Natural selection on the genetical component of variance in body condition in a wild bird population

Although there is substantial evidence that skeletal measures of body size are heritable in wild animal populations, it is frequently assumed that the nonskeletal component of body weight (or ‘condition’) is determined primarily by environmental factors, in particular nutritional state. We tested this assumption by quantifying the genetic and environmental components of variance in fledgling body condition index (=relative body weight) in a natural population of collared flycatchers (Ficedula albicollis), and compared the strength of natural selection on individual breeding values with that on phenotypic values. A mixed model analysis of the components of variance, based on an ‘animal model’ and using 18 years of data on 17 717 nestlings, revealed a significant additive genetic component of variance in body condition, which corresponded to a narrow sense heritability (h²) of 0.30 (SE=0.03). Nongenetic contributions to variation in body condition were large, but there was no evidence of dominance variance nor of contributions from early maternal or common environment effects (pre‐manipulation environment) in condition at fledging. Comparison of pre‐ and post‐selection samples revealed virtually identical h² of body condition index, despite the fact that there was a significant decrease (35%) in the levels of additive genetic variance from fledging to breeding. The similar h² in the two samples occurred because the environmental component of variance was also reduced by selection, suggesting that natural selection was acting on both genotypic and environmental variation. The effects of selection on genetic variance were confirmed by calculation of the selection differentials for both phenotypic values and best linear unbiased predictor (BLUP) estimates of breeding values: there was positive directional selection on condition index both at the phenotypic and the genotypic level. The significant h² of body condition index is consistent with data from human and rodent populations showing significant additive genetic variance in relative body mass and adiposity, but contrasts with the common assumption in ecology that body condition reflects an individual’s nongenetic nutritional state. Furthermore, the substantial reduction in the additive genetic component of variance in body condition index suggests that selection on environmental deviations cannot alone explain the maintenance of additive genetic variation in heritable traits, but that other mechanisms are needed to explain the moderate to high heritabilities of traits under consistent and strong directional selection.     

Why is there so much genetic variation for wing dimorphism?

Wing dimorphism appears in general to be determined either by a single locus, 2 allele system in which brachyptery is dominant, or by the additive action of numerous loci. In the latter case studies indicate that the heritability is typically quite large. It is generally postulated that wing dimorphism is under strong selection: why then is genetic variation not eroded? In this paper I consider three possible explanations. First, genetic variation may not be exposed to selection because environmental heterogeneity effectively makes heritability zero. Because wing dimorphisms are known to evolve it seems unlikely that this is the primary factor. Second, directional selection on a threshold trait may push the population almost to monomorphism but erodes genetic variance at a very slow rate. This mechanism cannot preserve variation but makes it possible for other factors to more easily maintain variability. Finally, I demonstrate that in a heterogeneous environment spatio-temporal variation in fitness will itself maintain a genetic polymorphism for wing dimorphism.     

Evolution in a changing environment: a case study with great tit fledging mass

Heritable phenotypic traits under significant and consistent directional selection often fail to show the expected evolutionary response. A potential explanation for this contradiction is that because environmental conditions change constantly, environmental change can mask an evolutionary response to selection. We combined an "animal model" analysis with 36 years of data from a long-term study of great tits (Parus major) to explore selection on and evolution of a morphological trait: body mass at fledging. We found significant heritability of this trait, but despite consistent positive directional selection on both the phenotypic and the additive genetic component of body mass, the population mean phenotypic value declined rather than increased over time. However, the mean breeding value for body mass at fledging increased over time, presumably in response to selection. We show that the divergence between the response to selection observed at the levels of genotype and phenotype can be explained by a change in environmental conditions over time, that is, related both to increased spring temperature before breeding and elevated population density. Our results support the suggestion that measuring phenotypes may not always give a reliable impression of evolutionary trajectories and that understanding patterns of phenotypic evolution in nature requires an understanding of how the environment has itself changed.     

Genotypic Variation for a Quantitative Character Maintained under Stabilizing Selection without Mutations: Epistasis

A model of the gene action on a quantitative character is suggested. The model takes into account epistasis by combining multiplicative with the traditional additive approximation of the action of loci. It is demonstrated on the basis of this model that a high level of genotypic variation can be maintained in a population for a quantitative character under stabilizing selection in the absence of mutations, if there is epistasis. It is also shown that a large amount of additive variation as well as high heritability can be "hidden" in such a population and "released" if stabilizing selection is relaxed.     

