, Jost's D,and FST are similarly constrained by allele frequencies: A mathematical,simulation, and empirical study

Statistics and Jost's D have been proposed for replacing F_ST as measures of genetic differentiation. A principal argument in favour of these statistics is the independence of their maximal values with respect to the subpopulation heterozygosity H_S, a property not shared by F_ST. Nevertheless, it has been unclear if these alternative differentiation measures are constrained by other aspects of the allele frequencies. Here, for biallelic markers, we study the mathematical properties of the maximal values of and D, comparing them to those of F_ST. We show that and D exhibit the same peculiar frequency‐dependence phenomena as F_ST, including a maximal value as a function of the frequency of the most frequent allele that lies well below one. Although the functions describing , D, and F_ST in terms of the frequency of the most frequent allele are different, the allele frequencies that maximize them are identical. Moreover, we show using coalescent simulations that when taking into account the specific maximal values of the three statistics, their behaviours become similar across a large range of migration rates. We use our results to explain two empirical patterns: the similar values of the three statistics among North American wolves, and the low D values compared to and F_ST in Atlantic salmon. The results suggest that the three statistics are often predictably similar, so that they can make quite similar contributions to data analysis. When they are not similar, the difference can be understood in relation to features of genetic diversity.     

Purging putative siblings from population genetic data sets: a cautionary view

Interest has surged recently in removing siblings from population genetic data sets before conducting downstream analyses. However, even if the pedigree is inferred correctly, this has the potential to do more harm than good. We used computer simulations and empirical samples of coho salmon to evaluate strategies for adjusting samples to account for family structure. We compared performance in full samples and sibling‐reduced samples of estimators of allele frequency (), population differentiation () and effective population size (). Results: (i) unless simulated samples included large family groups together with a component of unrelated individuals, removing siblings generally reduced precision of and ; (ii) based on the linkage disequilibrium method was largely unbiased using full random samples but became increasingly upwardly biased under aggressive purging of siblings. Under nonrandom sampling (some families over‐represented), using full samples was downwardly biased; removing just the right ‘Goldilocks’ fraction of siblings could produce an unbiased estimate, but this sweet spot varied widely among scenarios; (iii) weighting individuals based on the inferred pedigree (to produce a best linear unbiased estimator, BLUE) maximized precision of when the inferred pedigree was correct but performed poorly when the pedigree was wrong; (iv) a variant of sibling removal that leaves intact small sibling groups appears to be more robust to errors in inferences about family structure. Our results illustrate the complex challenges posed by presence of family structure, suggest that no single optimal solution exists and argue for caution in adjusting population genetic data sets for the presence of putative siblings without fully understanding the consequences.     

Sensitivity analysis of effective population size to demographic parameters in house sparrow populations

The ratio between the effective and the census population size, , is an important measure of the long‐term viability and sustainability of a population. Understanding which demographic processes that affect most will improve our understanding of how genetic drift and the probability of fixation of alleles is affected by demography. This knowledge may also be of vital importance in management of endangered populations and species. Here, we use data from 13 natural populations of house sparrow (Passer domesticus) in Norway to calculate the demographic parameters that determine . Using the global variance‐based Sobol’ method for the sensitivity analyses, we found that was most sensitive to demographic variance, especially among older individuals. Furthermore, the individual reproductive values (that determine the demographic variance) were most sensitive to variation in fecundity. Our results draw attention to the applicability of sensitivity analyses in population management and conservation. For population management aiming to reduce the loss of genetic variation, a sensitivity analysis may indicate the demographic parameters towards which resources should be focused. The result of such an analysis may depend on the life history and mating system of the population or species under consideration, because the vital rates and sex–age classes that is most sensitive to may change accordingly.     

