Effective size of density‐dependent two‐sex populations: the effect of mating systems

Density dependence in vital rates is a key feature affecting temporal fluctuations of natural populations. This has important implications for the rate of random genetic drift. Mating systems also greatly affect effective population sizes, but knowledge of how mating system and density regulation interact to affect random genetic drift is poor. Using theoretical models and simulations, we compare N_e in short‐lived, density‐dependent animal populations with different mating systems. We study the impact of a fluctuating, density‐dependent sex ratio and consider both a stable and a fluctuating environment. We find a negative relationship between annual N_e/N and adult population size N due to density dependence, suggesting that loss of genetic variation is reduced at small densities. The magnitude of this decrease was affected by mating system and life history. A male‐biased, density‐dependent sex ratio reduces the rate of genetic drift compared to an equal, density‐independent sex ratio, but a stochastic change towards male bias reduces the N_e/N ratio. Environmental stochasticity amplifies temporal fluctuations in population size and is thus vital to consider in estimation of effective population sizes over longer time periods. Our results on the reduced loss of genetic variation at small densities, particularly in polygamous populations, indicate that density regulation may facilitate adaptive evolution at small population sizes.     

Variance in Female Reproductive Success Differentially Impacts Effective Population Size in the Short-Nosed Fruit Bat, <Emphasis Type="Italic">Cynopterus sphinx</Emphasis>

Effective population size (N _e) quantifies the effects of micro-evolutionary processes and the rate of loss of genetic diversity in a population. Several demographic and mating parameters reduce N _e. Theoretical studies elucidate the impacts of various demographic and mating system parameters on N _e, while empirical studies illustrate realized N _e for species with differing life histories and mating systems. However, effect of intra-specific variation in mating system on effective size remains largely unexplored. In this paper we investigated the effect of promiscuous and polygynous mating on N _e in two wild populations of the short-nosed fruit bat, Cynopterus sphinx. N _e/N (ratio of effective population size to census size) was lower than unity in both populations, and much lower for the polygynous population compared to promiscuous population. Elasticity analyses reveal that N _e/N was sensitive to deviations in the sex ratio. Variance in female reproductive success had a higher impact on N _e compared to variance in male reproductive success in the promiscuous population. However, for the polygynous population, impact of variance in male reproductive success on N _e was higher than that of variance in female reproductive success. Our results suggest that depending on mating system, different populations of the same species could have alternate evolutionary trajectories. The rate of loss of genetic diversity would be lower for the promiscuous population compared to the polygynous population. Our study is the first to highlight which parameters would most significantly impact population specific N _e under different mating systems.     

Evolution of mating systems in coral reef gobies and constraints on mating system plasticity

Social and mating systems can be influenced by the distribution, abundance, and economic defendability of breeding partners and essential resources. Polygyny is predicted where males can economically defend multiple females or essential resources used by females. In contrast, monogamy is predicted where neither sex can monopolise multiple partners, either directly or through resource control, but where one mate is economically defendable. The mating system and reproductive behaviour of five species of coral reef goby were investigated and contrasted with population density and individual mobility. The two most abundant species (Asterropteryx semipunctatus and Istigobius goldmanni) were polygynous. In contrast, the less populous and more widely dispersed epibenthic species (Amblygobius bynoensis, Amblygobius phalaena and Valenciennea muralis) were pair forming and monogamous. All five species had low mobility, mostly remaining within metres (3 epibenthic species) or centimetres (2 cryptobenthic species) of a permanent shelter site. Interspecific differences in the mating system may have been shaped by differences in population density and the ability of reproductive individuals to economically defend breeding partners/sites. However, in a test of mating system plasticity, males of the three monogamous species did not mate polygynously when given the opportunity to do so in experimental manipulations of density and sex ratio. Mate guarding and complex spawning characteristics, which have likely co-evolved with the monogamous mating system, could contribute to mating system inflexibility by making polygynous mating unprofitable for individuals of the pair forming species, even when presented with current-day ecological conditions that usually favour polygyny.     

