The evolutionary genetics of paternal care: how good genes and extra-pair copulation affect the trade-off between paternal care and mating success

We investigate the evolution of a gene for paternal care, with pleiotropic effects on male mating fitness and offspring viability, with and without extra pair 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 poorpaternal care, where males harm their young. When non-random 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 non-random 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.

Methods
No empirical data. These files are mathematica notebooks which are used to solve equations and to generate simulations.

我们针对父本照料相关基因的演化展开研究，该基因对雄性交配适合度与后代存活力具有多效性效应，同时考量是否存在配偶外交配（extra pair copulations, EPCs）两种情境。我们构建种群遗传模型，以探究雄性交配优势与父本照料的多效性效应如何受「优质基因」与配偶外交配的影响。通过该研究框架，我们发现二者对适合度的相对效应并非总能准确预测演化方向。

我们推导得到一条由交配成功率与父本照料组合构成的边界线，可将所有可能取值构成的平面划分为基因频率正向变化区域与负向变化区域。当引入优质基因或配偶外交配时，该边界线会发生偏移，进而扩大或缩小基因频率正向变化的区域，对父本照料的演化产生显著影响。

可预见的是，能够提升后代存活力的「优质基因」直接存活力效应，会依据该存活力效应是否与父本照料等位基因相关，对父本照料可演化的参数空间产生约束或拓展作用。无论哪种情形，提升后代存活力的「优质基因」效应均十分显著；当其效应足够强时，甚至可能促成劣质父本照料的演化——此时雄性会对后代造成伤害。

当非随机交配后伴随随机配偶外交配时，父本与后代间的遗传回归会减弱，因此选择的相对强度会偏离父本照料，转向雄性交配优势。然而，当随机交配后伴随非随机配偶外交配（即雌性所谓的「择偶升级」策略）时，我们发现选择的偏向方向恰好相反：在配偶外交配频率的自然取值范围内，选择会偏离雄性交配优势，转向父本照料。

研究方法
本研究未使用实验数据。所用文件为Mathematica笔记本，用于求解方程并生成模拟结果。