Kin selection is implicated in partial sib-mating populations with constant viability differences before mating

The change in the frequency of a rare mutant allele under constant sex-differentiated viability selection in an infinite, partial full-sib mating population is studied. The diplo-diploid and haplo-diploid polygynous models are considered with a Poisson distribution for the number of offspring produced by every mated female. Reproduction is followed by weak selection among the offspring and then mating to form the next generation. It is shown that the rate of change with respect to the frequency of the mutant allele and the intensity of selection can be expressed in terms of costs or benefits of substituting the mutant type for the wild type, which correspond to average excesses in viability in females and males, multiplied by coefficients of relatedness to the individuals affected by such a substitution and reproductive values associated to the sexes of these individuals. This reveals hidden interactions between mated individuals and between males for mating, the former having positive effects on the reproductive success of related individuals and the latter having negative effects. Such interactions are the result of reproductive constraints when a fixed proportion of females must mate with a male sib and all females are fertilized as long as one mate is available. However, they affect the change in allele frequency because there is inbreeding or relatedness between mates and more generally relatedness between interacting individuals. Surprisingly, the effects of these interactions cancel out in a diploid population when the number of offspring is large enough so that the possibility for a female to have no male sib to mate with can be neglected and the viability differences are the same in both sexes.     

Selection, subdivision and extinction and recolonization

In a subdivided population, the interaction between natural selection and stochastic change in allele frequency is affected by the occurrence of local extinction and subsequent recolonization. The relative importance of selection can be diminished by this additional source of stochastic change in allele frequency. Results are presented for subdivided populations with extinction and recolonization where there is more than one founding allele after extinction, where these may tend to come from the same source deme, where the number of founding alleles is variable or the founders make unequal contributions, and where there is dominance for fitness or local frequency dependence. The behavior of a selected allele in a subdivided population is in all these situations approximately the same as that of an allele with different selection parameters in an unstructured population with a different size. The magnitude of the quantity N(e)s(e), which determines fixation probability in the case of genic selection, is always decreased by extinction and recolonization, so that deleterious alleles are more likely to fix and advantageous alleles less likely to do so. The importance of dominance or frequency dependence is also altered by extinction and recolonization. Computer simulations confirm that the theoretical predictions of both fixation probabilities and mean times to fixation are good approximations.     

Separation of time scales, fixation probabilities and convergence to evolutionary stable states under isolation by distance

To a first order of approximation, selection is frequency independent in a wide range of family structured models and in populations following an island model of dispersal, provided the number of families or demes is large and the population is haploid or diploid but allelic effects on phenotype are semidominant. This result underlies the way the evolutionary stability of traits is computed in games with continuous strategy sets. In this paper similar results are derived under isolation by distance. The first-order effect on expected change in allele frequency is given in terms of a measure of local genetic diversity, and of measures of genetic structure which are almost independent of allele frequency in the total population when the number of demes is large. Hence, when the number of demes increases the response to selection becomes of constant sign. This result holds because the relevant neutral measures of population structure converge to equilibrium at a rate faster than the rate of allele frequency changes in the total population. In the same conditions and in the absence of demographic fluctuations, the results also provide a simple way to compute the fixation probability of mutants affecting various ecological traits, such as sex ratio, dispersal, life-history, or cooperation, under isolation by distance. This result is illustrated and tested against simulations for mutants affecting the dispersal probability under a stepping-stone model.     

Separation of time scales, fixation probabilities and convergence to evolutionarily stable states under isolation by distance

To a first order of approximation, selection is frequency independent in a wide range of family structured models and in populations following an island model of dispersal, provided the number of families or demes is large and the population is haploid or diploid but allelic effects on phenotype are semidominant. This result underlies the way the evolutionary stability of traits is computed in games with continuous strategy sets. In this paper similar results are derived under isolation by distance. The first-order effect on expected change in allele frequency is given in terms of a measure of local genetic diversity, and of measures of genetic structure which are almost independent of allele frequency in the total population when the number of demes is large. Hence, when the number of demes increases the response to selection becomes of constant sign. This result holds because the relevant neutral measures of population structure converge to equilibrium at a rate faster than the rate of allele frequency changes in the total population. In the same conditions and in the absence of demographic fluctuations, the results also provide a simple way to compute the fixation probability of mutants affecting various ecological traits, such as sex ratio, dispersal, life-history, or cooperation, under isolation by distance. This result is illustrated and tested against simulations for mutants affecting the dispersal probability under a stepping-stone model.     