Effective number of breeders provides a link between interannual variation in stream flow and individual reproductive contribution in a stream salmonid

The effective number of breeders that give rise to a cohort (N_b) is a promising metric for genetic monitoring of species with overlapping generations; however, more work is needed to understand factors that contribute to variation in this measure in natural populations. We tested hypotheses related to interannual variation in N_b in two long‐term studies of brook trout populations. We found no supporting evidence for our initial hypothesis that reflects (defined as the number of adults in a population at the time of reproduction). was stable relative to and did not follow trends in abundance (one stream negative, the other positive). We used stream flow estimates to test the alternative hypothesis that environmental factors constrain N_b. We observed an intermediate optimum autumn stream flow for both (R² = 0.73, P = 0.02) and full‐sibling family evenness (R² = 0.77, P = 0.01) in one population and a negative correlation between autumn stream flow and full‐sib family evenness in the other population (r = ?0.95, P = 0.02). Evidence for greater reproductive skew at the lowest and highest autumn flow was consistent with suboptimal conditions at flow extremes. A series of additional tests provided no supporting evidence for a related hypothesis that density‐dependent reproductive success was responsible for the lack of relationship between N_b and N_C (so‐called genetic compensation). This work provides evidence that N_b is a useful metric of population‐specific individual reproductive contribution for genetic monitoring across populations and the link we provide between stream flow and N_b could be used to help predict population resilience to environmental change.     

Population genomics from pool sequencing

Next generation sequencing of pooled samples is an effective approach for studies of variability and differentiation in populations. In this paper we provide a comprehensive set of estimators of the most common statistics in population genetics based on the frequency spectrum, namely the Watterson estimator , nucleotide pairwise diversity Π, Tajima's D, Fu and Li's D and F, Fay and Wu's H, McDonald‐Kreitman and HKA tests and , corrected for sequencing errors and ascertainment bias. In a simulation study, we show that pool and individual θ estimates are highly correlated and discuss how the performance of the statistics vary with read depth and sample size in different evolutionary scenarios. As an application, we reanalyse sequences from Drosophila mauritiana and from an evolution experiment in Drosophila melanogaster. These methods are useful for population genetic projects with limited budget, study of communities of individuals that are hard to isolate, or autopolyploid species.     

Species turnover (β‐diversity) in ectomycorrhizal fungi linked to uptake capacity

Ectomycorrhizal (EcM) fungal communities may be shaped by both deterministic and stochastic processes, potentially influencing ecosystem development and function. We evaluated community assembly processes for EcM fungi of Pseudotsuga menziesii among 12 sites up to 400 km apart in southwest British Columbia (Canada) by investigating species turnover (β‐diversity) in relation to soil nitrogen (N) availability and physical distance. We then examined functional traits for an N‐related niche by quantifying net fluxes of , and protons on excised root tips from three contrasting sites using a microelectrode ion flux measurement system. EcM fungal communities were well aligned with soil N availability and pH, with no effect of site proximity (distance–decay curve) on species assemblages. Species turnover was significant (β_1/2 = 1.48) along soil N gradients, with many more Tomentella species on high N than low N soils, in contrast to Cortinarius species. Ammonium uptake was greatest in the spring on the medium and rich sites and averaged over 190 nmol/m²/s for Tomentella species. The lowest uptake rates of were by nonmycorrhizal roots of axenically grown seedlings (10 nmol/m²/s), followed by Cortinarius species (60 nmol/m²/s). EcM roots from all sites displayed only marginal uptake of nitrate (8.3 nmol/m²/s). These results suggest uptake capacity is an important functional trait influencing the assembly of EcM fungal communities. The diversity of EcM fungal species across the region arguably provides critical belowground adaptations to organic and inorganic N supply that are integral to temperate rainforest ecology.     

SEX RATIO AND DENSITY AFFECT SEXUAL SELECTION IN A SEX‐ROLE REVERSED FISH

Understanding how demographic processes influence mating systems is important to decode ecological influences on sexual selection in nature. We manipulated sex ratio and density in experimental populations of the sex‐role reversed pipefish Syngnathus typhle. We quantified sexual selection using the Bateman gradient (), the opportunity for selection (I), and sexual selection (I_s), and the maximum standardized sexual selection differential (). We also measured selection on body length using standardized selection differentials (s′) and mating differentials (m′), and tested whether the observed I and I_s differ from values obtained by simulating random mating. We found that I, I_s, and , but not , were higher for females under female than male bias and the opposite for males, but density did not affect these measures. However, higher density decreased sexual selection (m′ but not s′) on female length, but selection on body length was not affected by sex ratio. Finally, I_s but not I was higher than expected from random mating, and only for females under female bias. This study demonstrates that both sex ratio and density affect sexual selection and that disentangling interrelated demographic processes is essential to a more complete understanding of mating behavior and the evolution of mating systems.     

