23 o CONGRESSO BRASILEIRO DE NEMATOLOGIA March 14, 2001 Howard Ferris Department of Nematology
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Transcript of 23 o CONGRESSO BRASILEIRO DE NEMATOLOGIA March 14, 2001 Howard Ferris Department of Nematology
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Nematode Population Dynamics and Economic Thresholds
Dinâmica das Populações de Nematóides e Níveis de Dano Econômico
23o CONGRESSO BRASILEIRO DE NEMATOLOGIA
March 14, 2001
Howard FerrisDepartment of Nematology
University of California, Davis
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Basic components of the dynamics of populations:
• Birth and death rates
• Development and senescence rates
• Population size
• Density dependence– resource availability
• Predator pressure
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Birth Rates
• Intrinsic factors– oocytes and sperm– age effects
• Extrinsic factors– resource availability– mate availability– temperature
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Sex Ratios and Multiple Mating Effects
0
2000
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0 50 100Pi
Pf
1:1 F:M
0.3:0.7 F:M
0.7:0.3 F:M
•C. elegans produces 4x more eggs when multiple-mated than by hermaproditism.
•Females of Heterodera attract and are mated by several males
•R. pellio male does not supply sufficient sperm to fertilize all oocytes from a single female
Consequences of Multiple Mating
•Probability that female genes are perpetuated is increased•Population may increase at a greater rate when there are fewer females and more males
Rhabditis pellio
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3 5 7 9Male Age
Egg
s fe
rtili
zed Total sperm = 884
Female produces 600 oocytesOnly 150 fertilized at a single mating
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Ag
e-s
pe
cifi
c R
ep
rod
uct
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clk-1
age-1
Caenorhabditis elegans
Chen, Carey and Ferris (2001), Expt. Gerontology 36:431-440
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Lifetime egg production
wild type
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age-1
Chen, Carey and Ferris (2001), Expt. Gerontology 36:431-440
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Death Rates
• Intrinsic factors– natural longevity– relationships of fecundity and longevity
• Extrinsic factors– resource availability– environmental extremes– predation– management
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8 1 6 2 4 3 2 4 0 4 8 0A G E ( d a y s )
80 eggs/day40-79 eggs/day1-39 eggs/day0 eggs/day
C. elegans wild type
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A G E ( d a y s )
l xw i l d t y p ec l k - 1a g e - 1
NU
MB
ER
AL
IVE 24
48
0 8 16 24 32 40 48 0
AGE (days)
Chen, Carey and Ferris (2001), Expt. Gerontology 36:431-440
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Many types of models represent our understanding of the dynamics of populations….
• Continuous and discrete time models– differential equations and time steps– understand behavior through calculus or sensitivity
analysis• Age and stage structured models• Deterministic and stochastic models• Individual and event-based models
– time steps or event steps
Models with parameters related to properties of the organisms are usually more satisfying to biologists than equations that draw lines through points on a graph
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Continuous time models Nt=N0ert, Nt=N0 t
dN/dt=rN
r=dNt/Ntdt (growth rate/indiv.)
=er (pop. growth/unit time)
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Nt
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Nt
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Continuous time models Nt=N0ert, Nt=N0 t
dN/dt=rN
r=dNt/Ntdt (growth rate/indiv.)
