Effective population size in eusocial Hymenoptera with worker-produced males

In many eusocial Hymenoptera, a proportion of males are produced by workers. To assess the effect of male production by workers on the effective population size N_e, a general expression of N_e in Hymenoptera with worker-produced males is derived on the basis of the genetic drift in the frequency of a neutral allele. Stochastic simulation verifies that the obtained expression gives a good prediction of N_e under a wide range of conditions. Numerical computation with the expression indicates that worker reproduction generally reduces N_e. The reduction can be serious in populations with a unity or female-biased breeding sex ratio. Worker reproduction may increase N_e in populations with a male-biased breeding sex ratio, only if each laying worker produce a small number of males and the difference of male progeny number among workers is not large. Worker reproduction could be an important cause of the generally lower genetic variation found in Hymenoptera, through its effect on N_e.     

Sociality and the rate of molecular evolution

The molecular clock does not tick at a uniform rate in all taxa but may be influenced by species characteristics. Eusocial species (those with reproductive division of labor) have been predicted to have faster rates of molecular evolution than their nonsocial relatives because of greatly reduced effective population size; if most individuals in a population are nonreproductive and only one or few queens produce all the offspring, then eusocial animals could have much lower effective population sizes than their solitary relatives, which should increase the rate of substitution of "nearly neutral" mutations. An earlier study reported faster rates in eusocial honeybees and vespid wasps but failed to correct for phylogenetic nonindependence or to distinguish between potential causes of rate variation. Because sociality has evolved independently in many different lineages, it is possible to conduct a more wide-ranging study to test the generality of the relationship. We have conducted a comparative analysis of 25 phylogenetically independent pairs of social lineages and their nonsocial relatives, including bees, wasps, ants, termites, shrimps, and mole rats, using a range of available DNA sequences (mitochondrial and nuclear DNA coding for proteins and RNAs, and nontranslated sequences). By including a wide range of social taxa, we were able to test whether there is a general influence of sociality on rates of molecular evolution and to test specific predictions of the hypothesis: (1) that social species have faster rates because they have reduced effective population sizes; (2) that mitochondrial genes would show a greater effect of sociality than nuclear genes; and (3) that rates of molecular evolution should be correlated with the degree of sociality. We find no consistent pattern in rates of molecular evolution between social and nonsocial lineages and no evidence that mitochondrial genes show faster rates in social taxa. However, we show that the most highly eusocial Hymenoptera do have faster rates than their nonsocial relatives. We also find that social parasites (that utilize the workers from related species to produce their own offspring) have faster rates than their social relatives, which is consistent with an effect of lower effective population size on rate of molecular evolution. Our results illustrate the importance of allowing for phylogenetic nonindependence when conducting investigations of determinants of variation in rate of molecular evolution.     

Estimation of average number of nucleotide substitutions when the rate of substitution varies with nucleotide

Summary A formal mathematical analysis of Kimura's (1981) six-parameter model of nucleotide substitution for the case of unequal substitution rates among different pairs of nucleotides is conducted, and new formulae for estimating the number of nucleotide substitutions and its standard error are obtained. By using computer simulation, the validities and utilities of Jukes and Cantor's (1969) one-parameter formula, Takahata and Kimura's (1981) four-parameter formula, and our sixparameter formula for estimating the number of nucleotide substitutions are examined under three different schemes of nucleotide substitution. It is shown that the one-parameter and four-parameter formulae often give underestimates when the number of nucleotide substitutions is large, whereas the six-parameter formula generally gives a good estimate for all the three substitution schemes examined. However, when the number of nucleotide substitutions is large, the six-parameter and four-parameter formulae are often inapplicable unless the number of nucleotides compared is extremely large. It is also shown that as long as the mean number of nucleotide substitutions is smaller than one per nucleotide site the three formulae give more or less the same estimate regardless of the substitution scheme used.On leave of absence from the Department of Biology, Faculty of Science, Kyushu University 33, Fukuoka 812, Japan     

