10.00
10.08
10.05 – 10.11
0.65
6.5%
6.5%
0.8%
94.8%
1800
uniform 2 - r - 2.00 2.00 1.99 – 2.01 0.16 8.1% 8.1% 0.1% 99.3% 600uniform
2 - s - 2.00
2.27
2.25 – 2.29
0.49
24.3%
17.9%
13.5%
84.2%
1800
uniform 6 - r - 6.04 6.01 5.99 – 6.03 0.30 4.9% 4.9% 0.5% 98.5% 600
80
Table A-1. Continued Dist ODens TDens TL TNum TD D̂ 95% CI( D̂ ) RMSE RMSE% CV( D̂ ) Bias% 95% DCI Sim Runs uniform 6 - s - 6.04 5.75 5.73 – 5.77 0.59 9.8% 8.9% 4.8% 90.8% 1800
uniform 10 - r - 10.01 10.08 10.02 – 10.14 0.76 7.6% 7.5% 0.7% 96.0% 600uniform
10 - s - 10.01
11.22
11.08 – 11.36
3.26
32.6%
27.0%
12.1%
77.2%
1800
clumped 2 - - f 1.97 2.13 2.09 – 2.17 0.73 37.1% 33.6% 8.3% 72.2% 1200clumped
2 - - s 1.96
2.18
2.14 – 2.22
0.74
37.5%
32.5%
10.9%
73.1%
1200
clumped 6 - - f 5.75 6.06 5.96 – 6.17 1.83 31.8% 30.1% 5.4% 65.6% 1200clumped
6 - - s 5.75
6.10
6.00 – 6.20
1.81
31.5%
29.4%
6.0%
63.0%
1200
clumped 10 - - f 9.65 10.12 9.95 – 10.29 3.07 31.8% 30.3% 4.8% 66.8% 1200clumped
10 - - s 9.65
10.26
10.09 – 10.44
3.10
32.1%
29.9%
6.3%
67.0%
1200
random 2 - - f 2.00 2.02 2.00 – 2.04 0.28 14.1% 13.9% 1.0% 93.8% 1200random
2 - - s 2.00
2.04
2.02 – 2.06
0.29
14.6%
14.2%
2.0%
93.1%
1200
random 6 - - f 6.00 6.03 6.00 – 6.06 0.52 8.6% 8.6% 0.6% 94.5% 1200random
6 - - s 6.00
6.02
5.99 – 6.05
0.49
8.2%
8.2%
0.3%
94.1%
1200
random 10 - - f 10.00 10.09 10.05 – 10.13 0.67 6.7% 6.6% 0.9% 93.9% 1200random
10 - - s 10.00
10.06
10.02 – 10.09
0.65
6.5%
6.4%
0.6%
94.8%
1200
uniform 2 - - f 2.00 2.24 2.22 – 2.27 0.49 24.3% 18.7% 12.2% 86.3% 1200uniform
2 - - s 2.00
2.16
2.14 – 2.18
0.36
18.2%
15.1%
8.1%
89.6%
1200
uniform 6 - - f 6.04 5.79 5.76 – 5.82 0.55 9.1% 8.5% 4.1% 92.3% 1200uniform
6 - - s 6.04
5.84
5.81 – 5.86
0.51
8.5%
8.1%
3.3%
93.3%
1200
uniform 10 - - f 10.01 10.85 10.70 – 11.01 2.88 28.8% 25.4% 8.4% 79.8% 1200uniform 10 - - s 10.01 11.02 10.88 – 11.17 2.82 28.1% 23.9% 10.1% 84.0% 1200
LIST OF REFERENCES
Abrahamson, W. G. 1984. Species response to fire on the Florida Lake Wales Ridge. American Journal of Botany 71:35-43.
Alford, R. A. 1980. Population structure of Gopherus Polyphemus in northern Florida. Journal of Herpetology 14:177-182.
Ashton, P. S., and R. E. Ashton. in press. Natural history and management of the gopher tortoise (Gopherus polyphemus). Krieger Press, Malabar, Florida, USA.
Auffenberg, W., and R. Franz. 1982. The status and distribution of the gopher tortoise (Gopherus polyphemus). Wildlife Research Report 12, U.S. Department of Interior, Fish and Wildlife Service, Washington D.C., USA.
Borchers, D. L., S. T. Buckland, P. W. Goedhart, E. D. Clarke, and S. L. Hedley. 1998. Horvitz-Thompson estimators for double-platform line transect surveys. Biometrics 54:1221-1237.
