Effective population size/adult population size ratios in wildlife: a review

Genetic effective size is three orders of magnitude smaller than adult census size in an abundant, Estuarine-dependent marine fish (Sciaenops ocellatus)

Using eight microsatellite loci and a variety of analytical methods, we estimated genetic effective size (N(e)) of an abundant and long-lived marine fish species, the red drum (Sciaenops ocellatus), in the northern Gulf of Mexico (Gulf). The ratio N(e)/N, where short-term variance N(e) was estimated via the temporal method from shifts in allele-frequency data over four cohorts and where N reflected a current estimate of adult census size in the northern Gulf, was approximately 0.001. In an idealized population, this ratio should approximate unity. The extraordinarily low value of N(e)/N appears to arise from high variance in individual reproductive success and perhaps more importantly from variance in productivity of critical spawning and nursery habitats located in spatially discrete bays and estuaries throughout the northern Gulf. An estimate of N(e) based on a coalescent approach, which measures long-term, inbreeding effective size, was four orders of magnitude lower than the estimate of current census size, suggesting that factors presently driving N(e)/N to low values among red drum in the northern Gulf may have operated similarly in the past. Models that predict N(e)/N exclusively from demographic and life-history features will seriously overestimate N(e) if variance in reproductive success and variance in productivity among spatially discrete demes is underestimated. Our results indicate that these variances, especially variance in productivity among demes, must be large for red drum. Moreover, our study indicates that vertebrate populations with enormous adult census numbers may still be at risk relative to decline and extinction from genetic factors.

Population genetics of shortnose sturgeon Acipenser brevirostrum based on mitochondrial DNA control region sequences

Shortnose sturgeon is an anadromous North American acipenserid that since 1973 has been designated as federally endangered in US waters. Historically, shortnose sturgeon occurred in as many as 19 rivers from the St. John River, NB, to the St. Johns River, FL, and these populations ranged in census size from 10(1) to 10(4), but little is known of their population structure or levels of gene flow. We used the polymerase chain reaction (PCR) and direct sequence analysis of a 440 bp portion of the mitochondrial DNA (mtDNA) control region to address these issues and to compare haplotype diversity with population size. Twenty-nine mtDNA nucleotide-substitution haplotypes were revealed among 275 specimens from 11 rivers and estuaries. Additionally, mtDNA length variation (6 haplotypes) and heteroplasmy (2-5 haplotypes for some individuals) were found. Significant genetic differentiation (P < 0.05) of mtDNA nucleotide-substitution haplotypes and length-variant haplotypes was observed among populations from all rivers and estuaries surveyed with the exception of the Delaware River and Chesapeake Bay collections. Significant haplotype differentiation was even observed between samples from two rivers (Kennebec and Androscoggin) within the Kennebec River drainage. The absence of haplotype frequency differences between samples from the Delaware River and Chesapeake Bay reflects a probable current absence of spawning within the Chesapeake Bay system and immigration of fish from the adjoining Delaware River. Haplotypic diversity indices ranged between 0.817 and 0.641; no relationship (P > 0.05) was found between haplotype diversity and census size. Gene flow estimates among populations were often low (< 2.0), but were generally higher at the latitudinal extremes of their distribution. A moderate level of haplotype diversity and a high percentage (37.9%) of haplotypes unique to the northern, once-glaciated region suggests that northern populations survived the Pleistocene in a northern refugium. Analysis of molecular variance best supported a five-region hierarchical grouping of populations, but our results indicate that in almost all cases populations of shortnose sturgeon should be managed as separate units.

Evaluating the effect of stage-specific survivorship on the N(e)/N ratio

Evaluating effective population size (Ne) and the effective size to census size ratio (Ne/N) in species with Type III survivorship curves is complicated when key demographic parameters [mean (k macro) and variance (V(k)) of family size] are measured during early life stages. The method of Crow & Morton (1955) for scaling demographic data collected at a juvenile stage to expected values at adulthood is extended to consider sequential episodes of random and family correlated survival. Results show the following: (i) The order in which the episodes of random and family-correlated survival occur does not affect N(e) or N(e)/N; (ii) If a population experiences an episode of family-correlated survival, N(e)/N scaled to its expected value in a population of constant size (k macro= 2) is simply the survival rate during the family-correlated stage. If multiple such stages occur, scaled N(e)/N is the product of the survivals during all family-correlated life stages; (iii) Under the assumption of random post-enumeration survival, adjusting the variance effective size to its expected value at k macro= 2 is equivalent to computing the inbreeding effective size at the earlier life stage. Application to experimental data for hatchery populations of Pacific salmon (Oncorhynchus spp.) indicates that nonrandom survival during the marine phase led to estimated reductions in effective size of 0-62 (mean 19) in 12 different cohorts. This approach can provide insights into N(e)/N in highly fecund species, including some marine species in which N(e) has been estimated to be several orders of magnitude less than N.