Effective population size does not predict codon usage bias in mammals

Synonymous codons are not used at equal frequency throughout the genome, a phenomenon termed codon usage bias (CUB). It is often assumed that interspecific variation in the intensity of CUB is related to species differences in effective population sizes (N_e), with selection on CUB operating less efficiently in species with small N_e. Here, we specifically ask whether variation in N_e predicts differences in CUB in mammals and report two main findings. First, across 41 mammalian genomes, CUB was not correlated with two indirect proxies of N_e (body mass and generation time), even though there was statistically significant evidence of selection shaping CUB across all species. Interestingly, autosomal genes showed higher codon usage bias compared to X‐linked genes, and high‐recombination genes showed higher codon usage bias compared to low recombination genes, suggesting intraspecific variation in N_e predicts variation in CUB. Second, across six mammalian species with genetic estimates of N_e (human, chimpanzee, rabbit, and three mouse species: Mus musculus, M. domesticus, and M. castaneus), N_e and CUB were weakly and inconsistently correlated. At least in mammals, interspecific divergence in N_e does not strongly predict variation in CUB. One hypothesis is that each species responds to a unique distribution of selection coefficients, confounding any straightforward link between N_e and CUB.     

Effective/census population size ratio estimation: a compendium and appraisal

With an ecological-evolutionary perspective increasingly applied toward the conservation and management of endangered or exploited species, the genetic estimation of effective population size (N_e) has proliferated. Based on a comprehensive analysis of empirical literature from the past two decades, we asked: (i) how often do studies link N_e to the adult census population size (N)? (ii) To what extent is N_e correctly linked to N? (iii) How readily is uncertainty accounted for in both N_e and N when quantifying N_e/N ratios? and (iv) how frequently and to what degree might errors in the estimation of N_e or N affect inferences of N_e/N ratios? We found that only 20% of available N_e estimates (508 of 2617; 233 studies) explicitly attempted to link N_e and N; of these, only 31% (160 of 508) correctly linked N_e and N. Moreover, only 7% (41 of 508) of N_e/N ratios (correctly linked or not) reported confidence intervals for both N_e and N; for those cases where confidence intervals were reported for N_e only, 31% of N_e/N ratios overlapped with 1, of which more than half also reached below N_e/N = 0.01. Uncertainty in N_e/N ratios thus sometimes spanned at least two orders of magnitude. We conclude that the estimation of N_e/N ratios in natural populations could be significantly improved, discuss several options for doing so, and briefly outline some future research directions.     

Spatiotemporal relationship between adult census size and genetic population size across a wide population size gradient

Adult census population size (N) and effective number of breeders (N_b) are highly relevant for designing effective conservation strategies. Both parameters are often challenging to quantify, however, making it of interest to determine whether one parameter can be generalized from the other. Yet, the spatiotemporal relationship between N and N_b has not been well characterized empirically in many taxa. We analysed this relationship for 5–7 consecutive years in twelve brook trout populations varying greatly in N (49‐10032) and N_b (3‐567) and identified major environmental variables affecting the two parameters. N or habitat size alone explained 47–57% of the variance in N_b, and N_b was strongly correlated with effective population size. The ratio N_b/N ranged from 0.01 to 0.45 and increased at small N or following an annual decrease in N, suggesting density‐dependent constraints on N_b. We found no evidence for a consistent, directional difference between variability in N_b and/or N_b/N among small and large populations; however, small populations had more varying temporal variability in N_b/N ratios than large populations. Finally, N_b and N_b/N were 2.5‐ and 2.3‐fold more variable among populations than temporally within populations. Our results demonstrate a clear linkage between demographic and evolutionary parameters, suggesting that N_b could be used to approximate N (or vice versa) in natural populations. Nevertheless, using one variable to infer the other to monitor trends within populations is less recommended, perhaps even less so in small populations given their less predictable N_b vs. N dynamics.     

Patterns of protein evolution in Tetrahymena thermophila: implications for estimates of effective population size

High levels of synonymous substitutions among alleles of the surface antigen SerH led to the hypothesis that Tetrahymena thermophila has a tremendously large effective population size, one that is greater than estimated for many prokaryotes (Lynch, M., and J. S. Conery. 2003. Science 302:1401-1404.). Here we show that SerH is unusual as there are substantially lower levels of synonymous variation at five additional loci (four nuclear and one mitochondrial) characterized from T. thermophila populations. Hence, the effective population size of T. thermophila, a model single-celled eukaryote, is lower and more consistent with estimates from other microbial eukaryotes. Moreover, reanalysis of SerH polymorphism data indicates that this protein evolves through a combination of vertical transmission of alleles and concerted evolution of repeat units within alleles. SerH may be under balancing selection due to a mechanism analogous to the maintenance of antigenic variation in vertebrate immune systems. Finally, the dual nature of ciliate genomes and particularly the amitotic divisions of processed macronuclear genomes may make it difficult to estimate accurately effective population size from synonymous polymorphisms. This is because selection and drift operate on processed chromosomes in macronuclei, where assortment of alleles, disruption of linkage groups, and recombination can alter the genetic landscape relative to more canonical eukaryotic genomes.     

