Recombination can evolve in large finite populations given selection on sufficient loci

It is well known that an allele causing increased recombination is expected to proliferate as a result of genetic drift in a finite population undergoing selection, without requiring other mechanisms. This is supported by recent simulations apparently demonstrating that, in small populations, drift is more important than epistasis in increasing recombination, with this effect disappearing in larger finite populations. However, recent experimental evidence finds a greater advantage for recombination in larger populations. These results are reconciled by demonstrating through simulation without epistasis that for m loci recombination has an appreciable selective advantage over a range of population sizes (am, bm). bm increases steadily with m while am remains fairly static. Thus, however large the finite population, if selection acts on sufficiently many loci, an allele that increases recombination is selected for. We show that as selection acts on our finite population, recombination increases the variance in expected log fitness, causing indirect selection on a recombination-modifying locus. This effect is enhanced in those populations with more loci because the variance in phenotypic fitnesses in relation to the possible range will be smaller. Thus fixation of a particular haplotype is less likely to occur, increasing the advantage of recombination.     

Optimization of selection contribution and mate allocations in monoecious tree breeding populations

Background

The combination of optimized contribution dynamic selection and various mating schemes was investigated over seven generations for a typical tree breeding scenario. The allocation of mates was optimized using a simulated annealing algorithm for various object functions including random mating (RM), positive assortative mating (PAM) and minimization of pair-wise coancestry between mates (MCM) all combined with minimization of variance in family size and coancestry. The present study considered two levels of heritability (0.05 and 0.25), two restrictions on relatedness (group coancestry; 1 and 2%) and two maximum permissible numbers of crosses in each generation (100 and 400). The infinitesimal genetic model was used to simulate the genetic architecture of the trait that was the subject of selection. A framework of the long term genetic contribution of ancestors was used to examine the impacts of the mating schemes on population parameters.

Results

MCM schemes produced on average, an increased rate of genetic gain in the breeding population, although the difference between schemes was small but significant after seven generations (up to 7.1% more than obtained with RM). In addition, MCM reduced the level of inbreeding by as much as 37% compared with RM, although the rate of inbreeding was similar after three generations of selection. PAM schemes yielded levels of genetic gain similar to those produced by RM, but the increase in the level of inbreeding was substantial (up to 43%).

Conclusion

The main reason why MCM schemes yielded higher genetic gains was the improvement in managing the long term genetic contribution of founders in the population; this was achieved by connecting unrelated families. In addition, the accumulation of inbreeding was reduced by MCM schemes since the variance in long term genetic contributions of founders was smaller than in the other schemes. Consequently, by combining an MCM scheme with an algorithm that optimizes contributions of the selected individuals, a higher long term response is obtained while reducing the risk within the breeding program.     

Disequilibrium distribution of genotypes in the pairs of isozyme loci in the pine populations of the forest-steppe regions of Siberia

We performed an analysis of linkage disequilibrium of alleles of 15 allozyme loci in 35 populations of Scots pine in the Siberian part of the range between 50° and 56° N and 79° and 107° E. We found a significant deviation in the distribution of genotypes of 1–9 pairs of loci in the investigated samples. We established correlations between frequencies of certain pairs of linked loci with ecological conditions and geographical coordinates of habitats of the pine populations. We present the results of comparative analysis of the differences in certain morphological features of trees with significantly predominant genotypes for pairs of linked loci in three isolated populations: in the south of Krasnoyarsk krai, Khakassia, and Tuva.     

Lethals in finite populations

It has been assumed, based on theoretical studies, that lethals with the level of dominance estimated from experimental studies would have an allele frequency that is virtually independent of effective population size. However, here it is shown numerically that the expected frequency of lethals with low levels of dominance is also dependent on finite population size, although not as much as completely recessive lethals. This finding is significant in determining the standing level of inbreeding depression and the consequent potential for the evolution of self-fertilization. In addition, the architecture of genetic variation influencing inbreeding depression in populations with a history of small size may be of important consequence in endangered species. Finally, it is shown that the loss of lethal genetic variation often occurs much more quickly than the regeneration of lethal variation by mutation. This asymmetry may result in a lower standing genetic variation for inbreeding depression than expected from mutation rates and contemporary population size data.     

Genotype dynamics in populations with breeding pairs

A new model of pair fecundity is proposed for populations with breeding pairs. The model is based upon the assumption of strong predominance of male gamete production over female. Corresponding equations for genotype dynamics are derived. It is established that the usual equation for allele frequency dynamics in panmictic populations cannot be applied to the considered system. In spite of accidental pair formation and accidental gametic fusion within each pair, gamete panmixia of the population as a whole is violated and gene dynamics should be described by means of genotype frequencies. The condition of reduction to the “classical” dynamics is achieved.     

Dynamics of finite populations

Summary A time-homogeneous stochastic process was used to derive exact expressions for the ultimate probability of fixation or loss and the expected time to fixation or loss of an allele in a haploid population whose size is a Poisson random variable. The treatment included selection and multiple alleles.Contribution no. 165 Department of Statistics, Kansas Agricultural Experiment Station, Manhattan, Kansas 66502.     

On selection in finite populations

Journal of Mathematical Biology - Two major forces shaping evolution are drift and selection. The standard models of neutral drift—the Wright–Fisher (WF) and Moran processes—can...     

