The effect of temperature on the survival of Chinook salmon eggs and fry: a probabilistic model...
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Transcript of The effect of temperature on the survival of Chinook salmon eggs and fry: a probabilistic model...
The effect of The effect of temperature on the temperature on the survival of Chinook survival of Chinook
salmon eggs and fry: salmon eggs and fry: a probabilistic modela probabilistic model
Maarika TeoseMaarika TeoseOregon State UniversityOregon State University
Jorge Ramirez, Edward Waymire,Jorge Ramirez, Edward Waymire,Jason DunhamJason Dunham
Background – Cougar Background – Cougar DamDam
• LocationLocation• ESA-Listed Chinook SalmonESA-Listed Chinook Salmon• Temperature Control StructureTemperature Control Structure
http://www.bpa.gov/corporate/BPANews/Library/images/Dams/Cougar.jpg
Background - SalmonBackground - Salmon
Early Life HistoryEarly Life History Spawning, Egg, Alevin, FrySpawning, Egg, Alevin, Fry
Effect of TemperatureEffect of Temperature Studied exhaustivelyStudied exhaustively Some equations existSome equations exist ““Egg-Fry Conflict” Egg-Fry Conflict” (Quinn 2005)(Quinn 2005)
http://wdfw.wa.gov/wildwatch/salmoncam/hatchery.html
Background - IntentionBackground - Intention
Qualitative model Qualitative model Incubation temperature (T) vs. Incubation temperature (T) vs.
rearing temperature (Trearing temperature (T22)) Survival and fitness of salmonSurvival and fitness of salmon
Construction - ObjectiveConstruction - Objective
Measure of fitness: BiomassMeasure of fitness: Biomass
Biomass = avg. weight × Biomass = avg. weight × pop. sizepop. size
pop. sizepop. size = = (# eggs laid)(# eggs laid) × × P(P(EE))
where P(where P(EE) = probability that an egg survives to ) = probability that an egg survives to hatchinghatching
Construction - Objective Construction - Objective
NN = # eggs in reach = # eggs in reach
P(P(EE)) = Probability that an egg hatches = Probability that an egg hatches
E(E(WW||EE)) = Expected weight (i.e. average = Expected weight (i.e. average weight) given that the egg hatchedweight) given that the egg hatched
Biomass = Biomass = E(E(WW||EE)) × × NN × × P(P(EE))
It remains to find It remains to find E(E(WW||EE))
Construction - ObjectiveConstruction - Objective
Th
Weight
tm
Time
ConstructionConstruction
Fish weight at time tFish weight at time tmm= = W(t,TW(t,T22) ) (Elliott & Hurley 1997)(Elliott & Hurley 1997)
Amount of time the fish grows (t)Amount of time the fish grows (t) Rearing temperature (TRearing temperature (T22))
Need an expression for the amount Need an expression for the amount of time a fish has to grow.of time a fish has to grow.
ConstructionConstruction
Recall TRecall Thh has a has a density function: density function:
ffThTh(t,T)(t,T)
Equation for median Equation for median hatching time (Crisp hatching time (Crisp 2000)2000): :
DD22(T)(T)
DD22(T) determines (T) determines location of flocation of fThTh(t,T)(t,T)
ConstructionConstruction
TTgg = amt of time a fish has to grow = amt of time a fish has to grow before tbefore tmm
TTgg = t = tmm – T – Thh
Median of distribution of TMedian of distribution of Tgg given by given by
ttmm – D – D22(T)(T) Probability density function vProbability density function vTgTg(t,T)(t,T) Cumulative distribution function Cumulative distribution function
VVTgTg(t,T)(t,T)
ConstructionConstruction
Recall: Recall: Cumulative Distribution Function Cumulative Distribution Function
“G(x)”“G(x)”G(x) = P(X ≤ x)G(x) = P(X ≤ x)
In our caseIn our caseVVTgTg(t,T)(t,T) = P(T = P(Tgg ≤ t) ≤ t)
Probability that for some incubation temperature Probability that for some incubation temperature T, the time the fish has to grow once it hatches is T, the time the fish has to grow once it hatches is
less than t.less than t.
