My research area is theoretical population genetics; my aim is to augment our understanding of the genetic structure and evolution of natural populations. Most of my research concerns the formulation and analysis of models for geographical variation, random genetic drift, natural selection, and gene conversion in multigene families.
I have shown that, excluding a relatively narrow range of parameters, neutral and selective models of geographical variation may be treated dichotomously. In both cases, I incorporate migration into the models and investigate the amount and pattern of genetic variability. In neutral models, I replace selection by random genetic drift and mutation to new alleles.
No convincing biological rationale has been advanced for the Wright-Fisher model with (zygotic) selection. Therefore, I have formulated new models for the joint action of selection, mutation, and random genetic drift in panmictic populations. These models can be derived from explicit biological assumptions and may be more realistic than the Wright-Fisher model. The second aim of this part of my research program has been to establish a variety of useful and illuminating approximations for our models. This unified approach contrasts with the ad hoc modeling in most of the literature.
My studies of natural selection in panmictic populations have been primarily devoted to proving and extending the approximate validity of Fisher's Fundamental Theorem of Natural Selection (that the rate of increase of the mean fitness is equal to the additive component of the genetic variance) for weak selection or weak epistasis. This covers most situations of biological interest.
I am also interested in the evolution of multigene families under the joint action of gene conversion, equal crossing-over, random genetic drift, and mutation to new alleles. I have related my assumptions and parameters directly to current models of recombination. The results show that gene conversion may be an important mechanism for maintaining sequence homogeneity among repeated genes.
Selected Publications
Nagylaki, T., 1997. The diffusion model for migration and selection in a plant population. J. Math. Biol. 35: 409-431.
Nagylaki, T., 1997. Multinomial-sampling models for random genetic drift. Genetics 145: 485-491.
Nagylaki, T., 1998. The expected number of heterozygous sites in a subdivided population. Genetics 149: 1599-1604.
Nagylaki, T., J. Hofbauer, and P. Brunovsky 1999. Convergence of multilocus systems under weak epistasis or weak selection. J. Math. Biol. 38: 103-133.
Ayati, B. P., T. F. Dupont, and T. Nagylaki, 1999. The influence of spatial inhomogeneities on neutral models of geographical variation. IV. Discontinuities in the population density and migration rate. Theor. Pop. Biol. 56: 337-347.
Nagylaki, T., 2000. Geographical invariance and the strong-migration limit in subdivided populations. J. Math. Biol. 41: 123-142.
Nagylaki, T. and Y. Lou, 2001. Patterns of multiallelic polymorphism maintained by migration and selection. Theor. Pop. Biol. 59: 297-313.
Lou, Y. and T. Nagylaki, 2002. A semilinear parabolic system for migration and selection in population genetics. J. Diff. Eqs. 181: 388-418.
Nagylaki, T., 2002. When and where was the most recent common ancestor? J. Math. Biol. 44: 253-275.
Lou, Y. and T. Nagylaki, 2004. Evolution of a semilinear parabolic system for migration and selection in population genetics. J. Diff. Eqs. 204: 292-322.
Nagylaki, T., 2005. A stochastic model for a progressive chronic disease. J. Math. Biol. 51, 268-280.
Nagylaki, T. and Y. Lou, 2006. Multiallelic selection polymorphism. Theor. Pop. Biol. 69, 217-229.
Lou, Y. and T. Nagylaki, 2006. Evolution of a semilinear parabolic system for migration and selection without dominance. J. Diff. Eqs. 225, 624-665.
Nagylaki, T. and Y. Lou, 2006. Evolution under the multiallelic Levene model. Theor. Pop. Biol. 70, 401-411.
Nagylaki, T. and Y. Lou, 2007. Evolution under multiallelic migration-selection models. Theor. Pop. Biol. 72, 21-40.
Nagylaki, T. and Y. Lou, 2007. Evolution at a multiallelic locus under migration and uniform selection. J. Math. Biol. 54, 787-796.
Nagylaki, T. and Y. Lou, 2008. The dynamics of migration-selection models. In Tutorials in Mathematical Biosciences Vol. IV Evolution and Ecology (edited by A. Friedman), p. 119-172. Springer-Verlag, Berlin. Online at www.springerlink.com.