The effect of temperature on the survival of Chinook salmon eggs and fry: a probabilistic model

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
• ESA-Listed Chinook Salmon
• Temperature Control Structure

http//www.bpa.gov/corporate/BPANews/Library/image
s/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.ht
ml
4
Background - Intention

• Qualitative model
• Incubation temperature (T) vs. rearing
  temperature (T2)
• 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(WE) Expected weight (i.e. average weight)
  given that the egg hatched
• Biomass E(WE) N P(E)
• It remains to find E(WE)

7
Construction - Objective
Weight
tm
Time
8
Construction

• Fish weight at time tm W(t,T2) (Elliott Hurley
  1997)
• Amount of time the fish grows (t)
• Rearing temperature (T2)
• Need an expression for the amount of time a fish
  has to grow.

9
Construction

• Recall Th has a density function
• fTh(t,T)
• Equation for median hatching time (Crisp 2000)
• D2(T)
• D2(T) determines location of fTh(t,T)

10
Construction

• Tg amt of time a fish has to grow before tm
• Tg tm Th
• Median of distribution of Tg given by
• tm D2(T)
• Probability density function vTg(t,T)
• Cumulative distribution function VTg(t,T)

11
Construction

• Recall
• Cumulative Distribution Function G(x)
• G(x) P(X x)
• In our case
• VTg(t,T) P(Tg 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
• P(W w)P(Tg z)
• Solve W(t,T2) for time
• New expression
• z(w,T2)
• Gives time needed to grow to w grams when reared
  at temperature T2

VTg(z(w,T2) ,T)
13
Construction

• Formula for Expected Value

14
Results

• Let Th, Tg have symmetrical triangular
  distributions
• Assume no fry mortality

15
Results

• P(E)H(T)
• Fit curve to data
• (Current function is a very poor fit)
• N eggs
• Fecundity
• 2000-17,000

16
Results

• Biomass
• B(T,T2) E(WE) N P(E)

17
Results Cougar Dam

• USGS water temperature gauges
• Above reservoir (14159200)
• Below dam (14159500)
• According to current model
• Temp regime above reservoir ? 110.7 kg
• Temp regime below dam ? 156 kg
• By current model, dam encourages growth and
  survival!

18
Conclusion

• Improvements
• Realistic distribution for Th, Tg
• Introduce fry mortality into model
• Improved form of H(T)
• Further research
• Is T or T2 more decisive in determining a
  populations biomass?
• What is the implication of one generations
  biomass on successive generations?

19
Eco-Informatics

• Eco-informatics in my project
• Fish biology
• Probability theory
• Maple 10
• Other discipline Statistics

20

• 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
• 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.