Inconsistencies in standard approximations for selection coefficients at loci affecting a polygenic character

Inconsistencies exist in the standard expansions used to approximate selection coefficients for alleles at a locus underlying a quantitative character. Allelic (marginal) fitnesses obtained from expansions based on average excesses differ from allelic fitnesses obtained from expansions based on genotypic values. Similarly, the mean population fitness based on summing over either allelic or genotypic fitnesses usually differs mean population fitness obtained by averaging over the unrestricted phenotypic distribution. A consistent value of requires no variation in genotypic values. If, as suggested by Nagylaki (1984), expansions are corrected for the decrease in phenotypic variance resulting from conditioning on the presence of a particular allele or genotype, inconsistencies still exist. Unless W(z)[V _z p(z) + zp(z) + p(z)] dz = 0, where p(z) is the phenotypic probability density function, V _z the phenotypic variance, W( _z ) the fitness of phenotypic value z, the primes denote differentiation with respect to z, allelic fitnesses based on average effects differ from allelic fitnesses based on genotypic values. This condition must also be satisfied in order for either expansion to give a consistent , as first shown by Nagylaki. For arbitrary W(z), this is satisfied if and only if phenotypes are normally distributed.     

Relative roles of mutation and selection in the maintenance of genetic variability

The extent and pattern of protein and DNA polymorphisms are discussed with emphasis on the mechanism of maintenance of the polymorphisms. Statistical studies suggest that a large proportion of genetic variability at the molecular level is maintained by a mutation-drift balance. At some loci, such as those for histocompatibility in mammals, however, a form of overdominant selection seems to be involved. In the presence of overdominant selection, polymorphic alleles may be maintained for tens of millions of years, so that the number of nucleotide differences between alleles is often very large, as in the case of self-incompatibility alleles in plants. There are also an increasing number of examples in which an adaptive change of a morphological or physiological character is caused by a single nucleotide substitution. Nevertheless, these mutations seem to be a small proportion of the total nucleotide changes that contribute to genetic variability and evolution. Although there are many examples of frequency-dependent selection, this form of selection is apparently unimportant for the maintenance of genetic variability except in some special cases. Observations on the evolutionary change of DNA suggest that the driving force of evolution is mutation rather than selection.     

Detection of closely linked multiple quantitative trait loci using a genetic algorithm

The existence of a quantitative trait locus (QTL) is usually tested using the likelihood of the quantitative trait on the basis of phenotypic character data plus the recombination fraction between QTL and flanking markers. When doing this, the likelihood is calculated for all possible locations on the linkage map. When multiple QTL are suspected close by, it is impractical to calculate the likelihood for all possible combinations of numbers and locations of QTL. Here, we propose a genetic algorithm (GA) for the heuristic solution of this problem. GA can globally search the optimum by improving the "genotype" with alterations called "recombination" and "mutation." The "genotype" of our GA is the number and location of QTL. The "fitness" is a function based on the likelihood plus Akaike's information criterion (AIC), which helps avoid false-positive QTL. A simulation study comparing the new method with existing QTL mapping packages shows the advantage of the new GA. The GA reliably distinguishes multiple QTL located in a single marker interval.     

The genetic variance for multiple linked quantitative trait loci conditional on marker information in a crossed population

In the prediction of genetic values and quantitative trait loci (QTLs) mapping via the mixed model method incorporating marker information in animal populations, it is important to model the genetic variance for individuals with an arbitrary pedigree structure. In this study, for a crossed population originated from different genetic groups such as breeds or outbred strains, the variance of additive genetic values for multiple linked QTLs that are contained in a chromosome segment, especially the segregation variance, is investigated assuming the use of marker data. The variance for a finite number of QTLs in one chromosomal segment is first examined for the crossed population with the general pedigree. Then, applying the concept of the expectation of identity-by-descent proportion, an approximation to the mean of the conditional probabilities for the linked QTLs over all loci is obtained, and using it an expression for the variance in the case of an infinite number of linked QTLs marked by flanking markers is derived. It appears that the approach presented can be useful in the segment mapping using, and in the genetic evaluation of, crosses with general pedigrees in the population of concern. The calculation of the segregation variance through the current approach is illustrated numerically, using a small data-set.     

