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

Background – Cougar Dam Location Location ESA-Listed Chinook Salmon ESA-Listed Chinook Salmon Temperature Control Structure Temperature Control Structure

Background - Salmon  Early Life History  Spawning, Egg, Alevin, Fry  Effect of Temperature  Studied exhaustively  Some equations exist  “Egg-Fry Conflict” (Quinn 2005)

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

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

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)

Construction - Objective ThTh Weight tmtm Time

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.

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)

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)

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.

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)

Construction Formula for Expected Value:

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

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

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

Results – Cougar Dam USGS water temperature gauges USGS water temperature gauges Above reservoir ( ) Above reservoir ( ) Below dam ( ) Below dam ( ) According to current model: According to current model: Temp regime above reservoir → kg Temp regime above reservoir → 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!

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?

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

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, Quinn, Tom (2005). The behavior and ecology of Pacific salmon and trout. Seattle, WA: University of Washington Press.