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Group selection on the boundary of a stable population
1Society of Fellows and Department of Sociology, Harvard University, Cambridge, Massachusetts 02138.
Summary
Group selection models reveal that differential extinction in small populations can significantly impact gene frequencies. A critical allele frequency threshold, where extinction rates change abruptly, is key for population polymorphism.
Area of Science:
- Evolutionary biology
- Population genetics
- Mathematical modeling
Background:
- Group selection is a mechanism where differential extinction and colonization of groups affects gene frequencies.
- Previous models often overlooked the impact of extinction dynamics on small, peripheral populations.
Purpose of the Study:
- To develop a mathematical model of group selection focusing on differential extinction in boundary populations.
- To identify conditions under which differential extinction significantly influences population genetics.
Main Methods:
- Construction of a group selection model incorporating extinction operators near carrying capacity.
- Analysis of extinction rates relative to genetic parameters in boundary populations.
- Investigation of allele frequency distributions and their relationship to extinction thresholds.
Main Results:
- Differential extinction can significantly affect gene frequencies when extinction rates are high relative to genetic drift.
- A critical allele frequency, causing a sharp transition in extinction rates (from high to low), promotes population polymorphism.
- Linear extinction operators do not produce these qualitative effects.
Conclusions:
- Group selection via differential extinction is most effective under specific, limited conditions.
- The identified critical allele frequency threshold is crucial for observing significant group selection effects.
- Understanding extinction dynamics in boundary populations is essential for evolutionary theory.
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