Sex-specific meiotic drive and selection at an imprinted locus

We present a one-locus model that breaks two symmetries of Mendelian genetics. Whereas symmetry of transmission is breached by allowing sex-specific segregation distortion, symmetry of expression is breached by allowing genomic imprinting. Simple conditions for the existence of at least one polymorphic stable equilibrium are provided. In general, population mean fitness is not maximized at polymorphic equilibria. However, mean fitness at a polymorphic equilibrium with segregation distortion may be higher than mean fitness at the corresponding equilibrium with Mendelian segregation if one (or both) of the heterozygote classes has higher fitness than both homozygote classes. In this case, mean fitness is maximized by complete, but opposite, drive in the two sexes. We undertook an extensive numerical analysis of the parameter space, finding, for the first time in this class of models, parameter sets yielding two stable polymorphic equilibria. Multiple equilibria exist both with and without genomic imprinting, although they occurred in a greater proportion of parameter sets with genomic imprinting.     

Son preference among Filipino Muslims: A causal analysis

Abstract

A social selection model for deleterious genes has been studied by considering two alleles at one locus. The model allows for the fitness of an individual to be determined by parental phenotypes as well as by his/her own phenotype. We show that the equilibrium gene frequency depends on the loss of fitness of an individual due to the trait (γ) and due to affected parents (P), and the probability that the heterozygote develops the trait (h). We show that whenever an interior equilibrium point exists for given values of γ and β, it is unique and that the sufficient condition for the existence of the equilibrium point is given by     

Host mating system and the prevalence of disease in a plant population

A modified susceptible-infected-recovered (SIR) host-pathogen model is used to determine the influence of plant mating system on the outcome of a host-pathogen interaction. Unlike previous models describing how interactions between mating system and pathogen infection affect individual fitness, this model considers the potential consequences of varying mating systems on the prevalence of resistance alleles and disease within the population. If a single allele for disease resistance is sufficient to confer complete resistance in an individual and if both homozygote and heterozygote resistant individuals have the same mean birth and death rates, then, for any parameter set, the selfing rate does not affect the proportions of resistant, susceptible or infected individuals at equilibrium. If homozygote and heterozygote individual birth rates differ, however, the mating system can make a difference in these proportions. In that case, depending on other parameters, increased selfing can either increase or decrease the rate of infection in the population. Results from this model also predict higher frequencies of resistance alleles in predominantly selfing compared to predominantly outcrossing populations for most model conditions. In populations that have higher selfing rates, the resistance alleles are concentrated in homozygotes, whereas in more outcrossing populations, there are more resistant heterozygotes.     

The multiple-locus symmetric fertility model

Selection due to variation in the fecundity among matings of genotypes with respect to many loci each with two alleles is studied. The fitness of a mating depends only on the genotypic distinction between homozygote and heterozygote at each locus in the two individuals, and differences among loci are allowed. This symmetric fertility model is therefore a generalization of the multiple-locus symmetric viability model. The phenomena seen in the two-locus symmetric fertility model generalize—e.g., the possibility of joint stability of equilibria with linkage equilibrium and with linkage disequilibrium, and the existence of different types of totally polymorphic equilibria with the gametic proportions in linkage equilibrium. The central equilibrium with genotypic frequencies in Hardy-Weinberg proportions and gametic frequencies in Robbins proportions exists for all symmetric fertility models. For some symmetric fertility regimes additional equilibria exist with gametic frequencies in linkage equilibrium and with genotypic frequencies in Hardy-Weinberg proportions at all except one locus. These equilibria may exist in the dioecious symmetric viability model, and then they will be locally stable. For free recombination the stable equilibria show linkage equilibrium, but several of these with different numbers of polymorphic loci may be stable simultaneously.     

