Abstract
We investigate the evolution of a gene for paternal care, with pleiotropic effects on male mating fitness and offspring viability, with and without extrapair copulations (EPCs). We develop a population genetic model to examine how pleiotropic effects of a male mating advantage and paternal care are affected by "good genes" and EPCs. Using this approach, we show that the relative effects of each on fitness do not always predict the evolutionary change. We then find the line of combinations of mating success and paternal care that bisects the plane of possible values into regions of positive or negative gene frequency change. This line shifts when either good genes or EPCs are introduced, thereby expanding or contracting the region of positive gene frequency change and significantly affecting the evolution of paternal care. Predictably, a direct viability effect of "good genes" that enhances offspring viability constrains or expands the parameter space over which paternal care can evolve, depending on whether the viability effect is associated with the paternal care allele or not. In either case, the effect of a "good gene" that enhances offspring viability is substantial; when strong enough, it can even facilitate the evolution of poor paternal care, where males harm their young. When nonrandom mating is followed by random EPCs, the genetic regression between sire and offspring is reduced and, consequently, the relative strengths of selection are skewed away from paternal care and toward the male mating advantage. However, when random mating is followed by nonrandom EPCs, a situation called "trading up" by females, we show that selection is skewed in the opposite direction, away from male mating advantage and toward paternal care across the natural range of EPC frequencies.