Effective Size of Subpopulations in Early-Run Sockeye Salmon Oncorhynchus nerkafrom Azabach'e Lake (Kamchatka): The Effect of Density on Variance of Reproductive Success

Using Parensky's approach for estimating the number of breeding pairs, we determined effective subpopulation size N _e in early-run sockeye salmon Oncorhynchus nerka from Azabach'e Lake (Kamchatka) in 1977 through 1981. On average (over years and populations), biased sex ratio decreased N _e by 7% as compared to the number of fish on the spawning sites (N _i). High density reduced the N _e/N _i ratio by 62–66% because some fish were excluded from spawning. Dominance polygyny as compared to monogamy and random union of gametes could reduce N _e by about 17%.     

Punishment of polygyny

We investigated the evolution of monogamy (one male, one female) and polygyny (one male, more than one female). In particular, we studied whether it is possible for a mutant polygynous mating strategy to invade a resident population of monogamous breeders and, alternatively, whether a mutant monogamy can invade resident polygyny. Our population obeys discrete-time Ricker dynamics. The role of males and females in the breeding system is incorporated via the harmonic birth function. The results of the invasability analysis are straightforward. Polygyny is an evolutionarily stable strategy mating system; this holds throughout the examined range of numbers of offspring produced per female. So that the two strategies can coexist, polygyny has to be punished. The coexistence of monogamy and polygyny is achieved by reducing the offspring number for polygyny relative to monogamy. This yields long-term persistence of the strategies for all offspring numbers studied. An alternative punishment is to increase the sensitivity of polygynous breeders to population density. The coexistence is possible only with a limited range of offspring produced. The third way to achieve coexistence of the two mating strategies is to assume that individuals live in a spatially structured population, where dispersal links population subunits to a network. Reducing the dispersal rate of polygynous breeders relative to that of monogamous individuals makes the coexistence feasible. However, for monogamy to persist, the number of offspring produced has to be relatively high.     

Social structure and facultative mating systems of hoary marmots (Marmota caligata)

Mate-choice theory predicts different optimal mating systems depending on resource availability and habitat stability. Regions with limited resources are thought to promote monogamy. We tested predictions of monogamy in a social rodent, the hoary marmot (Marmota caligata), at the northern climatic extreme of its distribution. Mating systems, social structure and genetic relationships were investigated within and among neighbouring colonies of marmots within a 4 km(2) valley near Kluane National Park, Yukon, Canada, using 21 microsatellite loci. While both monogamous and polygynous populations of hoary marmots have been observed in the southern reaches of this species' range; northern populations of this species are thought to be predominantly monogamous. Contrary to previous studies, we did not find northern hoary marmot social groups to be predominantly monogamous; rather, the mating system seemed to be facultative, varying between monogamy and polygyny within, as well as among, social groups. These findings reveal that the mating systems within colonies of this species are more flexible than previously thought, potentially reflecting local variation in resource availability.     

Interval Estimation of the Effective Population Size from Heterozygote‐Excess in SNP Markers

The effective population size N_e is an important parameter in population genetics and conservation biology. In recent years, there has been great interest in the use of molecular markers to estimate N_e. Although the point estimates from molecular markers in general suffer from a low reliability, the use of single nucleotide polymorphism (SNP) markers over a wide range of genome is expected to remarkably improve the reliability. In this study, expressions were derived for interval estimates of N_e from one published method, the heterozygote‐excess method, when it is applied to SNP markers. The conditional variance theory is applied to the derivation of a confidence interval for N_e under random union of gametes, monogamy and polygyny. Stochastic simulation shows that the obtained confidence interval is slightly conservative, but fairly useful for practical applications. The result is illustrated with real data on SNP markers in a pig strain.     

