Evolutionarily stable mating decisions for sequentially searching females and the stability of reproductive isolation by assortative mating

The evolution of age-specific choosiness and reproductive isolation in a model with overlapping generations

The strength of mate choice (choosiness) often varies with age, but theory to understand this variation is scarce. Additionally, theory has investigated the evolution of choosiness in speciation scenarios but has ignored that most organisms have overlapping generations. We investigate whether speciation can result in variation of choosiness with age, and whether such variation can in turn affect speciation. We develop a population-genetic model of the evolution of choosiness in organisms with overlapping generations in the context of secondary contact between two divergent populations. We assume that females choose males that match their phenotype, such that choosiness evolves by sexual selection. We demonstrate that speciation can result in the evolution of age-specific choosiness when the mating trait is under divergent ecological selection and age is not used as a mating cue. The cause of this result is that allele frequencies differ between choosy females and males. However, we find that the evolution of age-specific choosiness does not affect the overall level of reproductive isolation compared to a case without age-structure, supporting previous speciation theory. Overall, our results connect life history and speciation theory, and the mechanisms that we highlight have implications for the understanding of the role of sex-specific selection in the evolution of choosiness.

Hamilton's rule, gradual evolution, and the optimal (feedback) control of phenotypically plastic traits

Most traits expressed by organisms, such as gene expression profiles, developmental trajectories, behavioural sequences and reaction norms are function-valued traits (colloquially "phenotypically plastic traits"), since they vary across an individual's age and in response to various internal and/or external factors (state variables). Furthermore, most organisms live in populations subject to limited genetic mixing and are thus likely to interact with their relatives. We here formalise selection on genetically determined function-valued traits of individuals interacting in a group-structured population, by deriving the marginal version of Hamilton's rule for function-valued traits. This rule simultaneously gives a condition for the invasion of an initially rare mutant function-valued trait and its ultimate fixation in the population (invasion thus implies substitution). Hamilton's rule thus underlies the gradual evolution of function-valued traits and gives rise to necessary first-order conditions for their uninvadability (evolutionary stability). We develop a novel analysis using optimal control theory and differential game theory, to simultaneously characterise and compare the first-order conditions of (i) open-loop traits - functions of time (or age) only, and (ii) closed-loop (state-feedback) traits - functions of both time and state variables. We show that closed-loop traits can be represented as the simpler open-loop traits when individuals do not interact or when they interact with clonal relatives. Our analysis delineates the role of state-dependence and interdependence between individuals for trait evolution, which has implications to both life-history theory and social evolution.

Fisher's lost model of runaway sexual selection

The bizarre elaboration of sexually selected traits such as the peacock's tail was a puzzle to Charles Darwin and his 19th century followers. Ronald A. Fisher crafted an ingenious solution in the 1930s, positing that female preferences would become genetically correlated with preferred traits due to nonrandom mating. These genetic correlations would translate selection for preferred traits into selection for stronger preferences, leading to a self-reinforcing process of ever-elaborating traits and preferences. It is widely believed that Fisher provided only a verbal model of this "runaway" process. However, in correspondence with Charles Galton Darwin, Fisher also laid out a simple mathematical model that purportedly confirms his verbal prediction of runaway sexual selection. Unfortunately, Fisher's model contains inconsistencies that render his quantitative conclusions inaccurate. Here, we correct Fisher's model and show that it contains all the ingredients of a working runaway process. We derive quantitative predictions of his model using numerical techniques that were unavailable in Fisher's time. Depending on parameter values, mean traits and preferences may increase until genetic variance is depleted by selection, exaggerate exponentially while their variances remain stable, or both means and variances may increase super-exponentially. We thus present the earliest mathematical model of runaway sexual selection.

The Evolution of Mutual Mate Choice under Direct Benefits

In nature, the intensity of mate choice (i.e., choosiness) is highly variable within and between sexes. Despite growing empirical evidence of male and/or mutual mate choice, theoretical investigations of the joint evolution of female and male choosiness are few. In addition, previous approaches have often assumed an absence of trade-off between the direct benefits per mating and the lower mating rate that results from being choosy. Here we model the joint evolution of female and male choosiness when it is solely ruled by this fundamental trade-off. We show that this trade-off can generate a diversity of stable combinations of choosiness. Mutual mate choice can evolve only if both females and males exhibit long latency after mating. Furthermore, we show that an increase in choosiness in one sex does not necessarily prevent the evolution of mutual mate choice; the outcome depends on details shaping the trade-off: the life history, the decision rule for mate choice, and how the fecundity of a pair is shaped by the quality of both individuals. Last, we discuss the power of the sensitivity of the relative searching time (i.e., of the proportion of a lifetime spent searching for mates) as a predictor of the joint evolution of choosiness.