Balancing selection and heterozygote advantage in major histocompatibility complex loci of the bottlenecked Finnish wolf population

Maintaining effective immune response is an essential factor in the survival of small populations. One of the most important immune gene regions is the highly polymorphic major histocompatibility complex (MHC). We investigated how a population bottleneck and recovery have influenced the diversity and selection in three MHC class II loci, DLA‐DRB1, DLA‐DQA1 and DLA‐DQB1, in the Finnish wolf population. We studied the larger Russian Karelian wolf population for comparison and used 17 microsatellite markers as reference loci. The Finnish and Karelian wolf populations did not differ substantially in their MHC diversities ( = 0.047, P = 0.377), but differed in neutral microsatellite diversities ( = 0.148, P = 0.008). MHC allele frequency distributions in the Finnish population were more even than expected under neutrality, implying balancing selection. In addition, an excess of nonsynonymous compared to synonymous polymorphisms indicated historical balancing selection. We also studied association between helminth (Trichinella spp. and Echinococcus canadensis) prevalence and MHC diversity at allele and SNP level. MHC‐heterozygous wolves were less often infected by Trichinella spp. and carriers of specific MHC alleles, SNP haplotypes and SNP alleles had less helminth infections. The associated SNP haplotypes and alleles were shared by different MHC alleles, which emphasizes the necessity of single‐nucleotide‐level association studies also in MHC. Here, we show that strong balancing selection has had similar effect on MHC diversities in the Finnish and Russian Karelian wolf populations despite significant genetic differentiation at neutral markers and small population size in the Finnish population.     

RISK OF POPULATION EXTINCTION FROM FIXATION OF NEW DELETERIOUS MUTATIONS

The fixation of new deleterious mutations is analyzed for a randomly mating population of constant size with no environmental or demographic stochasticity. Mildly deleterious mutations are far more important in causing loss of fitness and eventual extinction than are lethal and semilethal mutations in populations with effective sizes, N_e, larger than a few individuals. If all mildly deleterious mutations have the same selection coefficient, s against heterozygotes and 2s against homozygotes, the mean time to extinction, , is asymptotically proportional to for 4N_es > 1. Nearly neutral mutations pose the greatest risk of extinction for stable populations, because the magnitude of selection coefficient that minimizes is about ? = 0.4/N_e. The influence of variance in selection coefficients among mutations is analyzed assuming a gamma distribution of s, with mean and variance . The mean time to extinction increases with variance in selection coefficients if is near ?, but can decrease greatly if is much larger than ?. For a given coefficient of variation of , the mean time to extinction is asymptotically proportional to for . When s is exponentially distributed, (c = 1) is asymptotically proportional to . These results in conjunction with data on the rate and magnitude of mildly deleterious mutations in Drosophila melanogaster indicate that even moderately large populations, with effective sizes on the order of N_e = 10³, may incur a substantial risk of extinction from the fixation of new mutations.     

Crossing to safety: dispersal,colonization and mate choice in evolutionarily distinct populations of Steller sea lions,Eumetopias jubatus

Population growth typically involves range expansion and establishment of new breeding sites, while the opposite occurs during declines. Although density dependence is widely invoked in theoretical studies of emigration and colonization in expanding populations, few empirical studies have documented the mechanisms. Still fewer have documented the direction and mechanisms of individual transfer in declining populations. Here, we screen large numbers of pups sampled on their natal rookeries for variation in mtDNA (n = 1106) and 16 microsatellite loci (n = 588) and show that new Steller sea lion breeding sites did not follow the typical paradigm and were instead colonized by sea lions from both a declining (Endangered) population and an increasing population. Dispersing individuals colonized rookeries in the distributional hiatus between two evolutionarily distinct ( = 0.222,  = 0.053, K = 2) metapopulations recently described as separate subspecies. Hardy–Weinberg, mixed‐stock and relatedness analysis revealed levels of interbreeding on the new rookeries that exclude (i) assortative mating among eastern and western forms, and (ii) inbreeding avoidance as primary motivations for dispersal. Positive and negative density dependence is implicated in both cases of individual transfer. Migration distance limits, and conspecific attraction and performance likely influenced the sequence of rookery colonizations. This study demonstrates that resource limitation may trigger an exodus of breeding animals from declining populations, with substantial impacts on distribution and patterns of genetic variation. It also revealed that this event is rare because colonists dispersed across an evolutionary boundary, suggesting that the causative factors behind recent declines are unusual or of larger magnitude than normally occur.     

