My research area is mathematical population genetics. Population genetics is concerned with the study of the genetic composition of populations. This composition may be changed by segregation, selection, mutation, recombination, mating structure, migration, and other genetic, ecological, and evolutionary factors. Therefore, in population genetics these mechanisms and their interactions and evolutionary consequences are investigated. It provides the basis for understanding the evolutionary processes that have led to the diversity of life we encounter and admire. Mathematical models have played a central role in population genetics since its beginning in the early twentieth century. They are based on Mendel's laws and often seek to predict the between-generation change in gene frequencies or, more generally, in the distribution of trait values within a population that is subject to some of the above mentioned evolutionary forces. Other branches of population genetics are concerned with inferring the evolutionary processes that shaped contemporary populations from genetic data extracted from those populations.
Much of my research has been concerned with the equilibrium and evolutionary properties of the distribution of quantitative traits under various forms of selection. Such traits are typically determined by many gene loci, therefore multilocus models have to be investigated to explore such problems. Among others, I studied models of mutation, stabilizing selection, and random genetic drift, and derived approximations for the equilibrium distribution of a quantitative trait subject to these forces. I analyzed the response of equilibrium populations to various forms of directional and fluctuating selection, and investigated the role of recombination and sexual reproduction for the magnitude of the selection response. Moreover, I applied such models to problems of conservation genetics, for instance, to determine the extinction risk of a population that is experiencing a long-term environmental change, such as global warming.
More recently, I have been working on multilocus models of frequency-dependent selection on a quantitative trait, as it occurs if individuals of similar phenotype compete for resources from a continuous spectrum. In combination with assortative mating, such models are important to understand the conditions that may lead to sympatric speciation. Currently, most of my research focuses on the evolution in spatially subdivided populations, in particular, on the role of migration in maintaining polymorphism and genetic diversity at multiple loci. I am especially interested in the mechanisms maintaining and driving genetic differentiation between populations connected by gene flow. In this context, I have been exploring models designed to quantify the role of diversifying selection and of prezygotic or postzygotic isolation in generating divergence, thus leading to parapatric speciation.
I have also (co-)authored a number of papers on the evolution of multivariate quantitative traits and the G-matrix, on the evolutionary consequences of deleterious mutations, on the fixation probability of alleles in a finite population, on the evolution of dominance, on game theory, on the origin of life, on evolutionary explanations for the high phenotypic (i.e., those during transmission and transcription) mutation rates, on the extinction risk of small populations from genetic, demographic, and other causes, and on the role of genetic variation in community ecology.
My book The Mathematical Theory of Selection, Recombination, and Mutation (published in 2000 by John Wiley& Sons, Chichester, ISBN 0-471-98653-4) presents the basic mathematical theory of single- and multilocus genetic models. The emphasis is on models that provide the fundamental underpinning to our understanding of quantitative genetic variation and its evolutionary consequences. Also the relevant empirical literature is reviewed. Click here for a PDF-file with corrections, updates, further developments, etc. Reports on further deficiencies are welcome.
During the past fifteen years, my research has been supported by grants from FWF, WWTF, and NSF.