Lonely hearts or sex in the city? Density-dependent effects in mating systems

Two very basic ideas in sexual selection are heavily influenced by numbers of potential mates: the evolution of anisogamy, leading to sex role differentiation, and the frequency dependence of reproductive success that tends to equalize primary sex ratios. However, being explicit about the numbers of potential mates is not typical to most evolutionary theory of sexual selection. Here, we argue that this may prevent us from finding the appropriate ecological equilibria that determine the evolutionary endpoints of selection. We review both theoretical and empirical advances on how population density may influence aspects of mating systems such as intrasexual competition, female choice or resistance, and parental care. Density can have strong effects on selective pressures, whether or not there is phenotypic plasticity in individual strategies with respect to density. Mating skew may either increase or decrease with density, which may be aided or counteracted by changes in female behaviour. Switchpoints between alternative mating strategies can be density dependent, and mate encounter rates may influence mate choice (including mutual mate choice), multiple mating, female resistance to male mating attempts, mate searching, mate guarding, parental care, and the probability of divorce. Considering density-dependent selection may be essential for understanding how populations can persist at all despite sexual conflict, but simple models seem to fail to predict the diversity of observed responses in nature. This highlights the importance of considering the interaction between mating systems and population dynamics, and we strongly encourage further work in this area.     

Population density mediates the interaction between pre‐ and postmating sexual selection

When females mate with more than one male, sexual selection acts both before and after mating. The interaction between pre‐ and postmating episodes of selection is expected to be context dependent, but few studies have investigated how total sexual selection changes under different ecological conditions. We examined how population density mediates the interaction between pre‐ and postmating sexual selection by establishing replicate populations of the horned dung beetle Onthophagus taurus at low, medium, and high densities, and then using microsatellite‐based parentage analyses to measure male fitness. We found that mating success and fertilization success were positively correlated at all three densities, but the strength of the correlation decreased with increasing density. We also found a shift from negative to positive linear selection on testes mass as density increased, and opposing selection on weapons and testes at high densities. These patterns suggest that the importance of postmating processes increases with increasing population density, which reduces the selective advantage of weapons for premating contest competition, and increases the selective advantage of large ejaculates for postmating sperm competition. We expect that density‐dependent selection on testes mass has contributed to the phenotypic variation observed between natural populations of O. taurus that differ in density.     

Mating structure and the cost of deleterious mutation: I. Postponing inbreeding

Mating structure governs the distribution of alleles in populations and thus the extent to which the phenotypes associated with the alleles are manifested. A mating system which initially achieves more genetic identity within individuals than between individuals enhances the probability that a finite population without reproductive excess will become extinct from a recessive lethal or semidominant lethal mutation; however, such a mating system decreases the number of deaths that will ensue if the population size is maintained by replacement of inviable progeny with individuals engendered from the entire mating pool. This is illustrated with Markov chain models for half-sib and double-first-cousin mating in populations of four individuals and by various techniques for analogous large populations. An appropriate choice of mating strategy can mitigate the effect of deleterious mutations, but the determination of which strategy is appropriate depends on how much reproductive excess is available and on the relative costs assigned to individual deaths and the extinction of a population.     

A theoretical investigation of sympatric evolution of temporal reproductive isolation as illustrated by marine broadcast spawners

Recent theory suggests that frequency-dependent disruptive selection in combination with assortative mating can lead to the establishment of reproductive isolation in sympatry. Here we explore how temporal variation in reproduction might simultaneously generate both disruptive selection and assortative mating, and result in sympatric speciation. The conceptual framework of the model may be applicable to biological systems with negative frequency-dependent selection, such as marine broadcast spawners or systems with pollinator limitation. We present a model that is motivated by recent findings in marine broadcast spawners and is parameterized with data from the Montastraea annularis species complex. Broadcast spawners reproduce via external fertilization and synchronous spawning is required to increase the probability of successful fertilization, but empirical evidence shows that as density increases, so does the risk of polyspermy. Polyspermy is the fusion of multiple sperm with an egg at fertilization, a process that makes the embryo unviable. Synchrony can therefore also act as a source of negative density-dependent disruptive selection. Model analysis shows that the interaction between polyspermy and spawning synchrony can lead to temporal reproductive isolation in sympatry and that, more generally, increased density promotes maintenance of genetic variation.     

