Variance in reproductive success and effective population size

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Background

The effective population size \$N_e\$ is the size of the Wright-Fisher population that experience the same amount of drift than the population under consideration.

The higher the variance in reproductive success among individuals, the lower is the effective population. Consider for example, a case where the variance in reproductive success is so high that only one individual reproduces (selfing for example) and contribute to the next generation. In such a case the variance in reproductive success is so high that the effective population size is reduced to 1.

During a meeting I have encountered the following relationship between the population size \$N\$, the effective population size \$Ne\$ and the variance in reproductive success \$V\$.

\$\$N_e = frac{N}{V}\$\$

It makes intuitive sense to me. In the extreme case where \$V≈0\$, there is no drift and therefore no loss in diversity, everybody contribute as much to the next generation and therefore \$N_e=infty\$. By definition, in a Wright-Fisher population \$N=N_e\$ and therefore \$V=1\$ should be correct.

Questions

• Where does the equation \$N_e = frac{N}{V}\$ comes from? How to derive it? Is it an approximation or an equality?

• Is it true that \$V=1\$ in a Wright-Fisher population?

Variance in reproductive success and effective population size - Biology

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LARGE VARIANCE IN REPRODUCTIVE SUCCESS AND THE Ne/N RATIO

1 School of Life Sciences, Arizona State University, Tempe, Arizona 85287-4501 [email protected]

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The ratio of the effective population size to adult (or census) population size (Ne/N) is an indicator of the extent of genetic variation expected in a population. It has been suggested that this ratio may be quite low for highly fecund species in which there is a sweepstakes-like chance of reproductive success, known as the Hedgecock effect. Here I show theoretically how the ratio may be quite small when there are only a few successful breeders (Nb) and that in this case, the Ne/N ratio is approximately Nb/N. In other words, high variance in reproductive success within a generation can result in a very low effective population size in an organism with large numbers of adults and consequently a very low Ne/N ratio. This finding appears robust when there is a large proportion of families with exactly two progeny or when there is random variation in progeny numbers among these families.

Philip Hedrick "LARGE VARIANCE IN REPRODUCTIVE SUCCESS AND THE Ne/N RATIO," Evolution 59(7), 1596-1599, (1 July 2005). https://doi.org/10.1554/05-009

Received: 6 January 2005 Accepted: 16 April 2005 Published: 1 July 2005

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1. Introduction

The mating system can greatly influence the genetic structure of populations. Crosses between relatives and selfing reduce multilocus heterozygosity (MLH) and increase gametic disequilibria in the resulting progenies (Hedrick, Reference Hedrick 2000). At the population level, they also lead to a reduction of the effective size and an increase of inter-population differentiation. Moreover, demographic fluctuations (caused by variable ecological conditions) may result in transient bottlenecks that are expected to have the same effect on the population's diversity and differentiation (Cornuet & Luikart, Reference Cornuet and Luikart 1996). Marine species with high fecundity and high early mortality such as oysters (Elm-oyster model Williams, Reference Williams 1975), are particularly prone to display large variance in reproductive success, because of gametic (gamete quality and sperm–egg interaction) and zygotic (zygotic competition and differential viability of genotypes) effects (Boudry et al., Reference Boudry, Collet, Cornette, Hervouet and Bonhomme 2002), contributing to a reduction of their effective population size. Hence, many marine species have a combination of high fecundity and narrow conditions for spawning success that may lead to wide individual variation in realized reproductive success, such that an annual cohort is the result of only a few spawning events or individuals (Hedgecock, Reference Hedgecock and Beaumont 1994).