Usefulness of molecular markers for detecting population bottlenecks via monitoring genetic change

It is important to detect population bottlenecks in threatened and managed species because bottlenecks can increase the risk of population extinction. Early detection is critical and can be facilitated by statistically powerful monitoring programs for detecting bottleneck-induced genetic change. We used Monte Carlo computer simulations to evaluate the power of the following tests for detecting genetic changes caused by a severe reduction in a population's effective size ( N _e): a test for loss of heterozygosity, two tests for loss of alleles, two tests for change in the distribution of allele frequencies, and a test for small N _e based on variance in allele frequencies (the 'variance test'). The variance test was most powerful; it provided an 85% probability of detecting a bottleneck of size N _e = 10 when monitoring five microsatellite loci and sampling 30 individuals both before and one generation after the bottleneck. The variance test was almost 10-times more powerful than a commonly used test for loss of heterozygosity, and it allowed for detection of bottlenecks before 5% of a population's heterozygosity had been lost. The second most powerful tests were generally the tests for loss of alleles. However, these tests had reduced power for detecting genetic bottlenecks caused by skewed sex ratios. We provide guidelines for the number of loci and individuals needed to achieve high-power tests when monitoring via the variance test. We also illustrate how the variance test performs when monitoring loci that have widely different allele frequency distributions as observed in five wild populations of mountain sheep ( Ovis canadensis ).     

"Runaway" social evolution: reinforcing selection for inbreeding and altruism.

Kin selection theory predicts that altruistic behaviors, those that decrease the fitness of the individual performing the behavior but increase the fitness of the recipient, can increase in frequency if the individuals interacting are closely related. Several studies have shown that inbreeding therefore generally increases the effectiveness of kin selection when fitnesses are linear, additive functions of the number of altruists in the family, although with extreme forms of altruism, inbreeding can actually retard the evolution of altruism. These models assume that a constant proportion of the population mates at random and a constant proportion practices some form of inbreeding. In order to investigate the effect of inbreeding on the evolution of altruistic behavior when the mating structure is allowed to evolve, we examined a two-locus model by computer simulation of a diploid case and illustrated the important qualitative features by mathematical analysis of a haploid case. One locus determines an individual's propensity to perform altruistic social behavior and the second locus determines the probability that an individual will mate within its sibship. We assumed positive selection for altruism and no direct selection at the inbreeding locus. We observed that the altruistic allele and the inbreeding allele become positively associated, even when the initial conditions of the model assume independence between these loci. This linkage disequilibrium becomes established, because the altruistic allele increases more rapidly in the inbreeding segment of the population. This association subsequently results in indirect selection on the inbreeding locus. However, the dynamics of this model go beyond a simple "hitch-hiking" effect, because high levels of altruism lead to increased inbreeding, and high degrees of inbreeding accelerate the rate of change of the altruistic allele in the entire population. Thus, the dynamics of this model are similar to those of "runaway" sexual selection, with gene frequency change at the two loci interactively causing rapid evolutionary change.     

On the Theory of Partially Inbreeding Finite Populations. III. Fixation Probabilities under Partial Selfing When Heterozygotes Are Intermediate in Viability

In a previous paper by the senior author, an approximation to the probability of survival was given for a mutant, which is originally present in a single heterozygote, in a population that reproduces partly by selfing and partly by random mating. The population was assumed to be very large, but the result obtained is general with regard to the level of dominance in viability. In this paper two errors which were made in that earlier work are corrected. A general approximate expression is then derived for the probability that an allele A is fixed in a partially self fertilizing population of size N, if its initial frequency is p, selection is weak and heterozygotes with the allele are exactly intermediate in viability compared with genotypes AA and AA. A rigorous proof is given for a special case that is a generalization of the classical binomial sampling model. In this case, but not in general, the approximate fixation probability is independent of the probability of reproduction by selfing. Some implications are discussed.     

Allele age and a test for selection on rare alleles

An approximate expression for the probability distribution of the age of a neutral allele as a function of its frequency is derived for a population undergoing arbitrary changes in population size. A simple maximum-likelihood estimator of allele age based on frequency is also obtained. The distribution of allele age, combined with a model predicting the extent of intra-allelic variability generated by mutation and recombination, leads to a statistical test of whether a rare allele has experienced natural selection. The test is based on finding whether there is too little or too much intra-allelic variability to be consistent with the observed frequency. The test is applied to the locus, BRCA1, associated with early-onset breast cancer in humans and shows that two common disease-associated alleles (5382insC and 185delAG) appear to have been subject to natural selection.     

