Fixation of advantageous alleles in partially self-fertilizing populations. The effect of different selection modes

The expected fixation probability of an advantageous allele was examined in a partially self-fertilizing hermaphroditic plant species using the diffusion approximation. The selective advantage of the advantageous allele was assumed to be increased viability, increased fecundity, or an increase in male fitness. The mode of selection, as well as the selfing rate, the population size, and the dominance of the advantageous allele, affect the fixation probability of the allele. In general it was found that increases in selfing rate decrease the fixation probability under male sexual selection, increase fixation probability under fecundity selection, and increase when recessive and decrease when dominant under viability selection. In some cases the highest fixation probability of advantageous alleles under fecundity or under male sexual selection occurred at an intermediary selfing rate. The expected mean fixation times of the advantageous allele were also examined using the diffusion approximation.     

The average frequency of private alleles in a partially isolated population

An analytic model is developed to explore the relationship between gene flow, selection, and genetic drift. We assume that a single copy of a mutant allele appears in a finite, partially isolated population and allow for the effects of immigration, genic selection, and mutation on the frequency of the mutant. Our concern is with the distribution of the mutant's frequency before it either is lost from the population or emigrates. Before either of these events, the allele will be a “private allele” and would be found in only one of several populations in a larger collection. Slatkin [(1985) Evolution 39, 53–65] found several simple properties of private alleles in his simulations. We use the method developed by Karlin and Tavaré [(1980) Genet. Res. 37, 33–46; (1981a), Theor. Pop. Biol. 19, 187–214; (1981b) Theor. Pop. Biol. 19, 215–229] for a model similar to ours to obtain a diffusion equation with a “killing term” and obtain the mean and variance of the mutant's frequency and its expected frequency in samples of a specified size. There is only fair agreement between the analytic results from this model and those from Slatkin's (loc. cit.) simulations. The rescaling method used to obtain the results indicates that if emigration is relatively frequent, the distribution of rare alleles is governed largely by the balance between genetic drift and emigration, with selection, mutation, and immigration playing a lesser role.     

The population genetics of alleles affecting enzyme activity.

It is possible to predict the population genetics of allozymes by assuming that fitness is proportional to flux through a biochemical pathway. The model presented here extends previous work by incorporating two additional features of biological realism. Firstly, that more than one biochemical route may exist between any two metabolites. The major routes have been identified as the classical biochemical pathways but in the event of a mutation blocking a major route, minor routes become significant. These minor routes are named "bypass fluxes" and have profound effects on the population genetics of allozymes. Secondly, recent work has suggested that a metabolic cost is associated with enzyme synthesis; this will constitute an additional selective pressure on alleles which affect the amount of enzyme synthesized. The model generates a fitness curve which predicts the fitness associated with any level of enzyme activity. It can utilize data on null or near-null, structural or regulatory, mutations in the presence or absence of bypass fluxes. When data from natural populations of Drosophila are investigated, it is concluded that selection pressures acting on enzyme variants may be much higher than previously thought.     

Simultaneous estimation of null alleles and inbreeding coefficients

Although microsatellites are a very efficient tool for many population genetics applications, they may occasionally produce "null" alleles, which, when present in high proportion, may affect estimates of key parameters such as inbreeding and relatedness coefficients or measures of genetic differentiation. In order to account for the presence of null alleles, it is first necessary to estimate their frequency within studied populations. However, the commonly used null allele frequency estimators are not of general applicability because they can produce upwardly biased estimates when a population under study experiences some inbreeding. In such a case, 2 formerly described approaches, population inbreeding model and individual inbreeding model, can be applied for simultaneous estimation of null allele frequencies and of the inbreeding coefficient. In this study, we demonstrate the properties and utility of these 2 methods and show that they outperform the commonly used approaches in the estimation of null allele frequencies based on genotypic data. The methods are applied to empirical data from a natural population of European beech (Fagus sylvatica L.), and results are briefly discussed. The methods presented in this paper are implemented in the Windows-based user-friendly INEST computer program (available free of charge at http://genetyka.ukw.edu.pl/INEst10_setup.exe).     

