Should Individual Fitness Increase with Heterozygosity?

Natural selection influences not only gamete frequencies in populations but also the multilocus fitness structures associated with segregating gametes. In particular, only certain patterns of multilocus fitnesses are consistent with the maintenance of stable multilocus polymorphisms. This paper offers support for the proposition that, at stable, viability-maintained, multilocus polymorphisms, the fitness of a genotype tends to increase with the number of heterozygous loci it contains. Average fitness always increases with heterozygosity at stable product equilibria (i.e., those without linkage disequilibrium) maintained by either additive or multiplicative fitness schemes. Simulations suggest that it "generally" increases for arbitrary fitness schemes. The empirical literature correlating allozyme heterozygosity with fitness-correlated traits is discussed in the light of these and other theoretical results.     

Quantitative variability and multilocus polymorphism under epistatic selection

We study multilocus polymorphism under selection, using a class of fitness functions that account for additive, dominant, and pairwise additive-by-additive epistatic interactions. The dynamic equations are derived in terms of allele frequencies and disequilibria, using the notions of marginal systems and marginal fitnesses, without any approximations. Stationary values of allele frequencies and pairwise disequilibria under weak selection are calculated by regular perturbation techniques. We derive conditions for existence and stability of the multilocus polymorphic states. Using these results, we then analyze a number of models describing stabilizing selection on additive characters, with some other factors, and determine the conditions under which genetic quantitative variability is maintained.     

Introgressive hybridization as the breakdown of postzygotic isolation: a theoretical perspective

In this paper, both the empirical and theoretical genetic aspects of human-mediated introgressive hybridization are reviewed in terms of their association with the breakdown of postzygotic isolating mechanisms. I also compare several simulation models with an ecological or genetic focus that are relevant to the prediction and risk assessment of genetic extinction due to hybridization. One barrier to devising comprehensive risk assessment frameworks is a lack of sufficient population genetic studies that associate introgressive hybridization with specific isolating mechanisms. A gametic model based on multilocus underdominant fitness is one of the best genetic models for introgressive hybridization because it explicitly incorporates the postzygotic isolating mechanism known as Dobzhansky–Muller genetic incompatibility.     

Diagnosis of the Development and Pedological Clinical Care of Difficult Children

… Biology long ago discovered empirically that two phenotypically identical structures or processes may be wholly dissimilar from a causal-dynamic perspective, i.e., in terms of their causes and their effects. Physics and, recently, biology have demonstrated that phenotypical similarity may go hand in hand with an extreme difference in causal-dynamic properties and that, conversely, there may be considerable phenotypical difference between two phenomena or processes that are causally and dynamically very much alike.     

The effects of multilocus balancing selection on neutral variability

We studied the effect of multilocus balancing selection on neutral nucleotide variability at linked sites by simulating a model where diallelic polymorphisms are maintained at an arbitrary number of selected loci by means of symmetric overdominance. Different combinations of alleles define different genetic backgrounds that subdivide the population and strongly affect variability. Several multilocus fitness regimes with different degrees of epistasis and gametic disequilibrium are allowed. Analytical results based on a multilocus extension of the structured coalescent predict that the expected linked neutral diversity increases exponentially with the number of selected loci and can become extremely large. Our simulation results show that although variability increases with the number of genetic backgrounds that are maintained in the population, it is reduced by random fluctuations in the frequencies of those backgrounds and does not reach high levels even in very large populations. We also show that previous results on balancing selection in single-locus systems do not extend to the multilocus scenario in a straightforward way. Different patterns of linkage disequilibrium and of the frequency spectrum of neutral mutations are expected under different degrees of epistasis. Interestingly, the power to detect balancing selection using deviations from a neutral distribution of allele frequencies seems to be diminished under the fitness regime that leads to the largest increase of variability over the neutral case. This and other results are discussed in the light of data from the Mhc.     

X-ray-induced specific-locus mutations in the ad-3 region of two-component heterokaryons of Neurospora crassa. X. Heterozygous effects of multilocus deletion mutations of genotype ad-3A or ad-3B.