Language dynamics in finite populations

Any mechanism of language acquisition can only learn a restricted set of grammars. The human brain contains a mechanism for language acquisition which can learn a restricted set of grammars. The theory of this restricted set is universal grammar (UG). UG has to be sufficiently specific to induce linguistic coherence in a population. This phenomenon is known as "coherence threshold". Previously, we have calculated the coherence threshold for deterministic dynamics and infinitely large populations. Here, we extend the framework to stochastic processes and finite populations. If there is selection for communicative function (selective language dynamics), then the analytic results for infinite populations are excellent approximations for finite populations; as expected, finite populations need a slightly higher accuracy of language acquisition to maintain coherence. If there is no selection for communicative function (neutral language dynamics), then linguistic coherence is only possible for finite populations.     

Linkage disequilibria in finite populations

Four-locus recombination frequencies are summarized into two-locus pair frequencies and three-locus frequencies, and further, into two-locus frequencies such that higher-order frequencies are linear functions of lower-order frequencies. Frequencies of gene combinations are defined according to their position on the same or distinct gametes, and linear functions of these provide the measures of linkage disequilibria. These concepts are utilized to derive the transitional behavior of the gene combinations frequencies and the linkage disequilibria in a finite monoecious population with random union of gametes for up to four loci. The transitions of lower-order disequilibria in a higher-order (more loci) setting involve the higher-order disequilibria which must be taken into account in arriving at the final (fixation) frequencies. The methods allow different initial conditions. Since corresponding data functions of the gene combination frequencies provide unbiased estimates of the parameters, estimators follow naturally.     

Mapping quantitative trait loci in tetraploid populations

Knowledge of quantitative trait locus (QTL) mapping in polyploids is almost void, albeit many exquisite strategies of QTL mapping have been proposed and extensive investigations have been carried out in diploid animals and plants. In this paper we develop a simple algorithm which uses an iteratively reweighted least square method to map QTLs in tetraploid populations. The method uses information from all markers in a linkage group to infer the probability distribution of QTL genotype under the assumption of random chromosome segregation. Unlike QTL mapping in diploid species, here we estimate and test the compound 'gametic effect', which consists of the composite 'genic effect' of alleles and higher-order gene interactions. The validity and efficiency of the proposed method are investigated through simulation studies. Results show that the method can successfully locate QTLs and separates different sources (e.g. additive and dominance) of variance components contributed by the QTLs.     

ESS-theory for finite populations

On the basis of some principles from the philosophy of science, the inadequacy of the ESS-theory as introduced by Maynard Smith and Price as a biological theory is discussed, and an improved ESS-theory for finite populations is presented which can adopt the ideas of the original formalism, although modified. Resulting are explicit conditions on the population sizes that ensure certain strategies to be evolutionarily stable.     

Evolutionary game dynamics in finite populations

We introduce a model of stochastic evolutionary game dynamics in finite populations which is similar to the familiar replicator dynamics for infinite populations. Our focus is on the conditions for selection favoring the invasion and/or fixation of new phenotypes. For infinite populations, there are three generic selection scenarios describing evolutionary game dynamics among two strategies. For finite populations, there are eight selection scenarios. For a fixed payoff matrix a number of these scenarios can occur for different population sizes. We discuss several examples with unexpected behavior.     

Multistage index selection in finite populations

Multistage selection with fixed proportions and selection indices based on covariates of the target variable is studied. Assuming a multivariate normal distribution before the selection, expressions are presented for the expectation and the variance of the target variable in the retained subpopulation. As the numerical evaluation for finite populations requires lengthy computations, some approximations using methods for infinite populations are proposed. Numerical illustrations are given for selections in up to three stages.     

Fitness-dependent mutation rates in finite populations

Mutation rate may be condition dependent, whereby individuals in poor condition, perhaps from high mutation load, have higher mutation rates than individuals in good condition. Agrawal (J. Evol. Biol.15, 2002, 1004) explored the basic properties of fitness-dependent mutation rate (FDMR) in infinite populations and reported some heuristic results for finite populations. The key parameter governing how infinite populations evolve under FDMR is the curvature (k) of the relationship between fitness and mutation rate. We extend Agrawal's analysis to finite populations and consider dominance and epistasis. In finite populations, the probability of long-term existence depends on k. In sexual populations, positive curvature leads to low equilibrium mutation rate, whereas negative curvature results in high mutation rate. In asexual populations, negative curvature results in rapid extinction via 'mutational meltdown', whereas positive curvature sometimes allows persistence. We speculate that fitness-dependent mutation rate may provide the conditions for genetic architecture to diverge between sexual and asexual taxa.     

Epigenetic heterogeneity at imprinted loci in normal populations

Genomic imprinting is the phenomenon by which the two alleles of certain genes are differentially expressed according to their parental origin. Extensive analysis of allelic expression at multiple imprinted loci in a normal population has not performed so far. In the present study, we examined the allelic expression pattern of three imprinted genes in a panel of 262 Japanese normal individuals. We observed differences in the extent of maintenance of allele-specific expression of the three genes. The allelic expression of small nuclear ribonucleoprotein N (SNRPN) was stringently regulated while that of multimembrane-spanning polyspecific transporter-like gene 1 (IMPT1) showed a large degree of variation. Significant biallelic expression of insulin-like growth factor II (IGF2) was observed in about 10% of normal individuals. Our findings add to the accumulating evidence for variable allelic expression at multiple loci in a normal human population. This epigenetic heterogeneity can be a stable trait and potentially influence individual phenotypes.