Microsatellite diversity and genetic structure of fragmented populations of the rare, fire-dependent shrub Grevillea macleayana

Recent habitat loss and fragmentation superimposed upon ancient patterns of population subdivision are likely to have produced low levels of neutral genetic diversity and marked genetic structure in many plant species. The genetic effects of habitat fragmentation may be most pronounced in species that form small populations, are fully self-compatible and have limited seed dispersal. However, long-lived seed banks, mobile pollinators and long adult lifespans may prevent or delay the accumulation of genetic effects. We studied a rare Australian shrub species, Grevillea macleayana (Proteaceae), that occurs in many small populations, is self-compatible and has restricted seed dispersal. However, it has a relatively long adult lifespan (c. 30 years), a long-lived seed bank that germinates after fire and is pollinated by birds that are numerous and highly mobile. These latter characteristics raise the possibility that populations in the past may have been effectively large and genetically homogeneous. Using six microsatellites, we found that G. macleayana may have relatively low within-population diversity (3.2-4.2 alleles/locus; Hexp = 0.420-0.530), significant population differentiation and moderate genetic structure (FST = 0.218) showing isolation by distance, consistent with historically low gene flow. The frequency distribution of allele sizes suggest that this geographical differentiation is being driven by mutation. We found a lack mutation-drift equilibrium in some populations that is indicative of population bottlenecks. Combined with evidence for large spatiotemporal variation of selfing rates, this suggests that fluctuating population sizes characterize the demography in this species, promoting genetic drift. We argue that natural patterns of pollen and seed dispersal, coupled with the patchy, fire-shaped distribution, may have restricted long-distance gene flow in the past.

Pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance

A pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance is investigated. Mutations have effects on a metric trait and deleterious effects on fitness, for which a bivariate gamma distribution is assumed. Equations for calculating the strength of apparent stabilizing selection (V(s)) and the genetic variance maintained in segregating populations (V(G)) were derived. A large population can hold a high genetic variance but the apparent stabilizing selection may or may not be relatively strong, depending on other properties such as the distribution of mutation effects. If the distribution of mutation effects on fitness is continuous such that there are few nearly neutral mutants, or a minimum fitness effect is assumed if most mutations are nearly neutral, V(G) increases to an asymptote as the population size increases. Both V(G) and V(s) are strongly affected by the shape of the distribution of mutation effects. Compared with mutants of equal effect, allowing their effects on fitness to vary across loci can produce a much higher V(G) but also a high V(s) (V(s) in phenotypic standard deviation units, which is always larger than the ratio V(P)/V(m)), implying weak apparent stabilizing selection. If the mutational variance V(m) is approximately 10(-3)V(e) (V(e), environmental variance), the model can explain typical values of heritability and also apparent stabilizing selection, provided the latter is quite weak as suggested by a recent review.

Genetic effective size of a wild primate population: influence of current and historical demography

A comprehensive assessment of the determinants of effective population size (N(e)) requires estimates of variance in lifetime reproductive success and past changes in census numbers. For natural populations, such information can be best obtained by combining longitudinal data on individual life histories and genetic marker-based inferences of demographic history. Independent estimates of the variance effective size (N(ev), obtained from life-history data) and the inbreeding effective size (N((eI), obtained from genetic data) provide a means of disentangling the effects of current and historical demography. The purpose of this study was to assess the demographic determinants of N(e) in one of the most intensively studied natural populations of a vertebrate species: the population of savannah baboons (Papio cynocephalus) in the Amboseli Basin, southern Kenya. We tested the hypotheses that N(eV) < N < N(eI) (where N = population census number) due to a recent demographic bottleneck. N(eV) was estimated using a stochastic demographic model based on detailed life-history data spanning a 28-year period. Using empirical estimates of age-specific rates of survival and fertility for both sexes, individual-based simulations were used to estimate the variance in lifetime reproductive success. The resultant values translated into an N(eV)/N estimate of 0.329 (SD = 0.116, 95% CI = 0.172-0.537). Historical N(eI), was estimated from 14-locus microsatellite genotypes using a coalescent-based simulation model. Estimates of N(eI) were 2.2 to 7.2 times higher than the contemporary census number of the Amboseli baboon population. In addition to the effects of immigration, the disparity between historical N(eI) and contemporary N is likely attributable to the time lag between the recent drop in census numbers and the rate of increase in the average probability of allelic identity-by-descent. Thus, observed levels of genetic diversity may primarily reflect the population's prebottleneck history rather than its current demography.

