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PubMed1998

Should we expect substitution rate to depend on population size?

The rate of nucleotide substitution is generally believed to be a decreasing function of effective population size, at least for nonsynonymous substitutions. This view was originally based on consideration of slightly deleterious mutations with a fixed distribution of selection coefficients. A realistic model must include the occurrence and fixation of some advantageous mutations that compensate for the loss of fitness due to deleterious substitutions. Some such models, such as so-called "fixed" models, also predict a population size effect on substitution rate. An alternative model, presented here, predicts the near absence of a population size effect on substitution rate. This model is based on concave log-fitness functions and a fixed distribution of mutational effects on the selectively important trait. Simulations of an instance of the model confirm the approximate insensitivity of the substitution rate to population size. Although much experimental evidence has been claimed to support the existence of a population size effect, the body of evidence as a whole is equivocal, and much of the evidence that is supposed to demonstrate such an effect would also suggest that it is very small. Perhaps the proposed model applies well to some genes and not so well to others, and genes therefore vary with regard to the population size effect.

Amino Acid Substitution↗
PubMed2003

Conservation effort and assessment of population size in fluctuating environments.

We consider optimal conservation strategies for endangered populations. We assume that the survival of the population is affected by unpredictable environmental fluctuation and can be improved by conservation effort. Furthermore, the exact value of the initial population size is assumed to be unknown. The conservation strategy involves two aspects: investment of assessment effort, to improve the estimate of the initial population size and investment of conservation effort. Both types of effort imply economic costs. The optimal management strategy is assumed to minimize the weighted sum of extinction probability and the economic cost of the conservation and the assessment effort. (1) We first analyse the optimal conservation effort when the current population size is known accurately. (2) Next, we consider the situation in which there is limited information (i.e. a cue) on population size. (3) We subsequently discuss the cases where the cue accuracy can be improved by assessment of the population. We study the optimal level of the assessment effort and discuss its dependence on various parameters.

Animals↗
PubMed1973

Effects of population size and selection intensity on correlated responses to selection for postweaning gain in mice.

Correlated responses to selection for postweaning gain in mice were studied to determine the influence of population size and selection intensity. Correlated traits measured were three-, six- and eight-week body weights, litter size, twelve-day litter weight, proportion infertile matings and two indexes of reproductive performance. In general, the results agreed with observations made on direct response: correlated responses in the body weight traits and litter size increased as (1) selection intensity increased and (2) effective population size increased. Correlated responses in the body weight traits and litter size were positive in the large population size lines (16 pairs), as expected from the positive genetic correlation between these traits and postweaning gain. However, several negative correlated responses were observed at small population sizes (one and two pairs). Within each level of selection intensity, traits generally associated with fitness tended to decline most in the very small populations (one and two pairs) and in the large populations (16 pairs) for apparently different reasons. The fitness decline at the small effective population sizes was attributable to inbreeding depression. In contrast, it was postulated that the fitness decline at the large effective population size was due to selection moving the population mean for body weight and a trait positively correlated genetically with body weight (i.e., percent body fat) away from an optimum.

Age Factors↗
PubMed2003

Population size and identity influence the reaction norm of the rare, endemic plant Cochlearia bavarica across a gradient of environmental stress.

Habitat degradation and loss can result in population decline and genetic erosion, limiting the ability of organisms to cope with environmental change, whether this is through evolutionary genetic response (requiring genetic variation) or through phenotypic plasticity (i.e., the ability of a given genotype to express a variable phenotype across environments). Here we address the question whether plants from small populations are less plastic or more susceptible to environmental stress than plants from large populations. We collected seed families from small (<100) versus large natural populations (>1,000 flowering plants) of the rare, endemic plant Cochlearia bavarica (Brassicaceae). We exposed the seedlings to a range of environments, created by manipulating water supply and light intensity in a 2 x 2 factorial design in the greenhouse. We monitored plant growth and survival for 300 days. Significant effects of offspring environment on offspring characters demonstrated that there is phenotypic plasticity in the responses to environmental stress in this species. Significant effects of population size group, but mainly of population identity within the population size groups, and of maternal plant identity within populations indicated variation due to genetic (plus potentially maternal) variation for offspring traits. The environment x maternal plant identity interaction was rarely significant, providing little evidence for genetically- (plus potentially maternally-) based variation in plasticity within populations. However, significant environment x population-size-group and environment x population-identity interactions suggested that populations differed in the amount of plasticity, the mean amount being smaller in small populations than in large populations. Whereas on day 210 the differences between small and large populations were largest in the environment in which plants grew biggest (i.e., under benign conditions), on day 270 the difference was largest in stressful environments. These results show that population size and population identity can affect growth and survival differently across environmental stress gradients. Moreover, these effects can themselves be modified by time-dependent variation in the interaction between plants and their environment.