Bias in the prediction of genetic gain due to mass and half-sib selection in random mating populations

The prediction of gains from selection allows the comparison of breeding methods and selection strategies, although these estimates may be biased. The objective of this study was to investigate the extent of such bias in predicting genetic gain. For this, we simulated 10 cycles of a hypothetical breeding program that involved seven traits, three population classes, three experimental conditions and two breeding methods (mass and half-sib selection). Each combination of trait, population, heritability, method and cycle was repeated 10 times. The predicted gains were biased, even when the genetic parameters were estimated without error. Gain from selection in both genders is twice the gain from selection in a single gender only in the absence of dominance. The use of genotypic variance or broad sense heritability in the predictions represented an additional source of bias. Predictions based on additive variance and narrow sense heritability were equivalent, as were predictions based on genotypic variance and broad sense heritability. The predictions based on mass and family selection were suitable for comparing selection strategies, whereas those based on selection within progenies showed the largest bias and lower association with the realized gain.     

A meta-analysis of the heritability of developmental stability

The existence of additive genetic variance in developmental stability has important implications for our understanding of morphological variation. The heritability of individual fluctuating asymmetry and other measures of developmental stability have frequently been estimated from parent-offspring regressions, sib analyses, or from selection experiments. Here we review by meta-analysis published estimates of the heritability of developmental stability, mainly the degree of individual fluctuating asymmetry in morphological characters. The overall mean effect size of heritabilities of individual fluctuating asymmetry was 0.19 from 34 studies of 17 species differing highly significantly from zero (P < 0.0001). The mean heritability for 14 species was 0.27. This indicates that there is a significant additive genetic component to developmental stability. Effect size was larger for selection experiments than for studies based on parent-offspring regression or sib analyses, implying that genetic estimates were unbiased by maternal or common environment effects. Additive genetic coefficients of variation for individual fluctuating asymmetry were considerably higher than those for character size per se. Developmental stability may be significantly heritable either because of strong directional selection, or fluctuating selection regimes which prevent populations from achieving a high degree of developmental stability to current environmental and genetic conditions.     

The maintenance of phenotypic and genetic variation in threshold traits by frequency-dependent selection

Many traits are phenotypically dimorphic but determined by the action of many loci, the phenotype being a result of a threshold of sensitivity. Quantitative genetic analysis has shown that generally there is considerable additive genetic variation for the trait, the average heritability being 0.52. In numerous cases threshold traits have been shown, or are assumed, to be under frequency-dependent selection; examples include satellite-territorial behaviour, sex-determination, wing dimorphism and trophic dimorphism. In this paper I investigate the potential for frequency-dependent selection to maintain both phenotypic and additive genetic variation in threshold traits. The qualitative results are robust to the particular form of the frequency-dependent selection function. The equilibrium proportion is more or less independent of population size but the heritability increases with population size, typically approaching its maximal value at a population size of 5000, when the mutation rate is 10^?4. A tenfold decrease in the mutation rate requires an approximate doubling of the population size before an asymptotic value is approached. Thus frequency-dependent selection can account for both the existence of two morphs in a population and the observed levels of heritability. It is also shown, both via simulation and theory, that the quantitative genetic model and a simple phenotypic analysis predict the same equilibrium morph proportion.     

The mapping of epistatic effects onto a genealogical tree in haploid populations

In this paper we present a model that maps epistatic effects onto a genealogical tree for a haploid population. Prior work has demonstrated that genealogical structure causes the genotypic values of individuals to covary. Our results indicate that epistasis can reduce genotypic covariance that is caused by genealogical structure. Genotypic effects (both additive and epistatic) occur along the branches of a genealogical tree, from the base of the tree to its tips. Epistasis reduces genotypic covariance because there is a reweighting of the contribution of branches to the states of genotypes compared to the additive case. Branches near the tips of a genealogical tree contribute proportionally more genetic effects with epistasis than without epistasis. Epistatic effects are most numerous at basal positions in a genealogical tree when a population is constant in size and experiencing no selection, optimizing selection, diversifying selection or directional selection, indicating that epistatic effects are typically old. For a population that is growing in size, epistatic effects are most numerous at midpoints in a genealogical tree, indicating epistatic effects are of moderate age. Our results are important in that they suggest epistatic effects may typically explain deep (old) divergences and broad patterns of divergence that exist in populations, except in growing populations. In a growing population, epistatic effects may cause more within group divergence higher up in a tree and less between group divergence that is deep in a tree. The distribution of the number of epistatic effects and the expected variance and covariance in the number of epistatic effects is also provided assuming neutrality.     

