The spread of an advantageous allele across a barrier: the effects of random drift and selection against heterozygotes.

A local barrier to gene flow will delay the spread of an advantageous allele. Exact calculations for the deterministic case show that an allele that is favorable when rare is delayed very little even by a strong barrier: its spread is slowed by a time proportional to log((B/sigma) square root of 2S)/S, where B is the barrier strength, sigma the dispersal range, and fitnesses are 1:1 + S:1 + 2S. However, when there is selection against heterozygotes, such that the allele cannot increase from low frequency, a barrier can cause a much greater delay. If gene flow is reduced below a critical value, spread is entirely prevented. Stochastic simulations show that with additive selection, random drift slows down the spread of the allele, below the deterministic speed of sigma square root of 2S. The delay to the advance of an advantageous allele caused by a strong barrier can be substantially increased by random drift and increases with B/(2S rho sigma 2) in a one-dimensional habitat of density rho. However, with selection against heterozygotes, drift can facilitate the spread and can free an allele that would otherwise be trapped indefinitely by a strong barrier. We discuss the implications of these results for the evolution of chromosome rearrangements.

[1]  P. Brain,et al.  Karyotype and intermale aggression in wild house mice: Ecology and speciation , 1984, Behavior genetics.

[2]  N. Barton,et al.  A MODEL OF A HYBRID ZONE BETWEEN TWO CHROMOSOMAL RACES OF THE COMMON SHREW (SOREX ARANEUS) , 1992, Evolution; international journal of organic evolution.

[3]  K. Hadeler Travelling Population Fronts , 1976 .

[4]  A. N. Stokes On two types of moving front in quasilinear diffusion , 1976 .

[5]  N. Barton,et al.  Analysis of Hybrid Zones , 1985 .

[6]  N. Barton,et al.  THE PROBABILITY OF FIXATION OF A NEW KARYOTYPE IN A CONTINUOUS POPULATION , 1991, Evolution; international journal of organic evolution.

[7]  M. Slatkin,et al.  A COMPARISON OF THREE INDIRECT METHODS FOR ESTIMATING AVERAGE LEVELS OF GENE FLOW , 1989, Evolution; international journal of organic evolution.

[8]  T. Nagylaki,et al.  Conditions for the existence of clines. , 1975, Genetics.

[9]  N. Barton,et al.  The frequency of shifts between alternative equilibria. , 1987, Journal of theoretical biology.

[10]  M. Slatkin,et al.  The spatial distribution of transient alleles in a subdivided population: a simulation study. , 1978, Genetics.

[11]  E. Nevo,et al.  HYBRIDIZATION AND SPECIATION IN FOSSORIAL MOLE RATS , 1976, Evolution; international journal of organic evolution.

[12]  B. Charlesworth,et al.  Sex differences in fitness and selection for centric fusions between sex-chromosomes and autosomes. , 1980, Genetical research.

[13]  Denis Mollison,et al.  Spatial Contact Models for Ecological and Epidemic Spread , 1977 .

[14]  R. Lande EFFECTIVE DEME SIZES DURING LONG‐TERM EVOLUTION ESTIMATED FROM RATES OF CHROMOSOMAL REARRANGEMENT , 1979, Evolution; international journal of organic evolution.

[15]  W. Atchley,et al.  House Mice as Models in Systematic Biology , 1993 .

[16]  T. Nagylaki,et al.  Clines with variable migration. , 1976, Genetics.

[17]  M. King Species Evolution: The Role of Chromosome Change , 1993 .

[18]  R. May,et al.  Gene Frequency Clines in the Presence of Selection Opposed by Gene Flow , 1975, The American Naturalist.

[19]  M. Slatkin The Rate of Spread of an Advantageous Allele in a Subdivided Population , 1976 .

[20]  K. Key The Concept of Stasipatric Speciation , 1968 .

[21]  T. Maruyama,et al.  On the fixation probability of mutant genes in a subdivided population. , 1970, Genetical research.

[22]  B K Epperson Spatial and space-time correlations in systems of subpopulations with stochastic migration. , 1994, Theoretical population biology.

[23]  T. Nagylaki Random genetic drift in a cline. , 1978, Proceedings of the National Academy of Sciences of the United States of America.

[24]  R. Fisher THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES , 1937 .

[25]  M T Davisson,et al.  Recombination suppression by heterozygous Robertsonian chromosomes in the mouse. , 1993, Genetics.

[26]  M. Nachman,et al.  Why is the house mouse karyotype so variable? , 1995, Trends in ecology & evolution.

[27]  N. Barton Gene flow past a cline , 1979, Heredity.

[28]  V. Bauchau,et al.  Segregation and fertility in Mus musculus domesticus (wild mice) heterozygous for the Rb(4.12) translocation , 1992, Heredity.

[29]  M. Shaw,et al.  Simulation of population expansion and spatial pattern when individual dispersal distributions do not decline exponentially with distance , 1995, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[30]  P. Scriven Robertsonian translocations introduced into an island population of house mice , 1992 .