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PubMed2000

Inbreeding depression due to mildly deleterious mutations in finite populations: size does matter.

We studied the effects of population size on the inbreeding depression and genetic load caused by deleterious mutations at a single locus. Analysis shows how the inbreeding depression decreases as population size becomes smaller and/or the rate of inbreeding increases. This pattern contrasts with that for the load, which increases as population size becomes smaller but decreases as inbreeding rate goes up. The depression and load both approach asymptotic limits when the population size becomes very large or very small. Numerical results show that the transition between the small and the large population regimes is quite rapid, and occurs largely over a range of population sizes that vary by a factor of 10. The effects of drift on inbreeding depression may bias some estimates of the genomic rate of deleterious mutation. These effects could also be important in the evolution of breeding systems in hermaphroditic organisms and in the conservation of endangered populations.

Genetics, Population↗

PubMed1990

The effective population size of an age-structured population with a sex-linked locus.

Let a population have the same age distribution and age-specific sex ratios at times 0, 1, 2,..., and let M, F, and L, respectively, be the numbers of males and females in the youngest age group and the generation interval. It can then be shown that if there is a sex-linked locus the fixation probabilities of a neutral allele are respectively 1/3LM or 1/3LF if the allele first appears in one newborn male or in one newborn female. The effective population size can then be derived. It is the same as for a population with discrete generations having the same means, variances, and covariances of male and female progeny during a lifetime and the same number of individuals entering the population per generation.

Age Factors↗

PubMed2001

Is the detection of the first arrival date of migrating birds influenced by population size? A case study of the red-backed shrike Lanius collurio.

Many analyses do not consider the problems associated with the effects of population size on encounter recording. Population size could impact on the detection of bird arrival time as there is a higher probability of observing earlier arrival when the population size is greater and the song activity of birds is increased, as occurs with a larger population. As a case study, we have analysed data on the red-backed shrike Lanius collurio collected in Western Poland during 1983-2000. In this period the red-backed shrike's return to its breeding sites became significantly earlier whilst the contemporary population size increased significantly. To eliminate linear trends through time we have worked on the standardised residuals from regression of both arrival time and population size on year. The correlation between arrival time and population size residuals was significantly negative, further supporting the link between detection and population size. This finding suggests that, in studies of avian migration and its changes over time, the relationship between arrival date and population size needs to be considered.

Animals↗

PubMed1993

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.

Animals↗

PubMed2003

Population size and the nature of genetic load in Gentianella germanica.

Theory predicts a significant relationship between the size of a population and the magnitude and composition of its genetic load, but few natural populations have been investigated. We examined the magnitude of genetic load due to recessive deleterious alleles (GL) both segregating and fixed within Gentianella germanica populations of varying size by selfing and reciprocally crossing plants within and between natural populations according to a partial diallel design and by comparing the performance of the experimental progeny in a common-garden experiment. The results show that GL for total fitness in small populations (fewer than 200 plants) was mainly due to fixed recessive deleterious alleles, whereas GL for total fitness in larger populations (more than 200 plants) appeared to be mainly due to segregating deleterious recessive alleles. The total fitness of selfed plants increased with decreasing population size, indicating some purging of deleterious alleles associated with declining population sizes. The magnitudes of GL due to fixed deleterious alleles in small populations and segregating deleterious alleles in large populations, however, were overall similar, suggesting that purging selection was an insignificant force when compared to genetic drift in determining the magnitude of GL in small natural populations in this species. The results of this study highlight the importance of population size in determining the dynamics of genetic loads of natural populations and are overall in line with a large body of theoretical work indicating that small populations may face higher extinction risks due to the fixation and accumulation of deleterious alleles of small effect.

Alleles↗

PubMed2004

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.

Genetics, Population↗

PubMed1986

The homozygosity test after a change in population size.

The homozygosity of a population will be influenced by any recent change in the population size. The "homozygosity test" of the neutral mutation hypothesis might also be influenced by a population change. A computer simulation method is described that establishes the significance levels of observed homozygosities after a change in population size. Some numerical examples are given.

Alleles↗

PubMed2006

Estimating population size with noninvasive capture-mark-recapture data.

