Christoph Hauert

Professor

Research Classification

Modelization and Simulation
Evolution and Phylogenesis
Biological Behavior

Research Interests

evolution
game theory
social dilemmas
dynamical systems
stochastic processes

Relevant Degree Programs

 

Biography

Professor of Mathematical Biology, University of British Columbia, Vancouver

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Graduate Student Supervision

Doctoral Student Supervision (Jan 2008 - May 2019)
Essays on game theory and stochastic evolution (2016)

Evolutionary game theory is a popular framework for modeling the evolution of populations via natural selection. The fitness of a genetic or cultural trait often depends on the composition of the population as a whole and cannot be determined by looking at just the individual ("player") possessing the trait. This frequency-dependent fitness is quite naturally modeled using game theory since a player's trait can be encoded by a strategy and their fitness can be computed using the payoffs from a sequence of interactions with other players. However, there is often a distinct trade-off between the biological relevance of a game and the ease with which one can analyze an evolutionary process defined by a game. The goal of this thesis is to broaden the scope of some evolutionary games by removing restrictive assumptions in several cases. Specifically, we consider multiplayer games; asymmetric games; games with a continuous range of strategies (rather than just finitely many); and alternating games. Moreover, we study the symmetries of an evolutionary process and how they are influenced by the environment and individual-level interactions. Finally, we present a mathematical framework that encompasses many of the standard stochastic evolutionary processes and provides a setting in which to study further extensions of stochastic models based on natural selection.

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Master's Student Supervision (2010 - 2018)
In which the fixation probability of a superstar is determined (2014)

No abstract available.

Space matters : evolution and ecology in structured populations (2012)

The inclusion of spatial structure in biological models has revealed important phenomenon not observed in “well-mixed” populations. In particular, cooperation may evolve in a network-structured population whereas it cannot in a well-mixed population. However, the success of cooperators is very sensitive to small details of the model architecture. In Chapter 1 I investigate two popular biologically-motivated models of evolution in finite populations: Death-Birth (DB) and Birth-Death (BD) processes. Under DB cooperation may be favoured, while under BD it never is. In both cases reproduction is proportional to fitness and death is random; the only difference is the order of the two events at each time step. Whether structure can promote the evolution of cooperation should not hinge on a somewhat artificial ordering of birth and death. I propose a mixed rule where in each time step DB (BD) is used with probability δ (1 − δ). I then derive the conditions for selection favouring cooperation under the mixed rule for all social dilemmas. The only qualitatively different outcome occurs when using just BD (δ = 0). This case admits a natural interpretation in terms of kin competition counterbalancing the effect of kin selection. Finally I show that, for any mixed BD-DB update and under weak selection, cooperation is never inhibited by population structure for any social dilemma.Chapter 2 addresses the Competitive Exclusion Principle: the maximum number of species that can coexist is the number of habitat types (Hardin, 1960). This idea was borne out in island models, where each island represents a different well-mixed niche, with migration between islands. A specialist dominates each niche. However, these models assumed equal migration between each pair of islands, and their results are not robust to changing that assumption. Débarre and Lenormand (2011) numerically studied a two-niche model with local migration. At the boundary between niches, generalists may stably persist. The number of coexisting species may be much greater than the number of habitat types. Here, I derive the conditions for invasion of a generalist using an asymptotic approach. The prediction performs well (compared with numerical results) even for not asymptotically small parameter values (i.e. epsilon ≈ 1).

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Publications

 
 

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