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Adaptive Diversification and Speciation as Pattern Formation in Partial Differential Equation Models

Adaptive Diversification and Speciation as Pattern Formation in Partial Differential Equation Models

Chapter:
(p.217) Chapter Nine Adaptive Diversification and Speciation as Pattern Formation in Partial Differential Equation Models
Source:
Adaptive Diversification (MPB-48)
Author(s):
Michael Doebeli
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691128931.003.0009

This chapter discusses partial differential equation models. Partial differential equations can describe the dynamics of phenotype distributions of polymorphic populations, and they allow for a mathematically concise formulation from which some analytical insights can be obtained. It has been argued that because partial differential equations can describe polymorphic populations, results from such models are fundamentally different from those obtained using adaptive dynamics. In partial differential equation models, diversification manifests itself as pattern formation in phenotype distribution. More precisely, diversification occurs when phenotype distributions become multimodal, with the different modes corresponding to phenotypic clusters, or to species in sexual models. Such pattern formation occurs in partial differential equation models for competitive as well as for predator–prey interactions.

Keywords:   partial differential equation models, phenotype distributions, polymorphic populations, adaptive dynamics, diversification, pattern formation

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