Estimating population size of elusive and rare species is challenging. The difficulties in catching such species has triggered the use of samples collected noninvasively, such as feces or hair; from which genetic analysis yields data similar to capture-mark-recapture (CMR) data. There are, however two differences between classical CMR and noninvasive CMR. First, capture and recapture data are gathered over multiple sampling sessions in classical CMR, whereas in noninvasive CMR they can be obtained from a single sampling session. Second, because of genotyping errors and unlike classical CMR, there is no simple relationship between (genetic) marks and individuals in noninvasive CMR. We evaluated, through simulations, the reliability of population size estimates based on noninvasive CMR. For equal sampling efforts, we compared estimates of population size N obtained from accumulation curves, a maximum likelihood, and a Bayesian estimator. For a closed population and without sampling heterogeneity, estimates obtained from noninvasive CMR were as reliable as estimates from classical CMR. The sampling structure (single or multiple session) did not alter the results, the Bayesian estimator in the case of a single sampling session presented the best compromise between low mean squared error and a 95% confidence interval encompassing the parametric value of N in most simulations. Finally, when suitable field and lab protocols were used, genotyping errors did not substantially bias population size estimates (bias < 3.5% in all simulations). The ability to reliably estimate population size from noninvasive samples taken during a single session offers a new and useful technique for the management and conservation of elusive and rare species.

Animals↗

PubMed2000

Plant Species and Plant Incubation Conditions Influence Variability in Epiphytic Bacterial Population Size.

The influences of plant species and plant incubation conditions on the variability in bacterial population sizes among leaves were investigated in field and growth chamber studies. Pseudomonas syringae strains TLP2 and Cit7 were inoculated onto plants and population sizes were measured at intervals after inoculation. Total bacterial population sizes were also assessed in field studies. Levels of leaf-to-leaf variability in both P. syringae population size and bacterial community size differed significantly among plant species. For all plant species, variability among leaves in population sizes of inoculated bacteria was consistently greater than the leaf-to-leaf variability in numbers of total bacteria. Considering levels of variability in population size immediately prior to and following incubation under either wet or dry physical conditions, leaf-to-leaf variability in the population sizes of inoculated P. syringae strains increased significantly following incubation under dry, but not under wet, conditions. Measurements of leaf-to-leaf variability immediately prior to and following incubation were positively correlated regardless of whether the incubation was under wet or dry conditions, though the correlation was greater following dry incubation. These data provide insight into the biological and physical factors that may be important in generating variability in bacterial population sizes among leaves, and they have important implications for the design of appropriate strategies for sampling leaf surface microbial populations. </hea

Journal Article↗

PubMed1997

Historical analysis of genetic variation reveals low effective population size in a northern pike (Esox lucius) population.

Effective population size (Ne) of a natural fish population was estimated from temporal changes in allele frequencies at seven microsatellite loci. Use of a historical collection of fish scales made it possible to increase the precision of estimates by increasing the time interval between samples and to use an equation developed for discrete generations without correcting for demographic parameters. Estimates of Ne for the time intervals 1961-1977 and 1977-1993 were 35 and 72, respectively. For the entire interval, 1961-1993, the estimate of Ne was 48 when based on a weighted mean derived from the above two estimates or 125 when calculated from 1961 and 1993 samples only. Corresponding ratios of effective size to adult census size ranged from 0.03 to 0.14. An Ne of 48 over a 32-year period would imply that this population lost as much as 8% of its heterozygosity in that time. Results suggest the potential for using genetic methods based on microsatellite loci data to compare historical trends in Ne with population dynamic parameters. Such comparisons will help to evaluate the relationship between genetic diversity and long-term persistence of natural populations.

Animals↗

PubMed2006

Genetic diversity, population structure, effective population size and demographic history of the Finnish wolf population.