Breininger, D. R., P. A. Schmalzer, and C. R. Hinkle. 1991. Estimating occupancy of gopher tortoise (Gopherus-polyphemus) burrows in coastal scrub and slash pine flatwoods. Journal of Herpetology 25:317-321.
Brown, B. M., and A. Cowling. 1998. Clustering and abundance estimation for Neyman-Scott models and line transect surveys. Biometrika 85:427-438.
Buckland, S. T., D. R. Anderson, K. P. Burnham, J. L. Laake, D. L. Borchers, and L. Thomas. 2001. Introduction to Distance Sampling: Estimating abundance of biological populations. Oxford University Press, New York, New York, USA.
Buckland, S. T., B. J. Goudie, and D. L. Borchers. 2000. Wildlife population assessments: Past developments and future directions. Biometrics 56:1-12.
Burke, R. L., and J. Cox. 1988. Evaluation and review of field techniques used to study and manage gopher tortoises. Pages 205-215 in Management of amphibians, reptiles, and small mammals in North America. US. Department of Agriculture, Forest Service, Flagstaff, Arizona, USA.
Burnham, K. P., and D. R. Anderson. 2002. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd edition. Springer, New York, New York, USA.
Burnham, K. P., D. R. Anderson, and J. L. Laake. 1980. Estimation of density from line transect sampling of biological populations. Wildlife Monographs 72:1-202.
Calambokidis, J., and J. Barlow. 2004. Abundance of blue and humpback whales in the eastern North Pacific estimated by capture-recapture and line-transect methods. Marine Mammal Science 20:63-85.
81
Cassey, P., and B. H. Mcardle. 1999. An assessment of distance sampling techniques for estimating animal abundance. Environmetrics 10:271-278.
Conradt, L., P. A. Zollner, T. J. Roper, K. Frank, and C. D. Thomas. 2003. Foray search: an effective systematic dispersal strategy in fragmented landscapes. American Naturalist 161:905-915.
Cox, J., D. Inkley, and R. Kautz. 1987. Ecology and habitat protection needs of gopher tortoise (Gopherus polyphemus) populations found on lands slated for large-scale development in Florida. 4, Florida Game and Fresh Water Fish Commission, Tallahassee, Florida, USA.
Diemer, J. E. 1992. Demography of the tortoise Gopherus polyphemus in northern Florida. Journal of Herpetology 26:281-289.
Donnelly, M. A., and C. Guyer. 1994. Patterns of reproduction and habitat use in an assemblage of Neotropical hylid frogs. Oecologia 98:291-302.
Doonan, T. J. 1986. A demographic study of an isolated population of the gopher tortoise, Gopherus polyphemus: and an assessment of a relocation procedure for tortoises. Thesis. University of Central Florida, Orlando, Florida, USA.
Doonan, T. J., and D. M. Epperson. 2001. Gopher tortoise (Gopherus polyphemus) populations of Naval Air Station Cecil Field, Florida: Structure, prevalence of upper respiratory tract disease, and activity patterns. Final Performance Report Florida Fish and Wildlife Conservation Commission, Tallahassee, Florida, USA.
Eisenberg, J. F. 1983. The gopher tortoise as a keystone species. Pages 1-4 in R. J. Bryant and R. Franz, editors. 4th Annual Meeting of the Gopher Tortoise Council, Florida State Museum, Gainesville, Florida, USA.
Ellis, A. M., and R. T. F. Bernard. 2005. Estimating the density of kudu (Tragelaphus strepsiceros) in subtropical thicket using line transect surveys of dung and DISTANCE software. African Journal of Ecology 43:362-368.
Epperson, D. M. 1997. Gopher tortoise (Gopherus polyphemus) populations: Activity patterns, upper respiratory tract disease, and management on a military installation in northeast Florida. Thesis. University of Florida, Gainesville, Florida, USA.
Eubanks, J. O., W. K. Michener, and C. Guyer. 2003. Patterns of movement and burrow use in a population of gopher tortoises (Gopherus polyphemus). Herpetologica 59:311-321.
Federal Register. 1987. Determination of threatened status for the gopher tortoise (Gopherus polyphemus). Pages 25376-25380 in Federal Register. Federal Register - National Archives and Records Administration.
FFWCC. 2006. Draft gopher tortoise management plan. Florida Fish and Wildlife Conservation Commission. Tallahassee, Florida, USA.
82
Fowler. 1986. The development of sampling strategies for population studies of coral reef fishes. A case study. Coral Reefs 6:49-58.
