The strongmigration limit in geographically structured populations
 Thomas Nagylaki
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Some strongmigration limits are established for geographically structured populations. A diploid monoecious population is subdivided into a finite number of colonies, which exchange migrants. The migration pattern is fixed and ergodic, but otherwise arbitrary. Generations are discrete and nonoverlapping; the analysis is restricted to a single locus. In all the limiting results, an effective population number N _{ e } (⩽ N_{ T }) appears instead of the actual total population number N _{ T }. 1. If there is no selection, every allele mutates at rate u to types not preexisting in the population, and the (finite) subpopulation numbers N _{ i } are very large, then the ultimate rate and pattern of convergence of the probabilities of allelic identity are approximately the same as for panmixia. If, in addition, the N _{ i } are proportional to 1/u, as N _{ T }→∼8, the equilibrium probabilities of identity converge to the panmictic value. 2. With a finite number of alleles, any mutation pattern, an arbitrary selection scheme for each colony, and the mutation rates and selection coefficients proportional to 1/N _{ T }, let P _{ j } be the frequency of the allele A _{ j } in the entire population, averaged with respect to the stationary distribution of the backward migration matrix M. As N _{ T } → ∼8, the deviations of the allelic frequencies in each of the subpopulations from P _{ j } converge to zero; the usual panmictic mutationselection diffusion is obtained for P _{ j }, with the selection intensities averaged with respect to the stationary distribution of M. In both models, N _{ e } = N _{ T } and all effects of population subdivision disappear in the limit if, and only if, migration does not alter the subpopulation numbers.
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 Title
 The strongmigration limit in geographically structured populations
 Journal

Journal of Mathematical Biology
Volume 9, Issue 2 , pp 101114
 Cover Date
 19800401
 DOI
 10.1007/BF00275916
 Print ISSN
 03036812
 Online ISSN
 14321416
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Migration
 Random drift
 Geographical structure
 Markov chains
 Limit theorems
 Industry Sectors
 Authors

 Thomas Nagylaki ^{(1)}
 Author Affiliations

 1. Department of Biophysics and Theoretical Biology, University of Chicago, 920 East 58th Street, 60637, Chicago, IL, USA