Steroid 21-hydroxylase (P450c21): a new allele and spread of mutations through the pseudogene

Lesions in the gene encoding the adrenal enzyme steroid 21-hydroxylase (P450c21) result in defective adrenal cortisol synthesis, often accompanied by aldosterone deficiency. The symptoms range from severe neonatal disease to inconspicuous symptoms in adulthood depending on the nature of the mutations. The 21-hydroxylase gene is present in close proximity to a highly homologous pseudogene, and both genes show variation in copy number between individuals. For complete DNA sequence characterization, we have applied selective polymerase chain reaction amplification and direct sequencing of all full-length steroid 21-hydroxylase genes present in individuals. Using healthy individuals with only one remaining steroid 21-hydroxylase allele as normal references, a new allele was found in two siblings, in whom clinical and laboratory findings demonstrated moderate enzyme deficiency. Full-length sequencing of this allele displayed an Arg 484 to Pro codon change in exon 10, in the same position as a previously identified GG to C mutation found in a patient with severe 21 -hydroxylase deficiency. Arg 484 is located within a stretch of amino acids that are highly conserved between mammalian 21-hydroxylases. The finding of the presently reported 21-hydroxylase allele indicates that the GG to C mutation from the severely affected patient has arisen by a two-step mechanism, consisting of a G to C transversion accompanied by an adjacent G deletion. When sequencing 26 pseudogenes, both these mutations, which are not present in the pseudogenes hitherto reported, were found at low frequency together with a number of other polymorphisms. Thus, also rare mutations can spread via the pseudogene and can therefore be expected to arise independently in unrelated individuals.     

Allele frequencies for candidate genes in atherosclerosis and diabetes among Trinidadian neonates

Trinidadians of South Asian origin have a high prevalence of cardiovascular disease and diabetes compared to Trinidadians of African origin. The degree to which these differences are related to genetic and/or environmental factors is unclear. To determine whether there might be a genetic basis for this difference in prevalence of deleterious phenotypes we examined allele frequencies for candidate genes in atherosclerosis and diabetes. We genotyped 81 consecutive neonates of African origin and 103 consecutive neonates of South Asian origin. We evaluated common polymorphisms in 11 candidate genes for atherosclerosis and diabetes. We found differences between the two subpopulations in the allele frequencies of several candidate genes, including APOE, LIPC, APOC3, PON1, PON2, and PPP1R3. However, the differences in the allele frequencies were not all consistent with the pattern of CHD expression between these two ethnic groups in adulthood. Thus, differences in genetic architecture alone may not explain the wide disparities in disease prevalence between these two subpopulations. It is very likely that environmental factors, or unmeasured genetic factors, influence the genetic susceptibility to disease in these subpopulations.     

Selection and drift in subdivided populations: a straightforward method for deriving diffusion approximations and applications involving dominance, selfing and local extinctions

Population structure affects the relative influence of selection and drift on the change in allele frequencies. Several models have been proposed recently, using diffusion approximations to calculate fixation probabilities, fixation times, and equilibrium properties of subdivided populations. We propose here a simple method to construct diffusion approximations in structured populations; it relies on general expressions for the expectation and variance in allele frequency change over one generation, in terms of partial derivatives of a "fitness function" and probabilities of genetic identity evaluated in a neutral model. In the limit of a very large number of demes, these probabilities can be expressed as functions of average allele frequencies in the metapopulation, provided that coalescence occurs on two different timescales, which is the case in the island model. We then use the method to derive expressions for the probability of fixation of new mutations, as a function of their dominance coefficient, the rate of partial selfing, and the rate of deme extinction. We obtain more precise approximations than those derived by recent work, in particular (but not only) when deme sizes are small. Comparisons with simulations show that the method gives good results as long as migration is stronger than selection.     