An inclusive fitness model for the sex ratio in a partially sibmating population with inbreeding cost

Summary We construct an inclusive fitness model to find the evolutionarily stable sex ratios in a partially sibmating diploid or haplodiploid population. We assume a constant rate of sibmating with inbred offspring incurring a fitness penalty which, under haplodiploidy, is only suffered by females. We construct a one-locus genetic model for the same problem and observe that when selection is weak it gives the same numerical results as the inclusive fitness model.     

Distribution of genes affecting characteristics of the population

THE CHANGING POPULATION OF THE UNITED STATES: Conrad Taeuber and Irene B. Taeuber. A Volume in the Census Monograph Series. John Wiley and Sons, Inc., New York; Chapman and Hall, Limited, London; for the Social Science Research Council in cooperation with the U. S. Department of Commerce, Bureau of the Census; 1958; xi, 357 pp.; $7.75.

VARIABLES RELATED TO HUMAN BREAST CANCER: Elving Anderson, Harold J. GOODMAN and SHELDON C. REED. University of Minnesota Press, Minneapolis, 1958, 172 pp., 41 text, tables, 53 appendix tables, 7 figures. $4.00.

THE POPULATION AHEAD, Edited by Roy G. Francis. University of Minnesota Press, Minneapolis, 1958, x, 160 pp.

ABORTION IN THE UNITED STATES: Mary Calderone, M. D. (Editor). Hoeber‐Harper, New York, 1958, 224 pp. $5.50.

DIFFERENTIAL PSYCHOLOGY: Anne Anastasi. The Macmillan Company, New York, 1958 (3rd Edition), 664 pp + xii.

FIVE YEARS OF FAMILY PLANNING IN THE COUNTRYSIDE: Baljit Singh. J. K. Institute Monograph No. 6, J. K. Institute of Sociology &; Human Relations, Lucknow University. 1958. 118 pp.

POPULATION; AN INTERNATIONAL DILEMMA. A Summary of the Proceedings of the Conference on Population Problems— 1956–1957. Frederick Osborn. New York, Population Council, 1958. Pp. ix + 97. $2.00.     

Prediction of rates of inbreeding in selected populations

A method is presented for the prediction of rate of inbreeding for populations with discrete generations. The matrix of Wright's numerator relationships is partitioned into 'contribution' matrices which describe the contribution of the Mendelian sampling of genes of ancestors in a given generation to the relationship between individuals in later generations. These contributions stabilize with time and the value to which they stabilize is shown to be related to the asymptotic rate of inbreeding and therefore also the effective population size, Ne approximately 2N/(mu 2r + sigma 2r), where N is the number of individuals per generation and mu r and sigma 2r are the mean and variance of long-term relationships or long-term contributions. These stabilized values are then predicted using a recursive equation via the concept of selective advantage for populations with hierarchical mating structures undergoing mass selection. Account is taken of the change in genetic parameters as a consequence of selection and also the increasing 'competitiveness' of contemporaries as selection proceeds. Examples are given and predicted rates of inbreeding are compared to those calculated in simulations. For populations of 20 males and 20, 40, 100 or 200 females the rate of inbreeding was found to increase by as much as 75% over the rate of inbreeding in an unselected population depending on mating ratio, selection intensity and heritability of the selected trait. The prediction presented here estimated the rate of inbreeding usually within 5% of that calculated from simulation.     

Evolution in plant populations as a driver of ecological changes in arthropod communities