Males achieve greater reproductive success through multiple broods than through extrapair mating in house wrens

In polygynous species, it is unclear whether extrapair matings provide a better reproductive payoff to males than additional social mates. Male house wrens, Troglodytes aedon, show three types of social mating behaviour: single-brooded monogamy, sequential monogamy (two broods) and polygyny. Thus, male reproductive success can vary depending on the number of mates, the number of broods and the number of extrapair fertilizations. We used microsatellite markers to determine the realized reproductive success (total number of young sired from both within-pair and extrapair fertilizations) of males in these three categories. We found that polygynous males were more likely to be cuckolded than monogamous males; however, half of the polygynous males had a third brood, which resulted in similar reproductive success for sequentially monogamous and polygynous males. Despite the paternity gained from extrapair fertilizations by single-brooded males, males were more successful when they produced multiple broods during a season, either sequentially (monogamy) or simultaneously (polygyny). In our population, multibrooded males were more likely to have prior breeding experience and arrived earlier in the season, which provided a better opportunity to obtain more than one brood and, thus, produce more young.     

Sexual dimorphism,mating system,and effect of phylogeny in De Brazza's monkey (Cercopithecus neglectus)

De Brazza's monkey (Cercopithecus neglectus), like other guenons, shows marked sexual dimorphism in an array of features. While strong sexual dimorphism is generally associated with a polygynous mating system, populations of De Brazza's monkeys in Gabon are reportedly monogamous. An explanation of this unique phenomenon is offered here. Patterns of sexual dimorphism are examined for morphology, growth and development, behavior, and ecology, and field and captive studies on the social organization and mating system of De Brazza's monkey and congeneric guenon species are reviewed. Based on the findings, it is postulated that 1) De Brazza's monkeys are not strictly monogamous, but exhibit interpopulational variation in their mating system, from facultative monogamy to mild polygyny; 2) marked sexual dimorphism most likely reflects the effect of the historical-phylogenetic factor; ie, it represents a holdover of a degree of dimorphism established earlier in evolutionary history when the degree of polygyny Was higher; and 3) lessening in the degree of polygyny and a tendency toward monogamy represents a consequence of selection toward small group size. Small group size, a unique antipredator strategy, and failure to form polyspecific associations are ultimately most likely the result of intragroup and interspecific competition and predation pressure.     

THE EFFECTIVE SIZE OF A HIERARCHICALLY STRUCTURED POPULATION

A knowledge of the effective size of a population (N_e) is important in understanding its current and future evolutionary potential. Unfortunately, the effective size of a hierarchically structured population is not, in general, equal to the sum of its parts. In particular, the inbreeding structure has a major influence on N_e. Here I link N_e to Wright's hierarchical measures of inbreeding, F_IS and F_ST, for an island-structured population (or metapopulation) of size N_T. The influence of F_ST depends strongly on the degree to which island productivity is regulated. In the absence of local regulation (the interdemic model), interdemic genetic drift reduces N_e. When such drift is combined with local inbreeding under otherwise ideal conditions, the effects of F_IS and F_ST are identical: increasing inbreeding either within or between islands reduces N_e, with N_e = N_T/[(1 + F_IS)(1 + F_ST) ? 2F_ISF_ST]. However, if islands are all equally productive because of local density regulation (the traditional island model), then N_e = N_T/[(1 + F_IS)(1 –F_ST)] and the effect of F_ST is reversed. Under the interdemic model, random variation in the habitat quality (and hence productivity) of islands act to markedly decrease N_e. This variation has no effect under the island model because, by definition, all islands are equally productive. Even when no permanent island structure exists, spatial differences in habitat quality can significantly increase the overall variance in reproductive success of both males and females and hence lower N_e. Each of these basic results holds when other nonideal factors are added to the model. These factors, deviations from a 1:1 sex ratio, greater than Poisson variance in female reproductive success, and variation in male mating success due to polygynous mating systems, all act to lower N_e. The effects of male and female variance on N_e have important differences because only females affect island productivity. Finally, it is noted that to use these relationships, F_IS and F_ST must be estimated according to Wright's definition (and corrected to have a zero expectation under the null model). A commonly used partitioning (θ, θ_g) can be biased if either island size or the number of islands is small.     