Gentry, A. H., and L. H. Emmons. 1987. Geographical variation in fertility, phenology, and composition of the understory of neotropical forests. Biotropica 19:216-227.
Gregory, C. J., R. R. Carthy, and L. G. Pearlstine. 2006. Survey and monitoring of species at risk at Camp Blanding Training Site, northeastern Florida. Southeastern Naturalist 5:473-498.
Hanowski, J. M., G. J. Niemi, and J. G. Blake. 1990. Statistical perspectives and experimental design when counting birds on line transects. The Condor 92:326-335.
Hashimoto, C. 1995. Population census of the chimpanzees in the Kalinzu Forest, Uganda: Comparison between methods with nest counts. Primates 36:477-488.
Hedley, S. L., and S. T. Buckland. 2004. Spatial models for line transect sampling. Journal of Agricultural, Biological, and Environmental Statistics 9:181-199.
Hines, J. E. 2000. DOBSERV - A double-observer approach for estimating detection probability and abundance from avian point counts. US. Geological Survey - Patuxent Wildlife Research Center, Patuxent, Maryland, USA.
Jarvinen, O., and R. A. Vaisanen. 1975. Estimating relative densities of breeding birds by the line transect method. Oikos 26:316-322.
Jefferson, T. A. 1996. Estimates of abundance of cetaceans in offshore waters by the northwestern Gulf of Mexico, 1992-1993. Southwestern Naturalist 41:279-287.
Krebs, C. J. 1999. Ecological Methodology. Addison-Wesley Educational Publishers, Menlo Park, California, USA.
Krzysik, A. J. 2002. A landscape sampling protocol for estimating distribution and density patterns of desert tortoise at multiple spatial scales. Chelonian Conservation and Biology 4:366-379.
Kushlan, J. A., and F. J. Mazotti. 1984. Environmental effects on a coastal population of gopher tortoises. Journal of Herpetology 18:231-239.
Lacki, M. J., J. W. Hummer, and J. L. Fitzgerald. 1994. Application of line transects for estimating population density of the endangered copperbelly water snake in southern Indiana. Journal of Herpetology 28:241-245.
Lewis, D. L., G. T. Baxter, K. M. Johnson, and M. D. Stone. 1985. Possible extinction of the Wyoming toad, Bufo hemiophrys baxteri. Journal of Herpetology 19:166-168.
83
Lohoefener, R. 1990. Line transect estimation of gopher tortoise burrow density using a fourier series. Pages 44-69 in E. Wester, C. K. Dodd Jr, and R. Franz, editors. Eighth annual meeting gopher tortoise council, Florida Museum of Natural History, Gainesville, Florida, USA.
Lohoefener, R., and L. Lohmeier. 1984. The status of Gopherus polyphemus (Testudines, Testudinidae) west of the Tombigbee and Mobile Rivers (Report to the US Fish and Wildlife Service in support of petition to list this population under the Endangered Species Act of 1973).
Mackenzie, D. I., J. D. Nichols, G. B. Lachman, S. Droege, J. A. Royle, and C. A. Langtimm. 2002. Estimating site occupancy rates when detection probabilities are less than one. Ecology 83:2248-2255.
Mackenzie, D. I., J. D. Nichols, J. A. Royle, K. H. Pollock, L. L. Bailey, and J. E. Hines. 2006. Occupancy estimation and modeling: Inferring patterns and dynamics of species occurrence. Elsevier, San Diego, California, USA.
Mann, T. M. 1993. Tortoise densities and burrow occupancy rates for gopher tortoises on selected sites in Mississippi. Mississippi Department of Wildlife, Fisheries and Parks, Jackson, Mississippi, USA.
Marques, F. F. C., S. T. Buckland, D. Goffin, C. E. Dixon, D. L. Borchers, B. A. Mayle, and A. J. Peace. 2001. Estimating deer abundance from line transect surveys of dung: sika deer in southern Scotland. Journal of Applied Ecology 38:349-363.
Mathworks. 2006. MATLAB. Mathworks, Natick, Massachusetts, USA.
McCoy, E. D., and H. R. Mushinsky. 1992. Studying a species in decline - gopher tortoises and the dilemma of correction factors. Herpetologica 48:402-407.
McCoy, E. D., and H. R. Mushinsky. 1995. The demography of Gopherus polyphemus (Daudin) in relation to size of available habitat. Florida Game and Fresh Water Fish Commission, Tallahassee, Florida, USA.
