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.


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)


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)


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.


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))


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.

the effect of temperature on the survival of chinook salmon eggs and fry: a probabilistic model...

Documents