Previous studies on X-ray-induced irreparable adenine-3 mutations (designated [ad-3]IR), induced in heterokaryon 12 of Neurospora crassa, demonstrated that they were not recessive and exhibited heterozygous effects in terms of markedly reduced linear growth rates (de Serres, 1965). Complementation tests with a series of tester strains carrying multilocus deletion mutations in the ad-3 and immediately adjacent genetic regions demonstrated that X-ray-induced irreparable mutations map, in the main part, as a series of overlapping multilocus deletion mutations that extend both proximally and distally into the immediately adjacent genetic regions, as well as into the 'X' region (a region of unknown, but essential function) between ad-3A and ad-3B (de Serres, 1968, 1989). Further studies (de Serres and Miller, 1988) have shown that the heterozygous effects of multilocus deletion mutations in the ad-3 region can be modified genetically and biochemically. In the present paper, the heterozygous effects of X-ray-induced multilocus deletion mutations of genotype ad-3A or ad-3B, induced in heterokaryon 12 (Webber and de Serres, 1965; de Serres, 1988, 1989), have been determined. These data show that 57.7% (15/26) of X-ray-induced multilocus deletion mutations covering the ad-3A locus have heterozygous effects, in terms of reduced linear growth rates, in forced dikaryons with a gene/point mutant at the ad-3B locus and 80.0% (20/25) in forced dikaryons with a multilocus deletion mutation covering the ad-3B locus. In addition, 35.1% (20/57) of X-ray-induced multilocus deletion mutations covering the ad-3B locus have heterozygous effects in forced dikaryons with a gene/point mutant at the ad-3A locus, and 100.0% (35/35) in forced dikaryons with a multilocus deletion mutation covering the ad-3A locus. These results demonstrate that the dominant or recessive characteristics of X-ray-induced specific-locus mutations resulting from multilocus deletion mutations are allele specific.     

Evolutionary Stability for Interactions among Kin under Quantitative Inheritance

The theory of evolutionarily stable strategies (ESS) predicts the long-term evolutionary outcome of frequency-dependent selection by making a number of simplifying assumptions about the genetic basis of inheritance. I use a symmetrized multilocus model of quantitative inheritance without mutation to analyze the results of interactions between pairs of related individuals and compare the equilibria to those found by ESS analysis. It is assumed that the fitness changes due to interactions can be approximated by the exponential of a quadratic surface. The major results are the following. (1) The evolutionarily stable phenotypes found by ESS analysis are always equilibria of the model studied here. (2) When relatives interact, one of the two conditions for stability of equilibria differs between the two models; this can be accounted for by positing that the inclusive fitness function for quantitative characters is slightly different from the inclusive fitness function for characters determined by a single locus. (3) The inclusion of environmental variance will in general change the equilibrium phenotype, but the equilibria of ESS analysis are changed to the same extent by environmental variance. (4) A class of genetically polymorphic equilibria occur, which in the present model are always unstable. These results expand the range of conditions under which one can validly predict the evolution of pairwise interactions using ESS analysis.     

Some natural viability systems for a multiallelic locus: a theoretical study

The maintenance of genetic polymorphism under various natural structured viability regimes vs. general unrestricted fitness assignments are compared. The selection models considered include a generalized dominance fitness system, a generalized viability model based on allelic activity values, viability matrices based on multilocus activity levels, viability matrices defined by partitioned "resource" or "substrate" variables, and circulant-type viability matrices. A number of examples that support these formulations are discussed. Detailed results on the nature of the genotype frequency equilibrium configurations for the specified viability models are presented. An increased likelihood for a globally stable equilibrium is predicted for the more structured viability models.     

What is wrong with absolute individual fitness?

One of the most basic facts about evolution is that fitness is a relative concept. It does not matter how well an organism survives and reproduces, only that it does so better than other organisms bearing alternative traits. Nevertheless, many evolutionary arguments are framed in terms of absolute individual fitness. The absolute fitness criterion (AFC) can be justified in terms of relative fitness only given certain assumptions that are frequently violated in nature. In particular, interactions must occur in groups that are randomly formed and phenotypic variation among groups must be tightly coupled to genetic variation. Complicating the genotype-phenotype relationship can cause phenotypic variation among groups to become nonrandom, even when the groups are randomly formed, favoring traits that do not maximize absolute individual fitness. Complex genotype-phenotype relationships and complex population structures require explicit models of evolutionary change based on relative fitness differences within and among groups.     