THE MAINTENANCE OF POLYGENIC VARIATION IN FINITE POPULATIONS

Models of the maintenance of genetic variance in a polygenic trait have usually assumed that population size is infinite and that selection is weak. Consequently, they will overestimate the amount of variation maintained in finite populations. I derive approximations for the equilibrium genetic variance, in finite populations under weak stabilizing selection for triallelic loci and for an infinite “rare alleles” model. These are compared to results for neutral characters, to the “Gaussian allelic” model, and to Wright's approximation for a biallelic locus under arbitrary selection pressures. For a variety of parameter values, the three-allele, Gaussian, and Wrightian approximations all converge on the neutral model when population size is small. As expected, far less equilibrium genetic variance can be maintained if effective population size, N, is on the order of a few hundred than if N is infinite. All of the models predict that comparisons among populations with N less than about 10⁴ should show substantial differences in . While it is easier to maintain absolute when alleles interact to yield dominance or overdominance for fitness, less additivity also makes more susceptible to differences in N. I argue that experimental data do not seem to reflect the predicted degree of relationship between N and . This calls into question the ability of mutation-selection balance or simple balancing selection to explain observed . The dependence of on N could be used to test the adequacy of mutation-selection balance models.     

A new proposal for measurement of the adjusted mean crowding through consideration of size variability in habitat units

The mean crowding has previously been measured under the assumption that all quadrats or habitat units have the same size, even though the actual habitat units such as seeds or leaves are generally variable in size. A new index, ‘adjusted mean crowding’, which is adjusted for this variability can be given as where Q is the total number of habitat units in the whole area, x_j the number of individuals in the jth habitat unit, and a_j is defined as the ‘relative size’ of the jth habitat unit, i.e. a_y=y_y/(∑y_j/Q) where y_j is the actually measured size of the jth habitat unit. It is expected that and for the uniform distribution and the random distribution ‘per unit size’, respectively. The comparison between and regressions ( analysis) for the egg distribution pattern of Callosobruchus chinensis or C. maculatus proved that the regression is biased by a positive correlation between the egg number per seed and seed size rather than by a density-dependent change in the ovipositional behavior.     

MATERNAL INHERITANCE AND ITS EFFECT ON ADAPTIVE EVOLUTION: A QUANTITATIVE GENETIC ANALYSIS OF MATERNAL EFFECTS IN A NATURAL PLANT POPULATION

A mother can influence a trait in her offspring both by the genes she transmits (Mendelian inheritance) and by maternal attributes that directly affect that trait in her offspring (maternal inheritance). Maternal inheritance can alter the direction, rate, and duration of adaptive evolution from standard Mendelian models and its impact on adaptive evolution is virtually unexplored in natural populations. In a hierarchical quantitative genetic analysis to determine the magnitude and structure of maternal inheritance in the winter annual plant, Collinsia verna, I consider three potential models of inheritance. These range from a standard Mendelian model estimating only direct (i.e., Mendelian) additive and environmental variance components to a maternal inheritance model estimating six additive and environmental variance components: direct additive and environmental variances; maternal additive and environmental variances; and the direct-maternal additive () and environmental covariances. The structure of maternal inheritance differs among the 10 traits considered at four stages in the life cycle. Early in the life cycle, seed weight and embryo weight display substantial , a negative , and a positive . Subsequently, cotyledon diameter displays and of roughly the same magnitude and negative . For fall rosettes, leaf number and length are best described by a Mendelian model. In the spring, leaf length displays maternal inheritance with significant and and a negative . All maternally inherited traits show significant negative . Predicted response to selection under maternal inheritance depends on and as well as . Negative results in predicted responses in the opposite direction to selection for seed weight and embryo weight and predicted responses near zero for all subsequent maternally inherited traits. Maternal inheritance persists through the life cycle of this annual plant for a number of size-related traits and will alter the direction and rate of evolutionary response in this population.     

