Causal models of multilevel selection

Abstract

In social evolution, fitness of an individual depends not only on the phenotype of the individual itself but also on the phenotype of its social environment. When measuring the strength of selection in empirical data, this leads to the question of how selection is assigned to the individual and the population level. Two methods for carrying out this assignment have been primarily discussed in the literature. The multilevel Price approach uses a multilevel expansion of the Price equation to express the components of selection on the two evels in terms of covariances. Contextual analysis, on the other hand, uses linear regression to assign fitness components to the individual and the population level. However, the two methods generally do not agree in their results, and discussions which one is preferable have been inconclusive. In this thesis, I argue that the root of the problem lies in viewing the two approaches as correlational. While both are equally valid as correlational models, underlying an empirical scenario is a causal process that may or may not match the given approach. To find the correct approach I therefore suggest to regard contextual analysis and the Price approach as causal models, i.e., as processes that generate the given data. In order to implement the approaches as process models I view the process of selection as a transformation from metapopulations to populations. I show that transformations of this kind as well as other aspects of biological systems can be expressed in terms of monoidal categories. More precisely, probability monads can be used to capture essential features of metatpopulations and allow a convenient graphical representation. Using this formalism, I construct process models of multilevel selection that correspond to the multilevel Price

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ORCID for Richard Watson: orcid.org/0000-0002-2521-8255

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