Effective population size and population subdivision in demographically structured populations

A fast-timescale approximation is applied to the coalescent process in a single population, which is demographically structured by sex and/or age. This provides a general expression for the probability that a pair of alleles sampled from the population coalesce in the previous time interval. The effective population size is defined as the reciprocal of twice the product of generation time and the coalescence probability. Biologically explicit formulas for effective population size with discrete generations and separate sexes are derived for a variety of different modes of inheritance. The method is also applied to a nuclear gene in a population of partially self-fertilizing hermaphrodites. The effects of population subdivision on a demographically structured population are analyzed, using a matrix of net rates of movement of genes between different local populations. This involves weighting the migration probabilities of individuals of a given age/sex class by the contribution of this class to the leading left eigenvector of the matrix describing the movements of genes between age/sex classes. The effects of sex-specific migration and nonrandom distributions of offspring number on levels of genetic variability and among-population differentiation are described for different modes of inheritance in an island model. Data on DNA sequence variability in human and plant populations are discussed in the light of the results.     

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

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

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.     

Stabilizing the dynamics of laboratory populations of Drosophila melanogaster through upper and lower limiter controls

Although a large number of methods exist to control the dynamics of populations to a desired state, few of them have been empirically validated. This limits the scope of using these methods in real-life scenarios. To address this issue, we tested the efficacy of two well-known control methods in enhancing different kinds of stability in highly fluctuating, extinction-prone populations of Drosophila melanogaster. The upper limiter control (ULC) method was able to reduce the fluctuations in population sizes as well as the extinction probability of the populations. On the negative side, it had no effect on the effective population size and required a large amount of effort. On the other hand, lower limiter control (LLC) enhanced effective population size and reduced extinction probability at a relatively low amount of effort. However, its effects on population fluctuations were equivocal. We examined the population size distributions, with and without the control methods, to derive biologically intuitive explanations for how these control methods work. We also show that biologically realistic simulations, using a very general population dynamics model, are able to capture most of the trends of our data. This suggests that our results are likely to be generalizable to a wide range of scenarios.     

Creating outbred and inbred populations in haplodiploids to measure adaptive responses in the laboratory

Laboratory studies are often criticized for not being representative of processes occurring in natural populations. One reason for this is the fact that laboratory populations generally do not capture enough of the genetic variation of natural populations. This can be mitigated by mixing the genetic background of several field populations when creating laboratory populations. From these outbred populations, it is possible to generate inbred lines, thereby freezing and partitioning part of their variability, allowing each genotype to be characterized independently. Many studies addressing adaptation of organisms to their environment, such as those involving quantitative genetics or experimental evolution, rely on inbred or outbred populations, but the methodology underlying the generation of such biological resources is usually not explicitly documented. Here, we developed different procedures to circumvent common pitfalls of laboratory studies, and illustrate their application using two haplodiploid species, the spider mites Tetranychus urticae and Tetranychus evansi. First, we present a method that increases the chance of capturing high amounts of variability when creating outbred populations, by performing controlled crosses between individuals from different field‐collected populations. Second, we depict the creation of inbred lines derived from such outbred populations, by performing several generations of sib‐mating. Third, we outline an experimental evolution protocol that allows the maintenance of a constant population size at the beginning of each generation, thereby preventing bottlenecks and diminishing extinction risks. Finally, we discuss the advantages of these procedures and emphasize that sharing such biological resources and combining them with available genetic tools will allow consistent and comparable studies that greatly contribute to our understanding of ecological and evolutionary processes.     

Linkage disequilibrium in laboratory populations of Drosophila nasuta

Summary Natural populations of Drosophila nasuta are polymorphic for many gene arrangements. Two non-overlapping inversions of the third chromosome, III-2 and III-35, are most common and display extreme linkage disequilibrium. Six randomly mating laboratory stocks, each founded by one gravid female heterozygous in coupling for both III-2 and III-35, were observed after 32 generations. Significant linkage disequilibrium was observed in all stocks. Recombinants were found in only two stocks. The absence of effective recombination in some stocks and its presence in others might be due to different genotypic backgrounds. We suggest that natural selection, influencing recombination rates in several ways, and intrachromosomal epistasis between the two inversions were the main factors for the maintenance of linkage disequilibrium in D. nasuta.     