McCoy, E. D., and H. R. Mushinsky. 2005. Population consequences of upper respiratory tract disease on gopher tortoises. Florida Fish and Wildlife Conservation Commission, Tallahassee, Florida, USA.
McCoy, E. D., H. R. Mushinsky, and J. Lindzey. 2006. Declines of the gopher tortoise on protected lands. Biological Conservation 128:120-127.
McRae, W. A., J. L. Landers, and J. A. Garner. 1981. Movement patterns and home range of the gopher tortoise. American Midland Naturalist 106:165-179.
Moler, P., and J. E. Berish. 2001. An assessment of options for survey and monitoring of gopher tortoises on Commission-managed lands. Florida Fish and Wildlife Conservation Commission, Gainesville, Florida, USA.
84
Nichols, J. D., J. E. Hines, J. R. Sauer, F. W. Fallon, J. E. Fallon, and P. J. Heglund. 2000. A double-observer approach for estimating detection probability and abundance from point counts. Auk 117:393-408.
Plumptre, A. J. 2000. Monitoring mammal populations with line transect techniques in African forests. Journal of Applied Ecology 37:356-368.
Royle, J. A., and J. D. Nichols. 2002. Estimating abundance from repeated presence-absence data or point counts. Ecology 84:777-790.
Ruette, S., P. Stahl, and M. Albaret. 2003. Applying distance-sampling methods to spotlight counts of red foxes. Journal of Applied Ecology 40:32-43.
SAS Institute. 2004. SAS Institute, Inc., Cary, North Carolina, USA.
Schwartz, T. S., and S. A. Karl. 2005. Population and conservation genetics of the gopher tortoise (Gopherus Polyphemus). Conservation Genetics 6:917-928.
Seber, G. A. F. 1982. The estimation of animal abundance and related parameters, 2nd edition. Edward Arnold, London, England.
Smith, L. L. 1992. Nesting ecology, female home range and activity patterns, and hatchling survivorship in gopher tortoises (Gopherus polyphemus). M.S. Thesis. University of Florida, Gainesville, Florida, USA.
Smith, R. B., D. R. Breininger, and V. L. Larson. 1997. Home range characteristics of radio tagged gopher tortoises on Kennedy Space Center, Florida. Chelonian Conservation and Biology 2:358-362.
Smith, R. B., T. D. Tuberville, A. L. Chambers, K. M. Herpich, and J. E. Berish. 2005. Gopher tortoise burrow surveys: External characteristics, burrows cameras, and truth. Applied Herpetology 2:161-170.
Swann, D. E., R. C. Averill-Murray, and C. R. Schwalbe. 2002. Distance sampling for Sonoran Desert tortoises. Journal of Wildlife Management 66:969-975.
Thomas, L., J. L. Laake, S. Strindberg, F. F. C. Marques, S. T. Buckland, D. L. Borchers, D. R. Anderson, K. P. Burnham, S. L. Hedley, J. H. Pollard, and J. R. B. Bishop. 2003. DISTANCE. Research Unit for Wildlife Population Estimation. University of St. Andrews, U.K.
Wahlquist, H. 1991. Gopher Tortoise Conservation. Pages 77-79 in K. R. Beaman, F. Caporaso, S. McKeown, and M. Graff, editors. First International Symposium on Turtle & Tortoises, Chapman University, Orange, California, USA.
White, G. C., and K. P. Burnham. 1999. Program MARK: survival estimation from populations of marked animals. Bird Study 46:120-139.
85
Williams, B. K., J. D. Nichols, and M. J. Conroy. 2002. Analysis and Management of Animal Populations. Modeling, Estimation, and Decision Making. Academic Press.
Wilson, D. S., H. R. Mushinsky, and E. D. McCoy. 1994. Relationship between gopher tortoise body size and burrow width. Herpetological Review 22:122-124.
Zollner, P. A., and S. L. Lima. 1999. Search strategies for landscape-level interpatch movements. Ecology 80:1019-1030.
86
BIOGRAPHICAL SKETCH
Saif Z. Nomani was born in 1978 in Karachi, Pakistan. He graduated from Karachi
Grammar School in 1996 and attended college at the Lahore University of Management Science,
Lahore, Pakistan. He transferred to Rutgers University, New Brunswick, NJ, in January 1998.
Upon graduating in January 2002 with his B.S. in computer science he worked as a physical
security consultant at Constantin Walsh-Lowe LLC. After 4 years of working as a consultant he
was admitted to the Master of Science program at the Department of Wildlife Ecology and
Conservation at University of Florida, Gainesville, FL, in 2005.
87