True pedigree errors more frequent than apparent errors for single nucleotide polymorphisms

Single nucleotide polymorphisms (SNPs) are currently being developed for use in disequilibrium analyses. These SNPs consist of two alleles with varying degrees of polymorphism. A natural design for use with SNPs is the 'haplotype relative risk' sampling design in which a father, mother, and child are typed at an SNP locus. Given such a trio of genotypes, we ask: what is the probability that a pedigree error (a change from one allele to the other) at an SNP locus will be detected using only Mendel's laws as a check? We calculate the probability of detecting such errors for a hypothetical SNP locus with varying degrees of polymorphism and for various true error rates. For the sets of allele frequencies considered, we find that the detection rates range between 25 and 30%, the detection rate being lowest when the two alleles have equal frequencies and the highest when one allele has a frequency of 10%. Based on this detection rate, we determine that the true error rate is roughly 3.3-4 times that of the apparent error rate at an SNP locus. The greatest discrepancy between true and apparent error rates occurs when allele frequencies are equal.     

Fixation probability and time in subdivided populations

New alleles arising in a population by mutation ultimately are either fixed or lost. Either is possible, for both beneficial and deleterious alleles, because of stochastic changes in allele frequency due to genetic drift. Spatially structured populations differ from unstructured populations in the probability of fixation and the time that this fixation takes. Previous results have generally made many assumptions: that all demes contribute to the next generation in exact proportion to their current sizes, that new mutations are beneficial, and that new alleles have additive effects. In this article these assumptions are relaxed, allowing for an arbitrary distribution among demes of reproductive success, both beneficial and deleterious effects, and arbitrary dominance. The effects of population structure can be expressed with two summary statistics: the effective population size and a variant of Wright's F(ST). In general, the probability of fixation is strongly affected by population structure, as is the expected time to fixation or loss. Population structure changes the effective size of the species, often strongly downward; smaller effective size increases the probability of fixing deleterious alleles and decreases the probability of fixing beneficial alleles. On the other hand, population structure causes an increase in the homozygosity of alleles, which increases the probability of fixing beneficial alleles but somewhat decreases the probability of fixing deleterious alleles. The probability of fixing new beneficial alleles can be simply described by 2hs(1 - F(ST))N(e)/N(tot), where hs is the change in fitness of heterozygotes relative to the ancestral homozygote, F(ST) is a weighted version of Wright's measure of population subdivision, and N(e) and N(tot) are the effective and census sizes, respectively. These results are verified by simulation for a broad range of population structures, including the island model, the stepping-stone model, and a model with extinction and recolonization.     

Decompositions of Price’s formula in an inhomogeneous population structure

The central tool for the study of allele frequency change due to selection is the remarkably simple but powerful formula of Price [Nature 227 (1970) 520] . Here, I provide what might be called a structural analysis of this formula. The formula essentially accumulates the average allele frequency change over many instances of a fitness‐determining interaction, but there are different ways of organizing this average and these lead to quite different computational algorithms. I present three of these: an analysis by population state, an analysis by recipient and an analysis by actor. A comparison of these can lead to a heightened understanding of the different factors behind selective allele frequency change. In particular, I pay attention to the effects of structural inhomogeneity on reproductive value (RV) and emphasize that Price’s formula measures RV‐weighted allele frequency change. I examine in detail a simple example as a crucial way of cementing the different theoretical pathways. My aim was to produce a simple transparent presentation and therefore I work with a simple population structure and have omitted a number of technical details that are found elsewhere.     

Effective testing of gene-disease associations.

We propose a method for testing any hypothesized association between a candidate allele, for which there is a specific laboratory test, and a common chronic disease. Families in which this allele is segregating are identified through index individuals who are homozygous or heterozygous for the allele. The sample consists of the subset of identified families who also have at least one member with the common disease of interest. For each independent family in this subset, select one person with the disease and determine if he or she is heterozygous for the allele. The observed proportion of heterozygotes in this sample is compared to the proportion expected on the basis of each diseased relative's null probability of being heterozygous for the allele; this null probability depends only on the relative's relationship to the index individual and the population allele frequency. We provide these null probabilities, develop appropriate inference procedures, discuss sample size requirements, and compare this method to a standard case-control design. Results using this method are unlikely to be influenced by confounders, systematic bias, or genetic heterogeneity.     