A QUANTITATIVE-GENETIC MODEL FOR SELECTION ON DEVELOPMENTAL NOISE

We propose a simple model for analyzing the effects of microenvironmental variation in quantitative genetics. Our model assumes that the sensitivity of the phenotype to fluctuations in microenvironment has a genetic basis and allows for genetic correlation between trait value and microenvironmental sensitivity. We analyze the effects of short-term stabilizing and directional selection on the genotypic and microenvironmental components of phenotypic variance. Our model predicts that stabilizing selection on a quantitative trait increases developmental canalization. We show that stabilizing selection can result in an increase in the heritability. Our findings may provide an explanation for the results of selection experiments in which artificial stabilizing selection did not change the heritability coefficient or increased it.     

A macroscopic approach to population genetics

Conventional population genetics uses as primitive variables the frequencies and fitnesses of individual genes. This paper develops a formalism whose primitive variables are the frequencies and fitnesses of genotypes and environmental histories in a population. From the mathematical relation that describes genetic variation and selection of genotypes and environmental histories we derive a sequence of more specialized equations, including those of the conventional theory. Some familiar formulas of the conventional theory (including Fisher's fundamental theorem, the formula relating the rate of change of a metric character to selection pressure, and the definitions of broad and narrow heritability) are shown to be special cases of simpler and more general formulas. It is shown that the “genotypic value” of a trait, together with its heritability, may depend strongly on genotype-environment correlations.A generalization of Fisher's fundamental theorem shows that the rate of evolution of a trait depends on the skewness of its fitness distribution. An equation relating the second derivative of the mean fitness to the skewness is derived.Finally, the formalism is applied in a preliminary way to a recent theory of genetic variation (Layzer,1978a), according to which the genetic variability of a trait is selected along with the trait itself. It is shown that there is positive feedback between the two kinds of selection.     

Selection and genetic (co)variance in bighorn sheep

Genetic theory predicts that directional selection should deplete additive genetic variance for traits closely related to fitness, and may favor the maintenance of alleles with antagonistically pleiotropic effects on fitness-related traits. Trait heritability is therefore expected to decline with the degree of association with fitness, and some genetic correlations between selected traits are expected to be negative. Here we demonstrate a negative relationship between trait heritability and association with lifetime reproductive success in a wild population of bighorn sheep (Ovis canadensis) at Ram Mountain, Alberta, Canada. Lower heritability for fitness-related traits, however, was not wholly a consequence of declining genetic variance, because those traits showed high levels of residual variance. Genetic correlations estimated between pairs of traits with significant heritability were positive. Principal component analyses suggest that positive relationships between morphometric traits constitute the main axis of genetic variation. Trade-offs in the form of negative genetic or phenotypic correlations among the traits we have measured do not appear to constrain the potential for evolution in this population.     

Hemiclonal analysis reveals significant genetic, environmental and genotype x environment effects on sperm size in Drosophila melanogaster

Spermatozoa are the most diverse of all animal cells. Variation in size alone is enormous and yet there are still no clear evolutionary explanations that can account for such diversity. The basic genetics of sperm form is also poorly understood, although sperm size is known to have a strong genetic component. Here, using hemiclonal analysis of Drosophila melanogaster, we demonstrate that there is not only a significant additive genetic component contributing to phenotypic variation in sperm length but also a significant environmental effect. Furthermore, the plasticity of sperm size has a significant genetic component to it (a genotype x environment interaction). A genotype x environment interaction could contribute to the maintenance of the substantial genetic variation in this trait and thereby explain the persistent inter-male differences in sperm size seen in numerous taxa. We suggest that the low conditional dependence and high heritability but low evolvability (the coefficient of additive genetic variation) of sperm length is more consistent with a history of stabilizing selection rather than either sexual selection or strong directional selection.     

Speeding up microevolution: the effects of increasing temperature on selection and genetic variance in a wild bird population

The amount of genetic variance underlying a phenotypic trait and the strength of selection acting on that trait are two key parameters that determine any evolutionary response to selection. Despite substantial evidence that, in natural populations, both parameters may vary across environmental conditions, very little is known about the extent to which they may covary in response to environmental heterogeneity. Here we show that, in a wild population of great tits (Parus major), the strength of the directional selection gradients on timing of breeding increased with increasing spring temperatures, and that genotype-by-environment interactions also predicted an increase in additive genetic variance, and heritability, of timing of breeding with increasing spring temperature. Consequently, we therefore tested for an association between the annual selection gradients and levels of additive genetic variance expressed each year; this association was positive, but non-significant. However, there was a significant positive association between the annual selection differentials and the corresponding heritability. Such associations could potentially speed up the rate of micro-evolution and offer a largely ignored mechanism by which natural populations may adapt to environmental changes.     

