Diffusion model of intergroup selection, with special reference to evolution of an altruistic character

Area of Science:

• Evolutionary Biology
• Population Genetics
• Behavioral Ecology

Background:

• Altruism presents an evolutionary paradox: traits that benefit groups but harm individuals are difficult to explain through natural selection.
• Mathematical models are crucial for understanding the complex interplay of forces shaping allele frequencies within and between populations.

Purpose of the Study:

• To investigate the conditions under which an altruistic allele can be favored and maintained in a population structured into competing demes.
• To develop a predictive framework for determining the prevalence of group selection versus individual selection in maintaining altruism.

Main Methods:

• A mathematical model was developed using a partial differential equation to describe the distribution of an altruistic allele frequency across competing demes.
• The model incorporated individual selection, group selection, random genetic drift, mutation, and migration (using Wright's island model).
• Steady-state analysis was performed to balance these evolutionary forces.

Main Results:

• A key index, D = c/m - 4N(e)s", was derived, where 'c' is the benefit of the altruistic allele to a deme, 'm' is the migration rate, 'N(e)' is the effective population size, and 's epeated' is the individual disadvantage.
• If D > 0, the altruistic allele is predicted to predominate, indicating that group selection overcomes individual selection.
• If D < 0, the altruistic allele is predicted to be rare and unlikely to become established.

Conclusions:

• Group selection can effectively promote altruistic traits when the benefits to the group are sufficiently large relative to the costs to the individual and migration rates.
• The derived index provides a valuable tool for predicting the evolutionary outcome of altruism based on the balance of individual and group selection pressures.