The Finnish wolf population (Canis lupus) was sampled during three different periods (1996-1998, 1999-2001 and 2002-2004), and 118 individuals were genotyped with 10 microsatellite markers. Large genetic variation was found in the population despite a recent demographic bottleneck. No spatial population subdivision was found even though a significant negative relationship between genetic relatedness and geographic distance suggested isolation by distance. Very few individuals did not belong to the local wolf population as determined by assignment analyses, suggesting a low level of immigration in the population. We used the temporal approach and several statistical methods to estimate the variance effective size of the population. All methods gave similar estimates of effective population size, approximately 40 wolves. These estimates were slightly larger than the estimated census size of breeding individuals. A Bayesian model based on Markov chain Monte Carlo simulations indicated strong evidence for a long-term population decline. These results suggest that the contemporary wolf population size is roughly 8% of its historical size, and that the population decline dates back to late 19th century or early 20th century. Despite an increase of over 50% in the census size of the population during the whole study period, there was only weak evidence that the effective population size during the last period was higher than during the first. This may be caused by increased inbreeding, diminished dispersal within the population, and decreased immigration to the population during the last study period.

Animal Migration↗

PubMed2002

Likelihood and Bayes estimation of ancestral population sizes in hominoids using data from multiple loci.

Polymorphisms in an ancestral population can cause conflicts between gene trees and the species tree. Such conflicts can be used to estimate ancestral population sizes when data from multiple loci are available. In this article I extend previous work for estimating ancestral population sizes to analyze sequence data from three species under a finite-site nucleotide substitution model. Both maximum-likelihood (ML) and Bayes methods are implemented for joint estimation of the two speciation dates and the two population size parameters. Both methods account for uncertainties in the gene tree due to few informative sites at each locus and make an efficient use of information in the data. The Bayes algorithm using Markov chain Monte Carlo (MCMC) enjoys a computational advantage over ML and also provides a framework for incorporating prior information about the parameters. The methods are applied to a data set of 53 nuclear noncoding contigs from human, chimpanzee, and gorilla published by Chen and Li. Estimates of the effective population size for the common ancestor of humans and chimpanzees by both ML and Bayes methods are approximately 12,000-21,000, comparable to estimates for modern humans, and do not support the notion of a dramatic size reduction in early human populations. Estimates published previously from the same data are several times larger and appear to be biased due to methodological deficiency. The divergence between humans and chimpanzees is dated at approximately 5.2 million years ago and the gorilla divergence 1.1-1.7 million years earlier. The analysis suggests that typical data sets contain useful information about the ancestral population sizes and that it is advantageous to analyze data of several species simultaneously.

Algorithms↗

PubMedDate not supplied

Breeding population size of a fragmented population of a Costa Rican dry forest tree species.

Pollen immigration can offset the effects of genetic drift and inbreeding in small populations. To understand the genetic consequences of forest fragmentation, estimates of pollen flow into remnant fragments are essential. Such estimates are straightforward for plants with singly sired, multiseeded fruits, since the pollen donor genotype for each fruit can be unambiguously reconstructed through full-sib genealogical analyses. Allozyme analyses were used to estimate pollen donor numbers from the progeny of fruits of the tropical dry forest tree Enterolobium cyclocarpum in a small (9.8 ha) fragmented population (N = 11) over three reproductive seasons (1994, 1995, and 1996). These analyses indicate that each tree receives pollen from many pollen donors. When data are pooled for the site, estimated maximum pollen donor pool sizes in all years exceed the number of individuals (56) in the 227 ha study area. Although unidentified pollen donors may be located as close as 250 m to the study trees, the number of unidentified pollen donors indicates that individuals in this forest fragment are part of a large network of reproductively active individuals.

Costa Rica↗

PubMed1973

Effects of population size and selection intensity of short-term response to selection for postweaning gain in mice.

The effects of population size and selection intensity on the mean response was examined after 14 generations of within full-sib family selection for postweaning gain in mice. Population sizes of 1, 2, 4, 8 and 16 pair matings were each evaluated at selection intensities of 100% (control), 50% and 25% in a replicated experiment. Selection response per generation increased as selection intensity increased. Selection response and realized heritability tended to increase with increasing population size. Replicate variability in realized heritability was large at population sizes of 1, 2 and 4 pairs. Genetic drift was implicated as the primary factor causing the reduced response and lowered repeatability at the smaller population sizes. Lines with intended effective population sizes of 62 yielded larger selection responses per unit selection differential than lines with effective population sizes of 30 or less.

