No abstract

Polyphenisms are excellent models for studying phenotypic variation, yet few studies have focused on natural populations. Facultative paedomorphosis is a polyphenism in which salamanders either metamorphose or retain their larval morphology and eventually become paedomorphic. Paedomorphosis can result from selection for capitalizing on favorable aquatic habitats (paedomorph advantage), but could also be a default strategy under poor aquatic conditions (best of a bad lot). We tested these alternatives by quantifying how the developmental environment influences the ontogeny of wild Arizona tiger salamanders (Ambystoma tigrinum nebulosum). Most paedomorphs in our study population arose from slow-growing larvae that developed under high density and size-structured conditions (best of a bad lot), although a few faster-growing larvae also became paedomorphic (paedomorph advantage). Males were more likely to become paedomorphs than females and did so under a greater range of body sizes than females, signifying a critical role for gender in this polyphenism. Our results emphasize that the same phenotype can be adaptive under different environmental and genetic contexts and that studies of phenotypic variation should consider multiple mechanisms of morph production.

This paper is a review of many of the dozens of procedures currently available for testing a data set for goodness-of-fit to the multivariate normal distribution. A majority of the procedures can be placed into one of four basic categories. Most procedures are multivariate extensions or adaptations of procedures used for testing univariate normality. Results of several power studies are summarized, and an extensive bibliography of literature pertaining to testing for multivariate normality is provided.

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Equivalence testing, an alternative to testing for statistical significance, is little used in educational research. Equivalence testing is useful in situations where the researcher wishes to show that two means are not significantly different. A simulation study assessed the relationships between effect size, sample size, statistical significance, and statistical equivalence.