Biomedical subjects

Reinhard Bürger

Publications and source records attributed to Reinhard Bürger.

10 recordsLinked to original sources

PubMed2006

Intraspecific competitive divergence and convergence under assortative mating.

Ecologically driven sympatric speciation has received much attention recently. We investigate a multilocus model of a quantitative trait that is under frequency-dependent selection caused by intraspecific competition and acts as mating character for assortment. We identify the conditions that lead to the establishment of reproductively isolated clusters. This may be interpreted as evolutionary splitting or sympatric speciation. In our model, there are parameters that independently determine the strength of assortment, the costs for being choosy, and the strength of frequency-dependent natural selection. Sufficiently strong frequency dependence leads to disruptive selection on the phenotypes. The population consists of (sexual) haploid individuals. If frequency dependence is strong enough to induce disruptive selection and costs are absent or low, the result of evolution depends in a distinctive nonlinear way on the strength of assortment: under moderately strong assortment, less genetic variation is maintained than under weak or strong assortment, and sometimes there is none at all. Evolutionary splitting occurs only if frequency dependence and assortment are both strong enough and costs are low. Even then, the evolutionary outcome depends on the genetics and the initial conditions. The roles of the number of loci, of linkage, and of asymmetric selection are also explored.

Animals↗

PubMed2005

Why are phenotypic mutation rates much higher than genotypic mutation rates?

The evolution of genotypic mutation rates has been investigated in numerous theoretical and experimental studies. Mutations, however, occur not only when copying DNA, but also when building the phenotype, especially when translating and transcribing DNA to RNA and protein. Here we study the effect of such phenotypic mutations. We find a maximum phenotypic mutation rate, umax, that is compatible with maintaining a certain function of the organism. This may be called a phenotypic error threshold. In particular, we find a minimum phenotypic mutation rate, umin, with the property that there is (nearly) no selection pressure to reduce the rate of phenotypic mutations below this value. If there is a cost for lowering the phenotypic mutation rate, then umin is close to the optimum phenotypic mutation rate that maximizes the fitness of the organism. In our model, there is selective pressure to decrease the rate of genotypic mutations to zero, but to decrease the rate of phenotypic mutations only to a positive value. Despite its simplicity, our model can explain part of the huge difference between genotypic and phenotypic mutation rates that is observed in nature. The relevant data are summarized.

Animals↗

PubMed2004

A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait.

The equilibrium structure of an additive, diallelic multilocus model of a quantitative trait under frequency- and density-dependent selection is derived. The trait is under stabilizing selection and mediates intraspecific competition as induced, for instance, by differential resource utilization. It is assumed that stabilizing selection is weak, but the strength of competition may be arbitrary relative to it. Density dependence is caused by population regulation, which may be of a very general kind. The number and effects of loci are arbitrary, and stabilizing selection is not necessarily symmetric with respect to the range of phenotypic values. All previously studied models of intraspecific competition for a continuum of resources known to the author reduce to a special case of the present model if overall selection is weak. Therefore, in this case our results are applicable as approximations to all these models. Our central result is the (nearly) complete characterization of the equilibrium and stability structure in terms of all parameters. It is derived under the sole assumption that selection is weak enough relative to recombination to ignore linkage disequilibrium. In particular, necessary and sufficient conditions on the strength of competition relative to stabilizing selection are found that ensure the maintenance of multilocus polymorphism and the occurrence of disruptive selection. In this case, explicit formulas for the number of polymorphic loci at equilibrium, the allele frequencies, the genetic variance, and the strength of disruptive selection are obtained. For two loci, the effects of linkage are investigated analytically; for several loci, they are studied numerically.

Alleles↗

PubMed2004

Evolution and stability of the G-matrix on a landscape with a moving optimum.