Markov Model of Haploid Random Mating with Given Distribution of Population Size

An exact Markov chain model is formulated and computed for random mating in a haploid gamete pool. There are two versions of the gamete, and there is a finite number of diploid monoecious organisms. The founder population is given, and the subsequent generations allow a prescribed statistical distribution over different population sizes. The non-homogeneous Markov chain works on the haploid gamete level provided the probability of self-fertilization is 1/n, where n is the number of diploid individuals. Standard deviations of gamete frequencies and fixation probabilities are calculated. Effective population sizes for different population size distributions are estimated, including periodic bottlenecks.     

Monogamy Has a Fixation Advantage Based on Fitness Variance in an Ideal Promiscuity Group

We consider an ideal promiscuity group of females, which implies that all males have the same average mating success. If females have concealed ovulation, then the males’ paternity chances are equal. We find that male-based monogamy will be fixed in females’ promiscuity group when the stochastic Darwinian selection is described by a Markov chain. We point out that in huge populations the relative advantage (difference between average fitness of different strategies) determines primarily the end of evolution; in the case of neutrality (means are equal) the smallest variance guarantees fixation (absorption) advantage; when the means and variances are the same, then the higher third moment determines which types will be fixed in the Markov chains.     

More than just noise: Chance,mating success,and sexual selection

Chance plays a critical but underappreciated role in determining mating success. In many cases, we tend to think of chance as background noise that can be ignored in studies of mating dynamics. When the influence of chance is consistent across contexts, chance can be thought of as background noise; in other cases, however, the impact of chance on mating success can influence our understanding of how mates are acquired and how sexual selection operates. In particular, when the importance of chance covaries with biological or ecological factors in a systematic manner—that is, when chance becomes consistently more or less important under certain conditions—then chance is important to consider if we want to fully understand the operation of mate acquisition and sexual selection. Here, we present a model that explores how chance covaries with factors such as sex ratio, adult population size, and mating regime in determining variation in mating success. We find that in some cases, chance covaries with adult population size and the operational sex ratio to create variation in mating success. We discuss how chance can influence our more general understanding of the operation of mating dynamics and sexual selection.     

THE ROLES OF LIFE‐HISTORY SELECTION AND SEXUAL SELECTION IN THE ADAPTIVE EVOLUTION OF MATING BEHAVIOR IN A BEETLE

Although there is continuing debate about whether sexual selection promotes or impedes adaptation to novel environments, the role of mating behavior in such adaptation remains largely unexplored. We investigated the evolution of mating behavior (latency to mating, mating probability and duration) in replicate populations of seed beetles Callosobruchus maculatus subjected to selection on life‐history (“Young” vs. “Old” reproduction) under contrasting regimes of sexual selection (“Monogamy” vs. “Polygamy”). Life‐history selection is predicted to favor delayed mating in “Old” females, but sexual conflict under polygamy can potentially retard adaptive life‐history evolution. We found that life‐history selection yielded the predicted changes in mating behavior, but sexual selection regime had no net effect. In within‐line crosses, populations selected for late reproduction showed equally reduced early‐life mating probability regardless of mating system. In between‐line crosses, however, the effect of life‐history selection on early‐life mating probability was stronger in polygamous lines than in monogamous ones. Thus, although mating system influenced male–female coevolution, removal of sexual selection did not affect the adaptive evolution of mating behavior. Importantly, our study shows that the interaction between sexual selection and life‐history selection can result in either increased or decreased reproductive divergence depending on the ecological context.     