Detecting major genetic loci controlling phenotypic variability in experimental crosses

Traditional methods for detecting genes that affect complex diseases in humans or animal models, milk production in livestock, or other traits of interest, have asked whether variation in genotype produces a change in that trait’s average value. But focusing on differences in the mean ignores differences in variability about that mean. The robustness, or uniformity, of an individual’s character is not only of great practical importance in medical genetics and food production but is also of scientific and evolutionary interest (e.g., blood pressure in animal models of heart disease, litter size in pigs, flowering time in plants). We describe a method for detecting major genes controlling the phenotypic variance, referring to these as vQTL. Our method uses a double generalized linear model with linear predictors based on probabilities of line origin. We evaluate our method on simulated F₂ and collaborative cross data, and on a real F₂ intercross, demonstrating its accuracy and robustness to the presence of ordinary mean-controlling QTL. We also illustrate the connection between vQTL and QTL involved in epistasis, explaining how these concepts overlap. Our method can be applied to a wide range of commonly used experimental crosses and may be extended to genetic association more generally.QUANTITATIVE trait locus (QTL) analysis has traditionally focused on detection of major genes controlling the expected mean of a phenotype. But there is substantial evidence that not only the mean but also the variance, that is, the stochastic variability of the phenotype about its average value, may itself be under genetic control. The identification of such variance-controlling loci, which we call vQTL, can be helpful in a variety of contexts, including selection of livestock for uniformity, evaluating predictability of response to medical treatment, identification of key biomolecular stabilizers, and assessment of population resilience in ecology and evolution.One way of interpreting an increase in variability is as a decrease in stability. Waddington (1942) described the concept of canalization, whereby natural selection favors the relative constancy of some attributes, for example, well-formed organs and limbs, and thereby leads to the evolution of heritable architectures that buffer the impact of environmental or background genetic variation that would otherwise cause development to go astray. These architectures create virtual “canals” down which developmental programs flow. For a canalized phenotype, which modern usage expands to include nondevelopmental traits, the “zone of canalization” is the range of underlying liability over which potentially disruptive variation may be absorbed without serious consequence to the expressed trait value (Lynch and Walsh 1998). A well-studied example of a stabilizing architecture is that provided by heat-shock protein 90 (Hsp90), which buffers genetic and stochastic variation in the development of plants and flies (Rutherford and Lindquist 1998; Queitsch et al. 2002; Sangster et al. 2008).But in absorbing variation, such stabilizing architectures also hide it from view, and a sensitizing change in the stabilizer that shifts liability outside the zone of canalization can have a dramatic effect on the phenotype. Such shifts release the combined effects of previously “cryptic” genetic variation: now decanalized, the phenotype is more sensitive to internal (including genetic) and external environment, and as a result varies more greatly between individuals (Dworkin 2005; Hornstein and Shomron 2006). In this vein, decanalization has been proposed to explain why the genetic architectures of some diseases in human populations seem more amenable than others to genetic dissection through genome-wide association (Gibson and Goldstein 2007). Specifically, whereas some disease phenotypes in homogeneous populations may be heavily canalized and thereby harder to dissect, others may have been decanalized by modern living conditions (e.g., inflammatory diseases) or modern admixture, while yet others are simply too recent in evolutionary history for buffering networks to have evolved (e.g., response to HIV).Increased variability can also be adaptive. In natural populations disruptive selection favors diversity, with increased “capacitance” (Rice 2008) or “bet-hedging” (Beaumont et al. 2009) spreading risk over a variable fitness landscape. Feinberg and Irizarry (2010) recently proposed a heritable and selectable mechanism for this based on stochastic epigenetic variation. In controlled populations, variability can be increased through directional selection. For example, in a Drosophila selection experiment Clayton and Robertson (1957) reported increased bristle number variance, which is consistent with the idea that genotypes associated with higher environmental variance have a greater chance of being selected under directional selection (Hill and Zhang 2004). Moreover, genetic differences have been observed for phenotypic variability in body weight for chickens (Rowe et al. 2006) and snails (Ros et al. 2004) and litter size in rabbits (Ibanez-Escriche et al. 2008), sheep (Sancristobal-Gaudy et al. 1998), and pigs (Sorensen and Waagepetersen 2003).In natural populations with stabilizing selection we should expect to find alleles minimizing variance for fitness traits (Lande 1980; Houle 1992), whereas directional selection during domestication will favor alleles that increase variance. One may therefore expect to find vQTL in experimental crosses between wild and domestic animals (see Andersson 2001). Nonetheless, genetic buffering that leads to phenotypic robustness need not require an evolutionary explanation to be observed, nor to be useful in medicine and agriculture. Plainly, detecting vQTL and inferring how they arose are separate questions; here we concentrate on the first.