Effective population size associated with self-fertilization: lessons from temporal changes in allele frequencies in the selfing annual Medicago truncatula

Despite its significance in evolutionary and conservation biology, few estimates of effective population size (N(e)) are available in plant species. Self-fertilization is expected to affect N(e), through both its effect on homozygosity and population dynamics. Here, we estimated N(e) using temporal variation in allele frequencies for two contrasted populations of the selfing annual Medicago truncatula: a large and continuous population and a subdivided population. Estimated N(e) values were around 5-10% of the population census size suggesting that other factors than selfing must contribute to variation in allele frequencies. Further comparisons between monolocus allelic variation and changes in the multilocus genotypic composition of the populations show that the local dynamics of inbred lines can play an important role in the fluctuations of allele frequencies. Finally, comparing N(e) estimates and levels of genetic variation suggest that H(e) is a poor estimator of the contemporaneous variance effective population size.     

Gene genealogies when the sample size exceeds the effective size of the population

We study the properties of gene genealogies for large samples using a continuous approximation introduced by R. A. Fisher. We show that the major effect of large sample size, relative to the effective size of the population, is to increase the proportion of polymorphisms at which the mutant type is found in a single copy in the sample. We derive analytical expressions for the expected number of these singleton polymorphisms and for the total number of polymorphic, or segregating, sites that are valid even when the sample size is much greater than the effective size of the population. We use simulations to assess the accuracy of these predictions and to investigate other aspects of large-sample genealogies. Lastly, we apply our results to some data from Pacific oysters sampled from British Columbia. This illustrates that, when large samples are available, it is possible to estimate the mutation rate and the effective population size separately, in contrast to the case of small samples in which only the product of the mutation rate and the effective population size can be estimated.     

Variance effective population size is affected by census size in sub-structured populations

Measurement of allele frequency shifts between temporally spaced samples has long been used for assessment of effective population size (N_e), and this ‘temporal method’ provides estimates of N_e referred to as variance effective size (N_eV). We show that N_eV of a local population that belongs to a sub-structured population (a metapopulation) is determined not only by genetic drift and migration rate (m), but also by the census size (N_c). The realized N_eV of a local population can either increase or decrease with increasing m, depending on the relationship between N_e and N_c in isolation. This is shown by explicit mathematical expressions for the factors affecting N_eV derived for an island model of migration. We verify analytical results using high-resolution computer simulations, and show that the phenomenon is not restricted to the island model migration pattern. The effect of N_c on the realized N_eV of a local subpopulation is most pronounced at high migration rates. We show that N_c only affects local N_eV, whereas N_eV for the metapopulation as a whole, inbreeding (N_eI), and linkage disequilibrium (N_eLD) effective size are all independent of N_c. Our results provide a possible explanation to the large variation of N_e/N_c ratios reported in the literature, where N_e is frequently estimated by N_eV. They are also important for the interpretation of empirical N_e estimates in genetic management where local N_eV is often used as a substitute for inbreeding effective size, and we suggest an increased focus on metapopulation N_eV as a proxy for N_eI.     

Goodman et al.'s method for augmenting the number of nucleotide substitutions

Summary Statistical properties of Goodman et al.'s (1974) method of compensating for undetected nucleotide substitutions in evolution are investigated by using computer simulation. It is found that the method tends to overcompensate when the stochastic error of the number of nucleotide substitutions is large. Furthermore, the estimate of the number of nucleotide substitutions obtained by this method has a large variance. However, in order to see whether this method gives overcompensation when applied together with the maximum parsimony method, a much larger scale of simulation seems to be necessary.     

Small effective population size in the long-toed salamander

The effective population sizes (Ne) of six populations of the long-toed salamander (Ambystoma macrodactylum) from Montana and Idaho, USA were estimated from allozyme data from samples collected in 1978, 1996 and 1997 using the temporal allele frequency method. Five of the six estimates ranged from 23 to 207 (mean = 123 +/- 79); one estimate was indistinguishable from infinity. In order to infer the actual Ne of salamander populations, we compared the frequency distribution of our observed Ne estimates with distributions obtained from simulated populations of known Ne. Our observed Ne estimate distribution was consistent with distributions from simulated populations with Ne values of 10, 25, and 50, suggesting an actual Ne for each of the six salamander populations of less than 100. This Ne estimate agrees with most other Ne estimates for amphibians. We conclude by discussing the conservation implications of small Ne values in amphibians in the context of increasing isolation of populations due to habitat fragmentation.     

