Response surfaces for overdispersion in the study of the conditions for fish eggs hatching

Abstract

Response surface methodology, originally developed for determining optimal conditions in industrial experiments, was early adapted to experiments in marine ecology. However, these involved studying the shape of the complete response surface, not only detecting the optimum, and often had counts or durations as the response variable. Thus, nonlinear, nonnormal response models were required. For counts, binomial and beta-binomial models have been used, the latter because of substantial overdispersion. In closely controlled experiments, overdispersion among units held under the same conditions might indicate that some mishap has occurred in conducting the study. One possible check is to model the dispersion as a second response surface. This procedure is used to show that overdispersion in fish egg hatching experiments has a biological explanation in that it occurs only under suboptimal hatching conditions.