Transcript The effect of temperature on the survival of Chinook

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
• ESA-Listed Chinook Salmon
• Temperature Control Structure
http://www.bpa.gov/corporate/BPANews/Library/images/Dams/Cougar.jpg
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
Background - Intention
 Qualitative model
 Incubation temperature (T) vs. rearing
temperature (T2)
 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
Weight
Th
Time
tm
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.
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)
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)
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.
Construction
Notice:
P(W ≤ w)=P(Tg ≤ z) = VTg(z(w,T2) ,T)



Solve W(t,T2) for time
New expression:
z(w,T2)
Gives time needed to grow to
w grams when reared at
temperature T2
Construction
Formula for Expected Value:


0
0
(W | E )   (W  w)dw   1  (W  w)dw
Results


Let Th, Tg have symmetrical triangular
distributions
Assume no fry mortality
Results

Egg Survival
P(E)=H(T)
1.2
Fit curve to data
(Current function is
a very poor fit)
Percent Survival
1
0.8
0.6
0.4
y = 0.0006x3 - 0.0336x2 + 0.4256x - 0.5722

N = #eggs
0.2
0
0
2
4
6
8
10
12
Temperature (C)
Fecundity:
~2000-17,000
Survival (Murray & McPhail, 1988)
Survival (Beacham & Murray, 1989)
Poly. (Survival (Murray & McPhail, 1988))
14
16
Results

Biomass
B(T,T2)= E(W|E) × N × P(E)
Results – Cougar Dam

USGS water temperature gauges
Above reservoir (14159200)
 Below dam (14159500)



According to current model:

Temp regime above reservoir → 110.7

Temp regime below dam → 156
kg
kg
By current model, dam encourages growth
and survival!
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
population’s biomass?
 What is the implication of one generation’s
biomass on successive generations?

Eco-Informatics

Eco-informatics in my project
Fish biology
 Probability theory
 Maple 10


Other discipline: Statistics

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.