The association between polyploidy and clonal reproduction in diploid and tetraploid Chamerion angustifolium

Clonal reproduction is associated with the incidence of polyploidy in flowering plants. This pattern may arise through selection for increased clonality in polyploids compared to diploids to reduce mixed‐ploidy mating. Here, we test whether clonal reproduction is greater in tetraploid than diploid populations of the mixed‐ploidy plant, Chamerion angustifolium, through an analysis of the size and spatial distribution of clones in natural populations using AFLP genotyping and a comparison of root bud production in a greenhouse study. Natural tetraploid populations (N = 5) had significantly more AFLP genotypes ( = 10.8) than diploid populations ( = 6.0). Tetraploid populations tended to have fewer ramets per genotype and fewer genotypes with >1 ramet. In a spatial autocorrelation analysis, ramets within genotypes were more spatially aggregated in diploid populations than in tetraploid populations. In the greenhouse, tetraploids allocated 90.4% more dry mass to root buds than diploids, but tetraploids produced no more root buds and 44% fewer root buds per unit root mass than diploids. Our results indicate that clonal reproduction is significant in most populations, but tetraploid populations are not more clonal than diploids, nor are their clones more spatially aggregated. As a result, tetraploids may be less sheltered from mixed‐ploidy mating and diploids more exposed to inbreeding, the balance of which could influence the establishment of tetraploids in diploid populations.     

Tiller population dynamics of reciprocally transplanted Eriophorum vaginatum L. ecotypes in a changing climate

Moist tussock tundra, dominated by the sedge Eriophorum vaginatum L., covers approximately 3.36 × 10⁸ km² of arctic surface area along with large amounts of subarctic land area. Eriophorum vaginatum exhibits ecotypic differentiation along latitudinal gradients in Alaska. While ecotypic differentiation may be beneficial during periods of climate stability, it may be detrimental as climate changes, causing adaptational lag. Following harvest of a 30-year reciprocal transplant experiment, age-specific demographic data on E. vaginatum tillers were collected to parameterize a Leslie matrix. Yellow Taxi analysis, based on Tukey's Jackknife, was used to determine mean pseudovalues of tiller population growth rate () for four source populations of E. vaginatum tussocks that were transplanted to each of three gardens along a latitudinal gradient. Source populations responded differentially along the latitudinal gradient. Survival and daughter tiller production influenced differences seen at the mid-latitude garden, and the overall tiller population performance was generally improved by northward transplanting relative to southward transplanting. A comparison of home-source and away-source within the same transplant garden indicates no home-site advantage. Although populations were still growing when transplanted to home-sites ( = 1.056), tiller population growth rate increased as ΔGDD became more negative relative to the home site (i.e., as tussocks were transplanted north). These results imply that populations are affected by climate gradients in a manner consistent with adaptational lag. This study documenting the response of high-latitude ecotypes to climate gradients may be an indication of the possible future effects of climate shift in more southern latitudes.     

Application of the\mathop m\limits^* - m method to the analysis of spatial patterns by changing the quadrat sizemethod to the analysis of spatial patterns by changing the quadrat size

A method for the analysis of spatial pattern using quadrats of different sizes is developed on the basis of the relationship of mean crowding () to mean density (m). The -on-m regression obtained by successive changes in quadrat size in a single population (unit-size relation) shows a characteristic pattern according to the type of distribution. By aid of the ρ-index proposed here, we can distinguish the random, aggregated and uniform distributions of the basic components (individual or group of individuals). The ρ serves as an index of spatial correlation between neighbouring quadrats, and it also provides information on the approximate area occupied by clump (colony), distribution pattern of individuals within clumps, and possibly the distribution pattern of clumps themselves. Even in a specified type of distribution, the unit-size relation is not necessarily identical with the relation for a series of populations at a particular quadrat size (series relation). The changes in the series relationship with successive changes of quadrat sizes are also considered for some basic patterns of distributions. The combined use of the unit-size and the series relations for a set of populations of the species under study may provide a satisfactory picture of the spatial pattern characteristic of the species. Application of the method is illustrated by using distribution data of several species of animals and plants. The advantage of the present method over other methods are discussed, and the formulae for determining the optimum quadrat unit in sampling surveys are given.     