Genetic evidence on the demography of speciation in allopatric dolphin species

Under a neutral model, the stochastic lineage sorting that leads to gene monophyly proceeds slowly in large populations. Therefore, in many recent species with large population size, the genome will have mixed support for monophyly unless historical bottlenecks have accelerated coalescence. We use genealogical patterns in mitochondrial DNA and in introns of four nuclear loci to test for historical bottlenecks during the speciation and divergence of two temperate Lagenorhynchus dolphin species isolated by tropical Pacific waters (an antitropical distribution). Despite distinct morphologies, foraging behaviors, and mitochondrial DNAs, these dolphin species are polyphyletic at all four nuclear loci. The abundance of shared polymorphisms between these sister taxa is most consistent with the maintenance of large effective population sizes (5.09 x 10(4) to 10.9 x 10(4)) during 0.74-1.05 million years of divergence. A variety of population size histories are possible, however. We used gene tree coalescent probabilities to explore the rejection region for historical bottlenecks of different intensity given best estimates of effective population size under a strict isolation model of divergence. In L. obliquidens the data are incompatible with a colonization propagule of an effective size of 10 or fewer individuals. Although the ability to reject less extreme historical bottlenecks will require data from additional loci, the intermixed genealogical patterns observed between these dolphin sister species are highly probable only under an extended history of large population size. If similar demographic histories are inferred for other marine antitropical taxa, a parsimonious model for the Pleistocene origin of these distributions would not involve rare breaches of a constant dispersal barrier by small colonization propagules. Instead, a history of large population size in L. obliquidens and L. obscurus contributes to growing biological and environmental evidence that the equatorial barrier became permeable during glacial/interglacial cycles, leading to vicariant isolation of antitropical populations.

Insights into recently fragmented vole populations from combined genetic and demographic data

We combined demographic and genetic data to evaluate the effects of habitat fragmentation on the population structure of the California red-backed vole (Clethrionomys californicus). We analysed variation in the mitochondrial DNA (mtDNA) control region and five nuclear microsatellite loci in small samples collected from two forest fragments and an unfragmented control site in 1990-91. We intensively sampled the same forest fragments and two different control sites in 1998 and 1999. Vole abundances fluctuated greatly at sizes below 50 individuals per fragment. Fragment populations had significantly lower mtDNA allelic diversity than controls, but not nuclear heterozygosity or numbers of alleles. The use of only trapping and/or mtDNA marker data would imply that fragment populations are at least partially isolated and vulnerable to inbreeding depression. In contrast, the abundance estimates combined with microsatellite data show that small fragment populations must be linked to nearby forests by high rates of migration. These results provide evidence for the usefulness of combining genetic and demographic data to understand nonequilibrium population structure in recently fragmented habitats.

Likelihood-based estimation of the effective population size using temporal changes in allele frequencies: a genealogical approach

A new genetic estimator of the effective population size (N(e)) is introduced. This likelihood-based (LB) estimator uses two temporally spaced genetic samples of individuals from a population. We compared its performance to that of the classical F-statistic-based N(e) estimator (N(eFk)) by using data from simulated populations with known N(e) and real populations. The new likelihood-based estimator (N(eLB)) showed narrower credible intervals and greater accuracy than (N(eFk)) when genetic drift was strong, but performed only slightly better when genetic drift was relatively weak. When drift was strong (e.g., N(e) = 20 for five generations), as few as approximately 10 loci (heterozygosity of 0.6; samples of 30 individuals) are sufficient to consistently achieve credible intervals with an upper limit <50 using the LB method. In contrast, approximately 20 loci are required for the same precision when using the classical F-statistic approach. The N(eLB) estimator is much improved over the classical method when there are many rare alleles. It will be especially useful in conservation biology because it less often overestimates N(e) than does N(eLB) and thus is less likely to erroneously suggest that a population is large and has a low extinction risk.

Emerging Issues in Population Viability Analysis

Population viability analysis ( PVA) has become a commonly used tool in endangered species management. There is no single process that constitutes PVA, but all approaches have in common an assessment of a population's risk of extinction (or quasi extinction) or its projected population growth either under current conditions or expected from proposed management. As model sophistication increases, and software programs that facilitate PVA without the need for modeling expertise become more available, there is greater potential for the misuse of models and increased confusion over interpreting their results. Consequently, we discuss the practical use and limitations of PVA in conservation planning, and we discuss some emerging issues of PVA. We review extant issues that have become prominent in PVA, including spatially explicit modeling, sensitivity analysis, incorporating genetics into PVA, PVA in plants, and PVA software packages, but our coverage of emerging issues is not comprehensive. We conclude that PVA is a powerful tool in conservation biology for comparing alternative research plans and relative extinction risks among species, but we suggest caution in its use: (1) because PVA is a model, its validity depends on the appropriateness of the model's structure and data quality; (2) results should be presented with appropriate assessment of confidence; (3) model construction and results should be subject to external review, and (4) model structure, input, and results should be treated as hypotheses to be tested. We also suggest (5) restricting the definition of PVA to development of a formal quantitative model, (6) focusing more research on determining how pervasive density-dependence feedback is across species, and (7) not using PVA to determine minimum population size or (8) the specific probability of reaching extinction. The most appropriate use of PVA may be for comparing the relative effects of potential management actions on population growth or persistence.

