The genealogy of sequences containing multiple sites subject to strong selection in a subdivided population

A stochastic model for the genealogy of a sample of recombining sequences containing one or more sites subject to selection in a subdivided population is described. Selection is incorporated by dividing the population into allelic classes and then conditioning on the past sizes of these classes. The past allele frequencies at the selected sites are thus treated as parameters rather than as random variables. The purpose of the model is not to investigate the dynamics of selection, but to investigate effects of linkage to the selected sites on the genealogy of the surrounding chromosomal region. This approach is useful for modeling strong selection, when it is natural to parameterize the past allele frequencies at the selected sites. Several models of strong balancing selection are used as examples, and the effects on the pattern of neutral polymorphism in the chromosomal region are discussed. We focus in particular on the statistical power to detect balancing selection when it is present.     

Selective structure of the gene pool. IV. Estimation from the selection intensity index Rs

A new approach for investigating the selective structure of the gene pool reflecting the type and intensity of selection is proposed. Selection pressure is estimated on the basis of interpopulation gene diversity with the use of the selection intensity index: RS(i) = NeS(i) = 1/4(1/FST(i)-1/Fe). Distributions of RS(i) in gene pools of indigenous populations from all continents and five subregions of the northeastern Eurasia were examined. It was shown that, of all theoretical distributions, only beta-distributions provide a good approximation of RS(i) estimates. Based on the confidence intervals of RS obtained from beta-distributions, genes can be grouped into the three following classes according to their selective structure: LOWER DIFF, NEUTRAL, and SUPER DIFF. These classes, respectively, include genes subjected mainly to stabilizing selection (RS(i) > 0; LOWER DIFF), genes subjected mainly to differentiating selection (RS(i) < 0; SUPER DIFF), and arbitrarily selectively neutral genes (RS(i) approximately 0; NEUTRAL). Simulation of gene pool sampling (10(6) samples from 50 markers for each gene pool) allowed us to characterize the selective structure by determining markers that fall into the same selective class irrespective of the variant for the sampling process. The selective structure of gene pools from six continents (Europe, Asia, Africa, Australia, America, and southeastern Eurasia) and five subregions of northeastern Eurasia was characterized. It was shown that approximately one-third of genes is subjected to selection irrespective of the hierarchical level of the region. In gene pools of Europe, northeastern Eurasia, and European and Ural subregions, the proportion of genes under stabilizing selection was higher, the proportion of selectively neutral genes, lower. Debatable issues of tests for selective neutrality based on heterogeneity of interpopulation gene diversity are considered. These issues include the effect on FST of the hierarchical population structure, sample size, number of subpopulations, and other factors that shift estimates of gene selective values.     

G'ST and D do not replace FST

The genetic differentiation among populations is affected by mutation as well as by migration, drift and selection. For loci with high mutation rates, such as microsatellites, the amount of mutation can influence the values of indices of differentiation such as G(ST) and F(ST). For many purposes, this effect is undesirable, and as a result, new indices such as G'(ST) and D have been proposed to measure population differentiation. This paper shows that these new indices are not effective measures of the causes or consequences of population structure. Both G'(ST) and D depend heavily on mutation rate, but both are insensitive to any population genetic process when the mutation rate is high relative to the migration rate. Furthermore, D is specific to the locus being measured, and so little can be inferred about the population demography from D. However, at equilibrium, D may provide an index of whether a particular marker is more strongly affected by mutation than by migration. I argue that F(ST) is a more important summary of the effects of population structure than D and that R(ST) or other measures that explicitly account for the mutation process are much better than G(ST), G'(ST), or D for highly mutable markers. Markers with lower mutation rates will often be easier to interpret.     

Natural Selection and Age-Structured Populations

This paper studies the properties of a new class of demographic parameters for age-structured populations and analyzes the effect of natural selection on these parameters. Two new demographic variables are introduced: the entropy of a population and the reproductive potential. The entropy of a population measures the variability of the contribution of the different age classes to the stationary population. The reproductive potential measures the mean of the contribution of the different age classes to the Malthusian parameter. The Malthusian parameter is precisely the difference between the entropy and the reproductive potential. The effect of these demographic variables on changes in gene frequency is discussed. The concept of entropy of a genotype is introduced and it is shown that in a random mating population in Hardy-Weinberg equilibrium and under slow selection, the rate of change of entropy is equal to the genetic variance in entropy minus the covariance in entropy and reproductive potential. This result is an information theoretic analog of Fisher''s fundamental theorem of natural selection.     