EXTINCTION-RECOLONIZATION DYNAMICS IN THE MYCOPHAGOUS BEETLE PHALACRUS SUBSTRIATUS

The population structure of the mycophagous beetle Phalacrus substriatus is characterized by many small, local populations interconnected by migration over a small spatial scale (10 × 75 m²). Each local P. substriatus population has a relatively short expected persistence time, but persistence of the species occurs due to a balance between frequent local extinctions and recolonizations. This nonequilibrium population structure can have profound effects on how the genetic variation is structured between and within populations. Theoretical models have stated that the genetic differentiation among local populations will be enhanced relative to an island model at equilibrium if the number of colonizers is less than approximately twice the number of migrants among local populations. To study these effects, a set of 50 local P. substriatus populations were surveyed over a four-year period to record any naturally occurring extinctions and recolonizations. The per population colonization and extinction rate were 0.237 and 0.275, respectively. Mark-recapture techniques were used to estimate a number of demographic parameters: local population size (N = 11.1), migration rate , number of colonizers (k = 4.0), and the probability of common origin of colonizers (φ = 0.5). The theoretically predicted level of differentiation among local populations (measured as Wright's F_ST) was 0.070. Genetic data obtained from an electrophoretic survey of seven polymorphic loci gave an estimated degree of differentiation of 0.077. There was thus a good agreement between the empirical results and the theoretical predictions. Young populations had significantly higher levels of differentiation than old, more established populations . The extinction-recolonization dynamics resulted in an overall increase in the genetic differentiation among local populations by c. 40%. The global effective population size was also reduced by c. 55%. The results give clear evidence to how nonequilibrium processes shape the genetic structure of populations.     

When genes move farther than offspring: gene flow by male gamete dispersal in the highly philopatric bat species Thyroptera tricolor

For species characterized by philopatry of both sexes, mate selection represents an important behaviour for inbreeding avoidance, yet the implications for gene flow are rarely quantified. Here, we present evidence of male gamete‐mediated gene flow resulting from extra‐group mating in Spix's disc‐winged bat, Thyroptera tricolor, a species which demonstrates all‐offspring philopatry. We used microsatellite and capture–recapture data to characterize social group structure and the distribution of mated pairs at two sites in southwestern Costa Rica over four breeding seasons. Relatedness and genetic spatial autocorrelation analyses indicated strong kinship within groups and over short distances (<50 m), resulting from matrilineal group structure and small roosting home ranges (~0.2 ha). Despite high relatedness among‐group members, observed inbreeding coefficients were low (F_IS = 0.010 and 0.037). Parentage analysis indicated mothers and offspring belonged to the same social group, while fathers belonged to different groups, separated by large distances (~500 m) when compared to roosting home ranges. Simulated random mating indicated mate choice was not based on intermediate levels of relatedness, and mated pairs were less related than adults within social groups on average. Isolation‐by‐distance (IBD) models of genetic neighbourhood area based on father–offspring distances provided direct estimates of mean gamete dispersal distances () > 10 roosting home range equivalents. Indirect estimates based on genetic distance provided even larger estimates of , indicating direct estimates were biased low. These results suggest extra‐group mating reduces the incidence of inbreeding in T. tricolor, and male gamete dispersal facilitates gene flow in lieu of natal dispersal of young.     

Analysis of spatial association between two species based on the interspecies mean crowding

The measurement of spatial association between two species is considered on the basis of interspecies mean crowding. Two indices of overlapping, γ and C_p, are derived as geometric and weighted arithmetic means of the same component ratios related to inter-and intraspecies mean crowdings. Both indices behave in a similar way, ranging from 1 when the distributions of two species are completely overlapped to 0 when they are completely exclusive with each other. The former is essentially identical with indices proposed byKuno (1968) andPianka (1973), and the latter is a modified form ofMorisita's (1959)C_σ index. Indices to measure the degree of spatial correlation between species, Ω and R_μ, are then derived for both kinds of overlapping indices, which vary from 1 in complete overlapping, through 0 in independent occurrence, to −1 in complete exclusion. Various kinds of interspecies association are analyzed using these indices and an extended form of the regression graph which provides a convenient way of indicating the spatial interrelation between two species as well as distribution patterns of respective species. The method presented in this paper may also be applicable to compare temporal distribution patterns between species, similarity between communities, etc. For such a wider application which includes continuous as well as discrete distributions, the interpretation of intra-and interspecies mean crowdings is not necessarily appropriate, and hence the concept of mean concentration with the symbols and for intraspecies relation and and for interspecies relation is suggested.