Reduction of Gene Flow Due to the Partial Sterility of Heterozygotes for a Chromosome Mutation. I. Studies on a 'Neutral' Gene Not Linked to the Chromosome Mutation in a Two Population Model

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Media type:
E-Article

Title:
Reduction of Gene Flow Due to the Partial Sterility of Heterozygotes for a Chromosome Mutation. I. Studies on a 'Neutral' Gene Not Linked to the Chromosome Mutation in a Two Population Model

Contributor:
Spirito, Franco;
Rossi, Carla;
Rizzoni, Marco

Published:
Society for the Study of Evolution, 1983

Published in:
Evolution, 37 (1983) 4, Seite 785-797

Language:
English

ISSN:
0014-3820;
1558-5646

Origination:

Footnote:

Description:
<p>The problem of 'chromosomal speciation' is addressed by studying the efficiency of the sterility of the heterozygotes for a chromosome mutation in the reduction of gene flow. Our deterministic model considers two populations, each initially monomorphic for one of two alternative forms of a chromosome whose heterozygotes are partially sterile, and which differ in the frequency of two neutral alleles of a locus not linked with the chromosome mutation. As a function of two parameters, m (the symmetrical and reciprocal migration rate between the two populations) and s (the partial sterility of the heterozygote for the chromosome mutation), the time course was defined of: 1) the difference in frequency of the mutated chromosome in the two populations (p<sub>1</sub>
<sup>(n)</sup>- p<sub>2</sub>
<sup>(n)</sup>); 2) the difference in frequency of a neutral allele in the two populations (P<sub>1</sub>
<sup>(n)</sup>- P<sub>2</sub>
<sup>(n)</sup>); and 3) the gametic phase disequilibrium of the overall system of the two populations (D<sub>c</sub>
<sup>(n)</sup>). Analysis of the recurrence equations reveals that: 1) p<sub>1</sub>
<sup>(n)</sup>- p<sub>2</sub>
<sup>(n)</sup>reaches an equilibrium value<tex-math>$\sqrt$</tex-math>{1 - 4m/s} when m/s < 1/4, and zero when m/s ⩾ 1/4; and 2) the equilibrium values of P<sub>1</sub>
<sup>(n)</sup>- P<sub>2</sub>
<sup>(n)</sup>and D<sub>c</sub>
<sup>(n)</sup>are always equal to zero (for s < 1). We describe the velocity with which equilibrium is approached, using simulations with various values of s and m. In order to quantify the reduction of the gene flow we calculated the number of generations necessary to reach set values of p<sub>1</sub>
<sup>(n)</sup>- p<sub>2</sub>
<sup>(n)</sup>and D<sub>c</sub>
<sup>(n)</sup>equal to 1/10 and 1/100 of the initial value. Two parameters were introduced: 1) the ratio (TR) between the number of generations necessary to reach a given value of P<sub>1</sub>
<sup>(n)</sup>- P<sub>2</sub>
<sup>(n)</sup>and D<sub>c</sub>
<sup>(n)</sup>corresponding to a given s ≠ 0 and that necessary to reach the same value for s = 0; and 2) the ratio (MRE) between the migration rate for s = 0 and that corresponding to a given s ≠ 0 necessary to reach, in the same number of generations, the same value of P<sub>1</sub>
<sup>(n)</sup>- P<sub>2</sub>
<sup>(n)</sup>and D<sub>c</sub>
<sup>(n)</sup>. The analysis reveals that TR increases as s increases and as m decreases, and tends to be constant for very low values of m. Thus gene frequencies move toward equilibrium more slowly if migration or the fitness of the heterokaryotype is low. In the low migration pattern, for s ≠ 0 the number of generations necessary to obtain the same reduction of P<sub>1</sub>
<sup>(n)</sup>- P<sub>2</sub>
<sup>(n)</sup>and D<sub>c</sub>
<sup>(n)</sup>is the same, whereas for s = 0 the value for P<sub>1</sub>
<sup>(n)</sup>- P<sub>2</sub>
<sup>(n)</sup>is twice that for D<sub>c</sub>
<sup>(n)</sup>, ceteris paribus, the MRE values tend to be the inverse of the corresponding TR. The partial sterility of the heterozygote for a chromosome mutation has a limited effect in reducing gene flow, especially for the s values which are assumed to be involved in chromosomal speciation (0.05 ⩽ s ⩽ 0.3) as is proven by the somewhat low TR values; this efficiency is accentuated at low migration rates; but this sterility can keep the two karyomorphs apart when m/s < 1/4.</p>