Coalescent process with fluctuating population size and its effective size

We consider a Wright-Fisher model whose population size is a finite Markov chain. We introduce a sequence of two-dimensional discrete time Markov chains whose components describe the coalescent process and the fluctuation of population size. For the limiting process of the sequence of Markov chains, the relationship of the expectation of coalescence time to the harmonic and the arithmetic means of population sizes is shown, and the Laplace transform of the distribution of coalescence time is calculated. We define the coalescence effective population size (cEPS) by the expectation of coalescence time. We show that cEPS is strictly larger (resp. smaller) than the harmonic (resp. arithmetic) mean. As the population size fluctuates more quickly (resp. slowly), cEPS is closer to the harmonic (resp. arithmetic) mean. For the case of a two-valued Markov chain, we show the explicit expression of cEPS and its dependency on the sample size.     

Detecting populations in the 'ambiguous' zone: kinship-based estimation of population structure at low genetic divergence

Identifying population structure is one of the most common and important objectives of spatial analyses using population genetic data. Population structure is detected either by rejecting the null hypothesis of a homogenous distribution of genetic variation, or by estimating low migration rates. Issues arise with most current population genetic inference methods when the genetic divergence is low among putative populations. Low levels of genetic divergence may be as a result of either high ongoing migration or historic high migration but no current, ongoing migration. We direct attention to recent developments in the use of the tempo-spatial distribution of closely related individuals to detect population structure or estimate current migration rates. These 'kinship-based' approaches complement more traditional population-based genetic inference methods by providing a means to detect population structure and estimate current migration rates when genetic divergence is low. However, for kinship-based methods to become widely adopted, formal estimation procedures applicable to a range of species life histories are needed.     

Monitoring of the genetic structure of natural populations: change of the effective population size and inversion polymorphism in <Emphasis Type="Italic">Drosophila subobscura</Emphasis>

We analyzed changes in the genetic structure and effective population size of two ecologically distinct populations of Drosophila subobscura over several years. Population sizes of D. subobscura in beech and oak wood habitats for a period of 6 years were estimated by the capture-mark-release-recapture method. Inversion polymorphism parameters were also assessed in the same populations for a period of 3 years. Significant differences in the numbers of individuals were observed between sexes. This affected the effective population sizes between particular years. The ratio of the effective size over the cenzus dropped significantly in beech wood in 2 years. Although overall heterozygosity remained unchanged during the years in both habitats, frequencies of gene arrangements on five chromosomes show variability. After the bottleneck, some complex chromosomal arrangements appeared for the first time in both populations. Standard gene arrangements of chromosome A increased in frequency over the years in each habitat, while the complex arrangements remain rather stable and specific for each population. The results obtained indicate that the population structure may significantly change if the effective size of D. subobscura population is reduced, which is mostly related to microclimatic changes in habitats. Based on the results to date, monitoring of microevolutionary changes by using D. subobscura and its relatives seems a promising way to study the effects of global climate changes.     

Effective population size,genetic diversity,and coalescence time in subdivided populations

A formula for the effective population size for the finite island model of subdivided populations is derived. The formula indicates that the effective size can be substantially greater than the actual number of individuals in the entire population when the migration rate among subpopulations is small. It is shown that the mean nucleotide diversity, coalescence time, and heterozygosity for genes sampled from the entire population can be predicted fairly well from the theory for randomly mating populations if the effective population size for the finite island model is used.     

Temporal variation in genetic diversity and effective population size of Mediterranean and subalpine Arabidopsis thaliana populations

Currently, there exists a limited knowledge on the extent of temporal variation in population genetic parameters of natural populations. Here, we study the extent of temporal variation in population genetics by genotyping 151 genome-wide SNP markers polymorphic in 466 individuals collected from nine populations of the annual plant Arabidopsis thaliana during 4 years. Populations are located along an altitudinal climatic gradient from Mediterranean to subalpine environments in NE Spain, which has been shown to influence key demographic attributes and life cycle adaptations. Genetically, A. thaliana populations were more variable across space than over time. Common multilocus genotypes were detected several years in the same population, whereas low-frequency multilocus genotypes appeared only 1 year. High-elevation populations were genetically poorer and more variable over time than low-elevation populations, which might be caused by a higher overall demographic instability at higher altitudes. Estimated effective population sizes were low but also showed a significant decreasing trend with increasing altitude, suggesting a deeper impact of genetic drift at high-elevation populations. In comparison with single-year samplings, repeated genotyping over time captured substantially higher amount of genetic variation contained in A. thaliana populations. Furthermore, repeated genotyping of populations provided novel information on the genetic properties of A. thaliana populations and allowed hypothesizing on their underlying mechanisms. Therefore, including temporal genotyping programmes into traditional population genetic studies can significantly increase our understanding of the dynamics of natural populations.     

