MODELING AND STATISTICAL ANALYSIS OF A LABORATORY EXPERIMENT TO MEASURE CANNIBALISM IN HELIOTHIS VIRESCENS LARVAE

Statistical and biomathematical techniques are employed to analyze a simple laboratory experiment investigating genetic variation in the propensity for intraspecific predation (cannibalism) among eleven geographic strains of Heliothis virescens (F.) larvae.;The analysis is based on a statistical model of the replicated experiment and a complementary stochastic model of the relevant biological phenomena. The statistical model, based on the trinomial distribution, obtains from the usual assumption of independent replications. The biomathematical model defines a parameter which represents the propensity for cannibalism, and thereby quantifies the propensity for cannibalism in the sense that the statistical estimate of that parameter is an estimate of the propensity for cannibalism exhibited by each strain. The same model determines which statistical hypotheses ought to be tested in order to decide whether or not cannibalism occurs. As a result of the modeling process, the biological assumptions are explicitly recognized and exposed to critical scrutiny. The scope of inferences based on the experiment is delineated, and additional experiments that might be performed in the future are suggested.;A unique, uniformly most powerful size .05, Neyman structure randomized test of the hypothesis that cannibalism does not occur is derived from the Neyman-Pearson theory, and then implemented using an efficient computer program. (A more complex program is used to compute the power against 100 alternatives.) This test is compared with a supposedly size .05 chi-squared goodness-of-fit test that was used by previous investigators, and with two other tests based on normal approximations of the distribution of the relevant statistic.;The difference between the optimal Neyman structure test and each of the comparable approximate tests is excessive unless the sample size is extremely large. Since the actual size of each of the three approximate tests is subtantially greater than the supposed size, and since the exact Neyman structure test can be computed inexpensively, the exact Neyman structure test is preferable.;Comparison of the tests is facilitated by the introduction of the concept of an "expected critical region" for a randomized test (based on a discrete distribution) that is analogous to the critical region of a nonrandomized test (based on a continuous distribution). The nature of the inaccuracy of the approximate tests is investigated by computing and comparing the exact and assumed approximate distributions of the various test statistics.;The dissertation exemplifies the usefulness and importance of biomathematical modeling and the nonroutine practical application of statistical theory.