GENETIC COVARIANCE OF FITNESS CORRELATES: WHAT GENETIC CORRELATIONS ARE MADE OF AND WHY IT MATTERS

The genetic variance-covariance matrix, G, is determined in part by functional architecture, the pathways by which variation in genotype influences phenotype. I develop a simple architectural model for G for two traits under directional selection constrained by their dependence on a common limiting resource. I assume that genetic variance is maintained by mutation-selection balance. The relative numbers of loci that play a role in acquiring versus allocating a limiting resource play a crucial role in determining genetic covariance. If many loci are involved in acquiring a resource, genetic covariance may be either negative or positive at equilibrium, depending on the fitness function and the input of mutational variance. The form of G does not necessarily reveal the constraint on resource acquisition inherent in the system, and therefore studies estimating G do not test for the existence of life-history tradeoffs. Characters may evolve in patterns that are unpredictable from G. Experiments are suggested that would indicate if this model could explain observations of positive genetic covariance.     

用超显性模型估计遗传多态平衡的种群参数

基于超显性模型,采用数学方法阐述了种群遗传多样性的延续机制及平衡条件,从双等位基因导出的定律有较大的局限性,在许多教科书中常用的估计平衡态基因频数的定律只适用于双等位基因,本文用另一种方法导出一些公式,将其扩展到多等位基因,讨论了种群中基因数ｎ,遗传负载荷（Ｌ）,杂合频ＹＸ（Ｈｅ）和纯合频率（Ｈｏｍ）之间的关系。     

Genetic Variation in a Heterogeneous Environment. II. Temporal Heterogeneity and Directional Selection

The maintenance of genetic variation is investigated in a finite population where selection at an autosomal locus with two alleles varies temporally between two environments and the heterozygote has an intermediate fitness value. When there is additive gene action and equal selection in both environments, the autocorrelation between subsequent environments must be negative for more maintenance of genetic variation than for neutrality. The maximum maintenance occurs when there is equal selection in the two environments and the autocorrelation approaches ^-1.0 (for a stochastic model), or when there is short repeating cycle such as one related to seasons. Also comparison of the effects of stochastic variation in selection in finite and infinite populations is made by using Monte Carlo simulation. One situation was found where temporal environmental variation maintains genetic variation very effectively even in a small population and that is when there is evolution of dominance, i.e., the heterozygote is closer in fitness to the favored homozygote than the other homozygote. An important conclusion is that in a finite population genetic tracing of environmental change, particularly when there is a positive autocorrelation between environments or a long environmental cycle, leads to an increased loss of genetic variation making such a response undesirable in the long term, a result different from that in infinite populations.     

Measuring fitness by means of balancer chromosomes

We present the theoretical background to a new method for measuring genetic variation for total fitness in Drosophila. The method allows heterozygous effects on total fitness of whole wild-type chromosomes to be measured under normal demography with overlapping generations. The wild-type chromosomes are competed against two balancer chromosomes (B1, B2, say), providing a standard genotype B1/B2 against which variation in the fitness effects of the wild-type chromosomes can be assessed. Fitness can be assessed in two ways: (i) at equilibrium of all three chromosomes under heterozygote advantage, and (ii) during displacement of one balancer by the other. Equilibrium with all three chromosomes present will be achieved only if the wild-type homozygote is not too fit, and if the fitnesses of the three heterozygotes are not too unequal. These conditions were not satisfied for any of a sample of 12 lethal-bearing chromosomes isolated from a random-bred laboratory population of Drosophila. At equilibrium, genotypic frequencies show low sensitivity to changes in genotypic fitness. Furthermore, where all four genotypes are viable and fertile, supplementary information from cages with only two chromosomes present and from direct measurements of pre-adult viability are required to estimate fitnesses from frequencies. The invasion method has the advantages of a greater sensitivity and of not requiring further data to estimate fitnesses if the wild-type homozygote is fertile. However, it requires that multiple samples be taken as the invasion progresses. In a discrete generation model, generation time influences fitness estimates from this method and is difficult to estimate accurately from the data. A full age-structured model can also be applied to the data from both types of experiment. For the invasion method, this gives fitness estimates close to those from the discrete generation model.     

