TY - JOUR

T1 - Evolutionary principles for polynomial models of frequency-dependent selection

AU - Curtsinger, J. W.

PY - 1984

Y1 - 1984

N2 - A one-locus two-allele deterministic model of frequency-dependent selection is analyzed, where genotypic fitness [w(i)(q)] are assumed to be nth-degree polynomial functional of allele frequency (q). The model encompasses many modes of selection, including intraspecies competitive interaction, brood selection, meiotic drive, cyclical selection, and mixed models. Allelic frequencies converge monotonically to locally stable equilibria provided that [dw(i)(q)/dq] is not large. There exists a function T(q) that is nondecreasing and locally maximized at locally stable equilibria. The rate of change of T(q) per generation is approximately equal to the additive genetic variance in fitness. T(q) is a simple function of the average effect of an allelic substitution and is closely related to Wright's 'fitness function'. These results define 'evolutionary landscapes' for some complex selection processes and enlarge the scope of the classical methods embodied in Wright's 'mean fitness principle' and 'Fisher's 'fundamental theorem'.

AB - A one-locus two-allele deterministic model of frequency-dependent selection is analyzed, where genotypic fitness [w(i)(q)] are assumed to be nth-degree polynomial functional of allele frequency (q). The model encompasses many modes of selection, including intraspecies competitive interaction, brood selection, meiotic drive, cyclical selection, and mixed models. Allelic frequencies converge monotonically to locally stable equilibria provided that [dw(i)(q)/dq] is not large. There exists a function T(q) that is nondecreasing and locally maximized at locally stable equilibria. The rate of change of T(q) per generation is approximately equal to the additive genetic variance in fitness. T(q) is a simple function of the average effect of an allelic substitution and is closely related to Wright's 'fitness function'. These results define 'evolutionary landscapes' for some complex selection processes and enlarge the scope of the classical methods embodied in Wright's 'mean fitness principle' and 'Fisher's 'fundamental theorem'.

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U2 - 10.1073/pnas.81.9.2840

DO - 10.1073/pnas.81.9.2840

M3 - Article

AN - SCOPUS:0021246982

SN - 0027-8424

VL - 81

SP - 2840

EP - 2842

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 9 I

ER -