The anomalous effects of biased mutation

Assessment on induced genetic variability and divergence in the mutagenized lentil populations of microsperma and macrosperma cultivars developed using physical and chemical mutagenesis

Induced mutagenesis was employed to create genetic variation in the lentil cultivars for yield improvement. The assessments were made on genetic variability, character association, and genetic divergence among the twelve mutagenized populations and one parent population of each of the two lentil cultivars, developed by single and combination treatments with gamma rays and hydrazine hydrates. Analysis of variance revealed significant inter-population differences for the observed quantitative phenotypic traits. The sample mean of six treatment populations in each of the cultivar exhibited highly superior quantitative phenotypic traits compared to their parent cultivars. The higher values of heritability and genetic advance with a high genotypic coefficient of variation for most of the yield attributing traits confirmed the possibilities of lentil yield improvement through phenotypic selection. The number of pods and seeds per plant appeared to be priority traits in selection for higher yield due to their strong direct association with yield. The cluster analysis divided the total populations into three divergent groups in each lentil cultivar with parent genotypes in an independent group showing the high efficacy of the mutagens. Considering the highest contribution of yield trait to the genetic divergence among the clustered population, it was confirmed that the mutagenic treatments created a wide heritable variation for the trait in the mutant populations. The selection of high yielding mutants from the mutant populations of DPL 62 (100 Gy) and Pant L 406 (100Gy + 0.1% HZ) in the subsequent generation is expected to give elite lentil cultivars. Also, hybridization between members of the divergent group would produce diverse segregants for crop improvement. Apart from this, the induced mutations at loci controlling economically important traits in the selected high yielding mutants have successfully contributed in diversifying the accessible lentil genetic base and will definitely be of immense value to the future lentil breeding programmes in India.

The contribution of spontaneous mutations to thermal sensitivity curve variation in Drosophila serrata

Many traits studied in ecology and evolutionary biology change their expression in response to a continuously varying environmental factor. One well-studied example are thermal performance curves (TPCs); continuous reaction norms that describe the relationship between organismal performance and temperature and are useful for understanding the trade-offs involved in thermal adaptation. We characterized curves describing the thermal sensitivity of voluntary locomotor activity in a set of 66 spontaneous mutation accumulation lines in the fly Drosophila serrata. Factor-analytic modeling of the mutational variance-covariance matrix, M, revealed support for three axes of mutational variation in males and two in females. These independent axes of mutational variance corresponded well to the major axes of TPC variation required for different types of thermal adaptation; "faster-slower" representing changes in performance largely independent of temperature, and the "hotter-colder" and "generalist-specialist" axes, representing trade-offs. In contrast to its near-absence from standing variance in this species, a "faster-slower" axis, accounted for most mutational variance (75% in males and 66% in females) suggesting selection may easily fix or remove these types of mutations in outbred populations. Axes resembling the "hotter-colder" and "generalist-specialist" modes of variation contributed less mutational variance but nonetheless point to an appreciable input of new mutations that may contribute to thermal adaptation.

Fisher's geometrical model emerges as a property of complex integrated phenotypic networks

Models relating phenotype space to fitness (phenotype-fitness landscapes) have seen important developments recently. They can roughly be divided into mechanistic models (e.g., metabolic networks) and more heuristic models like Fisher's geometrical model. Each has its own drawbacks, but both yield testable predictions on how the context (genomic background or environment) affects the distribution of mutation effects on fitness and thus adaptation. Both have received some empirical validation. This article aims at bridging the gap between these approaches. A derivation of the Fisher model "from first principles" is proposed, where the basic assumptions emerge from a more general model, inspired by mechanistic networks. I start from a general phenotypic network relating unspecified phenotypic traits and fitness. A limited set of qualitative assumptions is then imposed, mostly corresponding to known features of phenotypic networks: a large set of traits is pleiotropically affected by mutations and determines a much smaller set of traits under optimizing selection. Otherwise, the model remains fairly general regarding the phenotypic processes involved or the distribution of mutation effects affecting the network. A statistical treatment and a local approximation close to a fitness optimum yield a landscape that is effectively the isotropic Fisher model or its extension with a single dominant phenotypic direction. The fit of the resulting alternative distributions is illustrated in an empirical data set. These results bear implications on the validity of Fisher's model's assumptions and on which features of mutation fitness effects may vary (or not) across genomic or environmental contexts.