The flat oyster, Ostrea edulis, an endemic European species, naturally occurs from Norway to Morocco in the North-Eastern Atlantic and in the whole Mediterranean Sea. It has been harvested for at least 6000 years (Goulletquer & Héral, Reference Goulletquer and Héral 1997). However, overharvesting and, more recently, the successive occurrence during the 1960s of two protozoan diseases caused by Marteilia refringens and Bonamia ostreae drastically decreased its production. For example, the French production was reduced from 20 000 tonnes in the 1950s to 1 900 tonnes at present (FAO, 2007). Hence, the native European flat oyster is listed in the OSPAR (Oslo-Paris) Convention for the Protection of the Marine Environment of the North-Eastern Atlantic (species and habitat protection). In the context of potential restoration along European coasts (Laing et al., Reference Laing, Walker and Areal 2005), it is important to assess the potential impact of hatchery-propagated stocks on the genetic variability and the effective population size of wild populations (Gaffney, Reference Gaffney 2006). Therefore, information is needed about the genetic variability of hatchery-propagated stocks (Lallias et al., Reference Lallias, Lapègue, Boudry, King and Beaumont 2010) and the structure and dynamics of wild populations to ensure the proper management of populations and aquaculture production.

The genetic structure of wild O. edulis populations has been analysed with microsatellite DNA (Launey et al., Reference Launey, Ledu, Boudry, Bonhomme and Naciri-Graven 2002) and mitochondrial DNA (12S) markers (Diaz-Almela et al., Reference Diaz-Almela, Boudry, Launey, Bonhomme and Lapègue 2004). Genetic differentiation based on mitochondrial data was 10-fold greater (F st=0·224 Diaz-Almela et al., Reference Diaz-Almela, Boudry, Launey, Bonhomme and Lapègue 2004) than the one established on microsatellite data (F st=0·019 Launey et al., Reference Launey, Ledu, Boudry, Bonhomme and Naciri-Graven 2002). This quantitative difference of a factor of 10 observed between the nuclear and mitochondrial F st was proposed to be attributable to a reduced female effective population size. This could be explained by several factors: (i) a biased effective sex-ratio towards males owing to the protandry of the species and the higher energy cost in oogenesis (Ledantec & Marteil, Reference Ledantec and Marteil 1976), leading to a lower probability of becoming female. This is aggravated by the B. ostreae-caused disease (Culloty & Mulcahy, Reference Culloty and Mulcahy 1996), which induces high mortalities within 2–3-year-old adults, (ii) a higher variance in female than male reproductive success (Boudry et al., Reference Boudry, Collet, Cornette, Hervouet and Bonhomme 2002 Taris et al., Reference Taris, Boudry, Bonhomme, Camara and Lapègue 2009). Other explanations are: (1) N ef is one-quarter of N e and (2) F st is proportional to (H SH T) (H S being the average subpopulation Hardy–Weinberg heterozygosity and H T being the total population heterozygosity) and H S approached 1·0 in the microsatellites used (Hedrick, Reference Hedrick 2005a).

Heterozygote deficiencies with regard to Hardy–Weinberg equilibrium expectations are common in marine bivalve populations (Zouros & Foltz, Reference Zouros and Foltz 1984 Huvet et al., Reference Huvet, Boudry, Ohresser, Delsert and Bonhomme 2000 Hare et al., Reference Hare, Allen, Bloomer, Camara, Carnegie, Murfree, Luckenbach, Meritt, Morrison, Paynter, Reece and Rose 2006) and were reported in O. edulis for allozymes (Wilkins & Mathers, Reference Wilkins and Mathers 1973 Saavedra et al., Reference Saavedra, Zapata, Guerra and Alvarez 1987 Alvarez et al., Reference Alvarez, Zapata, Amaro and Guerra 1989) and microsatellites (Launey et al., Reference Launey, Ledu, Boudry, Bonhomme and Naciri-Graven 2002). Microsatellite markers are particularly prone to PCR artefacts such as the presence of null alleles and upper allele drop-out, which are responsible for the commonly observed heterozygote deficiencies. Moreover, a positive correlation between MLH and life history traits such as growth or survival was reported in O. edulis based on allozymes (Alvarez et al., Reference Alvarez, Zapata, Amaro and Guerra 1989 Launey, Reference Launey 1998) and microsatellite markers (Bierne et al., Reference Bierne, Launey, Naciri-Graven and Bonhomme 1998). Two kinds of arguments were mentioned to explain heterozygote deficiencies and correlations heterozygosity-growth. The first hypothesis, overdominance, implies that selection acts directly on allozymic genotypes, questioning the allozyme's neutrality. This hypothesis was refuted by the evidence of the same phenomenon occurring with reputedly neutral markers like microsatellites (Bierne et al., Reference Bierne, Launey, Naciri-Graven and Bonhomme 1998 Launey & Hedgecock, Reference Launey and Hedgecock 2001). The second hypothesis, associative overdominance, stipulates that marker polymorphism is neutral but indirectly reflects variation in loci linked to fitness by genetic correlations. Genetic markers, whether allozymes or microsatellites, can therefore either represent neutral loci in gametic disequilibrium with physically close loci under selection (local effect) or represent neutral markers of the overall genomic heterozygosity (general effect, David et al., Reference David, Delay, Berthou and Jarne 1995). Whether local or general, the associative overdominance hypothesis takes root in the characteristics of reproductive biology and dynamics of these species. Indeed, according to Bierne et al. ( Reference Bierne, Launey, Naciri-Graven and Bonhomme 1998), an instantaneous reduced effective population size can induce gametic disequilibrium between genetic markers and loci linked to fitness (local effect), whereas partial inbreeding can generate a variation in the global genomic heterozygosity between individuals (general effect). Li & Hedgecock ( Reference Li and Hedgecock 1998) in Crassostrea gigas and Hedgecock et al. ( Reference Hedgecock, Launey, Pudovkin, Naciri, Lapègue and Bonhomme 2007) in O. edulis highlighted the fact that, under local circumstances, the effective population size can be drastically reduced by a high variance in reproductive success, which could in turn generate a temporary gametic phase disequilibrium (reinforcing the associative overdominance hypothesis).