Biological Evolution↗
PubMed1996

Demographic genetics of brown trout (Salmo trutta) and estimation of effective population size from temporal change of allele frequencies.

We studied temporal allele frequency shifts over 15 years and estimated the genetically effective size of four natural populations of brown trout (Salmo trutta L.) on the basis of the variation at 14 polymorphic allozyme loci. The allele frequency differences between consecutive cohorts were significant in all four populations. There were no indications of natural selection, and we conclude that random genetic drift is the most likely cause of temporal allele frequency shifts at the loci examined. Effective population sizes were estimated from observed allele frequency shifts among cohorts, taking into consideration the demographic characteristics of each population. The estimated effective sizes of the four populations range from 52 to 480 individuals, and we conclude that the effective size of natural brown trout populations may differ considerably among lakes that are similar in size and other apparent characteristics. In spite of their different effective sizes all four populations have similar levels of genetic variation (average heterozygosity) indicating that excessive loss of genetic variability has been retarded, most likely because of gene flow among neighboring populations.

Alleles↗
PubMed1989

The measurement of villus cell population size in the mouse small intestine in normal and abnormal states: a comparison of absolute measurements with morphometric estimators in sectioned immersion-fixed material.

From a functional viewpoint, the most important part of the small intestinal mucosa is the villus epithelium; in the experimental study of intestinal adaptation it is often necessary to estimate the size of the population. For these reasons, a systematic study of methods of measuring the size of the villus cell population was undertaken in villi of normal morphology from control animals, and in villi of abnormal morphology as produced by treatment of mice with cytosine arabinoside (Ara-C). The villus cell population can be measured with precision and accuracy in both normal and abnormal mucosal states, with a relative standard error usually less than 5%, with good reproducibility, and with very low counting errors. In the mouse a practically linear relationship between the villus cell population size and position in the small intestine can be shown. In normal, control animals, linear estimates of villus population, for example the villus height, the villus core height, and the villus row count measured in sections of immersion-fixed material, were found to be rough approximations as indicators of the villus cell population, and were highly correlated with it. Product variables, comprising the products of a height with a width measurement, show a large improvement over the linear variables as estimators of villus cell population. In populations of abnormally shaped villi produced by Ara-C, both linear and product variables showed a considerable decrease in correlation with the villus cell population. Consequently, indirect, linear measurements of the villus population size do not accurately reflect the size of the villus population in abnormal villi. Finally, a method comparing theoretical and measured surface: volume indices was used to indicate that the most appropriate shape for normal mouse villi is a simple cylinder; this method would also be applicable for other villus cell populations.

Animals↗
PubMed2006

Stochastic or deterministic: what is the effective population size of HIV-1?

Various studies have attempted to estimate the effective population size of HIV-1 to determine the strength of stochastic effects in within-host evolution. The largely discrepant estimates, the complexity of the concept of the effective population size and the resulting uncertainty about the underlying assumptions make the interpretation of these estimates difficult. Here, we explain the concept and critically assess the current estimates. We discuss the biologically relevant factors that affect the estimate and use of the effective population size. We argue that these factors lead to an underestimation of the effective population size and, thus, to an overestimation of the strength of stochastic effects in HIV-1 evolution.

Evolution, Molecular↗
PubMed1995

Population Sizes, Immigration, and Growth of Epiphytic Bacteria on Leaves of Different Ages and Positions of Field-Grown Endive (Cichorium endivia var. latifolia).