Temporal change in genetic structure and effective population size in steelhead trout (Oncorhynchus mykiss)

There is a wealth of published molecular population genetic studies, however, most do not include historic samples and thus implicitly assume temporal genetic stability. We tested for changes in genetic diversity and structure in three populations of steelhead trout (Oncorhynchus mykiss) from a northern British Columbia watershed using seven microsatellite loci over 40 years. We found little change in genetic diversity (mean allele numbers and observed and expected heterozygosity), despite large variation in the estimated numbers of steelhead returning to the watershed over the same time period. However, the temporal stability in genetic diversity is not reflected in population structure, which appears to be high among populations, yet significantly variable over time. The neighbour-joining tree showed that, overall, two of the populations (Zymoetz and Kispiox) clustered separately from the third (Babine); a finding which was not consistent with their geographical separation. The clustering pattern was also not temporally consistent. We used the temporal method to estimate the effective number of breeders (Nb ) for the three populations; our values (Nb = 17-102) were low for the large and presumed vigorous populations of steelhead trout sampled. The low Nb values were also not consistent with the generally high genetic diversity estimates, suggesting the possibility of intermittent gene flow among the three populations. The use of temporal analyses in population genetic samples should be a priority; first, to verify observed patterns in contemporary data, and second, to build a dataset of temporal analyses to allow generalizations to be made concerning temporal genetic stability and effective population size in natural populations.

Relationship of Effective to Census Size in Fluctuating Populations

The effective size of a population (   N_e    ) rather than the census size (   N) determines its rate of genetic drift. Knowing the ratio of effective to census size, N_e   /  N, is useful for estimating the effective size of a population from census data and for examining how different ecological factors influence effective size. Two different multigenerational ratios have been used in the literature based on either the arithmetic mean or the harmonic mean in the denominator. We clarify the interpretation and meaning of these ratios. The arithmetic mean N_e   /  N ratio compares the total number of real individuals to the long-term effective size of the population. The harmonic mean N_e   /  N ratio summarizes variation in the N_e   /  N ratio for each generation. In addition, we show that the ratio of the harmonic mean population size to the arithmetic mean population size provides a useful measure of how much fluctuation in size reduced the effective size of a population. We discuss applications of these ratios and emphasize how to use the harmonic mean N_e   /  N ratio to estimate the effective size of a population over a period of time for which census counts have been collected.

Male reproductive competition in spawning aggregations of cod (Gadus morhua, L.)

Reproductive competition may lead to a large skew in reproductive success among individuals. Very few studies have analysed the paternity contribution of individual males in spawning aggregations of fish species with huge census population sizes. We quantified the variance in male reproductive success in spawning aggregations of cod under experimental conditions over an entire spawning season. Male reproductive success was estimated by microsatellite-based parentage analysis of offspring produced in six separate groups of spawning cod. In total, 1340 offspring and 102 spawnings distributed across a spawning season were analysed. Our results show that multiple males contributed sperm to most spawnings but that paternity frequencies were highly skewed among males, with larger males on average siring higher proportions of offspring. It was further indicated that male reproductive success was dependent on the magnitude of the size difference between a female and a male. We discuss our results in relation to the cod mating system. Finally, we suggest that the highly skewed distribution of paternity success observed in cod may be a factor contributing to the low effective population size/census population size ratios observed in many marine organisms.

The annual number of breeding adults and the effective population size of syntopic newts (Triturus cristatus,T. marmoratus)

Pond-breeding amphibians are deme-structured organisms with a population genetic structure particularly susceptible to demographic threats. We estimated the effective number of breeding adults (Nb) and the effective population size (Ne) of the European urodele amphibians Triturus cristatus (the crested newt) and T. marmoratus (the marbled newt), using temporal shifts in microsatellite allele frequencies. Eight microsatellite loci isolated from a T. cristatus library were used, five of which proved polymorphic in T. marmoratus, albeit with high frequencies of null alleles at two loci. Three ponds in western France were sampled, situated 4-10 kilometers apart and inhabited by both species. Parent-offspring cohort comparisons were used to measure Nb; samples collected at time intervals of nine or 12 years, respectively, were used to measure Ne. The adult population census size (N) was determined by mark-recapture techniques. With one exception, genetic distances (FST) between temporal samples were lower than among populations. Nb ranged between 10.6 and 101.8 individuals, Ne ranged between 9.6 and 13.4 individuals. For the pond where both parameters were available, Nb/N (overall range: 0.10-0.19) was marginally larger than Ne/N (overall range: 0.09-0.16), which is reflected in the temporal stability of N. In line with the observed differences in reproductive life-histories between the species, Nb/N ratios for newts were about one order of magnitude higher than for the anuran amphibian Bufo bufo. Despite of the colonization of the study area by T. cristatus only some decades ago, no significant genetic bottleneck could be detected. Our findings give rise to concerns about the long-term demographic viability of amphibian populations in situations typical for European landscapes.