Effect of various parameter combinations on genetic gain in computer simulated two-character selection

Summary In a simulation study, the effect of various parameter combinations such as linkage, dominance, heritability, and economic weights on the individual trait means was investigated using additive genetic, genotypic and the phenotypic index of Elston (1963). The characters responded differently to these indices under various parameter combinations, indicating favourable and unfavourable effects of the mentioned parameters. Linkage was found to reduce the rate of progress through selection. Depression of genetic gain was greater where the genes governing a character showed dominance and/or heritability coefficients were low. It was, however, noticed that depression of genetic gain due to low heritability of a character could be avoided by assigning higher economic weight to that character. This suggests that desirable changes in the means of characters available for selection can be manipulated by choosing appropriate economic weights. The additive genetic index, where only the additive genetic variances and covariances go into its construction, does not seem to be affected by intra-allelic interactions since they add to variances and covariances due to dominance deviations and these have nothing to do with the additive genetic variances and covariances. It seems that from such studies, if conducted extensively incorporating still more parameters, conclusions may be drawn on the most suitable selection model for simultaneous selection under a given set of parameters available in real biological systems.     

GENETIC VARIATION AND COVARIATION FOR CHARACTERISTICS ASSOCIATED WITH CADMIUM TOLERANCE IN NATURAL POPULATIONS OF THE SPRINGTAIL ORCHESELLA CINCTA (L.)

Heavy metals can be strong and stable directional selective agents for metal-exposed populations. Genetic variation for the metal-tolerance characteristic “cadmium excretion efficiency” was studied in populations of the collembolan Orchesella cincta from a reference- and a metal-contaminated forest soil. Previously it has been shown that “excretion efficiency” influences tolerance through midgut-mediated immobilization and excretion of toxic metal ions, and that an increased mean excretion efficiency is present in animals inhabiting metal-contaminated litter. In the present research, offspring-parent regressions showed that additive genetic variation for cadmium excretion efficiency was present in the population from the reference site. The heritability estimate was 0.33. In the natural population exposed to heavy metals from an industrial source, additive genetic variation was not significantly different from zero. Differences in the heritability between the reference and the exposed population were not significant. Genetic variation for cadmium excretion efficiency allows for a response to selection in the reference population. Such a response has probably occurred in the metal-exposed population. Half-sib analysis with animals from the reference population was used to estimate genetic variation and maternal effects for excretion efficiency, relative growth rate and molting frequency, and to determine genetic correlations between these characteristics. Additive genetic variation was demonstrated for all three characteristics, heritability estimates were 0.48, 0.75 and 0.46, respectively. Maternal effects were low for excretion efficiency and molting frequency, but may be present for relative growth rate. Phenotypic and genetic correlations among these characteristics were positive. The environmental correlation between relative growth rate and molting frequency was positive, others were negative. Direct selection for any of the characteristics, or genetic correlations between tolerance characteristics and growth characteristics, or both may have caused the responses previously observed in field populations.     

COMPARING STRENGTHS OF DIRECTIONAL SELECTION: HOW STRONG IS STRONG?

The fundamental equation in evolutionary quantitative genetics, the Lande equation, describes the response to directional selection as a product of the additive genetic variance and the selection gradient of trait value on relative fitness. Comparisons of both genetic variances and selection gradients across traits or populations require standardization, as both are scale dependent. The Lande equation can be standardized in two ways. Standardizing by the variance of the selected trait yields the response in units of standard deviation as the product of the heritability and the variance-standardized selection gradient. This standardization conflates selection and variation because the phenotypic variance is a function of the genetic variance. Alternatively, one can standardize the Lande equation using the trait mean, yielding the proportional response to selection as the product of the squared coefficient of additive genetic variance and the mean-standardized selection gradient. Mean-standardized selection gradients are particularly useful for summarizing the strength of selection because the mean-standardized gradient for fitness itself is one, a convenient benchmark for strong selection. We review published estimates of directional selection in natural populations using mean-standardized selection gradients. Only 38 published studies provided all the necessary information for calculation of mean-standardized gradients. The median absolute value of multivariate mean-standardized gradients shows that selection is on average 54% as strong as selection on fitness. Correcting for the upward bias introduced by taking absolute values lowers the median to 31%, still very strong selection. Such large estimates clearly cannot be representative of selection on all traits. Some possible sources of overestimation of the strength of selection include confounding environmental and genotypic effects on fitness, the use of fitness components as proxies for fitness, and biases in publication or choice of traits to study.     