Inter-sexual combat and resource allocation into body parts in the spider, Stegodyphus lineatus

Abstract.  1. Sexual conflict, which results from the divergence of genetic interests between males and females, is predicted to affect multiple behavioural, physiological, and morphological traits.
2. Sexual conflict over mating may interact with population density to produce predictable changes in resource allocation into inter-sexual armament.
3. In the spider Stegodyphus lineatus , males fight with females over re-mating. The outcome of the fight is influenced by the cephalothorax size of the contestants. The investment in armament – the cephalothorax, may be traded-off against investment in abdomen, which is a trait that affects survival and fecundity. Pay-offs may depend on population density. Both sexes are expected to adjust resource allocation into different body parts accordingly.
4. Males had increased cephalothorax/body size ratio in low densities where probability of finding another receptive female is low and females had increased cephalothorax/body size ratio in high densities where cumulative costs of multiple mating are high.
5. The results support the theoretical conjecture that population density affects resource allocation into inter-sexual armament and call for further research on the interaction between sexual selection and population density.     

Assortative mating between two distinct micro-allopatric populations of Littorina saxatilis (Olivi) on the northeast coast of England

Size assortative mating is a common invertebrate mating pattern and is usually accompanied by male and female sexual selection, and these three behaviours can contribute to reproductive isolation. Two distinct populations of the marine prosobranch Littorina saxatilis, H and M, occur within 15 m of each other on the same shore. Previous studies have demonstrated that these two forms have different reproductive strategies and that the rare hybrids between the two forms show evidence of reproductive dysfunction and hence are less fit than the assumed parental forms. In both populations, female shell height was shown to be a predictor of the number of embryos contained within the brood pouch. The mean shell height of the M population was significantly larger than that of the H population, and the M population matures at a larger shell size than the H population. The two populations show complete assortative mating to type in the field, and occupy different microhabitats on the same shore. Therefore, laboratory-based experiments were performed to determine if assortative mating was maintained in sympatry and also to determine the effect of population density on mate choice. The males of both populations showed sexual selection for female size, choosing to mate with females approximately 10% larger than themselves from an assortment of female sizes. The M population showed complete assortative mating to type, irrespective of the density of H and M females, whereas at low densities the H males did occasionally mate with M females. The role of assortative mating and reinforcement (due to natural selection acting against the less fit hybrids), in maintaining the partial reproductive barrier between the two populations is discussed.     

The evolution of repeated mating under sexual conflict

In insects, repeated mating by females may have direct effects on female fecundity, fertility, and longevity. In addition, a female's remating rate affects her fitness through mortality costs of male harassment and ecological risks of mating such as predation. We analyse a model where these female fitness factors are put into their life-history context, and traded against each other, while accounting for limitations because of mate availability. We solve analytically for the condition when female multiple mating will evolve. We show that the probability that a female mates with a courting male decreases with increases in population density. The extent of conflict between the sexes thus automatically becomes larger at higher densities. However, because at higher densities females meet males at a higher rate, the resulting ESS female remating rate is independent of population density. The female remating probability is in conflict with male adaptations that increase male mating rate by persuading or forcing females to mate, and also in conflict with male adaptations for protecting the own sperm from being removed by future female mates. We show that the relative importance of these conflicts depends on population density.     

EQUILIBRIUM ANALYSIS OF SEXUAL SELECTION IN DROSOPHILA MELANOGASTER

Several models for sexual selection, both by male-male competition and female choice, predict that a character which covaries with mating success should be near an equilibrium where the intensity of sexual selection opposes viability selection. This prediction was used to design experiments for estimating the intensity of sexual and viability selection on wing length in a recently captured population of Drosophila melanogaster. Observations of matings by males color-marked for wing length indicated that the standardized sexual selection differential on wing length was 0.24 under a wide range of effective sex ratios. After estimating the heritability of wing length to be 0.62, the expected standardized response due to sexual selection was calculated as 0.15 (SE = 0.15). The response due to viability selection was then estimated by comparing wing lengths of progeny of flies that had been randomly mated, thereby preventing sexual selection, with progeny of flies that had been allowed to acquire mates in a mass-mating chamber. The results support an equilibrium model in that the standardized response due to viability selection (?0.31, SE = 0.08) was opposite in sign and similar in magnitude to the estimated response due to sexual selection. Observations of females orienting in front of males which differed in wing length indicated that the mating advantage accruing to long-winged males was not due to female choice. Instead, male-male competition in which the larger of two randomly chosen males succeeded in mating, explains the observed sexual selection. An experimental analysis of genotype-environment interaction revealed that larval density had a nonlinear effect on mean wing length within sibships. If a population is displaced from equilibrium, therefore, the evolutionary trajectory of mean wing length will depend both on the intensity of selection and the environment in which that selection is operating.     