A bias correction for estimates of effective population size based on linkage disequilibrium at unlinked gene loci*

Analysis of linkage disequilibrium (=mean squared correlation of allele frequencies at different gene loci) provides a means of estimating effective population size (N _e) from a single sample, but this method has seen much less use than the temporal method (which requires at least two samples). It is shown that for realistic numbers of loci and alleles, the linkage disequilibrium method can provide precision comparable to that of the temporal method. However, computer simulations show that estimates of N _e based on for unlinked, diallelic gene loci are sharply biased downwards ( in some cases) if sample size (S) is less than true N _e. The bias is shown to arise from inaccuracies in published formula for when S and/or N _e are small. Empirically derived modifications to for two mating systems (random mating and lifetime monogamy) effectively eliminate the bias (residual bias in % in most cases). The modified method also performs well in estimating N _e in non-ideal populations with skewed sex ratio or non-random variance in reproductive success. Recent population declines are not likely to seriously affect , but if N has recently increased from a bottleneck can be biased downwards for a few generations. These results should facilitate application of the disequilibrium method for estimating contemporary N _e in natural populations. However, a comprehensive assessment of performance of with highly polymorphic markers such as microsatellites is needed.The US Governmentȁ9s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

Variation in the mating system of oribi and its ecological determinants

Flexibility (varying from monogamy in South Africa to polygyny in East Africa) has been documented in the mating system of the oribi ( Ourebia ourebi ) by several authors. To investigate this, a population was studied in Northern KwaZulu-Natal (South Africa). The adult sex ratio was one male to 1.38 females and the mean group size was 2.1 (n = 13). Although monogamous and polygynous groups occurred in the study population, the polygynous groups were unstable and depended on seasonal food abundance. Comparison of oribi populations across Africa suggests that variation in the mating system is determined mainly by predation risk and altitude (most likely through its effect on graze quality). In areas of high predation risk, oribi can survive only when resource quality permits females to forage in groups, thereby allowing males to be polygynous.     

Decomposing demographic contributions to the effective population size with moose as a case study

Levels of random genetic drift are influenced by demographic factors, such as mating system, sex ratio and age structure. The effective population size (N_e) is a useful measure for quantifying genetic drift. Evaluating relative contributions of different demographic factors to N_e is therefore important to identify what makes a population vulnerable to loss of genetic variation. Until recently, models for estimating N_e have required many simplifying assumptions, making them unsuitable for this task. Here, using data from a small, harvested moose population, we demonstrate the use of a stochastic demographic framework allowing for fluctuations in both population size and age distribution to estimate and decompose the total demographic variance and hence the ratio of effective to total population size (N_e/N) into components originating from sex, age, survival and reproduction. We not only show which components contribute most to N_e/N currently, but also which components have the greatest potential for changing N_e/N. In this relatively long‐lived polygynous system we show that N_e/N is most sensitive to the demographic variance of older males, and that both reproductive autocorrelations (i.e., a tendency for the same individuals to be successful several years in a row) and covariance between survival and reproduction contribute to decreasing N_e/N (increasing genetic drift). These conditions are common in nature and can be caused by common hunting strategies. Thus, the framework presented here has great potential to increase our understanding of the demographic processes that contribute to genetic drift and viability of populations, and to inform management decisions.     

Mating system and demographic constraints on the opportunity for sexual selection

In monogamous systems the fitness difference between males due to competition for mates is limited to one female. This constraint presumably impedes the action of sexual selection relative to polygynous systems. In this paper, we use formal selection theory to show how population size and the adult sex ratio constrain the force of sexual selection and phenotypic evolution under monogamy and polygyny. The force of sexual selection is ultimately constrained by the number of males in a population and the theoretical limit to the rate of male phenotypic evolution is realized if a single male mates with one or many females. These results imply that the force of sexual selection is not strictly constrained by monogamy. The constraint on female phenotypic evolution is typically higher than the constraint on males under polygyny and similar to selection on males in monogamous systems. The sexual asymmetry in the force of selection under polygyny--not necessarily weak sexual selection on males of monogamous systems--may explain the prominence of sexual dimorphism in polygynous systems.     