A hidden Markov model approach to multilocus linkage analysis in a full-sib family

Statistical packages for constructing genetic linkage maps in inbred lines are well developed and applied extensively, while linkage analysis in outcrossing species faces some statistical challenges because of their complicated genetic structures. In this article, we present a multilocus linkage analysis via hidden Markov models for a linkage group of markers in a full-sib family. The advantage of this method is the simultaneous estimation of the recombination fractions between adjacent markers that possibly segregate in different ratios, and the calculation of likelihood for a certain order of the markers. When the number of markers decreases to two or three, the multilocus linkage analysis becomes traditional two-point or three-point linkage analysis, respectively. Monte Carlo simulations are performed to show that the recombination fraction estimates of multilocus linkage analysis are more accurate than those just using two-point linkage analysis and that the likelihood as an objective function for ordering maker loci is the most powerful method compared with other methods. By incorporating this multilocus linkage analysis, we have developed a Windows software, FsLinkageMap, for constructing genetic maps in a full-sib family. A real example is presented for illustrating linkage maps constructed by using mixed segregation markers. Our multilocus linkage analysis provides a powerful method for constructing high-density genetic linkage maps in some outcrossing plant species, especially in forest trees.     

Mutation-selection models solved exactly with methods of statistical mechanics

We reconsider deterministic models of mutation and selection acting on populations of sequences, or, equivalently, multilocus systems with complete linkage. Exact analytical results concerning such systems are few, and we present recent and new ones obtained with the help of methods from quantum statistical mechanics. We consider a continuous-time model for an infinite population of haploids (or diploids without dominance), with N sites each, two states per site, symmetric mutation and arbitrary fitness function. We show that this model is exactly equivalent to a so-called Ising quantum chain. In this picture, fitness corresponds to the interaction energy of spins, and mutation to a temperature-like parameter. The highly elaborate methods of statistical mechanics allow one to find exact solutions for non-trivial examples. These include quadratic fitness functions, as well as 'Onsager's landscape'. The latter is a fitness function which captures some essential features of molecular evolution, such as neutrality, compensatory mutations and flat ridges. We investigate the mean number of mutations, the mutation load, and the variance in fitness under mutation-selection balance. This also yields some insight into the 'error threshold' phenomenon, which occurs in some, but not all, examples.     

Heterozygosity is unrelated to adult fitness measures in a large, noninbred population of great tits (Parus major)

The extent to which heterozygosity-fitness correlations (HFCs) are expected in wild populations is an important and unresolved question in evolutionary biology, because it relates to our understanding of the genetic architecture of fitness. Here, we report a study of HFCs in a wild, noninbred population of great tits (Parus major), based on a sample comprising 281 individuals typed at 26 markers, resulting in a data set comprising over 5600 genotypes. We regressed pedigree-derived f-score and multilocus genetic diversity against eight life-history traits known to be associated with fitness in this population, including lifetime reproductive success (LRS), as well as several morphological traits under weak selection. We found no evidence for either multilocus or single-locus HFCs for any morphological or fitness trait, and further found no evidence that effect sizes were stronger for those life-history traits more closely associated with reproductive fitness. This result may, in part, be explained by the fact that we found no evidence that our set of 26 markers had any power to infer genome-wide heterozygosity in this population and that marker-derived heterozygosity was uncorrelated with pedigree-derived f-score. Overall, these results emphasize the fact that the often-reported strong HFCs detected in small, inbred populations do not reflect a general phenomenon of increasing individual reproductive fitness with increasing heterozygosity.     