Heritable variation in traits can have wide-ranging impacts on species interactions, but the effects that ongoing evolution has on the temporal ecological dynamics of communities are not well understood. Here, we identify three conditions that, if experimentally satisfied, support the hypothesis that evolution by natural selection can drive ecological changes in communities. These conditions are: (i) a focal population exhibits genetic variation in a trait(s), (ii) there is measurable directional selection on the trait(s), and (iii) the trait(s) under selection affects variation in a community variable(s). When these conditions are met, we expect evolution by natural selection to cause ecological changes in the community. We tested these conditions in a field experiment examining the interactions between a native plant (Oenothera biennis) and its associated arthropod community (more than 90 spp.). Oenothera biennis exhibited genetic variation in several plant traits and there was directional selection on plant biomass, life-history strategy (annual versus biennial reproduction) and herbivore resistance. Genetically based variation in biomass and life-history strategy consistently affected the abundance of common arthropod species, total arthropod abundance and arthropod species richness. Using two modelling approaches, we show that evolution by natural selection in large O. biennis populations is predicted to cause changes in the abundance of individual arthropod species, increases in the total abundance of arthropods and a decline in the number of arthropod species. In small O. biennis populations, genetic drift is predicted to swamp out the effects of selection, making the evolution of plant populations unpredictable. In short, evolution by natural selection can play an important role in affecting the dynamics of communities, but these effects depend on several ecological factors. The framework presented here is general and can be applied to other systems to examine the community-level effects of ongoing evolution.     

Predicting rates of inbreeding in populations undergoing selection

Tractable forms of predicting rates of inbreeding (DeltaF) in selected populations with general indices, nonrandom mating, and overlapping generations were developed, with the principal results assuming a period of equilibrium in the selection process. An existing theorem concerning the relationship between squared long-term genetic contributions and rates of inbreeding was extended to nonrandom mating and to overlapping generations. DeltaF was shown to be approximately (1)/(4)(1 - omega) times the expected sum of squared lifetime contributions, where omega is the deviation from Hardy-Weinberg proportions. This relationship cannot be used for prediction since it is based upon observed quantities. Therefore, the relationship was further developed to express DeltaF in terms of expected long-term contributions that are conditional on a set of selective advantages that relate the selection processes in two consecutive generations and are predictable quantities. With random mating, if selected family sizes are assumed to be independent Poisson variables then the expected long-term contribution could be substituted for the observed, providing (1)/(4) (since omega = 0) was increased to (1)/(2). Established theory was used to provide a correction term to account for deviations from the Poisson assumptions. The equations were successfully applied, using simple linear models, to the problem of predicting DeltaF with sib indices in discrete generations since previously published solutions had proved complex.     

Quantifying inbreeding in natural populations of hermaphroditic organisms

We review molecular methods for estimating selfing rates and inbreeding in populations. Two main approaches are available: the population structure approach (PSA) and progeny-array approach (PAA). The PSA approach relies on single-generation samples and produces estimates that integrate the inbreeding history over several generations, but is based on strong assumptions (for example, inbreeding equilibrium). The PSA has classically relied on single-locus inbreeding coefficients averaged over loci. Unfortunately PSA estimates are very sensitive to technical problems such as the occurrence of null alleles at one or more of the loci. Consequently inbreeding might be substantially overestimated, especially in outbred populations. However, the robustness of the PSA has recently been greatly improved by the development of multilocus methods free of such bias. The PAA, on the other hand, is based on the comparison between offspring and mother genotypes. As a consequence, PAA estimates do not reflect long-term inbreeding history but only recent mating events of the maternal individuals studied ('here and now' selfing). In addition to selfing rates, the PAA allows estimating other mating system parameters, including biparental inbreeding and the correlation of selfing among sibs. Although PAA estimates could also be biased by technical problems, incompatibilities between the mother's genotype and her offspring allow the identification and correction of such bias. For all methods, we provide guidelines on the required number of loci and sample sizes. We conclude that the PSA and PAA are equally robust, provided multilocus information is used. Although experimental constraints may make the PAA more demanding, especially in animals, the two methods provide complementary information, and can fruitfully be conducted together.     

Exact inbreeding coefficients in populations with overlapping generations

A theory is given that allows inbreeding coefficients to be calculated exactly for populations with overlapping generations. Emphasis is placed on providing equations well suited for computer iteration. Both monoecious and dioecious populations are considered and family size is not restricted to being Poisson. One-locus and two-locus inbreeding coefficients are evaluated, although the reader may omit the two-locus sections. The exact treatment is shown to be preferable to approximate treatments in that it applies to both early and late generations for all populations sizes. Inbreeding effective numbers found by the exact treatment are compared to various approximate numbers, and the approximate values are found to be generally very good.     