Habitat Patch Size,Facultative Monogamy and Sex Change in a Coral-dwelling Fish, <Emphasis Type="Italic">Caracanthus unipinna</Emphasis>

Synopsis We investigated the inter-relationships between coral colony size, social group size, mating system, and patterns of sex allocation in the pygmy coral croucher, Caracanthus unipinna (Caracanthidae), an obligate coral-dwelling fish. Histological examination of the gonads from all individuals in social groups revealed that the predominant mating system was harem polygyny. However, both group size and mating system co-varied with coral colony size, with pair forming and monogamy occurring on small corals and group forming and harem polygyny on large corals. This species therefore displays mating system plasticity in response to varying habitat patch size. Within-group sexual size dimorphism and individual gonad structure indicate that C. unipinna is also likely to be a protogynous hermaphrodite. These social and reproductive features of C. unipinna contrast with some other coral-dwelling fishes, which display a lack of social and mating system plasticity in response to habitat patch size, and either bi-directional or protandrous sex change. Possible reasons for this dichotomy include differences in spawning mode, parental care and levels of intrasexual aggression.     

The evolution of mating systems in bark and ambrosia beetles (Coleoptera: Scolytidae and Platypodidae)

The extraordinary array of mating systems in the Scolytidae and Platypodidae has been largely overlooked by researchers interested in the evolution of sexual behaviour. This paper provides the first overview of reproductive behaviour in this important and widespread group, known to most biologists only by the reputations of tree-killing taxa. Referred to generally as ‘bark beetles’, these insects chew egg tunnels inside a variety of (usually dead) plant tissues, though most species are either phloeophagous (breeding in the inner bark of woody plants) or xylomycetophagous (all stages feeding on mutualistic fungi growing on sapwood or heartwood). In most species, permanent records of many aspects of reproductive behaviour are etched in the host; in many, engravings reveal female fecundity, eggs sired per male, hatching success, and offspring survivorship. Each gallery arm represents a good portion of a given female's lifetime reproduction, but in many species females commonly re-emerge to reproduce in one or two additional sites. In most species of bark beetles, each female initiates her own gallery, to be joined later by a male. These monogynous gallery systems are associated with mating systems defined by how long males stay with females: in a few species, males seldom if ever join females under the bark; in the vast majority of species, males stay for part or all of the oviposition period then leave to seek other mates; and a few groups exhibit permanent monogamy, in that both sexes die in their only gallery system. While these patterns emerge from an overview of the world scolytid fauna, the length of male residency has seldom been quantified, and the costs and benefits associated with male mating strategies have not been measured for any bark beetle. Male-initiated monogyny is uncommon in Scolytidae, though the rule in Platypodidae; all instances of which I am aware are summarized from a phylogenetic perspective. Inbreeding polygyny with highly biased sex ratios has arisen at least seven times in Scolytidae. These taxa are usually characterized by males being dwarfed, flightless, and uncommon. Sex determination is known for only a few examples, but both haplodiploidy and diplodiploidy have been reported. Multiple origins of harem polygyny (otherwise rare in invertebrates) add an exciting dimension to the comparative and experimental study of scolytid mating systems. In harem polygynous taxa, males initiate gallery construction. I summarize what little can be learned from the literature about the fine structure of harem polygynous mating systems in bark beetles, and the problem of measuring reproductive success. Data on the nature of harem polygyny in Pityophthorus lautus are presented, illustrating (a) the fluidity of harems; (b) that average eggs laid per gallery arm is relatively unaffected by harem size, but strongly influenced by resource quality; (c) that male egg-gain is strongly correlated with territory quality (a consequence of (b) above); and (d) the temporal patterning of immigration and emigration and its effects on gallery system sex ratios. The second half of this paper is a discussion of the evolution of bark and ambrosia beetle mating Mating systems, emphasizing sexual selection and the role of resources. Male, residence is interpreted as postcopulalory guarding—preventing sexual liaisons with wandering males. Operational sex ratio, encounter rate, synchrony of breeding, ejaculate competition, and spatiotemporal distribution of resources are discussed as evolutionary forces moulding scolytid and platypodid male postmating behaviour. The nature of male male competition is reviewed. The paucity of information on male behaviour in gallery systems is mentioned; whether or not males significantly aid females is not known. Three hypotheses are presented for why females re-emerge, a feature which strongly affects operational sex ratios. Finally, I summarize features of bark beetle existence predisposing them to the evolution of post-inseminative guarding. Male-initiated monogyny presents a puzzle. I propose that most uncontested examples can be explained by monogyny re-evolving from (male-initiated) harem polygyny, and I present an argument for the evolution of harem polygyny leading to the development of male gallery initiation. The evolution of harem polygyny in birds and mammals has attracted considerable attention. The Verner Willson Orians polygyny threshold model is discussed with respect to bark beetles in general and P. lautus in particular. Resource quality is a major factor in P. lautus harem dynamics: the cost to females of joining harems is apparently slight compared to benefits accrued from moving into sites with higher quality inner bark. Female-biased adult sex ratios have been suggested to lead to harem polygyny, and literature and original data pertinent to this hypothesis are examined. The geometric constraints model, based on the polygyny threshold concept but tailored to bark beetles, is proposed to account for the failure of most species to evolve harem polygyny, and testable predictions are derived that interrelate breeding systems, habitat quality, and progeny size. The evolution of Inbreeding is briefly covered, and two routes to inbreeding polygyny are suggested.     

