Pollocks Robust Design: Model Extensions. Estimation of Temporary Emigration Temporary Emigration: =...
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Transcript of Pollocks Robust Design: Model Extensions. Estimation of Temporary Emigration Temporary Emigration: =...
Pollock’s Robust Design:
Model Extensions
Estimation of Temporary Emigration
Temporary Emigration:= individual emigrated from study area, but only temporarily (e.g., for one or a few years)
“emigrated”: individual is outside the study area during entire primary period=> NOT available for detection
“temporary”: animal will come back => not confounded with mortality, but bias detection low
Estimation of Temporary Emigration
Temporary Emigration (TE) = individual unavailable for detection a given year
We distinguish: = Pr(presence in sampled area) and = Pr(detection | presence in sampled area)
We have:
Estimation of Temporary Emigration
Robust Design: closed + open models
Closed model: Pr(detection | availability)
Open model:
= Pr(detection | availability) * Pr(availability)
We can thus estimate as =>
TE: Two possible directionsExiting vs. remaining outside study area (from one year to the next)
We define 2 distinct parameters:
• γ' = Probability that an individual that was not present in the previous sampling period become present in the current sampling period
• γ'' = Probability that an individual that was present in the previous sampling period remains present in the current sampling period
Temporary emigration
p1 p2 p3 p4
’ 1-” ’ 1-”
𝜙𝑖𝜙𝑖
Models for temporary emigration• No temporary emigration
γ’ = γ’’ = 1
• Random movement – emigration does not depend on last period
γ’ = γ’’
• Markovian movement – emigration depends on last period γ’ ≠ γ’’
Temporary Emigration: Biological Relevance
• Sometimes just local movement
• Breeding ground sampling: equates with P(nonbreeding) in various taxa (sea turtles, many bird species, some marine mammals, some toads)
Open Robust Design
Closed Robust Design
p1 p2 p3 p4
’ 1-” ’ 1-”
Closure assumption within primary periods (closed model)
No gain/loss
𝜙𝑖𝜙𝑖
Open Robust Design
p1 p2 p3 p4
’ 1-” 0 1 32
1 2 3
We model “staggered entries and departures” between secondary sampling occasions
= Each indiv. can enter () and depart () only once each year= Super-Population model applied inside primary periods
’ 1-”
Open Robust Design
Deals with the fact that an individual might:
- not be available yet at first sampling occasion and it might become= has not entered the sampled area yet
- might become unavailable before the last occasion = has departed the sampled area
Kendall and Bjorkland (2001)Hawksbill Sea Turtle
(Eretmochelys imbricata)
Hawksbill Sea Turtle(Eretmochelys imbricata)
• Jumby Bay, Long Island, Antigua• Collected 15 June – 15 November 1987-96• Female arrives, lays clutch returns to surf,
lays up to 4 more clutches every 14 days• Captured/resighted on nest, flipper tag
applied and shell notched.
Hawksbill Sea Turtle(Eretmochelys imbricata)
• Breeding season divided into 10 half-month periods to approximate 14-day cycle of egg depositionFemales are available for detection between first and last clutch
• NEVER breed in two consecutive years(Non-breeding = TE)
How do we account for no breeding in consecutive years?
Why do we need an OPEN robust design model here?
How do we interpret the ‘super-population’ estimate?
p1 p2 p3 p4
’ 1-”
*
0 1 32
1 2 3’ 1-”
*
Hawksbill Sea Turtles(Parameters involved)
1. Between breeding seasons:i* = prob. of survival/fidelity from year i to i+1
i” = prob. turtle is a breeder in year i if turtle was a breeder in year i-1
Never happens => i” = 0 ; (1 - i”) = 1
i’ = prob. turtle is a breeder in year i if turtle was a non-breeder in year i-1
Hawksbill Sea Turtles(Parameters involved)
2. Inside breeding season:ij = probability breeder in year i enters study area
between sample j and j+1 (first clutch)
ij = prob. breeder in year i lays last clutch betweensamples j and j+1
pij = prob. breeder is detected in sample j of year i
How do we account for no breeding in consecutive years?
We fix: i” = 0 ; (1 - i”) = 1
p1 p2 p3 p4
’ 1-”
*
0 1 32
1 2 3’ 1-”
*
p1 p2 p3 p4
’ 1-”
*
0 1 32
1 2 3’ 1-”
*
Use of the OPEN robust design?
Turtle only available between first and last clutch.
Dates of arrival/departure vary.
We use the j and j to model arrival/departures.
p1 p2 p3 p4
’ 1-”
*
0 1 32
1 2 3’ 1-”
*
Super-population?
= Total number of turtles that bred (in sampled area) this year
Multistate Robust Design
• Combine methods to improve estimates of state transitions (Nichols and Coffman 1999, Coffman et al. 2001)
• Reverse-time example in next section– Allows contributions of survival, reproduction,
and emigration to be separated