Implications of the variance effective population size on the genetic conservation of monoecious species

The concept of variance effective population size [Ne_(v)] and other expressions are reviewed and described for specific sampling steps in germplasm collection and regeneration of monoecious species. Special attention is given to procedures for computing the variance of the number of contributed gametes [V(k)] to the next generation. Drift, as it occurs between generations, was considered to contain a component due to the sampling of parents and a subsequent component due to the sampling of gametes. This demonstrates that drift, caused by reduction of seed viability, damages the genetic integrity of accessions stored in germplasm banks. The study shows how mating designs, such as plant-to-plant or chain crossings with additional female gametic control, can partially alleviate this problem. Optimal procedures for increasing Ne_(v) when collecting germplasm in the field are also discussed. The effect of different female and male gametic control strategies on Ne_(v) is considered under several situations. Practical examples illustrating the use of V(k) and Ne_(v) expressions are given.     

Methodologies for estimating the sample size required for genetic conservation of outbreeding crops

Summary The main purpose of germplasm banks is to preserve the genetic variability existing in crop species. The effectiveness of the regeneration of collections stored in gene banks is affected by factors such as sample size, random genetic drift, and seed viability. The objective of this paper is to review probability models and population genetics theory to determine the choice of sample size used for seed regeneration. A number of conclusions can be drawn from the results. First, the size of the sample depends largely on the frequency of the least common allele or genotype. Genotypes or alleles occurring at frequencies of more than 10% can be preserved with a sample size of 40 individuals. A sample size of 100 individuals will preserve genotypes (alleles) that occur at frequencies of 5%. If the frequency of rare genotypes (alleles) drops below 5%, larger sample sizes are required. A second conclusion is that for two, three, and four alleles per locus the sample size required to include a copy of each allele depends more on the frequency of the rare allele or alleles than on the number. Samples of 300 to 400 are required to preserve alleles that are present at a frequency of 1%. Third, if seed is bulked, the expected number of parents involved in any sample drawn from the bulk will be less than the number of parents included in the bulk. Fourth, to maintain a rate of breeding (F) of 1 %, the effective population size (N_e) should be at least 150 for three alleles, and 300 for four alleles. Fifth, equalizing the reproductive output of each family to two progeny doubles the effective size of the population. Based on the results presented here, a practical option is considered for regenerating maize seed in a program constrained by limited funds.Part of this paper was presented at the Global Maize Germplasm Workshop, CIMMYT, El Batan, Mexico, March 6–12, 1988     

The effective number of a population that varies cyclically in size. II. Overlapping generations

We consider haploid and dioecious age-structured populations that vary over time in cycles of length k. Results are obtained for both autosomal and sex-linked loci if the population is dioecious. It is assumed that k is small in comparison with numbers of haploid individuals (or of numbers of males and females) in any generation of a cycle. The inbreeding effective population size N(e) is then approximately given by the expression [T summation operator (k-1)(j=0)1/[N(e)(j)T(j)]](-1), where N(e)(j) and T(j) are, respectively, the effective population size and generation interval that would hold if the population was at all times generated in the same way as at time j. The constant T, which is the effective overall generation interval, is defined to be k times the harmonic mean of the quantities T(j). Our expressions for T and N(e), in terms of N(e)(j) and T(j), are general, but the N(e)(j)s are derived under the assumption that offspring are produced according to Poisson distributions.     

The genetic effective and adult census size of an Australian population of tiger prawns (Penaeus esculentus)

This study compares estimates of the census size of the spawning population with genetic estimates of effective current and long-term population size for an abundant and commercially important marine invertebrate, the brown tiger prawn (Penaeus esculentus). Our aim was to focus on the relationship between genetic effective and census size that may provide a source of information for viability analyses of naturally occurring populations. Samples were taken in 2001, 2002 and 2003 from a population on the east coast of Australia and temporal allelic variation was measured at eight polymorphic microsatellite loci. Moments-based and maximum-likelihood estimates of current genetic effective population size ranged from 797 to 1304. The mean long-term genetic effective population size was 9968. Although small for a large population, the effective population size estimates were above the threshold where genetic diversity is lost at neutral alleles through drift or inbreeding. Simulation studies correctly predicted that under these experimental conditions the genetic estimates would have non-infinite upper confidence limits and revealed they might be overestimates of the true size. We also show that estimates of mortality and variance in family size may be derived from data on average fecundity, current genetic effective and census spawning population size, assuming effective population size is equivalent to the number of breeders. This work confirms that it is feasible to obtain accurate estimates of current genetic effective population size for abundant Type III species using existing genetic marker technology.     