Effective size of harvested ungulate populations

The harvest of ungulate populations is often directed against certain sex or age classes to maximize the yield in terms of biomass, number of shot animals or number of trophies. Here we examine how such directional harvest affects the effective size of the population. We parameterize an age-specific model assumed to describe the dynamics of Fennoscandian moose. Based on expressions for the demographic variance     for a small subpopulation of heterozygotes Aa bearing a rare neutral allele a , we use this model to calculate how different harvest strategies influence the effective size of the population, given that the population remains stable after harvest. We show that the annual genetic drift, determined by     , increases with decreasing harvest rate of calves and increasing sex bias in the harvest towards bulls 1 year or older. The effective population size per generation decreased with reduced harvest of calves and increased harvest of bulls 1 year or older. The magnitude of these effects depends on the age-specific pattern of variation in reproductive success, which influences the demographic variance. This shows that the choice of harvest strategy strongly affects the genetic dynamics of harvested ungulate populations.     

Effects of population characteristics and structure on estimates of effective population size in a house sparrow metapopulation

Effective population size (N_e) is a key parameter to understand evolutionary processes and the viability of endangered populations as it determines the rate of genetic drift and inbreeding. Low N_e can lead to inbreeding depression and reduced population adaptability. In this study, we estimated contemporary N_e using genetic estimators (LDNE, ONeSAMP, MLNE and CoNe) as well as a demographic estimator in a natural insular house sparrow metapopulation. We investigated whether population characteristics (population size, sex ratio, immigration rate, variance in population size and population growth rate) explained variation within and among populations in the ratio of effective to census population size (N_e/N_c). In general, N_e/N_c ratios increased with immigration rates. Genetic N_e was much larger than demographic N_e, probably due to a greater effect of immigration on genetic than demographic processes in local populations. Moreover, although estimates of genetic N_e seemed to track N_c quite well, the genetic N_e‐estimates were often larger than N_c within populations. Estimates of genetic N_e for the metapopulation were however within the expected range (<N_c). Our results suggest that in fragmented populations, even low levels of gene flow may have important consequences for the interpretation of genetic estimates of N_e. Consequently, further studies are needed to understand how N_e estimated in local populations or the total metapopulation relates to actual rates of genetic drift and inbreeding.     

A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences

Summary Some simple formulae were obtained which enable us to estimate evolutionary distances in terms of the number of nucleotide substitutions (and, also, the evolutionary rates when the divergence times are known). In comparing a pair of nucleotide sequences, we distinguish two types of differences; if homologous sites are occupied by different nucleotide bases but both are purines or both pyrimidines, the difference is called type I (or transition type), while, if one of the two is a purine and the other is a pyrimidine, the difference is called type II (or transversion type). Letting P and Q be respectively the fractions of nucleotide sites showing type I and type II differences between two sequences compared, then the evolutionary distance per site is K = — (1/2) ln {(1 — 2P — Q) }. The evolutionary rate per year is then given by k = K/(2T), where T is the time since the divergence of the two sequences. If only the third codon positions are compared, the synonymous component of the evolutionary base substitutions per site is estimated by K'_S = — (1/2) ln (1 — 2P — Q). Also, formulae for standard errors were obtained. Some examples were worked out using reported globin sequences to show that synonymous substitutions occur at much higher rates than amino acid-altering substitutions in evolution.Contribution No. 1330 from the National Institute of Genetics, Mishima, 411 Japan     

Migration and inbreeding: the importance of recipient population size for genetic management