Variance in the individual reproductive success among parents has also been documented under experimental conditions using controlled crossing (e.g. Hedgecock & Sly, Reference Hedgecock and Sly 1990 Hedgecock et al., Reference Hedgecock, Chow and Waples 1992 and references therein Petersen et al., Reference Petersen, Ibarra, Ramirez and May 2008). The most direct evidence comes from studies of the Pacific oyster, C. gigas, in which changes in family representation in progenies resulting from factorial crosses were analysed using microsatellite markers for parentage analyses (Boudry et al., Reference Boudry, Collet, Cornette, Hervouet and Bonhomme 2002 Taris et al., Reference Taris, Ernande, McCombie and Boudry 2006). Their results showed large variance in parental contributions at several developmental stages, leading to a strong reduction of experiment-wide effective population size that could be attributed to four main factors: gamete quality, sperm–egg interaction, sperm competition and differential survival among families.

In order to document further the phenomena of variance in reproductive success both in natural- and hatchery-produced populations of O. edulis, we performed two complementary studies to answer two questions: (1) Is it possible to detect a variance in reproductive success which could result in a reduced effective population size? (2) How is this variance expressed temporally? To answer these questions, brooding females were firstly sampled in the wild and the number of males fertilizing each female estimated on the basis of microsatellite allele frequencies. Then, to get rid of drawbacks inherent to working with large natural populations and multiple environmental factors, parentage analyses were conducted under experimental conditions: successive cohorts were collected from a population of potential progenitors kept in the hatchery, whose genotypes were known, in order to infer a posteriori the relative contribution of each. The results of these two studies are discussed in the light of previous studies of wild- or hatchery-bred flat oysters.

Effective number of breeders, effective population size and their relationship with census size in an iteroparous species, Salvelinus fontinalis

The relationship between the effective number of breeders (Nb) and the generational effective size (Ne) has rarely been examined empirically in species with overlapping generations and iteroparity. Based on a suite of 11 microsatellite markers, we examine the relationship between Nb, Ne and census population size (Nc) in 14 brook trout (Salvelinus fontinalis) populations inhabiting 12 small streams in Nova Scotia and sampled at least twice between 2009 and 2015. Unbiased estimates of Nb obtained with individuals of a single cohort, adjusted on the basis of age at first maturation (α) and adult lifespan (AL), were from 1.66 to 0.24 times the average estimates of Ne obtained with random samples of individuals of mixed ages (i.e. [Formula: see text]). In turn, these differences led to adjusted Ne estimates that were from nearly five to 0.7 times the estimates derived from mixed-aged individuals. These differences translate into the same range of variation in the ratio of effective to census population size [Formula: see text] within populations. Adopting [Formula: see text] as the more precise and unbiased estimates, we found that these brook trout populations differ markedly in their effective to census population sizes (range approx. 0.3 to approx. 0.01). Using AgeNe, we then showed that the variance in reproductive success or reproductive skew varied among populations by a factor of 40, from Vk/k ≈ 5 to 200. These results suggest wide differences in population dynamics, probably resulting from differences in productivity affecting the intensity of competition for access to mates or redds, and thus reproductive skew. Understanding the relationship between Ne, Nb and Nc, and how these relate to population dynamics and fluctuations in population size, are important for the design of robust conservation strategies in small populations with overlapping generations and iteroparity.

