Stochastic Processes in Evolutionary and Disease Genetics

The broad subject area of the meeting was that of mathematical population genetics. It is concerned with the analysis of the generation, nature, and maintenance of genetic variation within and between biological populations. In its evolutionary aspects it describes the change in the genetic composition of populations under the influence of various evolutionary forces, the most important of which are mutation, selection, recombination, migration and random genetic drift. The latter is a consequence of the fact that even without fitness differences, some individuals may, just by chance, have more offspring than others, so that the offspring of one genotype may displace another one in a finite population. Thus there is a significant element of randomness in genetic systems. From the point of view of disease genetics, many diseases are caused by deleterious mutant genes, and the analysis of the variation in a population for the disease and the normal gene is a significant component of this area of research. These two components of the theory have hitherto been somewhat separate. However, recent trends in evolutionary genetics theory have brought them together, and one of the aims of this meeting was to further this fusion of two important areas of population genetics. Three new developments are shaping the area at present: a change in biological thinking, the emergence of new data, and new mathematic(ian)s; these are, of course, all interrelated. Let us explain this in some more detail. The basic processes of evolution are known in principle, along with fundamental equations which describe the effects of interactions between genes. Indeed, of the biological sciences, genetics is the one with the most clearly defined mathematical models. The evolutionary behavior of a population may be described by a stochastic model of gene frequency change, which is similar to corresponding models in interacting particle systems. These models are well understood if mutation and drift are the only forces present, or if selection is also present but acts on the genes at one or a small number of gene loci. In particular, the pattern of genetic variation generated under these scenarios is quite well known. But for several decades, the area suffered from a lack of data to support or reject the hypotheses about the evolutionary process and the genetic basis of various diseases. It was therefore often criticized as ”l’art pour l’art”. This situation has suddenly been reversed due to the wealth of molecular data flowing in during the past few years. The data come from the various genome projects, and from studies aimed at the genetic basis of human diseases. The most valuable data

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