A simple procedure to weight empirical potentials in a fitness function so as to optimize its performance in ab initio protein-folding problem

In an approach to the protein folding problem by a Genetic Algorithm, the fitness function plays a critical role. Empirical potentials are generally used to build the fitness function, and they must be weighted to obtain a valuable one. The weights are generally found by the comparison with a set of misfolded structures (decoys), but a dependence of the obtained fitness generally arises on the used decoys. Here we describe a general procedure to find out, from a given set of potentials, their better linear combination that could either identify the wild structure or prove their powerlessness. We use topological considerations over the hyperspace of the potentials, and a multiple linear inequalities solver. The iterated method flows through the following steps: it determines a direction in the hyperspace of the potentials, which identifies the native structure as a vertex among a set of misfolded decoys. A multiple linear inequalities solver obtains the direction. A Genetic Algorithm, tailored to the specific problem, uses the fitness function defined by this direction and generally reaches a new structure better than the experimental one, which is added to the ensemble. The decoys so generated are not dependent on a deterministic criterion. This iterative procedure can be stopped either by identifying an effective fitness function or by proving the impossibility of its achievement. In order to test the method under the hardest conditions, we choose numerous and heterogeneous quantities as components of the fitness function. This method could be a useful tool for the scientific community in order to test any fitness proposed and to recognize the most important components on which it is built.     

Age-specific effect of heterozygosity on survival in alpine marmots, Marmota marmota

The fitness consequences of heterozygosity and the mechanisms underpinning them are still highly controversial. Using capture–mark–recapture models, we investigated the effects of individual heterozygosity, measured at 16 microsatellite markers, on age-dependent survival and access to dominance in a socially monogamous mammalian species, the alpine marmot. We found a positive correlation between standardized multilocus heterozygosity and juvenile survival. However, there was no correlation between standardized multilocus heterozygosity and either survival of older individuals or access to dominance. The disappearance of a significant heterozygosity fitness correlation when individuals older than juveniles are considered is consistent with the prediction that differences in survival among individuals are maximal early in life. The lack of a correlation between heterozygosity and access to dominance may be a consequence of few homozygous individuals attaining the age at which they might reach dominance. Two hypotheses have been proposed to explain heterozygosity-fitness correlations: genome-wide effects reflected by all markers or local effects of specific markers linked to genes that determine fitness. In accordance with genome-wide effects of heterozygosity, we found significant correlations between heterozygosities calculated across single locus or across two sets of eight loci. Thus, the genome-wide heterozygosity effect seems to explain the observed heterozygosity-fitness correlation in the alpine marmot.     

The evolution of genetic canalization under fluctuating selection

Abstract.— If the direction of selection changes from generation to generation, the ability to respond to selection is maladaptive: the response to selection in one generation leads to reduced fitness in the next. Because the response is determined by the amount of genetic variance expressed at the phenotypic level, rapidly fluctuating selection should favor modifier genes that reduce the phenotypic effect of alleles segregating at structural loci underlying the trait. Such reduction in phenotypic expression of genetic variation has been named "genetic canalization." I support this argument with a series of two- and multilocus models with alternating linear selection and Gaussian selection with fluctuating optimum. A canalizing modifier gene affects the fitness of its carriers in three ways: (1) it reduces the phenotypic consequences of genetic response to previous selection; (2) it reduces the genetic response to selection, which is manifested as linkage disequilibrium between the modifier and structural loci; and (3) it reduces the phenotypic variance. The first two effects reduce fitness under directional selection sustained for several generations, but improve fitness when the direction of selection has just been reversed. The net effect tends to favor a canalizing modifier under rapidly fluctuating selection regimes (period of eight generations or less). The third effect improves fitness of the modifier allele if the fitness function is convex and reduces it if the function is concave. Under fluctuating Gaussian selection, the population is more likely to experience the concave portion of the fitness function when selection is stronger. Therefore, only weak to moderately strong fluctuating Gaussian selection favors genetic canalization. This paper considerably broadens the conditions that favor genetic canalization, which so far has only been postulated to evolve under long-term stabilizing selection.     

Multilocus heterozygosity and inbreeding in the Siberian jay

Because of its common negative association with fitness, inbreeding is a major concern in conservation biology. Traditionally it has been measured as individual inbreeding coefficient calculated from the pedigree, but recently multilocus heterozygosity estimates have become commonly used as proxies. However, theoretical and simulation studies have cast doubt on the validity of these surrogates especially when they are based on only a few molecular markers. Yet, empirical studies reporting the correlation between multilocus heterozygosity and inbreeding coefficient are rare. We studied this relationship in a wild Siberian jay (Perisoreus infaustus) population subject to a long-term field study over 30 years. The correlations between inbreeding coefficient and the employed heterozygosity measures—standardized heterozygosity and internal relatedness—based on 21 microsatellite loci were weak. These results together with results from theoretical and simulation studies caution against use of multilocus heterozygosity estimates to study inbreeding in natural populations.     

