The aim of this project is to understand better the role of selection in the genetics and evolution of natural populations through a study of the static and dynamic behavior of multilocus population genetic models. The models used in most of the analysis will be standard multilocus ones or quantitative genetics models as used in the study of mutation-selection balance. However, different methods of analysis will be used which will stress techniques and approaches which study the effects of weakening a prior assumptions made, such as the usual assumptions of normality of distributions and absence of epistasis in the study of the evolution of phenotypic characters. The static behavior of multilocus models with selection, both with and without mutation will be studied with the goal of understanding mechanisms underlying the maintenance of variability both at the phenotypic level and at the level of the single locus. Techniques based on bifurcation theory, perturbation theory and computer simulation will be used. Models where allele frequencies are explicitly included will be emphasized. The dynamics of multilocus systems will also be studied using perturbation techniques and computer simulation, again stressing phenotypic models based on underlying genetic models where allele frequencies are specified, with several goals.
One aim will be to understand the role of disequilibrium in the transient behavior of multilocus systems. In the context of phenotypic models, the importance of and implications of deviations from normality for the dynamics of continuous characters will be determined. Moreover, the role of epistasis will be investigated. Additionally, dynamics and statics in finite populations will be studied using both computer simulations and analytic techniques. The results of this study will help in understanding mechanisms which maintain variability in both natural and human populations.

National Institute of Health (NIH)
National Institute of General Medical Sciences (NIGMS)
Research Project (R01)
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Genetics Study Section (GEN)
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University of California Davis
Schools of Arts and Sciences
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Gavrilets, S; Hastings, A (1998) Coevolutionary chase in two-species systems with applications to mimicry. J Theor Biol 191:415-27
Gavrilets, S; Gravner, J (1997) Percolation on the fitness hypercube and the evolution of reproductive isolation. J Theor Biol 184:51-64
Gavrilets, S; Hastings, A (1995) Dynamics of polygenic variability under stabilizing selection, recombination, and drift. Genet Res 65:63-74
Gavrilets, S; Hastings, A (1995) Intermittency and transient chaos from simple frequency-dependent selection. Proc Biol Sci 261:233-8
Gavrilets, S; Hastings, A (1994) Maintenance of multilocus variability under strong stabilizing selection. J Math Biol 32:287-302
Gavrilets, S; Hastings, A (1994) Dynamics of genetic variability in two-locus models of stabilizing selection. Genetics 138:519-32
Gavrilets, S; Hastings, A (1993) Maintenance of genetic variability under strong stabilizing selection: a two-locus model. Genetics 134:377-86
Fox, G A; Hastings, A (1992) Inferring selective history from multilocus frequency data: Wright meets the Hamiltonian. Genetics 132:277-88
Hastings, A (1990) Second-order approximations for selection coefficients at polygenic loci. J Math Biol 28:475-83
Hastings, A (1990) Maintenance of polygenic variation through mutation-selection balance: bifurcation analysis of a biallelic model. J Math Biol 28:329-40

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