The effect of selection on genealogies

The coalescent process can describe the effects of selection at linked loci only if selection is so strong that genotype frequencies evolve deterministically. Here, we develop methods proposed by Kaplan, Darden, and Hudson to find the effects of weak selection. We show that the overall effect is given by an extension to Price's equation: the change in properties such as moments of coalescence times is equal to the covariance between those properties and the fitness of the sample of genes. The distribution of coalescence times differs substantially between allelic classes, even in the absence of selection. However, the average coalescence time between randomly chosen genes is insensitive to the current allele frequency and is affected significantly by purifying selection only if deleterious mutations are common and selection is strong (i.e., the product of population size and selection coefficient, Ns>3). Balancing selection increases mean coalescence times, but the effect becomes large only when mutation rates between allelic classes are low and when selection is extremely strong. Our analysis supports previous simulations that show that selection has surprisingly little effect on genealogies. Moreover, small fluctuations in allele frequency due to random drift can greatly reduce any such effects. This will make it difficult to detect the action of selection from neutral variation alone.     

A multi-dimensional coalescent process applied to multi-allelic selection models and migration models

For a sample of two genes from a population divided into an arbitrary number of allele classes, a general mathematical framework is developed to address the expectation and variance of the time of the most recent common ancestor. Depending on the meaning of allele classes and the manner in which genes can change among them, this framework can be applied to a diversity of population genetic models. By adoption of the infinite sites model, the effect on heterozygosity is modelled for balancing selection among allele classes, mutation between allele classes, migration among populations, and gene conversion between loci. Most results are described for a continuous time approximation to a discrete generation model. It is also shown how the discrete generation model can be used to study the hitch-hiking effect of favorable mutations.     

Maximum likelihood and Bayesian methods for estimating the distribution of selective effects among classes of mutations using DNA polymorphism data

Maximum likelihood and Bayesian approaches are presented for analyzing hierarchical statistical models of natural selection operating on DNA polymorphism within a panmictic population. For analyzing Bayesian models, we present Markov chain Monte-Carlo (MCMC) methods for sampling from the joint posterior distribution of parameters. For frequentist analysis, an Expectation-Maximization (EM) algorithm is presented for finding the maximum likelihood estimate of the genome wide mean and variance in selection intensity among classes of mutations. The framework presented here provides an ideal setting for modeling mutations dispersed through the genome and, in particular, for the analysis of how natural selection operates on different classes of single nucleotide polymorphisms (SNPs).     

Evolution of a plastic quantitative trait in an age-structured population in a fluctuating environment

We analyze weak fluctuating selection on a quantitative character in an age-structured population not subject to density regulation. We assume that early in the first year of life before selection, during a critical state of development, environments exert a plastic effect on the phenotype, which remains constant throughout the life of an individual. Age-specific selection on the character affects survival and fecundity, which have intermediate optima subject to temporal environmental fluctuations with directional selection in some age classes as special cases. Weighting individuals by their reproductive value, as suggested by Fisher, we show that the expected response per year in the weighted mean character has the same form as for models with no age structure. Environmental stochasticity generates stochastic fluctuations in the weighted mean character following a first-order autoregressive model with a temporally autocorrelated noise term and stationary variance depending on the amount of phenotypic plasticity. The parameters of the process are simple weighted averages of parameters used to describe age-specific survival and fecundity. The "age-specific selective weights" are related to the stable distribution of reproductive values among age classes. This allows partitioning of the change in the weighted mean character into age-specific components.     

Relationships among recent models for insect population dynamics with variable rates of development

A classification scheme for those population models which allow variation in development rates is proposed, based on two ways of modifying standard age-structured models. The resulting classes of models are termed development index models and sojourn time models. General formulations for the two classes of models are developed from two basic balance equations, and numerous specific models from the literature are shown to fit into the scheme. Concepts from competing risks theory are shown to be important in understanding the interplay between mortality and maturation. Relationships among the classes are investigated both for the most general forms of the models and for the simpler forms often used. The scheme can provide guidance in developing appropriate insect population models for specific modelling situations.Contribution 3878871     

Predicted accuracy of and response to genomic selection for new traits in dairy cattle