=er (pop. growth/unit time)
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Nt
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Nt
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Nt /N
0
Seasonal Multiplication:
Nt/N0=ert
Nt/N0=aN0b, Nt=aN0
(b+1)
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0
5
10
0 2 4 6 8 10Ln Initial Population (Pi) Sep 99
Ln F
inal
Pop
ulat
ion
(Pf)
Pf=(75/-Ln0.993)(1-0.993Pi)
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0 2 4 6 8 10Ln(Pi) Sep 99
Mul
tiplic
atio
n R
ate
(Pf/
Pi)
Pf/Pi=1018 Pi-0.71, r2=0.71
Pf/Pi=(400/-Ln0.90)(1-0.90Pi)/Pi
dN/dt=rN(1-N/K) Nt=K/(1+((K/N0-1)(e-rt))
dP/dt=aP(1-P/E) Pf=aEPi/((a-1)Pi+E) Pf=(a/-Lnq)(1-qPi)
Multiplication RatePf/Pi=((a/-Lnq)(1-qPi))/Pi
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Ln(Pi) Sep 99
Mul
tiplic
atio
n R
ate
(Pf/
Pi)
for PiPf/Pi=325, else
Pf/Pi=1018 Pi-0.71, r2=0.71
Kim and Ferris (2001)
Meloidogyne arenaria - oriental melon
Seasonal population change
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Discrete time models
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Soil Temperature
Rat
e
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Soil Moisture (bars)
Ra
te
Discrete time models
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Rat
e
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Soil Moisture (bars)
Ra
te
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0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
0
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Soil Temperature
Rat
e
Discrete time models
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Soil Temperature
Rat
e
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Soil Moisture (bars)
Ra
te
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Temperature
Rat
e
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Soil Moisture (bars)
Ra
te
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Soil Temperature
Rat
e
Discrete time models
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Soil Temperature
Rat
e
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Soil Moisture (bars)
Ra
te
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Temperature
Rat
e
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Temperature
Rat
e
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0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
0
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10 C 15 C 20 C 25 C 30 C 35 C
Soil Temperature
Rat
e
Discrete time models
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Soil Temperature
Rat
e
0
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0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
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Temperature
Rat
e
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Temperature
Rat
e
0
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10 C 15 C 20 C 25 C 30 C 35 C
Temperature
Rat
e
0
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0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
0
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10 C 15 C 20 C 25 C 30 C 35 C
Soil Temperature
Rat
e
Discrete time models
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Soil Temperature
Rat
e
0
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1
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0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
0
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1
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10 C 15 C 20 C 25 C 30 C 35 C
Temperature
Rat
e
0
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Temperature
Rat
e
0
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Temperature
Rat
e
0
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0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
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Soil Temperature
Rat
e
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Days
EggsJ2J3J4Ad
Discrete time models
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EggsJ2J3J4Ad
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Tot
al (
all s
tage
s)
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Tot
al (
all s
tage
s)Statistical Models
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Crop Yield in Relation to Nematode Population Density
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Total harvest
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Rel
ativ
e Y
ield
Late season
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0.81
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0 2 4 6 8 10Ln (Pi+1)
Rel
ativ
e Y
ield
Early season
00.20.40.60.8
11.2
0 2 4 6 8 10Ln (Pi+1)
Re
lativ
e Y
ield
Kim and Ferris (2001)
A: Early seasonY = 0.43+0.57*0.998Pi, ym=19743
B: Late seasonY = 0.03+0.97*0.998Pi, ym=10170
C: Total harvestY = 0.50+0.50*0.999Pi, ym=12312
A B
C
Oriental melon - Meloidogyne arenaria
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050000
100000150000200000250000300000
0 10 20 30 40 50 60Pi Sep 99
Val
ue L
oss
(WO
N)
Early
Late
Total
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0 10 20 30 40 50 60Pi Sep 99
Val
ue L
oss
(WO
N)
Early
Late
Total
Crop Value Panel A Panel BEarly Harvest 2019 won/kg 967 won/kgLate Harvest 967 won/kg 2019 won/kg
A
B
Kim and Ferris (2001)
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That initial population at which the loss in value due to nematode damage is equal to the cost of nematode management
The Economic Threshold
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That initial population at which the difference in crop value with and without management is equal to the cost of the management