Epistasis in the multiple locus symmetric viability model

The n-locus two-allele symmetric viability model is considered in terms of the parameters measuring the additive epistasis in fitness. The dynamics is analysed using a simple linear transformation of the gametic frequencies, and then the recurrence equations depend on the epistatic parameters and Geiringer's recombination distribution only. The model exhibits an equilibrium, the central equilibrium, where the 2 ⁿ gametes are equally frequent. The transformation simplifies the stability analysis of the central point, and provides the stability conditions in terms of the existence conditions of other equilibria. For total negative epistasis (all epistatic parameters are negative) the central point is stable for all recombination distributions. For free recombination either a central point (segregating one, two, ... or n loci) or the n-locus fixation states are stable. For no recombination and some epistatic parameters positive the central point is unstable and several boundary equilibria may be locally stable. The sign structure of the additive epistasis is therefore an important determinant of the dynamics of the n-locus symmetric viability model. The non-symmetric multiple locus models previously analysed are dynamically related, and they all have an epistatic sign structure that resembles that of the multiplicative viability model. A non-symmetric model with total negative epistasis which share dynamical properties with the similar symmetric model is suggested.Supported in part by NIH grant GM 28016, and by grant 81-5458 from the Danish Natural Science Research Council     

A fundamental relationship between genotype frequencies and fitnesses

The set of possible postselection genotype frequencies in an infinite, randomly mating population is found. Geometric mean heterozygote frequency divided by geometric mean homozygote frequency equals two times the geometric mean heterozygote fitness divided by geometric mean homozygote fitness. The ratio of genotype frequencies provides a measure of genetic variation that is independent of allele frequencies. When this ratio does not equal two, either selection or population structure is present. Within-population HapMap data show population-specific patterns, while pooled data show an excess of homozygotes.     

Genetic Variation in Heterogeneous Environments

A model of population structure in heterogeneous environments is described and conditions sufficient for maintaining a polymorphism are derived.

The absolute fitness of any genotype is regarded as a function of location in the niche space and the population density at that location. Two modes of habitat selection are examined: (1) organisms are distributed uniformly over the environment; and (2) each organism selects to occupy that habitat in which it is most fit ("optimal habitant selection").—Sufficient conditions for maintenance of genetic polymorphisms are derived for both models. In populations which do not practice habitat selection heterozygote superiority averaged over the environment is sufficient to guarantee the existence of polymorphisms. Comparable conditions for populations which practice optimal habitat selection are much less restrictive. If the heterozygotes are superior to one homozygote in any one part of the niche and to the other homozygote in any other part of the niche then a polymorphism will be defined.—A positive correlation between genetic and environmental variation follows from the model with habitat selection, but not from the other. The adaptive significance of polymorphisms thus depends on how animals behave.

     

Association between HLA-Cw*0602 polymorphism and psoriasis risk: a meta-analysis

Numerous studies have evaluated the association between human leukocyte antigen (HLA) Cw*0602 polymorphism and psoriasis risk. However, the results have been inconsistent. We made a meta-analysis of the association between HLA-Cw*0602 polymorphism and psoriasis risk. Eighteen studies were retrieved, reporting a total of 3419 psoriasis patients and 3297 healthy controls. The associations between HLA-Cw*0602 polymorphism and psoriasis risk were estimated by pooled odds ratio (OR) and 95% confidence interval (95%CI). We found significant associations between HLA-Cw*0602 polymorphism and psoriasis risk in the comparisons of positive versus negative alleles (OR = 4.55, 95%CI = 3.65-5.67, P < 0.00001); positive homozygote versus negative homozygote combined with heterozygote (OR = 14.00, 95%CI = 8.47-23.15, P < 0.00001); positive homozygote combined with heterozygote versus negative homozygote (OR = 5.11, 95%CI = 3.86-6.76, P < 0.00001); positive homozygote versus negative homozygote (OR = 23.03, 95%CI = 13.95-38.00, P < 0.00001), and positive homozygote versus heterozygote (OR = 4.21, 95%CI = 2.35- 7.00, P < 0.00001). In conclusion, the positive allele of HLA-Cw*0602 polymorphism appears to be a risk factor for psoriasis.     

