Inferring fitness landscapes

Since 1983, study of natural selection has relied heavily on multiple regression of fitness on the values for a set of traits via ordinary least squares (OLSs), as proposed by Lande and Arnold, to obtain an estimate of the quadratic relationship between fitness and the traits, the fitness surface. However, well-known statistical problems with this approach can affect inferences about selection. One key concern is that measures of lifetime fitness do not conform to a normal or any other standard sampling distribution, as needed to justify the usual statistical tests. Another is that OLS may yield an estimate of the sign of the fitness function's curvature that is opposite to the truth. We here show that the recently developed aster modeling approach, which explicitly models the components of fitness as the basis for inferences about lifetime fitness, eliminates these problems. We illustrate selection analysis via aster using simulated datasets involving five fitness components expressed in each of four years. We demonstrate that aster analysis yields accurate estimates of the fitness function in cases in which OLS misleads, as well as accurate confidence regions for directional selection gradients. Further, to evaluate selection when many traits are under consideration, we recommend model selection by information criteria and frequentist model averaging.