Total, fluorescent, and pectolytic epiphytic bacterial population sizes were quantified on leaves of different age groups of broad-leaved endive during field cultivation from leaf emergence until harvest. Greater bacterial population densities (log(inf10) CFU per square centimeter) were observed on outer leaves than on inner leaves of the plants throughout the growing season. These differences were statistically significant for total bacterial populations at all sampling times and were often significant for fluorescent and pectolytic bacterial populations. At harvest, a linear gradient of decreasing densities of epiphytic bacteria from outer (older) to inner (younger) leaves of the head was significant. Leaf age influenced the frequency distribution and variability of bacterial population sizes associated with leaves of broad-leaved endive. Total bacterial population sizes were greater at leaf emergence for leaves emerging during the second half of the cultivation period than for leaves emerging earlier. The size of fluorescent and pectolytic bacterial populations on newly emerged leaves increased throughout the season as plants aged. To assess the importance of plant age on bacterial immigration at leaf emergence, bacterial densities were quantified on leaves emerging simultaneously on plants of different ages. In two of the three experiments, greater bacterial population sizes were observed on leaves emerging on younger plants. This indicates that factors other than an increase in concentration of airborne bacteria can lead to increases in population sizes at leaf emergence as plants age in the field. Results of leaf pruning experiments suggested that adjacent leaves may act as a barrier for immigration of fluorescent bacteria on newly emerged leaves. Survival of an inoculated strain of Pseudomonas fluorescens on newly emerged leaves generally did not vary with the age of plants. However, these effects were not consistent among experiments, suggesting that interactions among micro- and macroenvironmental conditions, physiological condition of leaves, and accessibility of leaves to airborne bacteria are important in controlling epiphytic bacterial population sizes.

Journal Article↗
PubMed1998

The effective population size of Anopheles gambiae in Kenya: implications for population structure.

We estimated current and long-term effective population size (Ne) of two Anopheles gambiae (savanna cytotype) populations in Kenya. Temporal variation at nine microsatellite loci in each population sampled 7 and 9 years apart and genetic diversity in each sample were analyzed to answer the following questions. (1) Do bottlenecks occur in Kenyan populations of A. gambiae? (2) How variable are different populations with respect to their current and long-term Ne values? (3) What are the implications of these results on population structure and history? The estimates of Ne of Asembo and Jego were 6,359 and 4,258, respectively, and the lower 95% limits were 2,455 and 1,669, respectively. Thus, despite the typical observation of low density at the village level during the dry season, large populations are maintained annually. Large current Ne is consistent with previous studies showing low differentiation across the continent, especially under Wright's isolation-by-distance model. Current Ne in Asembo was 1.5-fold higher than in Jego, but this difference was not significant. Long-term Ne in Asembo (22,667) was 2.9-fold higher than that in Jego (7,855) based on the stepwise mutation model. The difference between populations was significant at both time points regardless of whether long-term Ne values were calculated based on the stepwise mutation model or the infinite-alleles model. Heterozygosity in Jego declined significantly between 1987 (59%) and 1996 (54%), whereas heterozygosity in Asembo was stable (66%-65%). Despite the relatively high and significant differentiation between Asembo and Jego (FST = 0.072-0.10, RST = 0.037-0.038), all alleles in Jego were found in Asembo but not vice versa. All of these findings suggest that lower Ne in Jego magnifies differentiation between the two populations. The long-term Ne was biased downward, because its calculation was based on an upper bound estimate of microsatellite mutation rate. Ne values based on mtDNA and allozymes were an order of magnitude higher. Long-term Ne therefore, is probably measured in hundreds of thousands and hence does not support a recent expansion of this species from a small population.

Animals↗
PubMed1979

Mutation rates, population sizes and amounts of electrophoretic variation of enzyme loci in natural populations.

A method is presented for estimating relative mutation rates or relative effective population sizes, under the hypothesis of adaptively neutral allelic variation. This method was applied to seven surveys of electrophoretic variation. It was observed that electrophoretic mutation rates so obtained follow the gamma distribution and, in Drosophila, are positively correlated with the molecular weights of the enzymes subunits. The variance in mutation rate is larger under the step-wise model of electrophoretic mutation than under the infinite-alleles model. Rates for the most variable loci may exceed rates for less variable loci by a factor of 500. For completely invariant loci, this factor may be as high as 4 X 10(4), an observation suggesting that these loci are subject to purifying selection. In contrast to mutation rates, effective population sizes may vary at the most by a factor of ten. These results support the hypothesis that differences in the amount of electrophoretic variability among polymorphic loci may reflect differences in the rate by which electrophoretically detectable variation is generated in population.

Animals↗
PubMed2004

Changes in Synechococcus population size and cellular ribosomal RNA content in response to predation and nutrient limitation.

