STOCHASTIC APPROACH TO PREDICT SURVIVAL 645 



during hot weather for the easily injured Gulf menhaden {Breuoortia 

 patroniis). Animals captured in the afternoon and evening were kept 

 in cages in the intake canal for later experimentation. The cylindrical 

 cages, 61 cm in diameter and 63.5 cm deep, were constructed of 

 plastic netting material of 0.325-cm or 1.3-cm mesh. 



Cessation of opercular motion was the criterion of death for the 

 fishes. Crustaceans were considered dead when appendages no longer 

 moved. Survival times were measured to 0.1 min with an elapsed- 

 time meter. Survivors were discarded. 



Treatment of Data 



After determining survival times of individual organisms at each 

 test temperature, we calculated seasonal survival percentages for 180 

 min by 10-min intervals for each species. The least-squares method 

 (Steel and Torrie, 1960) was used to estimate seasonal mortality 

 rates of 8 species of crustaceans and 46 fishes by season at each test 

 temperature. 



To estimate survival probabilities and expected survival times at 

 each test temperature, we used the stochastic approach (Matis and 

 Hartely, 1971; Gross and Clark, 1975): 



Pi(t) = e~^i^ for min < t < 180 min 



where t = time exposed 



Pi(t) = probability of survival to time t at test temperature i 

 Pi = constant death rate at test temperature i 

 T\ = expected survival time at test temperature i 



To estimate survival probabilities for the population of a species 

 exposed in the discharge canal afferent to the cooling towers, we 

 used the stochastic model: 



Pi(f)=e~^i*^ for min < t < 30 min 



where t is time exposed, Pi(t) is probability of survival in the 

 discharge canal afferent to the cooling towers, and Xj is death rate in 

 the discharge canal afferent to the cooling towers. 



To estimate expected population survival after exposure in the 

 discharge canal efferent to the cooling towers, we used the stochastic 

 model: 



P2(t) = (e~^' 3 0)[e-^2(t-3 0)j fQj. 30 j^^i^ < t< 180 min 