Keywords: Nb Ne age at maturation brook trout iteroparity small populations.

Figures

Streams sampled along the North…

Streams sampled along the North Mountain in Nova Scotia. Streams run into the…

Principal coordinate analysis (PCA) based…

Principal coordinate analysis (PCA) based on 11 loci for brook trout collected from…

Sex change and effective population size: implications for population genetic studies in marine fish

Large variance in reproductive success is the primary factor that reduces effective population size (Ne) in natural populations. In sequentially hermaphroditic (sex-changing) fish, the sex ratio is typically skewed and biased towards the 'first' sex, while reproductive success increases considerably after sex change. Therefore, sex-changing fish populations are theoretically expected to have lower Ne than gonochorists (separate sexes), assuming all other parameters are essentially equal. In this study, we estimate Ne from genetic data collected from two ecologically similar species living along the eastern coast of South Africa: one gonochoristic, the 'santer' sea bream Cheimerius nufar, and one protogynous (female-first) sex changer, the 'slinger' sea bream Chrysoblephus puniceus. For both species, no evidence of genetic structuring, nor significant variation in genetic diversity, was found in the study area. Estimates of contemporary Ne were significantly lower in the protogynous species, but the same pattern was not apparent over historical timescales. Overall, our results show that sequential hermaphroditism may affect Ne differently over varying time frames, and that demographic signatures inferred from genetic markers with different inheritance modes also need to be interpreted cautiously, in relation to sex-changing life histories.

Figures

Map: sampling locations off the…

Map: sampling locations off the KwaZulu-Natal Coast of South Africa.

Effective population size estimates: effective…

Effective population size estimates: effective population size of Cheimerius nufar (santer, in black)…

Historical female effective population size:…

Historical female effective population size: historical female effective population size ( N e…

Bayesian Skyline plots: Bayesian Skyline…

Bayesian Skyline plots: Bayesian Skyline plots for santer Cheimerius nufar and slinger Chrysoblephus…

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In: Evolution , Vol. 59, No. 7, 07.2005, p. 1596-1599.

Research output : Contribution to journal › Article › peer-review

T1 - Large variance in reproductive success and the Ne/N ratio

N2 - The ratio of the effective population size to adult (or census) population size (Ne/N) is an indicator of the extent of genetic variation expected in a population. It has been suggested that this ratio may be quite low for highly fecund species in which there is a sweepstakes-like chance of reproductive success, known as the Hedgecock effect. Here I show theoretically how the ratio may be quite small when there are only a few successful breeders (Nb) and that in this case, the Ne/N ratio is approximately Nb/N. In other words, high variance in reproductive success within a generation can result in a very low effective population size in an organism with large numbers of adults and consequently a very low N e/N ratio. This finding appears robust when there is a large proportion of families with exactly two progeny or when there is random variation in progeny numbers among these families.

AB - The ratio of the effective population size to adult (or census) population size (Ne/N) is an indicator of the extent of genetic variation expected in a population. It has been suggested that this ratio may be quite low for highly fecund species in which there is a sweepstakes-like chance of reproductive success, known as the Hedgecock effect. Here I show theoretically how the ratio may be quite small when there are only a few successful breeders (Nb) and that in this case, the Ne/N ratio is approximately Nb/N. In other words, high variance in reproductive success within a generation can result in a very low effective population size in an organism with large numbers of adults and consequently a very low N e/N ratio. This finding appears robust when there is a large proportion of families with exactly two progeny or when there is random variation in progeny numbers among these families.

