STOCHASTIC APPROACH TO PREDICT SURVIVAL 659 



This model has two weaknesses. First, death rates were estimated 

 from the laboratory experiments rather than directly from animals 

 passing through the discharge canal. Mortality rates may differ in the 

 discharge because of nonthermal factors. Second, cumulative dosage 

 and acclimation in the discharge canal afferent to the cooling towers 

 (30 min) were not considered. Animals exposed there for 30 min 

 might sustain critical damage and could die in the canal efferent to 

 the towers even though they would have survived if not previously 

 stressed. Laboratory data used to predict mortality past the cooling 

 towers did not consider previous thermal stresses occurring in the 

 canal above the towers. On the other hand, animals might survive 

 longer than expected since they will undergo some upward acclima- 

 tion in the discharge canal afferent to the towers. 



Despite the model's theoretical weaknesses, we accepted it as 

 adequately descriptive of seasonal survival of animal populations in 

 the discharge-canal system because expected survival determined by 

 the stochastic method at various test temperatures (Fig. 2) agreed 

 closely with actual percent of test animals surviving at test 

 temperatures in the laboratory (despite variations for some species 

 tested in small numbers). 



Fry, Brett, and Walker (1946) suggested a deterministic model 

 for fish mortality at lethally high temperatures, which, basically, 

 argues that a lethal dose is accumulated as the ratio of exposure time 

 at temperature T to median resistance time at temperature T. When 

 the accumulated dose reaches 1.0, the fish is dead. Their model 

 accurately predicted the results of laboratory tests, but it, too, has 

 not been tested under field conditions. 



ACKNOWLEDGMENTS 



The research reported here was funded by a grant from Houston 

 Lighting & Power Company to the Department of Wildlife and 

 Fisheries Sciences and the Texas Agricultural Experiment Station 

 (Project 1869-2898). 



This manuscript is taken in part from K. S. Chung's thesis 

 prepared in partial fulfillment of the requirement for the degree of 

 Doctor of Philosophy at Texas A. & M. University. 



We thank J. M. Matis, Institute of Statistics, Texas A. & M. 

 University, for suggestions in statistical analysis and W. H. Neill, 

 Department of Wildlife and Fisheries Sciences, Texas A. & M. 

 University, and F. G. Schlicht, Houston Lighting & Power Company, 

 for their criticism during the development of the manuscript. Thanks 