Complex mating system and dispersal patterns in a social lizard, Egernia whitii

In contrast to the polygynous mating systems typically displayed by most reptilian taxa, long-term genetic monogamy appears to be widespread within a lineage of group-living Australian scincid lizards, the Egernia group. We have recently shown that White's skink, Egernia whitii, lives in small but temporally stable social aggregations. Here, we examine the mating system, spatial organization, and dispersal patterns of E. whitii using behavioural field studies and data from four microsatellite loci. Parentage analysis of E. whitii litters revealed that its mating system is characterized by both polygyny and monogamy. Polygyny was the predominant mating system but within-season social and genetic monogamy was common (36-45% of breeding pairs). The incidence of between-season monogamy in E. whitii was rare compared to that reported for its congeners. Low levels of multiple paternity (12% of litters) and extra-group paternity (16%) were detected. Social groups are generally comprised of closely related individuals, but breeding pairs were not more closely related compared to other potential mates. Spatial autocorrelation analyses revealed significant positive local genetic structure over 50 m, which was consistent for all age-sex classes. There was no clear and consistent evidence for sex-biased dispersal, with assignment tests (mean assignment index) and relatedness analyses suggesting female-biased dispersal, but spatial autocorrelation analyses indicating a trend for male-biased dispersal. We discuss the implication of our results in regard to the factors promoting the evolution of monogamy within the Egernia group.     

Effect of Mating Structure on Variation in Linkage Disequilibrium

Measurement of linkage disequilibrium involves two sampling processes. First, there is the sampling of gametes in the population to form successive generations, and this generates disequilibrium dependent on the effective population size (N_e) and the mating structure. Second, there is sampling of a finite number (n) of individuals to estimate the population disequilibrium.——Two-locus descent measures are used to describe the mating system and are transformed to disequilibrium moments at the final sampling. Approximate eigenvectors for the transition matrix of descent measures are used to obtain formulae for the variance of the observed disequilibria as a function of N_e, mating structure, n, and linkage or recombination parameter.——The variance of disequilibrium is the same for monoecious populations with or without random selfing and for dioecious populations with random pairing for each progeny. With monogamy, the variance is slightly higher, the proportional difference being greater for unlinked loci.