Determinants of effective population size for loci with different modes of inheritance

Here we report an assessment of the determinants of effective population size (N(e)) in species with overlapping generations. Specifically, we used a stochastic demographic model to investigate the influence of different life-history variables on N(e)/N (where N = population census number) and the influence of sex differences in life-history variables on N(e) for loci with different modes of inheritance. We applied an individual-based modeling approach to two datasets: one from a natural population of savannah baboons (Papio cynocephalus) in the Amboseli basin of southern Kenya and one from a human tribal population (the Gainj of Papua New Guinea). Simulation-based estimates of N(e)/N averaged 0.329 for the Amboseli baboon population (SD = 0.116, 95% CI = 0.172 - 0.537) and 0.786 for the Gainj (SD = 0.184, 95% CI = 0.498 - 1.115). Although variance in male fitness had a substantial impact on N(e)/N in each of the two primate populations, ratios of N(e) values for autosomal and sex-linked loci exhibited no significant departures from Poisson-expected values. In each case, similarities in sex-specific N(e) values were attributable to the unexpectedly high variance in female fitness. Variance in male fitness resulted primarily from age-dependent variance in reproductive success, whereas variance in female fitness resulted primarily from stochastic variance in survival during the reproductive phase.

Genetic consequences of population decline in the European otter (Lutra lutra): an assessment of microsatellite DNA variation in Danish otters from 1883 to 1993

The European otter (Lutra lutra) was common in Denmark until the 1960s, but its present distribution encompasses only a minor part of the country. The aim of this study was to assess whether the recent population decline has resulted in loss of genetic variability and to gain further insight into the dynamics of the population decline. This was done by analysing microsatellite DNA variation in contemporary and historical samples, the latter encompassing DNA samples extracted from museum specimens covering a time-span from the 1880s to the 1960s. Tests for differences in expected heterozygosity and the numbers of alleles in contemporary versus historical samples and a test for detecting population bottlenecks provided few indications of a recent bottleneck and loss of variability. However, a procedure for detecting population expansions and declines, based on the genealogical history of microsatellite alleles, suggested that a drastic long-term population decline has taken place, which could have started more than 2000 years ago, possibly due to ancient anthropogenic pressure. Finally, assignment tests and pairwise F(ST) values suggested weak but statistically significant genetic differentiation between the extant population and historical samples of otters from other regions in Denmark, more likely reflecting differentiation among original populations rather than recent drift.

Genetic consequences of polygyny and social structure in an Indian fruit bat, Cynopterus sphinx. II. Variance in male mating success and effective population size

Variance in reproductive success is a primary determinant of genetically effective population size (Ne), and thus has important implications for the role of genetic drift in the evolutionary dynamics of animal taxa characterized by polygynous mating systems. Here we report the results of a study designed to test the hypothesis that polygynous mating results in significantly reduced Ne in an age-structured population. This hypothesis was tested in a natural population of a harem-forming fruit bat, Cynopterus sphinx (Chiroptera: Pteropodidae), in western India. The influence of the mating system on the ratio of variance Ne to adult census number (N) was assessed using a mathematical model designed for age-structured populations that incorporated demographic and genetic data. Male mating success was assessed by means of direct and indirect paternity analysis using 10-locus microsatellite genotypes of adults and progeny from two consecutive breeding periods (n = 431 individually marked bats). Combined results from both analyses were used to infer the effective number of male parents in each breeding period. The relative proportion of successfully reproducing males and the size distribution of paternal sibships comprising each offspring cohort revealed an extremely high within-season variance in male mating success (up to 9.2 times higher than Poisson expectation). The resultant estimate of Ne/N for the C. sphinx study population was 0.42. As a result of polygynous mating, the predicted rate of drift (1/2Ne per generation) was 17.6% higher than expected from a Poisson distribution of male mating success. However, the estimated Ne/N was well within the 0.25-0.75 range expected for age-structured populations under normal demographic conditions. The life-history schedule of C. sphinx is characterized by a disproportionately short sexual maturation period scaled to adult life span. Consequently, the influence of polygynous mating on Ne/N is mitigated by the extensive overlap of generations. In C. sphinx, turnover of breeding males between seasons ensures a broader sampling of the adult male gamete pool than expected from the variance in mating success within a single breeding period.

Sustaining genetic variation in a small population: evidence from the Mauritius kestrel

We obtained measures of genetic diversity in 10 kestrel species at a suite of 12 microsatellite loci. We estimated the relative effective size (Ne) of the species using a Markov chain Monte Carlo (MCMC) approach, which jointly estimated the locus specific mutation rates as nuisance parameters. There was surprisingly high genetic diversity found in museum specimens of the Mauritius kestrel. Being an endemic species on a small island, it is known to have a long history of small population size. Conversely, kestrels with a continental distribution had Ne estimates that were only one order of magnitude larger and similar to each other, despite having current population sizes that were between one and three orders of magnitude larger than the Mauritius kestrel. We show how many of the theoretical results describing the effective size of a subdivided population can be captured in terms of three rates which describe the branching pattern of the gene genealogy, and that they are useful in estimating the time to migration-drift and mutation-drift equilibrium. We use this approach to argue that population subdivision has helped retain genetic diversity in the Mauritius kestrel, and that the continental species' genetic diversity has yet to reach equilibrium after the range changes following the last ice age. We draw parallels with Hewitt's observation that genetic variation seems to survive species' range compression and is rather vulnerable to range expansion.

