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The effect of temperature on the survival of Chinook salmon eggs and fry: a probabilistic model Maarika Teose Oregon State University Jorge Ramirez, Edward.

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Presentation on theme: "The effect of temperature on the survival of Chinook salmon eggs and fry: a probabilistic model Maarika Teose Oregon State University Jorge Ramirez, Edward."— Presentation transcript:

1 The effect of temperature on the survival of Chinook salmon eggs and fry: a probabilistic model Maarika Teose Oregon State University Jorge Ramirez, Edward Waymire, Jason Dunham

2 Background – Cougar Dam Location Location ESA-Listed Chinook Salmon ESA-Listed Chinook Salmon Temperature Control Structure Temperature Control Structure http://www.bpa.gov/corporate/BPANews/Library/images/Dams/Cougar.jpg

3 Background - Salmon  Early Life History  Spawning, Egg, Alevin, Fry  Effect of Temperature  Studied exhaustively  Some equations exist  “Egg-Fry Conflict” (Quinn 2005) http://wdfw.wa.gov/wildwatch/salmoncam/hatchery.html

4 Background - Intention  Qualitative model  Incubation temperature (T) vs. rearing temperature (T 2 )  Survival and fitness of salmon

5 Construction - Objective Measure of fitness: Biomass Biomass = avg. weight × pop. size pop. size = (# eggs laid) × P(E) where P(E) = probability that an egg survives to hatching

6 Construction - Objective N = # eggs in reach P(E) = Probability that an egg hatches E(W|E) = Expected weight (i.e. average weight) given that the egg hatched Biomass = E(W|E) × N × P(E) It remains to find E(W|E)

7 Construction - Objective ThTh Weight tmtm Time

8 Construction Fish weight at time t m = W(t,T 2 ) (Elliott & Hurley 1997) Fish weight at time t m = W(t,T 2 ) (Elliott & Hurley 1997) Amount of time the fish grows (t) Amount of time the fish grows (t) Rearing temperature (T 2 ) Rearing temperature (T 2 ) Need an expression for the amount of time a fish has to grow.

9 Construction Recall T h has a density function: Recall T h has a density function: f Th (t,T) Equation for median hatching time (Crisp 2000) : Equation for median hatching time (Crisp 2000) : D 2 (T) D 2 (T) determines location of f Th (t,T) D 2 (T) determines location of f Th (t,T)

10 Construction T g = amt of time a fish has to grow before t m T g = t m – T h Median of distribution of T g given by t m – D 2 (T) Probability density function v Tg (t,T) Probability density function v Tg (t,T) Cumulative distribution function V Tg (t,T) Cumulative distribution function V Tg (t,T)

11 Construction Recall: Cumulative Distribution Function “G(x)” Cumulative Distribution Function “G(x)” G(x) = P(X ≤ x) In our case In our case V Tg (t,T) = P(T g ≤ t) Probability that for some incubation temperature T, the time the fish has to grow once it hatches is less than t.

12 Construction Notice: Notice: P(W ≤ w)=P(T g ≤ z) Solve W(t,T 2 ) for time Solve W(t,T 2 ) for time New expression: New expression: z(w,T 2 ) Gives time needed to grow to w grams when reared at temperature T 2 V Tg (z(w,T2),T) = V Tg (z(w,T2),T)

13 Construction Formula for Expected Value:

14 Results Let T h, T g have symmetrical triangular distributions Let T h, T g have symmetrical triangular distributions Assume no fry mortality Assume no fry mortality

15 Results P(E)=H(T) P(E)=H(T) Fit curve to data (Current function is a very poor fit) N = #eggs N = #eggsFecundity:~2000-17,000

16 Results Biomass Biomass B(T,T 2 )= E(W|E) × N × P(E)

17 Results – 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 → 110.7 kg Temp regime above reservoir → 110.7 kg Temp regime below dam → 156 kg Temp regime below dam → 156 kg By current model, dam encourages growth and survival! By current model, dam encourages growth and survival!

18 Conclusion Improvements: Improvements: Realistic distribution for T h, T g Realistic distribution for T h, T g Introduce fry mortality into model Introduce fry mortality into model Improved form of H(T) Improved form of H(T) Further research: Further research: Is T or T 2 more decisive in determining a population’s biomass? Is T or T 2 more decisive in determining a population’s biomass? What is the implication of one generation’s biomass on successive generations? What is the implication of one generation’s biomass on successive generations?

19 Eco-Informatics Eco-informatics in my project Eco-informatics in my project Fish biology Fish biology Probability theory Probability theory Maple 10 Maple 10 Other discipline: Statistics Other discipline: Statistics

20 Acknowledgements Acknowledgements Thanks to Jorge Ramirez, Jason Dunham, Edward Waymire, Desiree Tullos and the 2007 Eco-Informatics Summer Institute, everyone at the HJ Andrews Experimental Forest, and the National Science Foundation. References References Crisp, D.T. (2000). Trout and salmon: ecology, conservation and rehabilitation. Oxford, England: Blackwell Science. Elliott, J.M., & Hurley, M.A. (1997). A functional model for maximum growth of Atlantic salmon parr, salmo salar, from two populations in northwest England. Functional Ecology. 11, 592-603. Quinn, Tom (2005). The behavior and ecology of Pacific salmon and trout. Seattle, WA: University of Washington Press.

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