Skip navigation
Please use this identifier to cite or link to this item:
Title: PDE Models of Multilevel Selection: The Evolution of Cooperation and the Shadow of Selection
Authors: Cooney, Daniel Brendan
Advisors: Levin, Simon A
Contributors: Applied and Computational Mathematics Department
Keywords: Evolutionary Game Theory
Multilevel Selection
Replicator Equations
Subjects: Applied mathematics
Evolution & development
Issue Date: 2020
Publisher: Princeton, NJ : Princeton University
Abstract: In this thesis, we explore the fundamental evolutionary conflict between the individual incentive to cheat and the collective incentive to be part of a cooperative group. Our focus is on multilevel selection, in which individuals compete against peer group members and simultaneously compete together with their group members against other groups. Here we formulate these two levels of competition by considering group-structured populations in which each individual plays a two-strategy game with every other group member. Then the within-group competition depends on individual payoff, while between-group competition depends on the average payoff of group members. With this approach, we are able to explore a variety of individual-level and group-level incentives and the impact of relative incentives at the two level in establishing long-time defection or cooperation. In Chapter 2, we first formulate a finite population model for multilevel selection and then derive a PDE for the time evolution of the density of group compositions. The equation has an advection term corresponding to within-group competition and a non-local term corresponding to between-group competition. We then consider special cases of the Prisoners' Dilemma and Hawk-Dove game with solvable characteristic curves and find a threshold relative strength of between-group competition separating a regime in which defection dominates and one in which cooperation can survive in steady state. An interesting finding is the shadow of lower-level selection: when groups are best off with a mix of cooperators and defectors: no level of between-group selection strength can produce the optimal possible collective payoff. In Chapter 3, we study a broader class of payoff matrices, and use comparison principles and a preserved property of population distribution to show that the shadow of lower-level selection holds more generally. In Chapter 4, we apply the methods of chapter 3 to study how assortment, reciprocity, and network structure can work synergistically with multilevel selection. Chapter 5 presents alternate mathematical approaches and numerical methods for our model. In Chapter 6, we consider a model of protocell evolution, and then show how linking genes in a chromosome can help to overcome a cellular analogue to the shadow of lower- level selection.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Applied and Computational Mathematics

Files in This Item:
File Description SizeFormat 
Cooney_princeton_0181D_13359.pdf9.85 MBAdobe PDFView/Download

Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.