batemanater: a computer program to estimate and bootstrap mating system variables based on Bateman's principles

Bateman's principles continue to play a major role in the characterization of genetic mating systems in natural populations. The modern manifestations of Bateman's ideas include the opportunity for sexual selection (i.e. I-s - the variance in relative mating success), the opportunity for selection (i.e. I - the variance in relative reproductive success) and the Bateman gradient (i.e. (ss) - the slope of the least-squares regression of reproductive success on mating success). These variables serve as the foundation for one convenient approach for the quantification of mating systems. However, their estimation presents at least two challenges, which I address here with a new Windows-based computer software package called batemanater. The first challenge is that confidence intervals for these variables are not easy to calculate. batemanater solves this problem using a bootstrapping approach. The second, more serious, problem is that direct estimates of mating system variables from open populations will typically be biased if some potential progeny or adults are missing from the analysed sample. batemanater addresses this problem using a maximum-likelihood approach to estimate mating system variables from incompletely sampled breeding populations. The current version of batemanater addresses the problem for systems in which progeny can be collected in groups of half- or full-siblings, as would occur when eggs are laid in discrete masses or offspring occur in pregnant females. batemanater has a user-friendly graphical interface and thus represents a new, convenient tool for the characterization and comparison of genetic mating systems.