Population mixing and the adaptive divergence of quantitative traits in discrete populations: a theoretical framework for empirical tests

Empirical tests for the importance of population mixing in constraining adaptive divergence have not been well grounded in theory for quantitative traits in spatially discrete populations. We develop quantitative-genetic models to examine the equilibrium difference between two populations that are experiencing different selective regimes and exchanging individuals. These models demonstrate that adaptive divergence is negatively correlated with the rate of population mixing (m, most strongly so when m is low), positively correlated with the difference in phenotypic optima between populations, and positively correlated with the amount of additive genetic variance (G, most strongly so when G is low). The approach to equilibrium is quite rapid (fewer than 50 generations for two populations to evolve 90% of the distance to equilibrium) when either heritability or mixing are not too low (h2 > 0.2 or m > 0.05). The theory can be used to aid empirical tests that: (1) compare observed divergence to that predicted using estimates of population mixing, additive genetic variance/covariance, and selection; (2) test for a negative correlation between population mixing and adaptive divergence across multiple independent population pairs; and (3) experimentally manipulate the rate of mixing. Application of the first two of these approaches to data from two well-studied natural systems suggests that population mixing has constrained adaptive divergence for color patterns in Lake Erie water snakes (Nerodia sipedon), but not for trophic traits in sympatric pairs of benthic and limnetic stickleback (Gasterosteus aculeatus). The theoretical framework we outline should provide an improved basis for future empirical tests of the role of population mixing in adaptive divergence.

Mitochondrial mutations may decrease population viability

It is ironic that an organelle that is pivotal for the function of male gametes is inherited by sons only from their mother. A recent study of human fertility has provided the first definitive evidence that mitochondrial DNA mutations can reduce male fertility but with little or no effect on females. These results present the possibility that the viability of small populations might be reduced by increases in the frequency of mtDNA genotypes that lower the fitness of males.

Spatial structure of lemming populations (Dicrostonyx groenlandicus) fluctuating in density

The pattern and scale of the genetic structure of populations provides valuable information for the understanding of the spatial ecology of populations, including the spatial aspects of density fluctuations. In the present paper, the genetic structure of periodically fluctuating lemmings (Dicrostonyx groenlandicus) in the Canadian Arctic was analysed using mitochondrial DNA (mtDNA) control region sequences and four nuclear microsatellite loci. Low genetic variability was found in mtDNA, while microsatellite loci were highly variable in all localities, including localities on isolated small islands. For both genetic markers the genetic differentiation was clear among geographical regions but weaker among localities within regions. Such a pattern implies gene flow within regions. Based on theoretical calculations and population census data from a snap-trapping survey, we argue that the observed genetic variability on small islands and the low level of differentiation among these islands cannot be explained without invoking long distance dispersal of lemmings over the sea ice. Such dispersal is unlikely to occur only during population density peaks.

Detection of reduction in population size using data from microsatellite loci

We demonstrate that the mean ratio of the number of alleles to the range in allele size, which we term M, calculated from a population sample of microsatellite loci, can be used to detect reductions in population size. Using simulations, we show that, for a general class of mutation models, the value of M decreases when a population is reduced in size. The magnitude of the decrease is positively correlated with the severity and duration of the reduction in size. We also find that the rate of recovery of M following a reduction in size is positively correlated with post-reduction population size, but that recovery occurs in both small and large populations. This indicates that M can distinguish between populations that have been recently reduced in size and those which have been small for a long time. We employ M to develop a statistical test for recent reductions in population size that can detect such changes for more than 100 generations with the post-reduction demographic scenarios we examine. We also compute M for a variety of populations and species using microsatellite data collected from the literature. We find that the value of M consistently predicts the reported demographic history for these populations. This method, and others like it, promises to be an important tool for the conservation and management of populations that are in need of intervention or recovery.

The effects of deleterious mutations in cyclically parthenogenetic organisms

Cyclically parthenogenetic organisms experience benefits of both sexual and asexual reproductive modes in a constant environment. Sexual reproduction generates new genotypes and may facilitate the purging of deleterious mutations whereas asexuality has a two-fold advantage and enables maintenance of well-fitted genotypes. Asexual reproduction can have a drawback as increased linkage may lead to the accumulation of deleterious mutations. This study presents the results of Monte Carlo simulations of small and infinite diploid populations, with deleterious mutations occurring at multiple loci. The recombination rate and the length of the asexual period, interrupted by sexual reproduction, are allowed to vary. Here I show that the fitness of cyclical parthenogenetic population is dependent on the length of the asexual period. Increased length of the asexual period can lead both to increased segregational load following sexual reproduction and to a stronger effect of deleterious mutations on variation at a linked neutral marker, either by reducing or increasing the variation.