Methods for predicting rates of inbreeding in selected populations

Summary In selected populations, families superior for the selected trait are likely to contribute more offspring to the next generation than inferior families and, as a consequence, the rate of inbreeding is likely to be higher in selected populations than in randomly mated populations of the same structure. Methods to predict rates of inbreeding in selected populations are discussed. The method of Burrows based on probabilities of coselection is reappraised in conjunction with the transition matrix method of Woolliams. The method of Latter based on variances and covariances of family size is also examined. These methods are one-generation approaches in the sense that they only account for selective advantage over a single generation, from parents to offspring. Two-generation methods are developed that account for selective advantage over two generations, from grandparent to grandoffspring as well as from parent to offspring. Predictions are compared to results from simulation. The best one-generation method was found to underpredict rates of inbreeding by 10–25%, and the two-generation methods were found to underpredict rates of inbreeding by 9–18%.     

Evidence of inbreeding depression but not inbreeding avoidance in a natural house sparrow population

Inbreeding is common in small and threatened populations and often has a negative effect on individual fitness and genetic diversity. Thus, inbreeding can be an important factor affecting the persistence of small populations. In this study, we investigated the effects of inbreeding on fitness in a small, wild population of house sparrows (Passer domesticus) on the island of Aldra, Norway. The population was founded in 1998 by four individuals (one female and three males). After the founder event, the adult population rapidly increased to about 30 individuals in 2001. At the same time, the mean inbreeding coefficient among adults increased from 0 to 0.04 by 2001 and thereafter fluctuated between 0.06 and 0.10, indicating a highly inbred population. We found a negative effect of inbreeding on lifetime reproductive success, which seemed to be mainly due to an effect of inbreeding on annual reproductive success. This resulted in selection against inbred females. However, the negative effect of inbreeding was less strong in males, suggesting that selection against inbred individuals is at least partly sex specific. To examine whether individuals avoided breeding with close relatives, we compared observed inbreeding and kinship coefficients in the population with those obtained from simulations of random mating. We found no significant differences between the two, indicating weak or absent inbreeding avoidance. We conclude that there was inbreeding depression in our population. Despite this, birds did not seem to actively avoid mating with close relatives, perhaps as a consequence of constraints on mating possibilities in such a small population.     

Quantifying realized inbreeding in wild and captive animal populations

Most molecular measures of inbreeding do not measure inbreeding at the scale that is most relevant for understanding inbreeding depression—namely the proportion of the genome that is identical-by-descent (IBD). The inbreeding coefficient F_Ped obtained from pedigrees is a valuable estimator of IBD, but pedigrees are not always available, and cannot capture inbreeding loops that reach back in time further than the pedigree. We here propose a molecular approach to quantify the realized proportion of the genome that is IBD (propIBD), and we apply this method to a wild and a captive population of zebra finches (Taeniopygia guttata). In each of 948 wild and 1057 captive individuals we analyzed available single-nucleotide polymorphism (SNP) data (260 SNPs) spread over four different genomic regions in each population. This allowed us to determine whether any of these four regions was completely homozygous within an individual, which indicates IBD with high confidence. In the highly nomadic wild population, we did not find a single case of IBD, implying that inbreeding must be extremely rare (propIBD=0–0.00094, 95% CI). In the captive population, a five-generation pedigree strongly underestimated the average amount of realized inbreeding (F_Ped=0.013<propIBD=0.064), as expected given that pedigree founders were already related. We suggest that this SNP-based technique is generally useful for quantifying inbreeding at the individual or population level, and we show analytically that it can capture inbreeding loops that reach back up to a few hundred generations.     

Evolution of inbreeding coefficients and effective size in the population of Saguenay Lac-St.-Jean (Quebec)

We computed mean inbreeding coefficients (FIT, FIS, and FST) based on approximately 2,700 ascending pedigrees of contemporary people from Saguenay Lac-St-Jean (Québec, Canada). This allowed us to appreciate the accumulated inbreeding and to follow the evolution of these coefficients since the founding of Québec. One of the results was the expected increase in FST. Relying on this parameter, we computed the effective size (Ne) of the contemporary population, obtaining a value around 1,000, in agreement with previous estimations. We noticed a decrease of Ne through history despite the population's growing size.