In quantitative genetics, the genetic architecture of traits, described in terms of variances and covariances, plays a major role in determining the trajectory of evolutionary change. Hence, the genetic variance-covariance matrix (G-matrix) is a critical component of modern quantitative genetics theory. Considerable debate has surrounded the issue of G-matrix constancy because unstable G-matrices provide major difficulties for evolutionary inference. Empirical studies and analytical theory have not resolved the debate. Here we present the results of stochastic models of G-matrix evolution in a population responding to an adaptive landscape with an optimum that moves at a constant rate. This study builds on the previous results of stochastic simulations of G-matrix stability under stabilizing selection arising from a stationary optimum. The addition of a moving optimum leads to several important new insights. First, evolution along genetic lines of least resistance increases stability of the orientation of the G-matrix relative to stabilizing selection alone. Evolution across genetic lines of least resistance decreases G-matrix stability. Second, evolution in response to a continuously changing optimum can produce persistent maladaptation for a correlated trait, even if its optimum does not change. Third, the retrospective analysis of selection performs very well when the mean G-matrix (G) is known with certainty, indicating that covariance between G and the directional selection gradient beta is usually small enough in magnitude that it introduces only a small bias in estimates of the net selection gradient. Our results also show, however, that the contemporary G-matrix only serves as a rough guide to G. The most promising approach for the estimation of G is probably through comparative phylogenetic analysis. Overall, our results show that directional selection actually can increase stability of the G-matrix and that retrospective analysis of selection is inherently feasible. One major remaining challenge is to gain a sufficient understanding of the G-matrix to allow the confident estimation of G.

Adaptation, Biological↗

PubMed2004

The effects of intraspecific competition and stabilizing selection on a polygenic trait.

The equilibrium properties of an additive multilocus model of a quantitative trait under frequency- and density-dependent selection are investigated. Two opposing evolutionary forces are assumed to act: (i) stabilizing selection on the trait, which favors genotypes with an intermediate phenotype, and (ii) intraspecific competition mediated by that trait, which favors genotypes whose effect on the trait deviates most from that of the prevailing genotypes. Accordingly, fitnesses of genotypes have a frequency-independent component describing stabilizing selection and a frequency- and density-dependent component modeling competition. We study how the equilibrium structure, in particular, number, degree of polymorphism, and genetic variance of stable equilibria, is affected by the strength of frequency dependence, and what role the number of loci, the amount of recombination, and the demographic parameters play. To this end, we employ a statistical and numerical approach, complemented by analytical results, and explore how the equilibrium properties averaged over a large number of genetic systems with a given number of loci and average amount of recombination depend on the ecological and demographic parameters. We identify two parameter regions with a transitory region in between, in which the equilibrium properties of genetic systems are distinctively different. These regions depend on the strength of frequency dependence relative to pure stabilizing selection and on the demographic parameters, but not on the number of loci or the amount of recombination. We further study the shape of the fitness function observed at equilibrium and the extent to which the dynamics in this model are adaptive, and we present examples of equilibrium distributions of genotypic values under strong frequency dependence. Consequences for the maintenance of genetic variation, the detection of disruptive selection, and models of sympatric speciation are discussed.

Biological Evolution↗

PubMed2003

The two-locus model of Gaussian stabilizing selection.

We study the equilibrium structure of a well-known two-locus model in which two diallelic loci contribute additively to a quantitative trait that is under Gaussian stabilizing selection. The population is assumed to be infinitely large, randomly mating, and having discrete generations. The two loci may have arbitrary effects on the trait, the strength of selection and the recombination rate may also be arbitrary. We find that 16 different equilibrium patterns exist, having up to 11 equilibria; up to seven interior equilibria may coexist, and up to four interior equilibria, three in negative and one in positive linkage disequilibrium, may be simultaneously stable. Also, two monomorphic and two fully polymorphic equilibria may be simultaneously stable. Therefore, the result of evolution may be highly sensitive to perturbations in the initial conditions or in the underlying genetic parameters. For the special case of equal effects, global stability results are proved. In the general case, we rely in part on numerical computations. The results are compared with previous analyses of the special case of extremely strong selection, of an approximate model that assumes linkage equilibrium, and of the much simpler quadratic optimum model.

Alleles↗

PubMed2003

Stability of the G-matrix in a population experiencing pleiotropic mutation, stabilizing selection, and genetic drift.