A mathematical model of predator-prey interactions was used to predict the relationship between population size and cellular growth rate in a two-tiered trophic system consisting of Synechococcus PCC 6301 and Tetrahymena pyriformis. As predicted, axenic chemostat cultures of Synechococcus responded to increased nutrient availability by expanding the equilibrium population size without a concurrent change in growth rate. Likewise, the addition of the predator Tetrahymena pyriformis decreased the Synechococcus population size by 85% and increased the Synechococcus growth rate. Synechococcus populations in the surface waters of the Gulf of Mexico were sampled to ascertain whether the relationship between population size and cellular 16S rRNA concentration conformed to that predicted by the model. Direct counts of autofluorescent cells in size-fractionated seawater samples provided an estimate of Synechococcus population size. The growth rate of in situ populations was estimated by measuring the extent of hybridization of an oligonucleotide probes complementary to Synechococcus 16S rRNA, based on evidence that ribosomal RNA content increases concurrently with growth rate. The comparison of in situ population sizes and specific growth rates revealed that relatively large Synechococcus populations were growing slowly, indicative of nutrient limitation, and that quickly growing populations were relatively small, as predicted for predator-limited populations.

Animals↗
PubMedDate not supplied

The impact of supplementation in winter-run chinook salmon on effective population size.

Supplementation of young raised at a protected site, such as a hatchery, may influence the effective population size of an endangered species. A supplementation program for the endangered winter-run chinook salmon from the Sacramento River, California, has been releasing fish since 1991. A breeding protocol, instituted in 1992, seeks to maximize the effective population size from the captive spawners by equaling their contributions to the released progeny. As a result, the releases in 1994 and 1995 appear not to have decreased the overall effective population size and may have increased it somewhat. However, mistaken use of non-winter-run chinook spawners resulted in artificial crosses between runs with a potential reduction in effective population size, and imprinting of the released fish on Battle Creek, the site of the hatchery, resulted in limiting the contribution of the released fish to the target mainstem population. Rapid genetic analysis of captured spawners and a new rearing facility on the Sacramento River should alleviate these problems and their negative effect on the effective population size in future years.

Animals↗
PubMed2001

Variability levels, population size and structure of American and European Drosophila montana populations.

The level and patterns of nucleotide diversity have been characterized for two X-linked loci, fused (fu; a region of 2362 bp) and suppressor of sable (su(s); a region of 413 bp), in one European and one American D. montana population. Sequence variation at these loci shows that the two populations are divergent, although they may not be completely isolated. Data on the level of silent site variability at su(s) (1.1% and 0.5% for the European and American populations, respectively) suggest that the effective population sizes of the two populations may be similar. At the fused locus, one European sequence was highly divergent and may have resulted from gene conversion, and was excluded from the analysis. With this sequence removed, the level of silent site variability was significantly lower in the European population (0.28%) than in the American population (2.3%), which suggests a selective sweep at or near fu in the former population.

Animals↗
PubMed2000

Effective population sizes for cytoplasmic and nuclear genes in a gynodioecious species. The role of the sex determination system.

Equations are derived for the effective sizes of gynodioecious populations with respect to both nuclear and cytoplasmic genes (N(ec) and N(en), respectively). Compared to hermaphroditism, gynodioecy generally reduces effective population sizes for both kinds of loci to an extent depending on the frequency of females, the sex determination system, and the selfing rate of hermaphrodites. This reduction is due to fitness differences between the sexes and is highly influenced by the mode of inheritance of this fitness. In absence of selfing, nuclear gynodioecy results in a reduction of N(ec) that depends strongly on the dominance of male sterility alleles, while N(en) remains equal to the census number (N). With cytonuclear gynodioecy, both cytoplasmic and nuclear effective sizes are reduced, and at the extreme, dioecy results in the minimum N(ec) values and either minimum or maximum N(en) values (for low or high frequency of females, respectively). When selfing occurs, gynodioecy either increases or decreases N(en) as compared to hermaphroditism with the same selfing rate of hermaphrodites. Unexpectedly, N(ec) also varies with the selfing rate. Thus the genetic sex-determination system appears as a major factor for the nuclear and cytoplasmic genetic diversities of gynodioecious species.

Cell Nucleus↗
PubMed2003

Novel multilocus measure of linkage disequilibrium to estimate past effective population size.