The effect of a population bottleneck on the evolution of genetic variance/covariance structure

It is well known that standard population genetic theory predicts decreased additive genetic variance (V(a) ) following a population bottleneck and that theoretical models including interallelic and intergenic interactions indicate such loss may be avoided. However, few empirical data from multicellular model systems are available, especially regarding variance/covariance (V/CV) relationships. Here, we compare the V/CV structure of seventeen traits related to body size and composition between control (60 mating pairs/generation) and bottlenecked (2 mating pairs/generation; average F = 0.39) strains of mice. Although results for individual traits vary considerably, multivariate analysis indicates that V(a) in the bottlenecked populations is greater than expected. Traits with patterns and amounts of epistasis predictive of enhanced V(a) also show the largest deviations from additive expectations. Finally, the correlation structure of weekly weights is not significantly different between control and experimental lines but correlations between necropsy traits do differ, especially those involving the heart, kidney and tail length.     

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.     

Limited genetic structure and evidence for dispersal among populations of the endangered Florida grasshopper sparrow, Ammodramus savannarum floridanus

The Florida grasshopper sparrow, Ammodramus savannarum floridanus, is a non-migratory, endangered subspecies endemic to the prairie region of south-central Florida. It has experienced significant population declines and is currently restricted to five locations. We found substantial levels of variation in microsatellites and mtDNA control region sequences, estimates of inbreeding genetic effective population sizes that were much larger than the estimated census size, and no evidence of inbreeding within five sampled populations (n = 105). We also found a lack of genetic structure among populations (F _ST = 0.0123 for microsatellites and θ = 0.008 for mtDNA), and evidence for dispersal between populations, with 7.6% of all individuals identified as immigrants to their population of capture. We suggest that the subspecies be managed as a single management unit on a regional scale rather than as multiple management units on a local subpopulation scale. There is still a limited opportunity to preserve much of the present genetic variation in this subspecies, if immediate measures are taken to reverse the current population decline before this variation is reduced by genetic drift.     

The propagation of a cultural or biological trait by neutral genetic drift in a subdivided population

We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as the biological process. We focus on the growth of fixation times with the number of subpopulations, and variation of fixation probabilities and times with initial distributions of mutants. A general formula for the fixation probability for arbitrary initial condition is derived by extending a duality relation between forwards- and backwards-time properties of the model from a panmictic to a subdivided population. From this we obtain new formulae(formally exact in the limit of extremely weak migration) for the mean fixation time from an arbitrary initial condition for Wright's island model, presenting two cases as examples. For more general models of population subdivision, formulae are introduced for an arbitrary number of mutants that are randomly located, and a single mutant whose position is known. These formulae contain parameters that typically have to be obtained numerically, a procedure we follow for two contrasting clustered models. These data suggest that variation of fixation time with the initial condition is slight, but depends strongly on the nature of subdivision. In particular, we demonstrate conditions under which the fixation time remains finite even in the limit of an infinite number of demes. In many cases-except this last where fixation in a finite time is seen--the time to fixation is shown to be in precise agreement with predictions from formulae for the asymptotic effective population size.     

Reproductive fitness,population size and genetic variation in Muscari tenuiflorum (Hyacinthaceae): The role of temporal variation

In plant populations a positive correlation between population size, genetic variation and fitness components is often found, due to increased pollen limitation or reduced genetic variation and inbreeding depression in smaller populations. However, components of fitness also depend on environmental factors which can vary strongly between years. The dry grassland species Muscari tenuiflorum experiences long term habitat isolation and small population sizes. We analyzed seed production of M. tenuiflorum in four years and its dependence on population size and genetic variation. Genetic diversity within populations was high (AFLP: H_e = 0.245; allozymes: H_e = 0.348). An analysis of molecular variance revealed considerable population differentiation (AFLP: 26%; allozyme: 17%). An overall pattern of isolation by distance was found, which, however was not present at distances below 20 km, indicating stronger effects of genetic drift. Genetic diversity was positively correlated to population size. Self pollination reduced seed set by 24%, indicating inbreeding depression. Reproductive fitness was not correlated to genetic diversity and a positive correlation with population size was present in two of four study years. The absence of a general pattern stresses the importance for multi-year studies. Overall, the results show that despite long term habitat isolation M. tenuiflorum maintains seed production in many years independent of population size. The long term persistence of populations is thus expected to depend less on intrinsic genetic or demographic properties affecting seed production but on successful plant establishment and persistence, which latter are based on conservation and protection of suitable habitats.     