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Materials and methods

Sampling

C. puniceus and C. nufar specimens were collected from commercial ski-boat line fishermen between May and July 2007 at three locations along the KwaZulu-Natal coast: Port Edward, Park Rynie and Richards Bay (RB) (Figure 1). A total of 138 C. puniceus (122 females and 16 males) and 139 C. nufar (69 females and 67 males) were collected.

Map: sampling locations off the KwaZulu-Natal Coast of South Africa.

Fork length and weight were measured and sex was assessed by macroscopic gonad identification. We used previously published length–age relationships to derive age from fork length for both C. puniceus (Garratt et al., 1993) and C. nufar (Druzhinin, 1975 Coetzee and Baird, 1981). Fin clips were taken from the pectoral fins and stored in absolute ethanol for later DNA extraction.

Molecular analyses

DNA was extracted using a modified phenol–chloroform protocol (Sambrook and Russell, 2001). DNA concentration and quality were estimated on a NanoDropTM ND-1000 (Thermo Fisher Scientific Inc., Wilmington, DE, USA) spectrophotometer. Samples of both species were screened at 11 microsatellite loci, some specifically developed for this study (Chopelet et al., 2009a). Of the 11 microsatellites designed for C. puniceus, 5 cross-amplified in C. nufar. Six supplementary microsatellites were specifically developed for C. nufar, using the same protocol as in Chopelet et al. (2009a) (see Table 1 for details). Microsatellites were amplified using fluorescence-labelled forward primers (Applied Biosystems, Waltham, MA, USA) and 2X Multiplex PCR Master Mix (Qiagen, Hilden, Germany) in a final volume of 10 μl. Depending on size and dye, fragments were amplified into two multiplexed reactions for C. puniceus (Chopelet et al., 2009a), while another microsatellite (SL3) was amplified separately. For C. nufar, one reaction contained SL25 and SA2, and the other included the nine remaining loci (Table 1). All amplifications were carried out using the same conditions. An initial step of 15 min at 95 °C was followed by 30 cycles of 45 s at 94 °C, 45 s at 60 °C and 45 s at 72 °C, and a final extension step at 72 °C for 45 min. PCR products were sized on an ABI 3130xl alongside a GS600 ladder. Genemapper v 4 (Applied Biosystems) was used for allele scoring.

Universal primers Hsp1 and Lsp1 were also used to amplify the first hypervariable region of the mitochondrial DNA (mtDNA) control region (Ostellari et al., 1996). Each reaction was carried out using 300 ng of genomic DNA in Ready Mix (Applied Biosystems) in a final volume of 25 μl. PCR cycles were as follows: (a) 95 °C (5 min) (b) 30 cycles at 95 °C (50 s), 56 °C 1 min and 72 °C (2 min) and (c) a final 10 min elongation at 72 °C (10 min). Amplified products were purified with exonuclease I and shrimp alkaline phosphatase (Hanke & Wink 1994) and sequenced at GATC-Biotech (Konstanz, Germany).

Statistical analyses

Genetic diversity

Genetic analyses were first performed to detect patterns of spatial structure and estimate diversity within and between locations. For microsatellite data, frequencies of null alleles were estimated using FREENA (Chapuis and Estoup, 2007). For each location sample, number of alleles (Na), observed (Ho) and expected (He) heterozygozity and inbreeding coefficient (FIS) were assessed using GENEPOP ON THE WEB (http://genepop.curtin.edu.au/ Raymond and Rousset, 1995 Rousset, 2008). Marker neutrality was tested in LOSITAN (Antao et al., 2008). To correct for variance in the sample size among populations, we further estimated the allelic richness (AR) based on the minimum sample size (Table 1) using FSTAT 2.9.3 (Goudet, 1995) and the number of private alleles using the rarefaction method (Kalinowski, 2005) implemented in ADZE 1.0 (Szpiech et al., 2008). Population differentiation was estimated using the θ estimator of FST (Weir and Cockerham, 1984) and relative confidence intervals using 10 000 permutations on the individuals in GENETIX v.4.05.2 (Belkhir et al., 1996–2004). Although the mutation rate was in our instance likely to be orders of magnitude smaller than migration rates, the corrected F′ST (Hedrick, 2005) was calculated, and Jost’s Dest (Jost, 2008) estimated using SMOGD (Crawford, 2010), and reported as additional information on genetic substructure. POWSIM was used to evaluate the power of the data set to detect genetic differentiation (Ryman and Palm, 2006). Five hundred replications and different Ne/t ratios (500/0 2000/2 1000/5 1000/10 and 500/10) were used to obtain the expected FST according to this equation: FST=1−(1−1/2Ne) t , with t being the number of generations of isolation (Ryman and Palm, 2006). Bayesian assignment was performed in STRUCTURE 2.3 (Pritchard et al., 2000 Falush et al., 2003, 2007) to infer the most likely number of genetic clusters (K) present in the data sets using the admixture model, and 500 000 iterations, after 50 000 burn-in. The number of clusters was calculated by averaging the mean posterior probability of the data L(K) over 10 independent runs.