Isolation by distance in the Atlantic cod, Gadus morhua, at large and small geographic scales

Genetic isolation by distance (IBD) has rarely been described in marine species with high potential for dispersal at both the larval and adult life-history stages. Here, we report significant relationships between inferred levels of gene flow and geographic distance in the Atlantic cod, Gadus morhua, at 10 nuclear restriction-fragment-length-polymorphism (RFLP) loci at small regional scales in the western north Atlantic region (< 1,600 km) that mirror those previously detected over its entire geographic range (up to 7,300 km). Highly significant allele frequency differences were observed among eight northwestern Atlantic populations, although the mean FST for all 10 loci was only 0.014. Despite this weak population structuring, the distance separating populations explained between 54% and 62% of the variation in gene flow depending on whether nine or 10 loci were used to estimate Nm. Across the species' entire geographic range, highly significant differences were observed among six regional populations at nine of the 10 loci (mean FST = 0.068) and seven loci exhibited significant negative relationships between gene flow and distance. At this large geographic scale, natural selection acting in the vicinity of one RFLP locus (GM798) had a significant effect on the correlation between gene flow and distance, and eliminating it from the analysis caused the coefficient of determination to increase from 17% to 62%. The role of vicariance was assessed by sequentially removing populations from the analysis and was found to play a minor role in contributing to the relationship between gene flow and distance at either geographic scale. The correlation between gene flow and distance detected in G. morhua at small and large spatial scales suggests that dispersal distances and effective population sizes are much smaller than predicted for the species and that the recent age of populations, rather than extensive gene flow, may be responsible for its weak population structure. Our results suggest that interpreting limited genetic differences among populations as reflecting high levels of ongoing gene flow should be made with caution.

The evolution of trade-offs: effects of inbreeding on fecundity relationships in the cricket Gryllus firmus

The evolution of traits is modulated by their interrelationships with each other, particularly when those relationships result in a fitness trade-off. In this paper we explore the consequences of genetic architecture on functional relationships between traits. Specifically, we address the consequences of inbreeding on these relationships. We show that the linear regression between two traits will not be affected if there is no dominance genetic variance in either trait, whereas the intercept but not the slope of the regression will change if there is dominance genetic variance in one trait only. We test the latter hypothesis using fecundity relationships in the cricket Gryllus firmus. Data from pedigree analysis and an inbreeding experiment show that there is significant dominance genetic variance in fecundity, but not head width (an index of body size) or dorsal longitudinal muscle (DLM) mass. Fecundity increases with head width, but decreases with DLM mass. As predicted, the intercepts of the regressions of fecundity on these two morphological traits decrease with inbreeding, but there is little or no change in slope. Gryllus firmus is wing dimorphic, with the macropterous (LW) morph having a lower fecundity than the micropterous (SW) morph. We hypothesize that the difference in fecundity arises primarily because of a competition for resources in the LW females between DLM maintenance (i.e., mass) and egg production. As a consequence, we predict that the fecundity within each morph should decline linearly with the inbreeding coefficient at the same rate in both morphs. The result of this will be a change in the relative fitness of the two morphs, that of the SW morph increasing with inbreeding. This prediction is supported. These results indicate that trade-offs will evolve and such changes will affect evolutionary trajectories by altering the pattern of relationships among fitness components.

Density and Population Size of Mammals in Remnants of Brazilian Atlantic Forest

From October 1994 to April 1996, I surveyed six Atlantic forest reserves, two large (approximately 20,000 ha each), two medium-sized (approximately 2000 ha each), and two small (approximately 200 ha each), located in northern Espírito Santo, southeastern Brazil, for mammals openface> 1 kg body weight. My main objective was to assess the effects of fragmentation on population sizes and densities of five abundant species of forest-dwelling species (three primates and two rodents). I used line-transect sampling to survey mammals and estimated densities through the DISTANCE program. The average density of mammals increased from small to medium to large fragments, with small fragments having an average mammal density ( 7.6 individuals/km² ) significantly lower than that of large fragments (20.9 individuals/km² ). This trend was not significant when species that were extinct or absent in some fragments were excluded from the analysis. Shortage of food (  fruits) and predation by small cats (  Leopardus sp.) are the likely factors contributing to the demise of mammals, most of which are frugivores, in small fragments. Estimates of population sizes were on the order of several hundred to thousands of individuals for the large reserves, whereas comparable estimates for the other areas indicate a few hundred individuals for the medium-sized reserves and <100 individuals per species in the small reserves. The estimates provided here indicate that only Atlantic forest reserves of ≥20,000 ha can sustain viable populations (   N_e ≅ 500 individuals) of the five species studied, which represent only about 14% of all medium-sized to large species of mammals known to be present in fragments of this size. Given that only about 20% of all protected areas remaining in the Atlantic forest are equal to or larger than this size, management measures are badly needed to improve mammal conservation in this biome.

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.