Linkage disequilibrium (LD) between densely spaced, polymorphic genetic markers in humans and other species contains information about historical population size. Inferring past population size is of interest both from an evolutionary perspective (e.g., testing the "out of Africa" hypothesis of human evolution) and to improve models for mapping of disease and quantitative trait genes. We propose a novel multilocus measure of LD, the chromosome segment homozygosity (CSH). CSH is defined for a specific chromosome segment, up to the full length of the chromosome. In computer simulations CSH was generally less variable than the r(2) measure of LD, and variability of CSH decreased as the number of markers in the chromosome segment was increased. The essence and utility of our novel measure is that CSH over long distances reflects recent effective population size (N), whereas CSH over small distances reflects the effective size in the more distant past. We illustrate the utility of CSH by calculating CSH from human and dairy cattle SNP and microsatellite marker data, and predicting N at various times in the past for each species. Results indicated an exponentially increasing N in humans and a declining N in dairy cattle. CSH is a valuable statistic for inferring population histories from haplotype data, and has implications for mapping of disease loci.

Animals↗
PubMed2002

Effective Population Size during Grass Germplasm Seed Regeneration.

Effective population size (N(e)) is the key parameter for predicting genetic drift associated with germplasm regeneration. A major factor reducing N(e) below the census population size (N(c)) is variation in seed production among plants in a given population. The objectives of this study were to estimate N(e)/N(c) associated with variation in seed production in three model wind pollinated, perennial grass species [Lolium perenne L., Festuca pratensis Huds., and Pseudoroegneria spicata (Pursh) Á. Löve] and to recommend cost effective sampling methodology to maximize N(e)/N(c) during seed regeneration. Three accessions of each species were grown at two field locations and variation in seed number among plants and mean seed production per plant used to estimate N(e)/N(c). Mean seeds per whole plant, standard deviations, and N(e)/N(c) differed among species, and accessions within species (P < 0.05). For whole plant samples, average N(e)/N(c) for each species differed with values of 0.42, 0.51, and 0.63 for L. perenne, F. pratensis, and P. spicata, respectively. However, average N(e)/N(c) based on two inflorescences per plant was 0.69, 0.88, and 0.86 for L. perenne, F. pratensis, and P. spicata, respectively, which was higher than that of whole plant samples. This higher N(e)/N(c) resulted from the elimination of the variation in inflorescence number per plant, a major source of variation in seed number among plants. The results showed the high potential for genetic drift in small regeneration populations. Increased plant populations and harvesting a constant number of inflorescences per plant are recommended as cost-effective methods to minimize genetic drift during regeneration of outcrossing grass germplasm.

Journal Article↗
PubMed1997

Effective population size for a sex-linked locus in populations under selection.

The problem of selection in the prediction of effective population size for a sex-linked locus was addressed in terms of the cumulative effect of selection on change in frequency of a sex-linked neutral gene. To express the cumulative effect of selection, a transition matrix approach was used. It was found that the terms accounting for the cumulative change in gene frequency show different expressions, depending on the gametic pathways. This dependency is due to the fact that the heterogametic sex transmits a sex-linked gene only to offspring of the homogametic sex, whereas the homogametic sex transmits to offspring of both sexes. Monte Carlo simulation was carried out to check the obtained prediction equation. The result showed that there is a good agreement between observed and predicted effective sizes.

Animals↗
PubMed2005

A threefold genetic allee effect: population size affects cross-compatibility, inbreeding depression and drift load in the self-incompatible Ranunculus reptans.

A decline in population size can lead to the loss of allelic variation, increased inbreeding, and the accumulation of genetic load through drift. We estimated the fitness consequences of these processes in offspring of controlled within-population crosses from 13 populations of the self-incompatible, clonal plant Ranunculus reptans. We used allozyme allelic richness as a proxy for long-term population size, which was positively correlated with current population size. Crosses between plants of smaller populations were less likely to be compatible. Inbreeding load, assessed as the slope of the relationship between offspring performance and parental kinship coefficients, was not related to population size, suggesting that deleterious mutations had not been purged from small populations. Offspring from smaller populations were on average more inbred, so inbreeding depression in clonal fitness was higher in small populations. We estimated variation in drift load from the mean fitness of outbred offspring and found enhanced drift load affecting female fertility within small populations. We conclude that self-incompatibility systems do not necessarily prevent small populations from suffering from inbreeding depression and drift load and may exacerbate the challenge of finding suitable mates.

Alleles↗