Nucleotide and haplotype diversities were estimated from mtDNA sequences using DNASP v4.5 (Rozas et al., 2003). Median-Joining networks were constructed for both species using POPART (http://popart.otago.ac.nz).

Estimating effective population size

We used the linkage disequilibrium (LD) method implemented in LDNe (Waples and Do, 2008) to estimate contemporary Ne for each location from the microsatellite data, both including and excluding the markers that were not under Hardy-Weinberg equilibrium according to the exact test performed in Genepop. The LD method is based on the theoretical relationship (Hill, 1981) between a measure of LD (r 2 =squared correlation of alleles at pairs of unlinked gene loci), sample size (N) and Ne. LDNe implements a modification of Hill’s method that accounts for bias from ignoring second order terms in N and Ne. LDNe allows one to screen out rare alleles, which tend to upwardly bias Ne estimates, by selecting a minimum allowable allele frequency (PCrit). We focused especially on PCrit=0.02, which (given the minimum sample sizes of N=39–45 Table 2) ensured that any alleles that occurred in a single copy were not used (Waples and Do, 2010). Another estimate of effective population size was obtained using the Approximate Bayesian Computation method implemented in DIYABC 2.01 (Cornuet et al., 2014). Calculations were performed for each species, pooling samples from all locations in order to reflect the lack of genetic substructure detected in our data. Three simple scenarios were simulated. Each one represented one single population whose Ne remained constant (scenario 1), one where Ne increased after a time t1 (scenario 2) and the third where Ne decreased after t1. Priors were as follows: effective population size was between 10 and 10 6 and t1 between 10 and 10 4 generations.

A longer-term view of effective population size was also obtained through estimates of historical female Ne from mtDNA data. We first used the Watterson estimator of the mutation parameter theta (θ) obtained from the number of polymorphic sites (S) (Watterson, 1975). In DNASP v4.5, θ is defined as 2Neμ for mtDNA, where Ne is the effective population size and μ is the mutation rate per DNA sequence per generation (Tajima 1996). We estimated the female effective population size (Nef) from the haplotype mutation rate and generation time (T) according to this equation:

We assumed a widely accepted rate μ=11% per site per million year for the Sparid mtDNA control region (Bargelloni et al., 2003 Sala-Bozano et al., 2009 Coscia et al., 2012), equal to 0.055 substitutions per site per million years. The age at maximum egg production was estimated with Linf=47 cm for C. puniceus and Linf=75 cm for C. nufar (where Linf, a parameter of the von Bertalanffy growth equation, is defined as the length that an individual would reach if it grew indefinitely). This, according to Beverton (1992), can be used as an approximation of generation time (T=5 for C. puniceus and 7 for C. nufar). Therefore, to account for life-history plasticity, we estimated Ne in both species with generation time encompassing these values: T=3, 5 and 8.

Furthermore, we applied the Bayesian Skyline Plot approach implemented in BEAST v 1.7 (Drummond et al., 2012) to estimate trends in past effective population size. Firstly, jModelTest 0.1.1 (Posada, 2008 Guindon and Gascuel, 2003) was used to select the best model of substitution for each data set via the AIC (Akaike Information Criterion): GTR (Generalised Time Reversible described in Tavaré (1986)) was selected for C. nufar and HKY (Hasegawa 1985) for C. puniceus. To avoid convergence issues, several independent runs (each 10 6 generations and 10% burn-in) were used for each species until each effective sample size value reached

200 as per the user’s manual.