Effective size of fluctuating salmon populations

Pacific salmon are semelparous but have overlapping year classes, which presents special challenges for the application of standard population genetics theory to these species. This article examines the relationship between the effective number of breeders per year (N(b)) and single-generation and multigeneration effective population size (N(e)) in salmon populations that fluctuate in size. A simple analytical model is developed that allows calculation of N(e) on the basis of the number of spawners in individual years and their reproductive contribution (productivity) to the next generation. Application of the model to a 36-year time series of data for a threatened population of Snake River chinook salmon suggests that variation in population dynamic processes across years reduced the multigeneration N(e) by approximately 40-60%, and reductions may have been substantially greater within some generations. These reductions are comparable in magnitude to, and in addition to, reductions in N(b) within a year due to unequal sex ratio and nonrandom variation in reproductive success. Computer simulations suggest that the effects of variable population dynamics on N(e) observed in this dataset are not unexpected for species with a salmon life history, as random variation in productivity can lead to similar results.     

Effective size of harvested ungulate populations

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

Effective population size of a population with stochastically varying size

For a Wright–Fisher model with mutation whose population size fluctuates stochastically from generation to generation, a heterozygosity effective population size is defined by means of the equilibrium average heterozygosity of the population. It is shown that this effective population size is equal to the harmonic mean of population size if and only if the stochastic changes of population size are uncorrelated. The effective population size is larger (resp. smaller) than the harmonic mean when the stochastic changes of population size are positively (resp. negatively) autocorrelated. These results and those obtained so far for other stochastic models with fluctuating population size suggest that the property that effective population sizes are always larger than the harmonic mean under the fluctuation of population size holds only for continuous time models such as diffusion and coalescent models, whereas effective population sizes can be equal to or smaller than the harmonic mean for discrete time models.     

Effective size in management and conservation of subdivided populations

A numerical method for computing the eigenvalue variance effective size of a subdivided population connected by any fixed pattern of migration is described. Using specific examples it is shown that total effective size of a subdivided population can become less than the sum of the subpopulation sizes as a result of directionalities in the pattern of migration. For an extension of the model with threshold harvesting and local deterministic logistic population dynamic we consider the problem of maximizing the total harvesting yield with constraints on the total effective size. For some simple source-sink systems and more complicated population structures where subpopulations differ in their degree of isolation, it is shown to be optimal, for a given total effective size, to raise the harvesting thresholds relatively more in small and in isolated populations. Finally, we show how the method applies to populations which are supplemented, either intentionally or unintentionally. It is shown that the total effective size can be reduced by several orders of magnitude if the captive component of a population is much smaller than the wild component, even with symmetric backward migration.     

Resource availability and population size in cactophilic Drosophila

1. Four species of Drosophila, Drosophila nigrospiracula ( Patterson & Wheeler 1942 ) , Drosophila mettleri ( Heed 1977 ) , Drosophila pachea ( Patterson & Wheeler 1942 ) , and Drosophila mojavensis ( Patterson & Crow 1940 ) , are endemic to the Sonoran Desert of North America and breed in different species of necrotic columnar cacti. Differences in resource availability have been suggested to explain the interspecific variability in fly population biology, but resource availability for these species has not been quantitatively assessed thoroughly in either spatial or temporal terms. The resource availability was quantified quarterly at three sites for 3 years and population sizes for each Drosophila species were estimated.
2. Spatial and temporal availability of resources differed significantly among species of host cacti, with organpipe cactus ( Stenocereus thurberi ) being the least abundant and senita ( Lophocereus schottii ) the most abundant spatially.
3. Drosophila species differed significantly in population size. The largest population sizes were found for D. nigrospiracula and D. mojavensis and smallest for D. pachea . Populations of D. mettleri were intermediate to these.
4. Population size was greatest for fly species utilizing host species having the largest and longest lasting necroses.
5. Resource availability does not explain the reduction of fly populations in the summer. Necroses were most abundant when flies were absent.     

Simulation of local evolutionary dynamics of small populations

A simple stochastic model assuming continuous traits, normally distributed modifications, selection for fertility and multiplicative fitness was used to simulate phenotypic evolution by reproducing individuals in a given fitness landscape. Of particular interest was how small populations cross saddles separating distinct adaptive peaks. The simulated evolution exhibits a strong dualism: at the same level of reproductive errors, sexual reproduction provides significantly better local adaptation and asexual repreduction provides significantly better adaptive dynamics.