Heterozygosity-fitness correlations in a migratory bird: an analysis of inbreeding and single-locus effects

Studies in a multitude of taxa have described a correlation between heterozygosity and fitness and usually conclude that this is evidence for inbreeding depression. Here, we have used multilocus heterozygosity (MLH) estimates from 15 microsatellite markers to show evidence of heterozygosity-fitness correlations (HFCs) in a long-distance migratory bird, the light-bellied Brent goose. We found significant, positive heterozygosity-heterozygosity correlations between random subsets of the markers we employed, and no evidence that a model containing all loci as individual predictors in a multiple regression explained significantly more variation than a model with MLH as a single predictor. Collectively, these results lend support to the hypothesis that the HFCs we have observed are a function of inbreeding depression. However, we do find that fitness correlations are only detectable in years where population-level productivity is high enough for the reproductive asymmetry between high and low heterozygosity individuals to become apparent. We suggest that lack of evidence of heterozygosity-fitness correlations in animal systems may be because heterozygosity is a poor proxy measure of inbreeding, especially when employing low numbers of markers, but alternatively because the asymmetries between individuals of different heterozygosities may only be apparent when environmental effects on fitness are less pronounced.     

A Generalization of the Transmission/Disequilibrium Test for Uncertain-Haplotype Transmission

A new transmission/disequilibrium-test statistic is proposed for situations in which transmission is uncertain. Such situations arise when transmission of a multilocus marker haplotype is considered, since haplotype phase is often unknown in a substantial number of instances. Even for single-locus markers, transmission is uncertain if one or both parents are missing. In both these situations, uncertainty may be reduced by the typing of further siblings, whose disease status may be unaffected or unknown. The proposed test is a score test based on a partial score function that omits the terms most influenced by hidden population stratification.     

Prognostic criterion in the mendelian analysis of quantitative traits

Prediction test for estimation of genetical parameters and the fitness of the hypothesis is proposed. The test is based on coincidence of values of quantitative character in individuals predicted on the basis of the genetic analysis and the empirical measured values. The method gives a higher correctness of prediction of phenotypical values than statistical methods. The problem of a choice of the boundary values for the test is considered.     

The long-term evolution of multilocus traits under frequency-dependent disruptive selection

Frequency-dependent disruptive selection is widely recognized as an important source of genetic variation. Its evolutionary consequences have been extensively studied using phenotypic evolutionary models, based on quantitative genetics, game theory, or adaptive dynamics. However, the genetic assumptions underlying these approaches are highly idealized and, even worse, predict different consequences of frequency-dependent disruptive selection. Population genetic models, by contrast, enable genotypic evolutionary models, but traditionally assume constant fitness values. Only a minority of these models thus addresses frequency-dependent selection, and only a few of these do so in a multilocus context. An inherent limitation of these remaining studies is that they only investigate the short-term maintenance of genetic variation. Consequently, the long-term evolution of multilocus characters under frequency-dependent disruptive selection remains poorly understood. We aim to bridge this gap between phenotypic and genotypic models by studying a multilocus version of Levene's soft-selection model. Individual-based simulations and deterministic approximations based on adaptive dynamics theory provide insights into the underlying evolutionary dynamics. Our analysis uncovers a general pattern of polymorphism formation and collapse, likely to apply to a wide variety of genetic systems: after convergence to a fitness minimum and the subsequent establishment of genetic polymorphism at multiple loci, genetic variation becomes increasingly concentrated on a few loci, until eventually only a single polymorphic locus remains. This evolutionary process combines features observed in quantitative genetics and adaptive dynamics models, and it can be explained as a consequence of changes in the selection regime that are inherent to frequency-dependent disruptive selection. Our findings demonstrate that the potential of frequency-dependent disruptive selection to maintain polygenic variation is considerably smaller than previously expected.