A new statistical test of fitness set data from reciprocal transplant experiments involving intermediate phenotypes

Experimental biologists use reciprocal transplant experiments (RTEs) involving divergent forms to test hypotheses about fitness trade-offs across, and local adaptation to, native environments. Additional evolutionary hypotheses about diversifying selection, the evolution of specialization, and the coexistence of specialists and generalists are only testable when the RTE also includes intermediate (or alternatively generalist) forms. Environmental variation makes such RTEs challenging, and so strategies that increase their effectiveness are useful. Here, we focus on improvements to the efficiency of RTEs involving intermediate forms with respect to the experimental design and the analysis of the resulting data. We provide a likelihood ratio-based test that offers increased statistical power and robustness relative to another test involving nonlinear regression, when used both for simulated data sets and for data from a study of two divergent fish species and their hybrids transplanted between two lake habitats. The test can be used with unequal numbers of observations, unequal variances, and binomial-type survival data and other nonnormal data. Simulations suggest that having equal numbers of experimental units in each phenotype-environment combination is reasonable. The intentional pairing of observations between environmental conditions (by using clones, full sibs, or half-sibs) is beneficial when paired observations have fitnesses that are negatively related between conditions but is detrimental with positive relatedness. Our methods can be extended to study more than two divergent forms.