Mating preference in the invasion of growth enhanced fish

Fish with a transgene for growth hormone grow faster than the wild type and may have an advantage in sexual selection due to their larger size and earlier maturation. The cost in these genetically modified organisms (GMOs) is a lower viability of their offspring. The Trojan gene effect is a hypothesis that predicts that the release of such fish in nature can lead to an invasion by GMOs but ultimately decrease population size to extinction. We modelled GMO invasion with Mendelian inheritance of two alleles in one locus and the resulting mating and population dynamics of wild, GMO and hybrid genotypes. Invasion was attempted over a range of initial densities, representing scenarios from accidental escape to large-scale deliberate introduction of the transgenic genotype. Our results show that invasion strongly depends on hybrid fitness, requiring only a low initial density when GMOs and hybrids are preferred in mating. Preference against hybrids results in an invasion threshold, above which mating between GMOs are sufficiently frequent for invasion to take place. GMO invasion may decrease population size, but contrary to earlier studies on the Trojan gene effect, extinctions do not occur. This is due to the lower viability of GMOs being balanced by the decreased number of competitors reducing the effects of density dependence. The results emphasize the importance of initial density, hybrid fitness and density dependence when considering invasion through hybridization.     

Survival of small populations under demographic stochasticity.

We estimate the mean time to extinction of small populations in an environment with constant carrying capacity but under stochastic demography. In particular, we investigate the interaction of stochastic variation in fecundity and sex ratio under several different schemes of density dependent population growth regimes. The methods used include Markov chain theory, Monte Carlo simulations, and numerical simulations based on Markov chain theory. We find a strongly enhanced extinction risk if stochasticity in sex ratio and fluctuating population size act simultaneously as compared to the case where each mechanism acts alone. The distribution of extinction times deviates slightly from a geometric one, in particular for short extinction times. We also find that whether maximization of intrinsic growth rate decreases the risk of extinction or not depends strongly on the population regulation mechanism. If the population growth regime reduces populations above the carrying capacity to a size below the carrying capacity for large r (overshooting) then the extinction risk increases if the growth rate deviates from an optimal r-value.     

Host mating system and the spread of a disease-resistant allele in a population

The model presented here modifies a susceptible-infected (SI) host–pathogen model to determine the influence of mating system on the outcome of a host–pathogen interaction. Both deterministic and stochastic (individual-based) versions of the model were used. This model considers the potential consequences of varying mating systems on the rate of spread of both the pathogen and resistance alleles within the population. We assumed that a single allele for disease resistance was sufficient to confer complete resistance in an individual, and that both homozygote and heterozygote resistant individuals had the same mean birth and death rates. When disease invaded a population with only an initial small fraction of resistant genes, inbreeding (selfing) tended to increase the probability that the disease would soon be eliminated from a small population rather than become endemic, while outcrossing greatly increased the probability that the population would become extinct due to the disease.     

Logistic growth in the presence of non-white environmental noise

A method is given for studying realistic random fluctuations in the carrying capacity of the logistic population growth model. This method is then applied using an environmental noise based on a Poisson process, and the time-dependent moments of the population probability density calculated. These moments are expressed in terms of a parameter obtained by dividing the correlation time of the environmental fluctuations by the characteristic response time of the population. When this quotient is large (very slow fluctuations tracked by the population) or small (very rapid fluctuations which are averaged), exact solutions are obtained for the probability density itself. It is also shown that at equilibrium, the average population sizes given by these two exact solutions bound all other cases.Numerical simulations confirm these developments and point to a trade-off between population stability and average population size. Additional simulations show that the probability of becoming extinct in a given time is greatest for populations intermediate between tracking and averaging the carrying capacity fluctuations. In addition to specifying when environmental noise can be ignored, these results indicate the direction in which growth parameters evolve in a fluctuating environment.     