The Economic Threshold amended
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That initial population level at which net returns become zero
Profitability Limit constraint
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Management Efficacy = 90%
7.055.54.3
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800
0 2 4 6 8Ln (Pi+1)
Ne
t Re
turn
s ET = 74PL1 = 245PL2 = 1153
Management Efficacy = 100%
4.15 5.5
0
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400
600
800
0 2 4 6 8
Ln (Pi+1)
Net
Ret
urns
ET = 63PL1 = 245
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Fixed Cost Economic Threshold
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Net
Ret
urns
($)
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Continuous Model Optimization
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0 2 4 6 8 10log2 Pi
$
a = 15b = 50
Pi = 550m = 0.1T = 50z = 0.999
$max = 1000E.T. = 110
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Discrete Model
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$
a = 600Pi = 200m = 0.1T = 20z = 0.99
$max = 1000E.T. = 78.48428
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Optimized Discrete Model
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Seasonal Multiplication Rates (Host Crop)
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Pi
Pf/P
ia = 500b = -0.2
amax = 500p = 1q = -0.1s = 0.65
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Overwinter Survival Rates
0
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1
0 500 1000 1500 2000Pf1
Pi2
/Pf1
a = 500b = -0.2
amax = 500p = 1q = -0.1s = 0.65
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Annual Population Change (Host Crop)
0
20000
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60000
80000
100000
120000
0 500 1000 1500 2000Pi1
Pi1
* (
Pi2
/Pi1
)a = 500b = -0.2
amax = 500p = 1q = -0.1s = 0.65
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Annual Population Change (Non-host)
0
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600
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1400
0 500 1000 1500 2000Pi(t)
Pi(t
+x)
Pi1
Pi2
Pi3a = 500b = -0.2
amax = 500p = 1q = -0.1s = 0.65
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0
200
400
600
800
1000
1200
1400
1600
0 1 2 3 4 5 6 7 8
Years After Planting Host Crop
Pi(t
+x)
a = 300b = 0.6s = 0.4
Pi(0) = 70
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Population Convergence
0
1000
2000
3000
0 5 10 15Year
Po
pu
lati
on
Le
vel
0NHR
2NHR
4NHR
6NHR
Optimum Rotation Length
-200
-100
0
100
200
300
0 1 2 3 4 5 6 7 8 9 10
Years of Non-host
Ave
. An
nu
al R
etu
rns
($
)
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Perennial Crop Considerations
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0
2000
4000
6000
8000
10000
12000
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
Days
Mes
ocric
onem
a xe
nopl
ax
Lovell
Nemaguard
0
2000
4000
6000
8000
10000
12000
0 2000 4000 6000 8000 10000 12000 14000
Degree-Days
Mes
ocric
onem
a xe
nopl
ax
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Year 1
0
20
40
60
80
100
0 1000 2000 3000DD
AU
C LU
LT
NU
NT
Year 2
02000400060008000
1000012000
0 1000 2000 3000DD
AU
C LU
LT
NU
NT
Year 3
05000
1000015000200002500030000
0 1000 2000 3000DD
AU
C LU
LT
NU
NT
Year 4
05000
1000015000200002500030000
0 1000 2000 3000DD
AU
C LU
LT
NU
NT
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Year 1
0
20
40
60
80
100
0 1000 2000 3000DD
AU
C LU
LT
NU
NT
Year 2
02000400060008000
1000012000
0 1000 2000 3000DD
AU
C LU
LT
NU
NT
Year 3
05000
1000015000200002500030000
0 1000 2000 3000DD
AU
C LU
LT
NU
NT
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0
2
4
6
8
10
12
Year 2 Year 3 Year 4 Year 5
Co
eff
icie
nt
LT-Full
LT-S/F
LU-Full
LU-S/F
NT-Full
NT-S/F
NU-Full
NU-S/F
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0
10
20
30
40
0 20 40 60 80 100AUC
Alfl
afa
Yie
ld L
oss y=1.15+0.37x, r2=0.89
0
20
40
60
80
0 2000 4000DD
Are
a U
nder
Cur
ve
Pi2170
Pi4
Pi43
Pi434
Noling and Ferris(1987)
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References
Burt, O. R. and H. Ferris. 1996. Sequential decision rules for managing nematodes with crop rotations. J. Nematology 28:457-474.
Chen, J., J.R. Carey and H. Ferris. 2001. Comparative demography of isogenic populations of Caenorhabditis elegans Expt. Gerontology 36:431-440.
Ferris, H. 1978. Nematode economic thresholds: derivation, requirements and theoretical considerations. J. Nematology 10:341-350.
Ferris, H. 1985. Density-dependent nematode seasonal multiplication and overwinter survivorship: a critical point model. J. Nematology 17:93-100.
Hsin, H. and C. Kenyon. 1999. Signals from the reproductive system regulate the lifespan of C. elegans. Nature 399:362-366.
Kim D.G. and H. Ferris. 2001. Relationship between crop losses and initial population densities of Meloidogyne arenaria in winter-grown oriental melon in Korea. J. Nematology (subm.)
Noling, J.W. and H. Ferris. 1987. Nematode-degree days, a density-time model for relating epidemiology and crop losses in perennials. J. Nematology 19:108-118.
Seinhorst, J.W. 1965. The relationship between nematode density and damage to plants. Nematologica 11:137-154.
Seinhorst, J.W. 1967. The relationship between population increase and population density in plant parasitic nematodes. II. Sedentary nematodes. Nematologica 13:157-171.
Somers, J.A., H.H. Shorey and L.K. Gaston. 1977. Reproductive biology and behavior of Rhabditis pellio (Schneider) (Rhabditida:Rhabditidae). J. Nematology 9:143-148.
More information:http://plpnemweb.ucdavis.edu/nemaplex/nemaplex.htm