Measuring natural selection on multivariate phenotypic traits: a protocol for verifiable and reproducible analyses of natural selection: supplementary material
PalacioFacundo Xavier
OrdanoMariano
Benitez-VieyraSantiago
2019
<p>The
use of multiple regression analysis to quantify the regime and strength of
natural selection in nature has been an influential approach in evolutionary
biology over the last 36 years. However, many studies fail to report the
protocol of estimation of selection coefficients (selection gradients) and the
specific model assumptions, thus failing to verify and reproduce the estimation
of selection coefficients. We present a brief overview of the Lande and
Arnold’s approach and a step-by-step R routine to aid researchers to perform a
verifiable and reproducible regression analysis of natural selection. The steps
involved in the analysis include: (1) assessing collinearity between phenotypic
traits, (2) testing normality of model residuals, and (3) testing multivariate
normality of phenotypic traits. We also performed a series of simulations to
test the effect of non-symmetrical (skewed) phenotypic traits on the estimation
of linear selection gradients. These showed that the bias in the linear
gradient increased with increased skewness in phenotypic traits for the
quadratic model, whereas the linear gradient of a model with only linear terms
was nearly independent of trait skewness. If none of the above assumptions are
met, selection gradients need to be estimated from two separate equations,
whereas standard errors must be computed using other methods (e.g.
bootstrapping). We expect that the procedure outlined here and the availability
of analytical codes motivate the verifiability and reproducibility of the Lande
and Arnold’s approach in the study of microevolution.</p>