Measures of success in a class of evolutionary models with fixed population size and structure

We investigate a class of evolutionary models, encompassing many established models of well-mixed and spatially structured populations. Models in this class have fixed population size and structure. Evolution proceeds as a Markov chain, with birth and death probabilities dependent on the current population state. Starting from basic assumptions, we show how the asymptotic (long-term) behavior of the evolutionary process can be characterized by probability distributions over the set of possible states. We then define and compare three quantities characterizing evolutionary success: fixation probability, expected frequency, and expected change due to selection. We show that these quantities yield the same conditions for success in the limit of low mutation rate, but may disagree when mutation is present. As part of our analysis, we derive versions of the Price equation and the replicator equation that describe the asymptotic behavior of the entire evolutionary process, rather than the change from a single state. We illustrate our results using the frequency-dependent Moran process and the birth–death process on graphs as examples. Our broader aim is to spearhead a new approach to evolutionary theory, in which general principles of evolution are proven as mathematical theorems from axioms.     

The effects of primiparity on reproductive performance in the brown bear

We studied the effects of primiparity on litter size, offspring size, and cub loss in brown bears (Ursus arctos) in two study areas (north, south) in Sweden from 1987 to 2006. Sexually selected infanticide (SSI) has been suggested previously as a mortality factor in our study populations. Females in the south became primiparous earlier than females in the north. Primiparous females had significantly smaller litters of cubs than multiparous females. We found no evidence that primiparity was costly in terms of the interlitter interval. Primiparous mothers had a higher probability of cub loss than multiparous mothers. The probability of cub loss was analyzed separately for the pre-mating and the mating season. The probability of cub loss by primiparous females in the pre-mating season increased with both increasing population density and deteriorating food conditions, whereas the probability of cub loss during the mating season decreased with increasing age of primiparity and increased with male turnover (a variable predicting SSI). The temporal patterns of cub loss by primiparous females suggested that the critical times for reproductive success by primiparous females were the pre-mating season (from birth to shortly after leaving the den) and the mating season. Cub loss in these periods was independent and caused by different factors. Cub loss before the mating season seemed to be most influenced by food conditions, whereas that during the mating season appeared to be caused by SSI.     

Fixation of new alleles and the extinction of small populations: drift load, beneficial alleles, and sexual selection

With a small effective population size, random genetic drift is more important than selection in determining the fate of new alleles. Small populations therefore accumulate deleterious mutations. Left unchecked, the effect of these fixed alleles is to reduce the reproductive capacity of a species, eventually to the point of extinction. New beneficial mutations, if fixed by selection, can restore some of this lost fitness. This paper derives the overall change in fitness due to fixation of new deleterious and beneficial alleles, as a function of the distribution of effects of new mutations and the effective population size. There is a critical effective size below which a population will on average decline in fitness, but above which beneficial mutations allow the population to persist. With reasonable estimates of the relevant parameters, this critical effective size is likely to be a few hundred. Furthermore, sexual selection can act to reduce the fixation probability of deleterious new mutations and increase the probability of fixing new beneficial mutations. Sexual selection can therefore reduce the risk of extinction of small populations.     

Assortative mating by diet in a phenotypically unimodal but ecologically variable population of stickleback

Speciation with gene flow may be driven by a combination of positive assortative mating and disruptive selection, particularly if selection and assortative mating act on the same trait, eliminating recombination between ecotype and mating type. Phenotypically unimodal populations of threespine stickleback (Gasterosteus aculeatus) are commonly subject to disruptive selection due to competition for alternate prey. Here we present evidence that stickleback also exhibit assortative mating by diet. Among-individual diet variation leads to variation in stable isotopes, which reflect prey use. We find a significant correlation between the isotopes of males and eggs within their nests. Because egg isotopes are derived from females, this correlation reflects assortative mating between males and females by diet. In concert with disruptive selection, this assortative mating should facilitate divergence. However, the stickleback population remains phenotypically unimodal, highlighting the fact that assortative mating and disruptive selection do not guarantee evolutionary divergence and speciation.