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Professor of Mathematical Biology, University of British Columbia, Vancouver
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Graduate Student Supervision
Doctoral Student Supervision
Dissertations completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest dissertations.
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.
Master's Student Supervision
Theses completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest theses.
From the microscopic to the macroscopic level, biological life exhibits directed migration in response to environmental conditions. Chemotaxis enables microbes to sense and move towards nutrient-rich regions or to avoid toxic ones. Socio-economic factors drive human populations from rural to urban areas. However, migration affects the quantity and quality of desirable resources. The effect of collective movement is especially significant when in response to the generation of public goods. Microbial communities can, for instance, alter their environment through the secretion of extracellular substances. Some substances provide antibiotic-resistance, others provide access to nutrients or promote motility. However, in all cases the maintenance of such public goods requires costly cooperation and is consequently susceptible to exploitation. The threat of exploitation becomes even more acute with motile individuals as defectors can avoid the consequences of their cheating. Here, we propose a model to investigate the effects of targeted migration based on the production of ecological public goods and analyze the interplay between social conflicts and migration. In particular, individuals can locate attractive regions by moving towards higher cooperator densities or avoid unattractive regions by moving away from defectors. Both migration patterns not only shape an individual's immediate environment but also affects the population as a whole. For example, defectors hunting cooperators in search of the public good have a homogenizing effect on population densities. They limit the production of the public good and hence inhibit the growth of the population. In contrast, aggregating cooperators promote the spontaneous formation of heterogeneous density distributions. The positive feedback between cooperator aggregation and public goods production, however, poses analytical and numerical challenges due to its tendency to develop discontinuous distributions. Thus, different modes of directed migration bear the potential to enhance or inhibit the emergence of complex and sometimes dynamic spatial arrangements. Interestingly, whenever patterns emerge in the form of heterogeneous density distributions, cooperation is promoted, on average, population densities rise, and the risk of extinction is reduced.
Population structures can be crucial determinants of evolutionary processes. For the spatial Moran process certain structures suppress selective pressure, while others amplify it (Lieberman et al. 2005 Nature 433 312-316). Evolutionary amplifiers suppress random drift and enhance selection. Recently, some results for the most powerful known evolutionary amplifier, the superstar, have been invalidated by a counter example (Diaz et al. 2013 Proc. R. Soc. A 469 20130193). Here we correct the original proof and derive improved upper and lower bounds, which indicate that the fixation probability remains close to 1-1/ r⁴ H for population size N → ∞ and structural parameter H > 1. This correction resolves the differences between the two aforementioned papers. We also confirm that in the limit N,H → ∞ superstars remain capable of providing arbitrarily strong selective advantages to any beneficial mutation, eliminating random drift. In addition, we investigate the robustness of amplification in superstars,and find that it appears to be a fragile phenomenon with respect to changes in the selection or mutation processes.
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).