Genomic selection relaxes the requirement of traditional selection tools to have phenotypic measurements on close relatives of all selection candidates. This opens up possibilities to select for traits that are difficult or expensive to measure. The objectives of this paper were to predict accuracy of and response to genomic selection for a new trait, considering that only a cow reference population of moderate size was available for the new trait, and that selection simultaneously targeted an index and this new trait. Accuracy for and response to selection were deterministically evaluated for three different breeding goals. Single trait selection for the new trait based only on a limited cow reference population of up to 10 000 cows, showed that maximum genetic responses of 0.20 and 0.28 genetic standard deviation (s.d.) per year can be achieved for traits with a heritability of 0.05 and 0.30, respectively. Adding information from the index based on a reference population of 5000 bulls, and assuming a genetic correlation of 0.5, increased genetic response for both heritability levels by up to 0.14 genetic s.d. per year. The scenario with simultaneous selection for the new trait and the index, yielded a substantially lower response for the new trait, especially when the genetic correlation with the index was negative. Despite the lower response for the index, whenever the new trait had considerable economic value, including the cow reference population considerably improved the genetic response for the new trait. For scenarios with a zero or negative genetic correlation with the index and equal economic value for the index and the new trait, a reference population of 2000 cows increased genetic response for the new trait with at least 0.10 and 0.20 genetic s.d. per year, for heritability levels of 0.05 and 0.30, respectively. We conclude that for new traits with a very small or positive genetic correlation with the index, and a high positive economic value, considerable genetic response can already be achieved based on a cow reference population with only 2000 records, even when the reliability of individual genomic breeding values is much lower than currently accepted in dairy cattle breeding programs. New traits may generally have a negative genetic correlation with the index and a small positive economic value. For such new traits, cow reference populations of at least 10 000 cows may be required to achieve acceptable levels of genetic response for the new trait and for the whole breeding goal.     

长期指数选择的遗传效果分析—计算机模拟研究

本文利用Monte Carlo模拟技术研究比较了普通选择指数、实际选择指数、约束指数和单性状选择四种方法的长期选择效果及对群体遗传结构的影响。50世代的结果表明:群体大小和遗传参数能明显影响长期指数选择的反应;实际指数选择是有效的,其总体效果好于普通指数;约束选择的早期反应虽低于普通指数,但后期效果好,而且对群体遗传结构影响较小。同时,指数选择使性状加性遗传方差和遗传力衰减变化,而遗传相关依指数公式的系数呈定向改变。建议多性状长期选择时应用实际指数法或约束指数法。     

Gene frequency patterns in the levene subdivided population model

In the context of a multideme population structure subject to selection, migration, and mating forces, it is desired to ascertain the stable evolutionary outcomes for various classes of selection regimes. These include selection patterns as (i) a mosaic of local directed selection effects, (ii) overdominance throughout with varying intensities of the local heterozygote advantage, (iii) varying degrees of underdominance throughout, (iv) a mixed underdominant-overdominant regime. An accounting of the nature of the equilibrium configurations in the Levene population subdivision model was done with respect to the above classes of selection regimes. In particular, it is established that multiple polymorphic equilibria do not arise for selection structures (i) and (ii), while for the mixed underdominant-overdominant selection form (iv) with appropriate parameter ranges there can exist two stable internal equilibria. A surprising finding is that the number and/or character of the equilibria is not changed by increased population division beyond that of two habitats, while there is a significant difference in the equilibrium possibilities for a one- as against a two-deme population. These results appear to be a special limiting feature of the Levene population subdivision formulation.     

Prediction of genetic contributions and generation intervals in populations with overlapping generations under selection

A method to predict long-term genetic contributions of ancestors to future generations is studied in detail for a population with overlapping generations under mass or sib index selection. An existing method provides insight into the mechanisms determining the flow of genes through selected populations, and takes account of selection by modeling the long-term genetic contribution as a linear regression on breeding value. Total genetic contributions of age classes are modeled using a modified gene flow approach and long-term predictions are obtained assuming equilibrium genetic parameters. Generation interval was defined as the time in which genetic contributions sum to unity, which is equal to the turnover time of genes. Accurate predictions of long-term genetic contributions of individual animals, as well as total contributions of age classes were obtained. Due to selection, offspring of young parents had an above-average breeding value. Long-term genetic contributions of youngest age classes were therefore higher than expected from the age class distribution of parents, and generation interval was shorter than the average age of parents at birth of their offspring. Due to an increased selective advantage of offspring of young parents, generation interval decreased with increasing heritability and selection intensity. The method was compared to conventional gene flow and showed more accurate predictions of long-term genetic contributions.     

Habitat selection reduces extinction of populations subject to Allee effects

Theoretical studies indicate that a single population under an Allee effect will decline to extinction if reduced below a particular threshold, but the existence of multiple local populations connected by random dispersal improves persistence of the global population. An additional process that can facilitate persistence is the existence of habitat selection by dispersers. Using analytic and simulation models of population change, I found that when habitat patches exhibiting Allee effects are connected by dispersing individuals, habitat selection by these dispersers increases the likelihood that patches persist at high densities, relative to results expected by random settlement. Populations exhibiting habitat selection also attain equilibrium more quickly than randomly dispersing populations. These effects are particularly important when Allee effects are large and more than two patches exist. Integrating habitat selection into population dynamics may help address why some studies have failed to find extinction thresholds in populations, despite well-known Allee effects in many species.     

