Models of selection on a modifier locus affecting the degree of polymorphism in a population which has two or three distinct phenotypic classes are considered. Frequency-dependent interactions between the different types in the population and both internally and externally induced fluctuations in population size are also considered. Two types of models are analyzed, difference-equation models of populations with discrete, nonoverlapping generations and differential-equation models of populations with overlapping generations but no age structure. The basic result is that under many circumstances natural selection at the modifier locus will tend to equilibrate the fitnesses of the phenotypic classes in the population to the extent possible given the genetic constraints of the character being analyzed. For the model of frequency-dependent interactions considered, the long-term evolutionary trend of the population would not be to maximize the total population size or the mean fitness of the population. This is a different result from that found in other models of selection, including models of density-dependent selection and models of selection on a modifier system, because of the frequency dependence caused by the interference of the different morphs. It is also shown that the evolution of parameters that directly affect the fitnesses of different morphs in a population will tend to maximize the total population size given the constraint that the fitnesses of the different morphs are equal at equilibrium.
[1]
B. Charlesworth.
Selection in Populations with Overlapping Generations. V. Natural Selection and Life Histories
,
1973,
The American Naturalist.
[2]
Brian Charlesworth,et al.
Selection in Density‐Regulated Populations
,
1971
.
[3]
J. McGregor,et al.
Towards a theory of the evolution of modifier genes.
,
1974,
Theoretical population biology.
[4]
R M May,et al.
Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos
,
1974,
Science.
[5]
J M Smith,et al.
Evolution and the theory of games
,
1976
.
[6]
John L. Harper,et al.
The Shapes and Sizes of Seeds
,
1970
.
[7]
J. Roughgarden.
Resource partitioning among competing species--a coevolutionary approach.
,
1976,
Theoretical population biology.
[8]
M. Slatkin.
The Evolutionary Response to Frequency- and Density-Dependent Interactions
,
1979,
The American Naturalist.
[9]
M. Slatkin,et al.
Niche Width in a Fluctuating Environment-Density Independent Model
,
1976,
The American Naturalist.
[10]
J. M. Smith,et al.
The Coevolution and Stability of Competing Species
,
1976,
The American Naturalist.
[11]
S. Wright,et al.
Evolution in Mendelian Populations.
,
1931,
Genetics.
[12]
R. Lewontin,et al.
The Genetic Basis of Evolutionary Change
,
2022
.
[13]
C. Strobeck,et al.
Selection in a Fine-Grained Environment
,
1975,
The American Naturalist.