Size-specific fecundity and the influence of lifetime size variation upon effective population size in Abies balsamea

The hierarchy of plant size often present in dense populations of plants and the close correlation found between size and fecundity can result in an unequal distribution of fecundity, which reduces the ratio of effective population size/census number (Ne/N). Such an effect has been found previously in annuals, but no study has hitherto tested for the effect in the lifetime fecundity variation of a perennial population. We use the demographically stable size distribution to be found in natural, wave-regenerating populations of balsam fir, Abies balsamea, in order to estimate Ne/N. In both wave-regenerating and normal forests our estimated values of Ne/N were about twice those previously reported for annuals. We suggest that fecundity variance is expected to be smaller in trees and other long-lived perennials than in annuals because density-dependent mortality operates more strongly in the prereproductive phase of long-lived plants.

High genetic variation in leopards indicates large and long-term stable effective population size

In this paper we employ recently developed statistical and molecular tools to analyse the population history of the Tanzanian leopard (Panthera pardus), a large solitary felid. Because of their solitary lifestyle little is known of their past or present population dynamics. Eighty-one individuals were scored at 18 microsatellite loci. Overall, levels of heterozygosity were high (0.77 +/- 0.03), with a small heterozygote deficiency (0.06 +/- 0.03). Effective population size (Ne) was calculated to be 38 000-48 000. A Ne:N ratio of 0.42 (average from four cat studies) gives a present population size of about 100 000 leopards in Tanzania. Four different bottleneck tests indicated that this population has been large and stable for a minimum of several thousand years. FST values were low and no significant genetic structuring of the population could be detected. This concurs well with the large migration values (Nm) obtained (>3.3 individuals/generation). Our analysis reveals that ecological factors (e.g. disease), which are known to have had major impact on other carnivore populations, are unlikely to have impacted strongly on the population dynamics of Tanzanian leopards. The explanation may be found in their solitary life-style, their often nonconfrontational behaviour toward interspecific competitors, or that any bottlenecks have been of limited size, localized, or too short to have affected genetic variation to any measurable degree. Since the genetic structuring is weak, gene flow is not restricted to within protected areas. Local loss of genetic variation is therefore not of immediate concern.

RAPD variation among and within small and large populations of the rare clonal plant Ranunculus reptans (Ranunculaceae)

In the pre-alpine region of Europe numbers and sizes of populations of the clonal lake shore plant Ranunculus reptans have declined because of the regulation of lake water levels. We investigated genetic variation among and within 17 populations of different size (cover 1-10 000 m) in R. reptans with RAPD (random amplified polymorphic DNA) profiles. We sampled 127 rosettes in 14 populations at Lake Constance and three populations at or near Lake Como. There was significant genetic variation between plants from the two lake regions (5.9%, analysis of molecular variance [AMOVA], P < 0.001), among populations within lake regions (20.4%, P < 0.001), and within populations (73.7%, P < 0.001). Under the assumptions of Wright's island model the variation among populations corresponds to a gene flow of N(e)m = 0.70. Within the 14 Lake Constance populations we detected significant genetic variation among subpopulations separated by only a few metres (4.0% of the within-population variation; P < 0.05). Molecular variance was 24% smaller in small populations covering <100 m area than in larger ones (P < 0.03), indicating that samples from large populations were genetically more variable than samples representing comparable areas of smaller populations. We conclude that gene flow among populations is very limited and that genetic drift has caused reduced genetic variability of smaller populations. Conservation of genetic variability in R. reptans requires persistence of large and also of small populations (because of population differentiation), and it could be enhanced by increasing the size of small populations (to counter genetic drift).

The effective number of a population that varies cyclically in size. I. Discrete generations

We consider a dioecious population having numbers of males and females that vary over time in cycles of length k. It is shown that if k is small in comparison with the numbers of males and females in any generation of the cycle, the effective population number (or size), N(e), is approximately equal to the harmonic mean of the effective population sizes during any given cycle. This result holds whether the locus under consideration is autosomal or sex-linked and whether inbreeding effective population numbers or variance effective population numbers are involved in the calculation of N(e). If, however, only two successive generations in the cycle are considered and the population changes in size between these generations, the inbreeding effective population number, N(eI), differs from the variance effective population number, N(eV). The mutation effective population number turns out to be the same as the number derived using calculations involving probabilities of identity by descent. It is also shown that, at least in one special case, the eigenvalue effective population number is the same as N(eV).

Local drift load and the heterosis of interconnected populations

We use Wright's distribution of equilibrium allele frequency to demonstrate that hybrids between populations interconnected by low to moderate levels of migration can have large positive heterosis, especially if the populations are small in size. Beneficial alleles neither fix in all populations nor equilibrate at the same frequency. Instead, populations reach a mutation-selection-drift-migration balance with sufficient among-population variance that some partially recessive, deleterious mutations can be masked upon crossbreeding. This heterosis is greatest with intermediate mutation rates, intermediate selection coefficients, low migration rates and recessive alleles. Hybrid vigour should not be taken as evidence for the complete isolation of populations. Moreover, we show that heterosis in crosses between populations has a different genetic basis than inbreeding depression within populations and is much more likely to result from alleles of intermediate effect.