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Social Evolution and Inclusive Fitness TheoryAn Introduction$
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James A.R. Marshall

Print publication date: 2015

Print ISBN-13: 9780691161563

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691161563.001.0001

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Nonadditive Interactions and Hamilton’s Rule

Nonadditive Interactions and Hamilton’s Rule

(p.59) Chapter Five Nonadditive Interactions and Hamilton’s Rule
Social Evolution and Inclusive Fitness Theory

James A.R. Marshall

Princeton University Press

This chapter examines what happens in nonadditive interactions when such interactions take place between relatives, and how Hamilton's rule can be extended in two different ways to accommodate such nonadditivity. It first considers the selective pressures on nonadditive behaviors directed towards relatives by making use of the replicator dynamics to capture interactions within structured populations, so that on average, interactions within the population occur between relatives. It then describes two extensions to Hamilton's rule to deal with nonadditive interactions. One approach takes deviations from additivity and accounts for them all in a single synergistic coefficient. The other approach applies partial regression to keep a version of Hamilton's rule with only three parameters, in which costs and benefits vary according to the frequency of social individuals in a population. The chapter also explains the use of the Price equation to study nonadditive social interactions between relatives.

Keywords:   nonadditive interactions, Hamilton's rule, nonadditive behaviors, replicator dynamics, structured populations, additivity, synergistic coefficient, partial regression, Price equation

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