The effect of varying the number of Schistosoma mansoni miracidia on the reproduction and survival of Biomphalaria pfeifferi

The number of young snails emerging from egg masses of Biomphalaria pfeifferi (Kampala strain) is reduced by exposure to an increasing number of miracidia of Schistosoma mansoni (West Nile strain). Snails exposed to four miracidia are rendered sterile. Survival of infected snails is inversely proportional to the number of miracidia to which an individual snail is exposed.     

The influence of persistent individual differences and age at maturity on effective population size

Ratios of effective populations size, N(e), to census population size, N, are used as a measure of genetic drift in populations. Several life-history parameters have been shown to affect these ratios, including mating system and age at sexual maturation. Using a stochastic matrix model, we examine how different levels of persistent individual differences in mating success among males may affect N(e)/N, and how this relates to generation time. Individual differences of this type are shown to cause a lower N(e)/N ratio than would be expected when mating is independent among seasons. Examining the way in which age at maturity affects N(e)/N, we find that both the direction and magnitude of the effect depends on the survival rate of juveniles in the population. In particular, when maturation is delayed, lowered juvenile survival causes higher levels of genetic drift. In addition, predicted shifts in N(e)/N with changing age at maturity are shown to be dependent on which of the commonly used definitions of census population size, N, is employed. Our results demonstrate that patterns of mating success, as well as juvenile survival probabilities, have substantial effects on rates of genetic drift.     

Inbreeding coefficients for stochastically varying small population sizes-bias of calculation based on effective numbers

The commonly used procedure to calculate inbreeding coefficients by effective population numbers (Ne) by the harmonic mean of generation-by-generation population sizes involves a computational bias. If the individual population sizes are considered as realizations of a binomially distributed random variable with sample size N and probability p, this bias can be investigated for the two cases p = constant and p = variable (Markov chain). The bias is of practical relevance only for small probabilities p, short period of initial successive generations, and small population sizes. The largest values for this computational bias are in the range of 0.05-0.06. It is concluded that for most practical purposes the approximate procedure is appropriate.     

Concurrent habitat and life history influences on effective/census population size ratios in stream-dwelling trout

Lower effective sizes (N(e)) than census sizes (N) are routinely documented in natural populations, but knowledge of how multiple factors interact to lower N(e)/N ratios is often limited. We show how combined habitat and life-history influences drive a 2.4- to 6.1-fold difference in N(e)/N ratios between two pristine brook trout (Salvelinus fontinalis) populations occupying streams separated by only 750 m. Local habitat features, particularly drainage area and stream depth, govern trout biomass produced in each stream. They also generate higher trout densities in the shallower stream by favoring smaller body size and earlier age-at-maturity. The combination of higher densities and reduced breeding site availability in the shallower stream likely leads to more competition among breeding trout, which results in greater variance in individual reproductive success and a greater reduction in N(e) relative to N. A similar disparity between juvenile or adult densities and breeding habitat availability is reported for other species and hence may also result in divergent N(e)/N ratios elsewhere. These divergent N(e)/N ratios between adjacent populations are also an instructive reminder for species conservation programs that genetic and demographic parameters may differ dramatically within species.     

Population genetic structure and effective population size of ayu (Plecoglossus altivelis), an amphidromous fish

The temporal and spatial population genetic structure of ayu Plecoglossus altivelis (Salmoniformes: Plecoglossidae), an amphidromous fish, was examined using analysis of variation at six microsatellite DNA loci. Intracohort genetic diversities, as measured by the number of alleles and heterozygosity, were similar among six cohorts (2001–2006) within a population (Nezugaseki River), with the mean number of alleles per cohort ranging from 11·0 to 12·5 and the expected heterozygosity ranging from 0·74 to 0·77. Intrapopulational genetic diversities were also similar across the three studied populations along the 50 km coast, with the mean number of alleles and the expected heterozygosity ranging from 11·33 to 11·67 and from 0·75 to 0·76, respectively. The authors observed only one significant difference in pair-wise population differentiation ( F _ST-value) between the cohorts within a population and among three populations. Estimates of the effective population size ( N _e) based on maximum-likelihood method yielded small values (ranging from 94·8 to 135·5), whereas census population size ranged from c. 4800 to 24 000. As a result, the ratio of annual effective population sizes to census population size ( N _e/ N ) ranged from 0·004 to 0·023. These estimates of N _e/ N agree more closely with estimates for marine fishes than that of the larger estimates for freshwater fishes. The present study suggests that ayu which is highly fecund and shows low survival during the early life stages is also characterized by having low value of N _e/ N , similar to marine species with a pelagic life cycle.     

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.