Using genetic markers to directly estimate male selection gradients

We present an analysis of Raphanus raphanistrum and simulations illustrating the utility of directly estimating male phenotypic selection gradients using genetic markers. The method offers a much more refined characterization of selection than attempting to assign paternity to individual progeny. Our analysis of R. raphanistrum reveals selection on remarkably fine features of floral morphology, including anther exsertion, that were opaque to previous approaches. The new results also undermine a previous conclusion that selection on wild radish floral morphology acts primarily through female fitness. Simulation results show that selection gradients on the order of beta = 0.1-0.2 can be readily detected with allozyme markers in moderate-sized (< 200 paternal individuals) populations. Highly polymorphic (e.g., microsatellite) markers will likely detect fine scale selection (beta < 0.1) in larger populations (> or = 400 individuals). Increased progeny sample size, by sampling either additional maternal families or more progeny per maternal parent, partly compensates for low exclusion probability. Increasing the number of possible fathers without changing progeny sample size decreases the ability to detect selection, especially at lower exclusion probabilities. Sampling only some male genotypes reduces the power to detect selection and biases (underestimates) the magnitude of the selection gradient estimate.