Strong gender differences in reproductive success variance, and the times to the most recent common ancestors

The Time to the Most Recent Common Ancestor (TMRCA) based on human mitochondrial DNA (mtDNA) is estimated to be twice that based on the non-recombining part of the Y chromosome (NRY). These TMRCAs have special demographic implications because mtDNA is transmitted only from mother to child, while NRY is passed along from father to son. Therefore, the former locus reflects female history, and the latter, male history. To investigate what caused the two-to-one female–male TMRCA ratio r F / M = T F / T M in humans, we develop a forward-looking agent-based model (ABM) with overlapping generations. Our ABM simulates agents with individual life cycles, including life events such as reaching maturity or menopause. We implemented two main mating systems: polygynandry and polygyny with different degrees in between. In each mating system, the male population can be either homogeneous or heterogeneous. In the latter case, some males are ‘alphas’ and others are ‘betas’, which reflects the extent to which they are favored by female mates. A heterogeneous male population implies a competition among males with the purpose of signaling as alpha males. The introduction of a heterogeneous male population is found to reduce by a factor 2 the probability of finding equal female and male TMRCAs and shifts the distribution of r F / M to higher values. In order to account for the empirical observation of the factor 2, a high level of heterogeneity in the male population is needed: less than half the males can be alphas and betas can have at most half the fitness of alphas for the TMRCA ratio to depart significantly from 1. In addition, we find that, in the modes that maximize the probability of having 1.5 < r F / M < 2.5 , the present generation has 1.4 times as many female as male ancestors. We also tested the effect of sex-biased migration and sex-specific death rates and found that these are unlikely to explain alone the sex-biased TMRCA ratio observed in humans. Our results support the view that we are descended from males who were successful in a highly competitive context, while females were facing a much smaller female–female competition.

Highlights

► We develop a novel agent-based model (ABM) of a population of women and men. ► Our population has overlapping generation and different mating systems. ► We classify conditions reproducing the observed human female–male TMRCA ratio of 2. ► We find that high male–male competition is necessary to yield the TMRCA ratio of 2.

Population structure and variance effective size of red snapper (Lutjanus campechanus) in the northern Gulf of Mexico

We assayed allelic variation at 19 nuclear-encoded microsatellites among 1622 Gulf red snapper (Lutjanus campechanus) sampled from the 1995 and 1997 cohorts at each of three offshore localities in the northern Gulf of Mexico (Gulf). Localities represented western, central, and eastern subregions within the northern Gulf. Number of alleles per microsatellite per sample ranged from four to 23, and gene diversity ranged from 0.170 to 0.917. Tests of conformity to Hardy-Weinberg equilibrium expectations and of genotypic equilibrium between pairs of microsatellites were generally nonsignificant following Bonferroni correction. Significant genic or genotypic heterogeneity (or both) among samples was detected at four microsatellites and over all microsatellites. Levels of divergence among samples were low (FST ≤0.001). Pairwise exact tests revealed that six of seven “significant” comparisons involved temporal rather than spatial heterogeneity. Contemporaneous or variance effective size (NeV) was estimated from the temporal variance in allele frequencies by using a maximum-likelihood method. Estimates of NeV ranged between 1098 and >75,000 and differed significantly among localities the NeV estimate for the sample from the northcentral Gulf was >60 times as large as the estimates for the other two localities. The differences in variance effective size could reflect differences in number of individuals successfully reproducing, differences in patterns and intensity of immigration, or both, and are consistent with the hypothesis, supported by life-history data, that different “demographic stocks” of red snapper are found in the northern Gulf. Estimates of NeV for red snapper in the northern Gulf were at least three orders of magnitude lower than current estimates of census size (N). The ratio of effective to census size (Ne/N) is far below that expected in an ideal population and may reflect high variance in individual reproductive success, high temporal and spatial variance in productivity among subregions or a combination of the two.