Gene Replacement by Zinc Finger Nucleases in Medaka Embryos

Gene replacement (GR) via homologous recombination is a powerful tool for genome editing. Recently, direct GR is achieved successfully by coinjection of mRNAs for engineered endonucleases such as zinc finger nucleases (ZFNs) and donor DNA in developing embryos of diverse organisms. Here, we report the procedures and efficiency for direct GR by using ZFNs in the fish medaka. Upon zygotic coinjection of mRNAs encoding ZFNs that target the gonad-specifically expressed gsdf locus, linear DNA of GR vector pGRgsdf containing the red fluorescent protein (rfp) gene flanked by two homology arms of ~1-kb each underwent GR via homologous recombination. Specifically, 15 of 231 adults from manipulated embryos contained a GR allele in the caudal fin, producing an efficiency of ~7 % for somatic GR. Progeny test revealed that two out of nine fertile fish containing the GR allele in the fin were capable of transmitting the GR allele to ~6 % of F₁ generation at adulthood, generating an efficiency of ~22 % for germline transmission. Sequencing and Southern blotting validated precise GR. We show that the GR allele expressed a chimeric gsdf:rfp RNA between gsdf and cointegrated rfp specifically in the gonad, demonstrating recapitulation of endogenous RNA expression as predicted for the defined GR allele. Most importantly, RFP expression coincides faithfully with the gonad-specific gsdf expression in developing embryos and adults. These results demonstrate, for the first time, the feasibility and efficiency of ZFN-mediated precise GR directly in the developing embryo of medaka as a lower vertebrate model.     

Neofunctionalization of duplicated genes under the pressure of gene conversion

Neofunctionalization occurs when a neofunctionalized allele is fixed in one of duplicated genes. This is a simple fixation process if duplicated genes accumulate mutations independently. However, the process is very complicated when duplicated genes undergo concerted evolution by gene conversion. Our simulations demonstrate that the process could be described with three distinct stages. First, a newly arisen neofunctionalized allele increases in frequency by selection, but gene conversion prevents its complete fixation. These two factors (selection and gene conversion) that work in opposite directions create an equilibrium, and the time during which the frequency of the neofunctionalized allele drifts around the equilibrium value is called the temporal equilibrium stage. During this temporal equilibrium stage, it is possible that gene conversion is inactivated by mutations, which allow the complete fixation of the neofunctionalized allele. And then, permanent neofunctionalization is achieved. This article develops basic population genetics theories on the process to permanent neofunctionalization under the pressure of gene conversion. We obtain the probability and time that the frequency of a newly arisen neofunctionalized allele reaches the equilibrium value. It is also found that during the temporal equilibrium stage, selection exhibits strong signature in the divergence in the DNA sequences between the duplicated genes. The spatial distribution of the divergence likely has a peak around the site targeted by selection. We provide an analytical expression of the pattern of divergence and apply it to the human red- and green-opsin genes. The theoretical prediction well fits the data when we assume that selection is operating for the two amino acid differences in exon 5, which are believed to account for the major part of the functional difference between the red and green opsins.     

Estimates of natural selection due to protein tertiary structure inform the ancestry of biallelic loci

We consider the inference of which of two alleles is ancestral when the alleles have a single nonsynonymous difference and when natural selection acts via protein tertiary structure. Whereas the probability that an allele is ancestral under neutrality is equal to its frequency, under selection this probability depends on allele frequency and on the magnitude and direction of selection pressure. Although allele frequencies can be well estimated from intraspecific data, small fitness differences have a large evolutionary impact but can be difficult to estimate with only intraspecific data. Methods for predicting aspects of phenotype from genotype can supplement intraspecific sequence data. Recently developed statistical techniques can assess effects of phenotypes, such as protein tertiary structure on molecular evolution. While these techniques were initially designed for comparing protein-coding genes from different species, the resulting interspecific inferences can be assigned population genetic interpretations to assess the effect of selection pressure, and we use them here along with intraspecific allele frequency data to estimate the probability that an allele is ancestral. We focus on 140 nonsynonymous single nucleotide polymorphisms of humans that are in proteins with known tertiary structures. We find that our technique for employing protein tertiary structure information yields some biologically plausible results but that it does not substantially improve the inference of ancestral human allele types.     

Inclusive fitness models with two sexes

Much recent work has focused on the transition from G. R. Price's (1970, Nature 227, 520-521) formula for allele frequency change to an inclusive fitness condition for the selective advantage of a certain behaviour. In case there is any kind of asymmetry between the sexes, the analysis must keep track of the two sexes separately, and this leads to a number of different forms of the expression for inclusive fitness. In this paper I gather these forms together and note the assumptions needed to make each valid. I also show how inclusive fitness should be formulated when the behaviour of the actor is controlled by another individual. I illustrate the inclusive fitness approach with a sex allocation example in a haplodiploid population with a local breeding structure.