Analysis of Variance↗

PubMed2001

Is the population size of a species relevant to its evolution?

This paper examines aspects of genetic draft, the stochastic force induced by substitutions at one locus on the dynamics of a closely linked locus. Of particular interest is the role of population size on genetic draft. Remarkably, the rate of substitution of weakly selected advantageous mutations decreases with increasing population size, whereas that for deleterious mutations increases with population size. This dependency on population size is the opposite of that for genetic drift. Moreover, these rates are only weakly dependent on population size, again contrary to the strong dependency of drift-based dynamics. Four models of the strongly selected loci responsible for genetic draft are examined. Three of these exhibit a very weak dependency on population size, which implies that their induced effects will also be weakly dependent on population size. Together, these results suggest that population size and binomial sampling may not be relevant to a species' evolution. If this is the case, then a number of evolutionary conundrums are resolved.

Alleles↗

PubMed1997

On the estimation of ancestral population sizes of modern humans.

The theory developed by Takahata and colleagues for estimating the effective population size of ancestral species using homologous sequences from closely related extant species was extended to take account of variation of evolutionary rates among loci. Nuclear sequence data related to the evolution of modern humans were reanalysed and computer simulations were performed to examine the effect of rate variation on estimation of ancestral population sizes. It is found that the among-locus rate variation does not have a significant effect on estimation of the current population size when sequences from multiple loci are sampled from the same species, but does have a significant effect on estimation of the ancestral population size using sequences from different species. The effects of ancestral population size, species divergence time and among-locus rate variation are found to be highly correlated, and to achieve reliable estimates of the ancestral population size, effects of the other two factors should be estimated independently.

Animals↗

PubMed1993

Effective population size in organisms with complex life-histories.

A method for determining effective population size in organisms with arbitrarily complex life-histories, including clonal reproduction, is developed. A coalescent model that focuses on the time at which two alleles last shared a common ancestor leads to a method for determining an inbreeding effective population size. Comparisons with previously developed approximate methods for haploid age-structured models show close, but not exact, agreement. A diploid population with both clonal and sexual reproduction is considered; examples from published demographic studies are used to show the effects of within-individual versus between-individual coalescence times and different definitions of generation time in calculating effective population size. These examples show relatively small differences in effective population sizes calculated using within- and between-individual coalescence times; however, in one case, different definitions of generation time lead to a large change in ratios of effective population size to census size (Ne/N). The Ne/N calculated for clonally reproducing organisms in this paper seem to be substantially smaller than published values for organisms lacking clonal reproduction.

Age Factors↗

PubMed1989

Diel Variation in Population Size and Ice Nucleation Activity of Pseudomonas syringae on Snap Bean Leaflets.

The extent to which diel changes in the physical environment affect changes in population size and ice nucleation activity of Pseudomonas syringae on snap bean leaflets was determined under field conditions. To estimate bacterial population size and ice nucleation activity, bean leaflets were harvested at 2-h intervals during each of three 26-h periods. A tube nucleation test was used to assay individual leaflets for ice nuclei. Population sizes of P. syringae were determined by dilution plating of leaflet homogenates. The overall diel changes in P. syringae population sizes differed during each of the 26-h periods. In one 26-h period, there was a continuous increase in the logarithm of P. syringae population size despite intense solar radiation, absence of free moisture on leaf surfaces, and low relative humidity during the day. A mean doubling time of approximately 4.9 h was estimated for the 28-fold increase in P. syringae population size that occurred from 0900 to 0900 h during the 26-h period. However, doubling times of 3.3 and 1.9 h occurred briefly during this period from 1700 to 2300 h and from 0100 to 0700 h, respectively. Thus, growth rates of P. syringae in association with leaves in the field were of the same order of magnitude as optimal rates measured in the laboratory. The frequency with which leaflets bore ice nuclei active at -2.0, -2.2, and -2.5 degrees C varied greatly within each 26-h period. These large diel changes were inversely correlated primarily with the diel changes in air temperature and reflected changes in nucleation frequency rather than changes in population size of P. syringae. Thus, the response of bacterial ice nucleation activity to the physical environment was distinct from the changes in population size of ice nucleation-active P. syringae.

Journal Article↗