The maintenance (or not) of polygenic variation by soft selection in heterogeneous environments

On the basis of single-locus models, spatial heterogeneity of the environment coupled with strong population regulation within each habitat (soft selection) is considered an important mechanism maintaining genetic variation. We studied the capacity of soft selection to maintain polygenic variation for a trait determined by several additive loci, selected in opposite directions in two habitats connected by dispersal. We found three main types of stable equilibria. Extreme equilibria are characterized by extreme specialization to one habitat and loss of polymorphism. They are analogous to monomorphic equilibria in singe-locus models and are favored by similar factors: high dispersal, weak selection, and low marginal average fitness of intermediate genotypes. At the remaining two types of equilibria the population mean is intermediate but variance is very different. At fully polymorphic equilibria all loci are polymorphic, whereas at low-variance equilibria at most one locus remains polymorphic. For most parameters only one type of equilibrium is stable; the transition between the domains of fully polymorphic and low-variance equilibria is typically sharp. Low-variance equilibria are favored by high marginal average fitness of intermediate genotypes, in contrast to single-locus models, in which marginal overdominance is particularly favorable for maintenance of polymorphism. The capacity of soft selection to maintain polygenic variation is thus more limited than extrapolation from single-locus models would suggest, in particular if dispersal is high and selection weak. This is because in a polygenic model, variance can evolve independently of the mean, whereas in the single-locus two-allele case, selection for an intermediate mean automatically leads to maintenance of polymorphism.     

Constrained evolution of a quantitative character by pleiotropic mutation

The long-term response to directional selection and its selection limit are derived for a quantitative character that is controlled by pleiotropic mutations with direct deleterious effect on fitness. Directional selection is assumed to be weaker than the selection acting directly on mutations via deleterious effects (purging selection), which renders all mutations to eventual elimination. The analysis embedding this restrictive assumption indicates that the evolutionary response of the character starting from an equilibrium state, in which mutation and purging selection balance but no directional selection is operating, decreases monotonically with time at an exponential rate. And the fading rate of responses is mostly determined by the direct deleterious effect. Contrary to the expectation by the standard selection limit theory based on fixation of extant genetic variation, the present model predicts that the selection limit depends on the intensity of directional selection, the limit being proportional to the ratio of the directional selection intensity to the direct deleterious effect. A slightly larger genetic variance is maintained at the selection limit than would be without directional selection.     

