Design and analysis of experiments on random drift and inbreeding depression.

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Abstract
While the genetic consequences of inbreeding and small population size are of fundamental importance in many areas of biology, empirical research on these phenomena has proceeded in the absence of a well-developed statistical methodology. The usual approach is to compare observed means and variances with the expectations of Wright's neutral, additive genetic model for quantitative characters. If the observations deviate from the expectations more than can be accounted for by sampling variance of the parameter estimates, the null hypothesis is routinely rejected in favor of alternatives invoking evolutionary forces such as selection or nonadditive gene action. This is a biased procedure because it treats sequential samples from the same populations as independent, and because it ignores the fact that the expectations of the neutral additive genetic model will rarely be realized when only a finite number of lines are studied. Even when genes are perfectly additive and neutral, the variation among the properties of founder populations, the random development of linkage disequilibrium within lines, and the variance in inbreeding between lines reduce the likelihood that Wright's expectations will be realized in any particular set of lines. Under most experimental designs, these sources of variation are much too large to be ignored. Formulas are presented for the variance-covariance structure of the realized within- and between-line variance under the neutral additive genetic model. These results are then used to develop statistical tests for detecting the operation of selection and/or inbreeding depression in small populations. A number of recommendations are made for the optimal design of experiments on drift and inbreeding, and a method is suggested for the correction of data for general environmental effects. In general, it appears that we can best understand the response of populations to inbreeding and finite population size by studying a very large number (>100) of self-fertilizing or full-sib mated lines in parallel with one or more stable control populations.