Effects of bottlenecks on quantitative genetic variation in the butterfly Bicyclus anynana

The effects of a single population bottleneck of differing severity on heritability and additive genetic variance was investigated experimentally using a butterfly. An outbred laboratory stock was used to found replicate lines with one pair, three pairs and 10 pairs of adults, as well as control lines with approximately 75 effective pairs. Heritability and additive genetic variance of eight wing pattern characters and wing size were estimated using parent-offspring covariances in the base population and in all daughter lines. Individual morphological characters and principal components of the nine characters showed a consistent pattern of treatment effects in which average heritability and additive genetic variance was lower in one pair and three pair lines than in 10 pair and control lines. Observed losses in heritability and additive genetic variance were significantly greater than predicted by the neutral additive model when calculated with coefficients of inbreeding estimated from demographic parameters alone. However, use of molecular markers revealed substantially more inbreeding, generated by increased variance in family size and background selection. Conservative interpretation of a statistical analysis incorporating this previously undetected inbreeding led to the conclusion that the response to inbreeding of the morphological traits studied showed no significant departure from the neutral additive model. This result is consistent with the evidence for minimal directional dominance for these traits. In contrast, egg hatching rate in the same experimental lines showed strong inbreeding depression, increased phenotypic variance and rapid response to selection, highly indicative of an increase in additive genetic variance due to dominance variance conversion.     

Potential bias in inbreeding depression estimates when using pedigree relationships to assess the degree of homozygosity for loci under selection

A potential bias in estimation of inbreeding depression when using pedigree relationships to assess the degree of homozygosity for loci under selection is indicated. A comparison of inbreeding coefficients based on either pedigree or genotypic frequencies indicated that, as a result of selection, the inbreeding coefficient based on pedigree might not correspond with the random drift of allelic frequencies. Apparent differences in average levels of both inbreeding coefficients were obtained depending on the genetic model (additive versus dominance, initial allelic frequencies, heritability) and the selection system assumed (no versus mass selection). In the absence of selection, allelic frequencies within a small population change over generations due to random drift, and the pedigree-based inbreeding coefficient gives a proper assessment of the accompanying probability of increased homozygosity within a replicate by indicating the variance of allelic frequencies over replicates. With selection, in addition to random drift, directional change in allelic frequencies is not accounted for by the pedigree-based inbreeding coefficient. This result implies that estimation of inbreeding depression for traits under either direct or indirect selection, estimated by a regression of performance on pedigree-based coefficients, should be carefully interpreted.Deceased     

The heritability of fitness: some single gene models

Summary Because directional selection exhausts additive-genetic variance, it is frequently claimed that the heritability of fitness should be very close to zero. However, mutation-selection balance generates a certain amount of additive-genetic variance, so that even parent-offspring measures of heritability may be greater than zero at equilibrium. Intra-generation heritability may also be non-zero, providing the potentials for genetic change following environmental change.     

Smaller, scale-free gene networks increase quantitative trait heritability and result in faster population recovery

One of the goals of biology is to bridge levels of organization. Recent technological advances are enabling us to span from genetic sequence to traits, and then from traits to ecological dynamics. The quantitative genetics parameter heritability describes how quickly a trait can evolve, and in turn describes how quickly a population can recover from an environmental change. Here I propose that we can link the details of the genetic architecture of a quantitative trait--i.e., the number of underlying genes and their relationships in a network--to population recovery rates by way of heritability. I test this hypothesis using a set of agent-based models in which individuals possess one of two network topologies or a linear genotype-phenotype map, 16-256 genes underlying the trait, and a variety of mutation and recombination rates and degrees of environmental change. I find that the network architectures introduce extensive directional epistasis that systematically hides and reveals additive genetic variance and affects heritability: network size, topology, and recombination explain 81% of the variance in average heritability in a stable environment. Network size and topology, the width of the fitness function, pre-change additive variance, and certain interactions account for ～75% of the variance in population recovery times after a sudden environmental change. These results suggest that not only the amount of additive variance, but importantly the number of loci across which it is distributed, is important in regulating the rate at which a trait can evolve and populations can recover. Taken in conjunction with previous research focused on differences in degree of network connectivity, these results provide a set of theoretical expectations and testable hypotheses for biologists working to span levels of organization from the genotype to the phenotype, and from the phenotype to the environment.