Closely linked genetic loci required for swarm cell differentiation and multicellular migration by Proteus mirabilis

The pathogenic bacterium Proteus mirabilis exhibits a form of multicellular behaviour called swarming migration. This involves the differentiation of vegetative cells at the colony margin into swarm cells which are long, aseptate, multinucleate, hyper-flagellated filaments able to undergo repeated cycles of co-ordinated population migration and consolidation (reversion to vegetative cells). Transposon mutagenesis of uropathogenic P. mirabilis strain U6450 with Tn5 generated 4860 chromosomal insertions and, of these, 75 (1.6%) caused visibly abnormal swarming behaviour, indicating that at least 45 genes are involved in directing motility, cell differentiation and multicellular behaviour. While about one fifth of the swarm-defective mutants lacked flagella and were non-motile non-swarming (NMNS) the majority were normally flagellated and motile but were unable to form swarm cells (motile non-swarming, MNS), or were motile and able to form swarm cells but displayed aberrant patterns of multicellular migration (dendritic swarming, DS) or consolidation (frequent and infrequent consolidation, FC and IC). Restriction enzyme mapping of representative mutant DNAs by Southern hybridization with transposon DNA probes identified eight different mutated genetic loci within the five phenotypic classes. Subsequent Southern analysis of large restriction fragments separated by pulsed-field electrophoresis showed that these eight mutated loci required for motility, cell differentiation and multicellular migration were clustered on a region of DNA spanning approximately 8% of the 4.2 mbp P. mirabilis chromosome. Further linkage analysis showed that the DS locus involved in the ordered migration of the swarm cell population mapped separately from two main clusters of swarm loci, one cluster containing, within 112 kbp, genetic determinants of motility (NMNS) and also differentiation into swarm cells (MNS1, MNS2), and a second within a neighbouring 95 kbp DNA sequence containing three loci involved in the control of consolidation (FC, IC1, IC2).     

Mechanism of insolubilization by a single-point mutation in alphaA-crystallin linked with hereditary human cataracts

AlphaA-crystallin is a small heat shock protein that functions as a molecular chaperone and a lens structural protein. The R49C single-point mutation in alphaA-crystallin causes hereditary human cataracts. We have previously investigated the in vivo properties of this mutant in a gene knock-in mouse model. Remarkably, homozygous mice carrying the alphaA-R49C mutant exhibit nearly complete lens opacity concurrent with small lenses and small eyes. Here we have investigated the 90 degrees light scattering, viscosity, refractive index, and bis-ANS fluorescence of lens proteins isolated from the alphaA-R49C mouse lenses and found that the concentration of total water-soluble proteins showed a pronounced decrease in alphaA-R49C homozygous lenses. Light scattering measurements on proteins separated by gel permeation chromatography showed a small amount of high-molecular mass aggregated material in the void volume which still remains soluble in alphaA-R49C homozygous lens homogenates. An increased level of binding of beta- and gamma-crystallin to the alpha-crystallin fraction was observed in alphaA-R49C heterozygous and homozygous lenses but not in wild-type lenses. Quantitative analysis with the hydrophobic fluorescence probe bis-ANS showed a pronounced increase in fluorescence yield upon binding to alpha-crystallin from mutant as compared with the wild-type lenses. These results suggest that the decrease in the solubility of the alphaA-R49C mutant protein was due to an increase in its hydrophobicity and supra-aggregation of alphaA-crystallin that leads to cataract formation. Our study further shows that analysis of mutant proteins from the mouse model is an effective way to understand the mechanism of protein insolubilization in hereditary cataracts.     

Recent developments in statistical methods for detecting genetic loci affecting phenotypic variability

ABSTRACT: A number of recent works have introduced statistical methods for detecting genetic loci that affect phenotypic variability, which we refer to as variability-controlling quantitative trait loci (vQTL). These are genetic variants whose allelic state predicts how much phenotype values will vary about their expected means. Such loci are of great potential interest in both human and non-human genetic studies, one reason being that a detected vQTL could represent a previously undetected interaction with other genes or environmental factors. The simultaneous publication of these new methods in different journals has in many cases precluded opportunity for comparison. We survey some of these methods, the respective trade-offs they imply, and the connections between them. The methods fall into three main groups: classical non-parametric, fully parametric, and semi-parametric two-stage approximations. Choosing between alternatives involves balancing the need for robustness, flexibility, and speed. For each method, we identify important assumptions and limitations, including those of practical importance, such as their scope for including covariates and random effects. We show in simulations that both parametric methods and their semi-parametric approximations can give elevated false positive rates when they ignore mean-variance relationships intrinsic to the data generation process. We conclude that choice of method depends on the trait distribution, the need to include non-genetic covariates, and the population size and structure, coupled with a critical evaluation of how these fit with the assumptions of the statistical model.     