Stabilizing selection, purifying selection, and mutational bias in finite populations

Genomic traits such as codon usage and the lengths of noncoding sequences may be subject to stabilizing selection rather than purifying selection. Mutations affecting these traits are often biased in one direction. To investigate the potential role of stabilizing selection on genomic traits, the effects of mutational bias on the equilibrium value of a trait under stabilizing selection in a finite population were investigated, using two different mutational models. Numerical results were generated using a matrix method for calculating the probability distribution of variant frequencies at sites affecting the trait, as well as by Monte Carlo simulations. Analytical approximations were also derived, which provided useful insights into the numerical results. A novel conclusion is that the scaled intensity of selection acting on individual variants is nearly independent of the effective population size over a wide range of parameter space and is strongly determined by the logarithm of the mutational bias parameter. This is true even when there is a very small departure of the mean from the optimum, as is usually the case. This implies that studies of the frequency spectra of DNA sequence variants may be unable to distinguish between stabilizing and purifying selection. A similar investigation of purifying selection against deleterious mutations was also carried out. Contrary to previous suggestions, the scaled intensity of purifying selection with synergistic fitness effects is sensitive to population size, which is inconsistent with the general lack of sensitivity of codon usage to effective population size.

Change and maintenance of variation in quantitative traits in the context of the Price equation

The Price equation is a general description of evolutionary change in any character from one generation to the next due to natural selection and other forces such as mutation and recombination. Recently it has been widely utilised in many fields including quantitative genetics, but these applications have focused mainly on the response to selection in the mean of characters. Many different and, in some cases, conflicting models have been investigated by quantitative geneticists to examine the change and maintenance of both genetic and environmental variance of quantitative traits under selection and other forces. In this study, we use the Price equation to derive many such well-known results for the dynamics and equilibria of variances in a straightforward way and to develop them further.

The anomalous effects of biased mutation revisited: mean-optimum deviation and apparent directional selection under stabilizing selection

Empirical evidence indicates that the distribution of the effects of mutations on quantitative traits is not symmetric about zero. Under stabilizing selection in infinite populations with normally distributed mutant effects having a nonzero mean, Waxman and Peck showed that the deviation of the population mean from the optimum is expected to be small. We show by simulation that genetic drift, leptokurtosis of mutational effects, and pleiotropy can increase the mean-optimum deviation greatly, however, and that the apparent directional selection thereby caused can be substantial.

A generative bias towards average complexity in artificial cell lineages

The evolution of life on earth has been characterized by generalized long-term increases in phenotypic complexity. Although natural selection is a plausible cause for these trends, one alternative hypothesis--generative bias--has been proposed repeatedly based on theoretical considerations. Here, we introduce a computational model of a developmental system and use it to test the hypothesis that long-term increasing trends in phenotypic complexity are caused by a generative bias towards greater complexity. We use our model to generate random organisms with different levels of phenotypic complexity and analyse the distributions of mutational effects on complexity. We show that highly complex organisms are easy to generate but there are trade-offs between different measures of complexity. We also find that only the simplest possible phenotypes show a generative bias towards higher complexity, whereas phenotypes with high complexity display a generative bias towards lower complexity. These results suggest that generative biases alone are not sufficient to explain long-term evolutionary increases in phenotypic complexity. Rather, our finding of a generative bias towards average complexity argues for a critical role of selective biases in driving increases in phenotypic complexity and in maintaining high complexity once it has evolved.

Mutational bias for body size in rhabditid nematodes

Mutational bias is a potentially important agent of evolution, but it is difficult to disentangle the effects of mutation from those of natural selection. Mutation-accumulation experiments, in which mutations are allowed to accumulate at very small population size, thus minimizing the efficiency of natural selection, are the best way to separate the effects of mutation from those of selection. Body size varies greatly among species of nematode in the family rhabditidae; mutational biases are both a potential cause and a consequence of that variation. We report data on the cumulative effects of mutations that affect body size in three species of rhabditid nematode that vary fivefold in adult size. Results are very consistent with previous studies of mutations underlying fitness in the same strains: two strains of Caenorhabditis briggsae decline in body size about twice as fast as two strains of C. elegans, with a concomitant higher point estimate of the genomic mutation rate; the confamilial Oscheius myriophila is intermediate. There is an overall mutational bias, such that mutations reduce size on average, but the bias appears consistent between species. The genetic correlation between mutations that affect size and those underlying fitness is large and positive, on average.

