Existing insight suggests that maternal effects have a substantial impact on evolution, yet these predictions assume that maternal effects themselves are evolutionarily constant. Hence, it is poorly understood how natural selection shapes maternal effects in different ecological circumstances. To overcome this, the current study derives an evolutionary model of maternal effects in a quantitative genetics context. In constant environments, we show that maternal effects evolve to slight negative values that result in a reduction of the phenotypic variance (canalization). By contrast, in populations experiencing abrupt change, maternal effects transiently evolve to positive values for many generations, facilitating the transmission of beneficial maternal phenotypes to offspring. In periodically fluctuating environments, maternal effects evolve according to the autocorrelation between maternal and offspring environments, favoring positive maternal effects when change is slow, and negative maternal effects when change is rapid. Generally, the strongest maternal effects occur for traits that experience very strong selection and for which plasticity is severely constrained. By contrast, for traits experiencing weak selection, phenotypic plasticity enhances the evolutionary scope of maternal effects, although maternal effects attain much smaller values throughout. As weak selection is common, finding substantial maternal influences on offspring phenotypes may be more challenging than anticipated.

Mathematical models have played an important role in the development of sexual selection theory. These models come in different flavors and they differ in their assumptions, often in a subtle way. Similar questions can be addressed by modeling frameworks from population genetics, quantitative genetics, evolutionary game theory, or adaptive dynamics, or by individualbased simulations. Confronted with such diversity, nonspecialists may have difficulties judging the scope and limitations of the various approaches. Here we review the major modeling frameworks, highlighting their pros and cons when applied to different research questions. We also discuss recent developments, where classical models are enriched by including more detail regarding genetics, behavior, demography, and population dynamics. It turns out that some seemingly well-established conclusions of sexual selection theory are less general than previously thought. Linking sexual selection to other processes such as sex-ratio evolution or speciation also reveals that enriching the theory can lead to surprising new insights.

Many studies have suggested that reproductive performance improves during the pair-bond, which might explain why individuals remate with the same partner in many species. However, discussion exists about whether the association between reproductive performance and pair-bond duration that is reported in these studies reflects a causal relationship. Usually it is unclear whether a positive association is caused by pairs improving during their pair-bond or by high-quality pairs staying together for longer. Furthermore, reproductive performance often also depends on the age or breeding experience of parents, which all covary with pair-bond duration. A much needed experimental approach is lacking so far. We investigated the effect of pair-bond duration on reproductive performance in a long-lived monogamous bird species based on natural as well as experimental variation. The duration of oystercatcher (Haematopus ostralegus) pair-bonds, which were followed for 21 years, strongly affected reproductive output, even after controlling for effects of age and breeding experience. Pairs improved during their pair-bond, and there were no indications of selective disappearance of low-quality pairs; however, pairs that stayed together for very long performed badly. Experimental removal of one partner showed that the reproductive cost of divorce depended on the pair-bond duration with the old partner. In addition, after remating, the newly formed pairs strongly improved again, independent of the age and breeding experience of the remated pair members. As such, this study provides the first experimental evidence of a causal effect of pairbond duration on reproductive performance.