Quantitative genetics theory provides a framework that predicts the effects of selection on a phenotype consisting of a suite of complex traits. However, the ability of existing theory to reconstruct the history of selection or to predict the future trajectory of evolution depends upon the evolutionary dynamics of the genetic variance-covariance matrix (G-matrix). Thus, the central focus of the emerging field of comparative quantitative genetics is the evolution of the G-matrix. Existing analytical theory reveals little about the dynamics of G, because the problem is too complex to be mathematically tractable. As a first step toward a predictive theory of G-matrix evolution, our goal was to use stochastic computer models to investigate factors that might contribute to the stability of G over evolutionary time. We were concerned with the relatively simple case of two quantitative traits in a population experiencing stabilizing selection, pleiotropic mutation, and random genetic drift. Our results show that G-matrix stability is enhanced by strong correlational selection and large effective population size. In addition, the nature of mutations at pleiotropic loci can dramatically influence stability of G. In particular, when a mutation at a single locus simultaneously changes the value of the two traits (due to pleiotropy) and these effects are correlated, mutation can generate extreme stability of G. Thus, the central message of our study is that the empirical question regarding G-matrix stability is not necessarily a general question of whether G is stable across various taxonomic levels. Rather, we should expect the G-matrix to be extremely stable for some suites of characters and unstable for others over similar spans of evolutionary time.

Analysis of Variance↗

PubMed2003

Chromosome pairing does not contribute to nuclear architecture in vegetative yeast cells.

There are several reports of a closer-than-random colocalization of homologous chromosomes in the vegetative nuclei of diploid budding yeast. Here, we studied by fluorescence in situ hybridization (FISH) the nuclear distribution of chromosomes and found a slight tendency toward closer proximity between homologous (allelic) loci than between any nonhomologous chromosomal regions. We show that most of this preferential association is not due to vegetative (also known as somatic) pairing but is caused by the polar orientation of interphase chromosomes (Rabl orientation). We quantified the occasional loss of detectable fluorescence signals that is inherent to the FISH method. Signal loss leads to the occurrence of a single signal that may be misinterpreted as the close association of two homologous chromosomal sites. The nuclear distribution of homologous loci, when corrected for the influence of nuclear architecture and methodological faults, was not different or was only marginally different from a random relative positioning as predicted by computer simulation. We discuss here several possibilities for the residual homologous proximity that do not invoke homology-dependent vegetative pairing, and we conclude that, in diploid budding yeast, constitutive vegetative pairing is a negligible factor for the organization of the interphase nucleus.

Cell Nucleus↗

PubMed2002

Additive genetic variation under intraspecific competition and stabilizing selection: a two-locus study.

A diallelic two-locus model is investigated in which the loci determine the genotypic value of a quantitative trait additively. Fitness has two components: stabilizing selection on the trait and a frequency-dependent component, as induced, for instance, if the ability to utilize different food resources depends on this trait. Since intraspecific competition induces disruptive selection, this model leads to a conflict of selective forces. We study how the underlying genetics (recombination rate and allelic effects) interacts with the selective forces, and explore the resulting equilibrium structure. For the special case of equal effects, global stability results are proved. Unless the locus effects are sufficiently different, the genetic variance maintained at equilibrium displays a threshold-like dependence on the strength of competition. For loci with equal effects, the equilibrium fitnesses of genotypic values exhibit disruptive selection if and only if competition is strong enough to maintain a stable two-locus polymorphism. For unequal effects, disruptive selection can be observed for weaker competition and in the absence of a stable polymorphism.

Animals↗

PubMed2002

Fluctuating environments and the role of mutation in maintaining quantitative genetic variation.

We study a class of genetic models in which a quantitative trait determined by several additive loci is subject to temporally fluctuating selection. Selection on the trait is assumed to be stabilizing but with an optimum that varies periodically and might be perturbed stochastically. The population mates at random, is infinitely large and has discrete generations. We pursue a statistical and numerical approach, covering a wide range of ecological and genetic parameters, to determine the potential of fluctuating environments to maintain quantitative genetic variation. Whereas, in contrast to some recent claims, this potential seems to be rather limited in the absence of recurrent mutation, fluctuating environments might, in combination with it, often generate high levels of additive genetic variation. We investigate how the genetic variation maintained depends on the ecological parameters and on the underlying genetics.

Genetic Variation↗