Fisher's geometrical model of evolutionary adaptation--beyond spherical geometry

Fisher's geometrical model of evolutionary adaptation has recently been used in a variety of contexts of interest to evolutionary biologists. The renewed interest in this model strongly motivates generalizations that make it a more realistic description of evolutionary adaptation. Previously, the distribution of mutant effects has, for analytical tractability, rather than biological realism, been taken as spherically symmetric. Here we substantially extend Fisher's model, by allowing a wider class of mutational distributions that incorporate mutational bias and more general deviations from spherical symmetry such as correlations between mutant effects. We also incorporate work on generalized fitness landscapes, thereby reducing the number of artificial assumptions underlying the model. The generalized model exhibits a substantially increased flexibility and a far richer underlying geometry. We find that the distribution characterizing selection coefficients of new mutations is expressed in terms of a number of geometrical invariants associated with mutation, selection and the parental phenotype.

Near-periodic substitution and the genetic variance induced by environmental change

We investigate a model that describes the evolution of a diploid sexual population in a changing environment. Individuals have discrete generations and are subject to selection on the phenotypic value of a quantitative trait, which is controlled by a finite number of bialleic loci. Environmental change is taken to lead to a uniformly changing optimal phenotypic value. The population continually adapts to the changing environment, by allelic substitution, at the loci controlling the trait. We investigate the detailed interrelation between the process of allelic substitution and the adaptation and variation of the population, via infinite population calculations and finite population simulations. We find a simple relation between the substitution rate and the rate of change of the optimal phenotypic value.

Evolution of mechanoregulation of bone growth will lead to non-optimal bone phenotypes

Mechanical forces acting on the bones during growth affect their final shape and strength. Mechanoregulation of bone growth may be recognized in embryogenesis, and also in the adaptation of the adult skeleton to changes in mechanical loading. Mechanoregulatory responses for tissues have arisen during evolution, but does evolution give rise to responses that produce optimal skeletal phenotypes? In this paper, we investigate the emergence of an optimal mechanoregulation response in a population. By combining equations describing long bone growth with a genetic algorithm to describe evolutionary change, we created a computational model to simulate the evolution of mechanoregulation in bone growth. A population of individuals is created where each individual is assigned a diploid gene set which controls the growth and remodelling of the bone. At maturity, each bone is assessed and its 'fitness' calculated; fitness is quantified as bone strength relative to bone mass. The simulation continues for many generations, and includes mutations and a varying environment. The genes present in the population are tracked and the evolution of parameters governing mechanoregulation is calculated. The results indicate that a population may converge to one bone growth algorithm but, more usually, a range of mechanoregulation algorithms for different individuals will persist after many generations. Even if the population converges to one mechanoregulation law, convergence to the 'optimum' bone was never found. Although many researchers propose that natural selection has pushed skeletal structure towards an optimum, our computational model suggests that this is unlikely to be the case.

Dynamics of a quantitative character subject only to stabilising selection

The implications of stabilising selection on a quantitative trait, in the absence of other evolutionary forces, are theoretically investigated in a randomly mating population. The dynamics of various statistics that describe the alleles contributing to the trait are determined and used to infer the behaviour of the trait. Dynamical solutions of the distribution of allelic effects and the distribution of the trait are found when all initial distributions of allelic effects are Gaussian and linkage disequilibria are neglected. Some results for the behaviour of the mean and the variance of genotypic effects of the population, when subject to a moving optimum, are derived. When the initial distributions of allelic effects are not Gaussian, but possess a small asymmetry, the mean and the variance of the allelic effects differ only slightly from the Gaussian results. By contrast, the third central moments of allelic effects, are, at all loci, strictly zero in the Gaussian case but are generally non-zero for non-symmetric initial distributions. To leading order in a quantitative measure of the asymmetry of the distribution, we determine the third central moment of allelic effects.

A one locus, biased mutation model and its equivalence to an unbiased model

Experimental data suggests that for some continuously-varying characters under stabilising selection, mutation may cause a mean change in the value of the character. A one locus, mathematical model of a continuously-varying biological character with this property of biased mutation is investigated. Via a mathematical transformation, the equilibrium equation describing a large population of individuals is reduced to the equilibrium equation describing a mutationally unbiased problem. Knowledge of an unbiased problem is thus sufficient to determine all equilibrium properties of the corresponding biased problem. In the biased mutation problem, the dependence of the mean equilibrium value of the character, as a function of the mutational bias, is non-monotonic and remains small, for all levels of mutational bias. The analysis presented in this work sheds new light on Turelli's House of Cards Approximation.