Variation in continuous reaction norms: quantifying directions of biological interest

Thermal performance curves are an example of continuous reaction norm curves of common shape. Three modes of variation in these curves-- Vertical shift, horizontal shift, and generalist-specialist tradeoffs-- are of special interest to evolutionary biologists. Since two of these modes are nonlinear, traditional methods such as Principal Component Analysis fail to decompose the variation into biological modes and to quantify the variation associated with each mode. Here we present the results of a new method, Template Mode of Variation (TMV), that decomposes the variation into predetermined modes of variation for a particular set of thermal performance curves. We illustrate the method using data on thermal sensitivity of growth rate in Pieris rapae caterpillars. The TMV model explains 67% of the variation in thermal performance curves among families; generalist-specialist tradeoffs account for 38% of the total between-family variation. The TMV method implemented here is applicable to both differences in mean and patterns of variation, and can be used with either phenotypic or quantitative genetic data for thermal performance curves or other continuous reaction norms that have a template shape with a single maximum. The TMV approach may also apply to growth trajectories, age-specific life history traits and other function-valued traits.