The divergence of a polygenic system subject to stabilizing selection, mutation and drift

Polygenic variation can be maintained by a balance between mutation and stabilizing selection. When the alleles responsible for variation are rare, many classes of equilibria may be stable. The rate at which drift causes shifts between equilibria is investigated by integrating the gene frequency distribution W2N II (pq)4N mu-1. This integral can be found exactly, by numerical integration, or can be approximated by assuming that the full distribution of allele frequencies is approximately Gaussian. These methods are checked against simulations. Over a wide range of population sizes, drift will keep the population near an equilibrium which minimizes the genetic variance and the deviation from the selective optimum. Shifts between equilibria in this class occur at an appreciable rate if the product of population size and selection on each locus is small (Ns alpha 2 less than 10). The Gaussian approximation is accurate even when the underlying distribution is strongly skewed. Reproductive isolation evolves as populations shift to new combinations of alleles: however, this process is slow, approaching the neutral rate (approximately mu) in small populations.     

Features of genetic variability in microsatellite DNA loci in the French Bulldog dog breed

Genetic variability in microsatellite markers PEZ1, PEZ3, PEZ6, PEZ8, FHC2010, and FHC2054 from a panel recommended by the International Society for Animal Genetics has been assessed for a micropopulation of dogs of the French Bulldog breed. The number and size of alleles, the number of alleles per locus, the effective number of alleles, the polymorphism index, expected and actual heterozygosity, and Wright’s fixation index have been determined to characterize each locus investigated. Deficit of heterozygous genotypes was observed in the micropopulation investigated, which is indicative of inbreeding. The relationship between the degree of homozygosity for six microsatellite loci and the degree of inbreeding has been analyzed. The results obtained point at a trend for increase of the relative abundance of homozygous loci upon an increase in the inbreeding coefficient of individuals.     

Genetic effects at pleiotropic loci are context-dependent with consequences for the maintenance of genetic variation in populations

Context-dependent genetic effects, including genotype-by-environment and genotype-by-sex interactions, are a potential mechanism by which genetic variation of complex traits is maintained in populations. Pleiotropic genetic effects are also thought to play an important role in evolution, reflecting functional and developmental relationships among traits. We examine context-dependent genetic effects at pleiotropic loci associated with normal variation in multiple metabolic syndrome (MetS) components (obesity, dyslipidemia, and diabetes-related traits). MetS prevalence is increasing in Western societies and, while environmental in origin, presents substantial variation in individual response. We identify 23 pleiotropic MetS quantitative trait loci (QTL) in an F₁₆ advanced intercross between the LG/J and SM/J inbred mouse strains (Wustl:LG,SM-G16; n = 1002). Half of each family was fed a high-fat diet and half fed a low-fat diet; and additive, dominance, and parent-of-origin imprinting genotypic effects were examined in animals partitioned into sex, diet, and sex-by-diet cohorts. We examine the context-dependency of the underlying additive, dominance, and imprinting genetic effects of the traits associated with these pleiotropic QTL. Further, we examine sequence polymorphisms (SNPs) between LG/J and SM/J as well as differential expression of positional candidate genes in these regions. We show that genetic associations are different in different sex, diet, and sex-by-diet settings. We also show that over- or underdominance and ecological cross-over interactions for single phenotypes may not be common, however multidimensional synthetic phenotypes at loci with pleiotropic effects can produce situations that favor the maintenance of genetic variation in populations. Our findings have important implications for evolution and the notion of personalized medicine.