The dynamics of two-species allelopathic competition with optimal harvesting

This paper analyses a bionomic model of two competitive species in the presence of toxicity with different harvesting efforts. An interesting dynamics in the first quadrant is analysed and two saddle-node bifurcations are detected for different bifurcation parameters. It is noted that under certain parametric restrictions, the model has a unique positive equilibrium point that is globally asymptotically stable whenever it is locally stable. It is also noted that the model can have zero, one or two feasible equilibria appearing through saddle-node bifurcations. The non-existence of a limit cycle in the interior of the first quadrant is also discussed using the Poincare–Dulac criteria. The saddle-node bifurcations are studied using Sotomayor's theorem. Numerical simulations are carried out to validate the analytical findings. The conditions for the existence of bionomic equilibria are discussed and an optimal harvesting policy is derived using Pontryagin's maximum principle.     

THE FITNESS CONSEQUENCES OF MULTIPLE-LOCUS HETEROZYGOSITY: THE RELATIONSHIP BETWEEN HETEROZYGOSITY AND GROWTH RATE IN PITCH PINE (PINUS RIGIDA MILL.)

Positive correlations between measures of “fitness” and the number of electrophoretic loci for which an individual is heterozygous have been observed in many species. Two major hypotheses have been proposed to explain this phenomenon: inbreeding depression and overdominance. Until recently, there has been no way to distinguish between these hypotheses. The overdominance model devised by Smouse (1986) is used here in a reanalysis of Ledig et al.‘s (1983) study of heterozygosity and growth rate in eight populations of pitch pine and is contrasted with an inbreeding-depression analysis. Ledig et al. (1983) regressed mean growth rate per heterozygosity class on the number of heterozygous loci, a method of analysis which, although it points to general trends in the data, does not differentiate between hypotheses. The correlations they obtained in four populations were significant only because regressing on the means eliminates most of the sum of squares for error and does not weight the unequally sized heterozygosity classes. Reanalysis of Ledig et al.‘s data using individuals, not means, showed no significant correlations between heterozygosity and fitness. A major assumption of Smouse's overdominance model is that genetic polymorphism is in part a reflection of selection for heterozygotes at genetic equlibrium. The homozygote for the most frequent allele at a locus should be more fit than a homozygote for a less frequent allele, with the heterozygote superior to both homozygotes. Smouse's model predicts a negative, linear relationship between fitness and “adaptive distance,” a variable that for a heterozygote is zero and for homozygotes is equal to the inverse of the frequency of the corresponding allele. The adaptive-distance model accounted for between 15% and 50% of the variation in growth rate within eight P. rigida population samples by accounting for genotypic differences at eight polymorphic loci. This is over twice as much of the variation in growth rate accounted for by Ledig et al.'s (1983) analysis using individuals. Significant correlations were found between adaptive distance and growth rate in four of the eight populations, but in only two of the populations were more of the partial coefficients negative than positive, as would be predicted by the overdominance hypothesis. The remaining two populations in which correlations were significant did not lend themselves to such clear-cut interpretation, as the majority of the partial coefficients were positive. Positive partial coefficients indicate that the growth rate of the heterozygote is inferior to that of at least one of the homozygotes. The adaptive-distance analysis provides evidence that specific genotypes do play a role in determining growth rate in pitch pine. The correlation between growth rate and adaptive distance increased significantly with the age of the population, possibly reflecting competition subsequent to crown closure.     

The dynamics of two-species allelopathic competition with optimal harvesting

This paper analyses a bionomic model of two competitive species in the presence of toxicity with different harvesting efforts. An interesting dynamics in the first quadrant is analysed and two saddle-node bifurcations are detected for different bifurcation parameters. It is noted that under certain parametric restrictions, the model has a unique positive equilibrium point that is globally asymptotically stable whenever it is locally stable. It is also noted that the model can have zero, one or two feasible equilibria appearing through saddle-node bifurcations. The non-existence of a limit cycle in the interior of the first quadrant is also discussed using the Poincare-Dulac criteria. The saddle-node bifurcations are studied using Sotomayor's theorem. Numerical simulations are carried out to validate the analytical findings. The conditions for the existence of bionomic equilibria are discussed and an optimal harvesting policy is derived using Pontryagin's maximum principle.     