Genetic steady-state under BLUP selection for an infinite and homogeneous population with discrete generations

A matrix derivation is proposed to analytically calculate the asymptotic genetic variance-covariance matrix under BLUP selection according to the initial genetic parameters in a large population with discrete generations. The asymptotic genetic evolution of a homogeneous population with discrete generations is calculated for a selection operating on an index including all information (pedigree and records) from a non-inbred and unselected base population (BLUP selection) or on an index restricted to records of a few ancestral generations. Under the first hypothesis, the prediction error variance of the selection index is independent of selection and is calculated from the genetic parameters of the base population. Under the second hypothesis, the prediction error variance depends on selection. Furthermore, records of several generations of ancestors of the candidates for selection must be used to maintain a constant prediction error variance over time. The number of ancestral generations needed depends on the population structure and on the occurrence of fixed effects. Without fixed effects to estimate, accounting for two generations of ancestors is sufficient to estimate the asymptotic prediction error variance. The amassing of information from an unselected base population proves to be important in order not to overestimate the asymptotic genetic gains and not to underestimate the asymptotic genetic variances.     

The origin of ancestral bacterial metabolism

A model for metabolism of the last bacterial common ancestor based on biomimetic analysis of the metabolic systems of phylogenetically ancient bacteria is developed. The mechanism of natural selection and evolution of the autocatalytic chemical systems under the effect of natural homeostatic parameters, such as chemical potentials, temperature, and pressure of environment is proposed. Competition between particular parts of the autocatalytic network with positive-plus-negative feedback resulted in the formation of particular systems of primary autotrophic, mixotrophic, and heterotrophic metabolism. The model of the last common ancestor as a combination of coupled metabolic cycles among population of protocells is discussed. Physicochemical features of these metabolic cycles determined the major principles of natural selection towards ancestral bacterial taxa.     

Genetic improvement of production while maintaining fitness

Selection for production tends to decrease fitness, in particular, major components such as reproductive performance. Under an infinitesimal genetic model restricted index selection can maintain reproductive performance while improving production. However, reproductive traits are thought to be controlled by a finite number of recessive alleles at low frequency. Culling for low reproduction may weed out the negative homozygous genotypes for reproduction in any generation, thus controlling the frequencies of alleles negative for reproduction. Restricted index selection, culling for low reproduction and a new method called empirical restricted index selection were compared for their efficiency in improving production while maintaining reproduction. Empirical restricted index selection selects animals that have on average the highest estimated breeding values for production and on average the same estimated breeding values for reproduction as the base population. An infinitesimal genetic model and models with a finite number of loci for reproduction with rare deleterious recessive alleles, which have additive, dominant or no pleiotropic effects on production, were considered. When reproduction was controlled by a finite number of loci with rare recessive alleles, restricted index selection could not maintain reproduction. The culling of 20% of the animals on reproduction maintained reproduction with all genetic models, except for the model where loci for reproduction had additive effects on production. Empirical restricted selection maintained reproduction with all models and yielded higher production responses than culling on reproduction, except when there were dominant pleiotropic effects on production.     

A representative model of the hierarchic structure of human populations]

The paper deals with the concept of a hierarchy population. The population is hierarchial, if it can be divided into a certain amount of subpopulations in such a way that the set may naturally break into classes (levels). A migration may exist from each sub-population or into a higher one. Such population structures are frequently encountered among the human populations. It is shown that in a hierarchial population a selection is more efficient than in a non-subdivided one. In this respect the role of small populations in evolution is suggested. It was possible to demonstrate that in a hierarchial population there was a higher degree of polymorphism, a higher velocity of the evolutional process, that in a non-subdivided population of the same size. Besides, the level of polymorphism in the hierarchial population increases monotomously with the growth of the amount of generations during rather a long period of time.     

Relaxed selection when you least expect it: why declining bird populations might fail to respond to phenological mismatches

Ongoing climate change threatens to cause mismatches between the phenology of many organisms and their resources. Populations of migratory birds may need to undergo ‘evolutionary rescue’ if resource availability moves to earlier dates in the year, as shifted arrival dates at the breeding grounds may be required for persistence under new environmental schedules. Here we show a counterintuitive process that can reduce the strength of selection for early arrival when the resource peaks earlier. This happens when two processes combine to determine selection for early arrival: breeding success is higher if a bird does not miss the resource peak, but this occurs together with a ‘zero‐sum game’ where birds acquire good territories ahead of their competitors if they arrive early. The latter process can relax if the population has experienced a recent decline. Therefore, climate change can have two opposing effects: its direct effect on breeding success strengthens selection for early arrival, but this combines with an indirect effect of relaxed selection due to population declines, if territoriality is a significant determinant of population dynamics and fitness. We show that the latter process can predominate, and this can cause a failure for a population to adapt to a new schedule under changing environmental conditions.