Sewall Wright demonstrated 70 years ago thatthe number of migrants required to maintainspecified levels of gene flow (i.e. avoidexcessive inbreeding) is virtually independentof the size of the recipient population. According to conventional wisdom, this idea isvalid provided population size exceeds 20. Itis well known that this independence implicitlyassumes that a population's effective size(N _e) is equal to its census size(N). However, it is not obvious whetherindependence between the required number ofmigrants (to avoid excessive inbreeding) andpopulation size constitutes a reasonableassumption for real populations of conservationconcern. Relying on empirical data, wedemonstrate that for real populations, theassumption (i.e. N _e = N) isroutinely violated to a degree such that therequired number of migrants is stronglydependent on the size of the recipientpopulation. Because a population's effectivesize (N _e) is typically much smallerthan its census size (N), the number ofmigrants required to avoid inbreeding isactually dependent on N even when it isconsiderably greater than 20. For example,when N _e/N = 0.1, the number ofmigrants required to maintain the inbreedingcoefficient (F) at 0.2 doubles (from 4 to8) as N increases from 9 to 60. Similarly, when N _e/N = 0.05, thenumber of migrants required increases by 50%as N increases from 18 to 45, andincreases again by 50% as N increasesfrom 45 to 260. Thus, for populations muchlarger than 20, the required number of migrantsincreases asymptotically with N, anddramatically so when N _e/N1. Simple conventions regarding the requisitenumber of migrants may not apply to manypopulations of conservation concern. Geneticmanagement should routinely rely on models thatexplicitly account for this and other recentconsiderations. Failure to do so mayjeopardize the viability of populations thatare sensitive to altered levels of inbreeding.     

Generation time and effective population size in Polar Eskimos

North Greenland Polar Eskimos are the only hunter-gatherer population, to our knowledge, who can offer precise genealogical records spanning several generations. This is the first report from Eskimos on two key parameters in population genetics, namely, generation time (T) and effective population size (Ne). The average mother-daughter and father-son intervals were 27 and 32 years, respectively, roughly similar to the previously published generation times obtained from recent agricultural societies across the world. To gain an insight for the generation time in our distant ancestors, we calculated maternal generation time for two wild chimpanzee populations. We also provide the first comparison among three distinct approaches (genealogy, variance and life table methods) for calculating Ne, which resulted in slightly differing values for the Eskimos. The ratio of the effective to the census population size is estimated as 0.6-0.7 for autosomal and X-chromosomal DNA, 0.7-0.9 for mitochondrial DNA and 0.5 for Y-chromosomal DNA. A simulation of alleles along the genealogy suggested that Y-chromosomal DNA may drift a little faster than mitochondrial DNA in this population, in contrast to agricultural Icelanders. Our values will be useful not only in prehistoric population inference but also in understanding the shaping of our genome today.     

Effective population size of natural populations of Drosophila buzzatii, with a comparative evaluation of nine methods of estimation

Allozyme and microsatellite data from numerous populations of Drosophila buzzatii have been used (i) to determine to what degree N(e) varies among generations within populations, and among populations, and (ii) to evaluate the congruence of four temporal and five single-sample estimators of N(e) . Effective size of different populations varied over two orders of magnitude, most populations are not temporally stable in genetic composition, and N(e) showed large variation over generations in some populations. Short-term N(e) estimates from the temporal methods were highly correlated, but the smallest estimates were the most precise for all four methods, and the most consistent across methods. Except for one population, N(e) estimates were lower when assuming gene flow than when assuming populations that were closed. However, attempts to jointly estimate N(e) and immigration rate were of little value because the source of migrants was unknown. Correlations among the estimates from the single-sample methods generally were not significant although, as for the temporal methods, estimates were most consistent when they were small. These single-sample estimates of current N(e) are generally smaller than the short-term temporal estimates. Nevertheless, population genetic variation is not being depleted, presumably because of past or ongoing migration. A clearer picture of current and short-term effective population sizes will only follow with better knowledge of migration rates between populations. Different methods are not necessarily estimating the same N(e) , they are subject to different bias, and the biology, demography and history of the population(s) may affect different estimators differently.     

Temporal genetic variation of mitochondrial DNA and the female effective population size of red drum (Sciaenops ocellatus) in the northern Gulf of Mexico

We studied genetic drift of mitochondrial DNA (mtDNA) haplotype frequencies in a natural population of red drum (Sciaenops ocellatus) from the northern Gulf of Mexico (Gulf). The amount of genetic drift observed across temporally adjacent year classes (1986–89) was used to estimate variance effective (female) population size (N_ef). N_ef was estimated to be 14 308 and the ratio of female effective size to adult female census size was approximately 0.004, which is among the lowest value reported for vertebrate animals. Low effective size relative to census size among red drum in the northern Gulf may result from yearly fluctuations in the number of breeding females, high variance in female reproductive success, or both. Despite low genetic effective size relative to census size, the genetic effective population size of red drum in the northern Gulf appears sufficiently large to preclude potentially deleterious effects of inbreeding.