ConstructionConstruction
Notice:Notice:
P(W ≤ w)=P(TP(W ≤ w)=P(Tgg ≤ z) ≤ z)
Solve Solve W(t,TW(t,T22)) for for timetime
New expression: New expression:
z(w,Tz(w,T22))
Gives time needed to Gives time needed to grow to w grams when grow to w grams when reared at temperature reared at temperature TT22
= VVTgTg((z(w,T2)z(w,T2) ,T,T))
ConstructionConstruction
Formula for Expected Value:Formula for Expected Value:
00
)(1)()|( dwwWdwwWEW
ResultsResults
Let TLet Thh, T, Tgg have symmetrical have symmetrical triangular distributionstriangular distributions
Assume no fry mortalityAssume no fry mortality
ResultsResults
P(P(EE)=H(T)=H(T))
Fit curve to Fit curve to datadata
(Current (Current function is a function is a very poor fit)very poor fit)
N = #eggsN = #eggs
Fecundity:Fecundity:~2000-17,000~2000-17,000
Egg Survival
y = 0.0006x3 - 0.0336x2 + 0.4256x - 0.5722
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12 14 16
Temperature (C)
Pe
rce
nt
Su
rviv
al
Survival (Murray & McPhail, 1988)
Survival (Beacham & Murray, 1989)
Poly. (Survival (Murray & McPhail, 1988))
ResultsResults
BiomassBiomass
B(T,TB(T,T22)= )= E(E(WW||EE)) × × NN × × P(P(EE))
Results – Cougar DamResults – Cougar Dam
USGS water temperature gauges USGS water temperature gauges Above reservoir (14159200)Above reservoir (14159200) Below dam (14159500)Below dam (14159500)
According to current model:According to current model: Temp regime above reservoir → Temp regime above reservoir → 110.7 kg110.7 kg
Temp regime below dam → Temp regime below dam → 156 kg156 kg By current model, dam By current model, dam
encourages growth and survival!encourages growth and survival!
ConclusionConclusion
Improvements:Improvements: Realistic distribution for TRealistic distribution for Thh, T, Tgg
Introduce fry mortality into modelIntroduce fry mortality into model Improved form of H(T)Improved form of H(T)
Further research:Further research: Is T or TIs T or T22 more decisive in more decisive in
determining a population’s biomass?determining a population’s biomass? What is the implication of one What is the implication of one
generation’s biomass on successive generation’s biomass on successive generations?generations?
Eco-InformaticsEco-Informatics
Eco-informatics in my projectEco-informatics in my project Fish biology Fish biology Probability theory Probability theory Maple 10Maple 10
Other discipline: StatisticsOther discipline: Statistics
AcknowledgementsAcknowledgementsThanks to Jorge Ramirez, Jason Dunham, Edward Thanks to Jorge Ramirez, Jason Dunham, Edward
Waymire, Desiree Tullos and the 2007 Eco-Waymire, Desiree Tullos and the 2007 Eco-Informatics Summer Institute, everyone at the HJ Informatics Summer Institute, everyone at the HJ Andrews Experimental Forest, and the National Andrews Experimental Forest, and the National Science Foundation.Science Foundation.
ReferencesReferencesCrisp, D.T. (2000). Crisp, D.T. (2000). Trout and salmon: ecology, Trout and salmon: ecology,
conservation and rehabilitationconservation and rehabilitation. Oxford, England: . Oxford, England: Blackwell Science.Blackwell Science.
Elliott, J.M., & Hurley, M.A. (1997). A functional Elliott, J.M., & Hurley, M.A. (1997). A functional model for maximum growth of Atlantic salmon parr, model for maximum growth of Atlantic salmon parr, salmo salar, from two populations in northwest salmo salar, from two populations in northwest England. England. Functional EcologyFunctional Ecology. . 1111, 592-603., 592-603.
Quinn, Tom (2005). Quinn, Tom (2005). The behavior and ecology of The behavior and ecology of Pacific salmon and troutPacific salmon and trout. Seattle, WA: University of . Seattle, WA: University of Washington Press.Washington Press.