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In this work, testing of factor effects to the observed data from finite mixture distributions are discussed. Likelihood ratio tests are used to test whether factors of interest have significant effects to the mixture distribution model. To carry out the likelihood ratio tests, different methods about the computation algorithm for the maximum likelihood estimation (MLE) of the parameters in the mixture models are studied. These methods are applied to the data obtained from a laboratory study on emergence of Pontomyia oceana, where the effects of factors, such as sex and temperature, to the distribution of the dates that Pontomyia oceana emerged are investigated. From the results obtained, in some cases, three-component logistic distributions are fitted to the data with two peaks very close to each other. This is somewhat surprising as merely from the histogram, it is not easy to see and usually not expected to say there are two very close peaks. From the practical point of view, as the laboratory conditions excluded the possible effects related to semi-lunar tidal fluctuations that may have a dominating influence in nature. Thus the laboratory results helps to identify all the possible factors that have minor effects. Based on the results of this study, the difference between males and females, nevertheless, suggests that sex hormone may be involved in affecting the emergence dates. The suggestion of a third peak is unexpected from our point of view and it implies that there are factors we never suspected. It is worth noting that through rigorous statistical analysis presented here, it helps to provide an objective estimation on the distribution of the emergence dates as well as the corresponding proportions and the peak synchronous emergence dates in each period under different factor effects. We only start to speculate its possible adaptive meaning after the differences have been established as a true phenomenon. From this study, it reveals some additional biological phenomena worthy of more investigations.

Factor Effects Testing for Mixture Distributions with Application to the Study of Emergence of Pontomyia Oceana