Stable Equilibria at Two Loci in Populations with Large Selfing Rates

The equilibrium structure of two-locus, two-allele models with very large selfing rates is found using perturbation techniques. For free recombination, r = 1/2, the following results hold. If the heterozygotes do not have at least an approximate 30% advantage in fitness relative to homozygotes, a stable equilibrium with all alleles present is possible only if all of the homozygote fitnesses differ at most by approximately the outcrossing rate, t, and all stable polymorphic equilibria have disequilibrium values, D, that are at most on the order of the outcrossing rate. Once the heterozygote fitnesses are above the threshold, there are stable equilibria possible with D near its maximum possible value. The results show that the observed disequilibria in highly selfed plant populations are not likely to result from selection leading to an equilibrium.     

The significance of over- and underdominance for the maintenance of genetic polymorphisms. I. Underdominance and stability

It is pointed out that the standard selection models in population genetics all require some form of heterozygote advantage in fitness in order to guarantee the maintenance or stability of genetic polymorphisms. Even more recent results demonstrating the existence of stable two-locus polymorphisms with marginal underdominance at both loci are based on certain epistatically acting heterosis assumptions. This raises the question as to whether heterozygote advantage in fitness is indeed a generally valid principle of maintaining polymorphisms. To avoid ambiguity in definition of heterozygote advantage (overdominance) as it appears in multiallele or multilocus systems, a one-locus-two-allele model is considered. This model allows for sexually asymmetric selection and random mating. It is shown that the model produces globally stable polymorphisms exhibiting underdominance in fitness for a considerable and biologically reasonable range of selection values. Having thus properly refuted the general validity of the common overdominance principle, a modified version is suggested which covers the classical viability selection model and its extension to arbitrary, sexually asymmetric viability and fertility selection. This modified overdominance principle is based on the notion of fractional fitnesses and relates protectedness of biallelic polymorphisms to the extent to which each genotype reproduces its own type. The fact that the model treated displays frequency dependent fitnesses which may change in ranking while approaching equilibrium is discussed in relation to problems of the evolution of overdominance and underdominance.     

Heterosis as an explanation for large amounts of genic polymorphism

By using both numerical and analytical approaches, we have shown that heterosis alone is not a mechanism for maintaining many alleles segregating at a locus. Even when all heterozygous are more fit than all homozygotes, the proportion of fitness arrays that will lead to a stable, feasible equilibrium of more than 6 or 7 alleles is vanishingly small. More alleles can be maintained if, in addition to heterosis, it is assumed that there is very little variation in fitness from heterozygote to heterozygote, with the ratio of mean heterosis to standard deviation of fitness among heterozygotes in the neighborhood of 10. When such conditions hold, the allelic frequency distribution and equilibrium will be very uniform, with all alleles very close to equal frequency (see PDF). It is much more likely that stable equilibria for multiple alleles will be best explained by multiple niche selection.     

Uniqueness of polymorphic equilibria under soft selection

Any two allele polymorphic equilibrium of a subdivided haploid population subject to soft selection is stable. This provides that for a two allele system in a subdivided haploid population there is a globally attracting equilibrium which is polymorphic if a polymorphic equilibrium exists, otherwise monomorphic. These results extend to diploid populations if within each habitat the heterozygote viability is greater than or equal to the geometric mean of the homozygote viabilities.     

Behavioural analysis of two prey-two predator model

To deal with real-life diversity of our ecosystem, this paper analyzes two prey-two predator model including both Type-I and Type-II functional responses. The interior equilibrium point of the proposed model is calculated; and behaviour of the model around that point is studied. Local stability at an interior equilibrium point is discussed; and possibility of Hopf-bifurcation with probable direction is studied. A generalized form of the Poincaré-Bendixon criterion is applied to establish the sufficient conditions for global stability of the proposed model surrounding at an interior equilibrium point. Numerical simulations are also conducted in support of our work. Conclusions of our findings and some probable future directions are also included at the end.