- Intriguing effects of selection intensity on the evolution of prosocial behaviors (2021)
PLOS Computational Biology, 17 (11), e1009611
- On the importance of evolving phenotype distributions on evolutionary diversification (2021)
PLOS Computational Biology, 17 (2), e1008733
- Origin of diversity in spatial social dilemmas (2021)
- Spatial social dilemmas promote diversity (2021)
Proceedings of the National Academy of Sciences, 118 (42)
- Global dynamics of microbial communities emerge from local interaction rules (2020)
- A sheep in wolf’s clothing: levels of deceit and detection in the evolution of cue-mimicry (2019)
Proceedings of the Royal Society B: Biological Sciences, 286 (1910), 20191425
- Asymmetric evolutionary games with environmental feedback (2019)
Journal of Theoretical Biology, 462, 347--360
- Directed migration shapes cooperation in spatial ecological public goods games (2019)
PLOS Computational Biology,
- Effort Perception is Made More Accurate with More Effort and When Cooperating with Slackers (2019)
- Effects of sampling interaction partners and competitors in evolutionary games (2018)
- Public goods games in populations with fluctuating size (2018)
Theoretical Population Biology, 121, 72--84
- Autocratic strategies for alternating games (2017)
Theoretical Population Biology, 113, 13-22
- Autocratic strategies for iterated games with arbitrary action spaces (2016)
Proceedings of the National Academy of Sciences, 113 (13), 3573--3578
- Eco-evolutionary dynamics of social dilemmas (2016)
Theoretical Population Biology, 111, 28-42
- Leadership in Mammalian Societies: Emergence, Distribution, Power, and Payoff (2016)
Trends in Ecology and Evolution, 31 (1), 54-66
- Structure coefficients and strategy selection in multiplayer games (2016)
Journal of Mathematical Biology, 72 (1-2), 203-238
- Targeted cooperative actions shape social networks (2016)
PLoS ONE, 11 (1)
- Asymmetric Evolutionary Games (2015)
PLoS Computational Biology, 11 (8)
- Cooperation and coauthorship in scientific publishing (2015)
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 91 (1)
- Fixation probabilities on superstars, revisited and revised (2015)
Journal of Theoretical Biology, 382, 44-56
- Stochastic game dynamics under demographic fluctuations (2015)
Proceedings of the National Academy of Sciences of the United States of America, 112 (29), 9064-9069
- Structural symmetry in evolutionary games (2015)
Journal of the Royal Society Interface, 12 (111)
- Evolutionary Game Dynamics in Populations with Heterogenous Structures (2014)
PLoS Computational Biology, 10 (4)
- Fixation Times in Deme Structured, Finite Populations with Rare Migration (2014)
Journal of Statistical Physics, 156 (4), 739-759
- Origin and structure of dynamic cooperative networks (2014)
Scientific Reports, 4
- Social evolution in structured populations (2014)
Nature Communications, 5
- A comment on "Towards a rigorous framework for studying 2-player continuous games" by Shade T. Shutters, Journal of Theoretical Biology 321, 40-43, 2013 (2013)
Journal of Theoretical Biology, 336, 240-241
- Consolidating Birth-Death and Death-Birth Processes in Structured Populations (2013)
PLoS ONE, 8 (1)
- Extrapolating Weak Selection in Evolutionary Games (2013)
PLoS Computational Biology, 9 (12)
- Intra- and intergenerational discounting in the climate game (2013)
Nature Climate Change, 3 (12), 1025-1028
- Could shame and honor save cooperation? (2012)
Communicative & Integrative Biology, 5 (2), 209-13
- Emergence of stable polymorphisms driven by evolutionary games between mutants (2012)
Nature Communications, 3
- Evolutionary games in deme structured, finite populations (2012)
Journal of Theoretical Biology, 299, 106-112
- Stochastic differential equations for evolutionary dynamics with demographic noise and mutations (2012)
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 85 (4)
- Pattern formation and chaos in spatial ecological public goodsgames (2011)
Journal of Theoretical Biology, 268 (1), 30-38
- Public goods games with reward in finite populations (2011)
Journal of Mathematical Biology, 63 (1), 109-123
- Shame and honour drive cooperation (2011)
Biology Letters, 7 (6), 899-901
- Social control and the social contract: The emergence of sanctioning systems for collective action (2011)
Dynamic Games and Applications, 1 (1), 149-171
- Diversity of Cooperation in the Tragedy of the Commons (2010)
Biological Theory, 5 (1), 3--6
- Freedom, enforcement, and the social dilemma of strong altruism (2010)
Journal of Evolutionary Economics, 20 (2), 203-217
- Invasion and expansion of cooperators in lattice populations: Prisoner's dilemma vs. snowdrift games (2010)
Journal of Theoretical Biology, 266 (3), 358-366
- Replicator dynamics of reward & reputation in public goods games (2010)
Journal of Theoretical Biology, 267 (1), 22-28
- Social learning promotes institutions for governing the commons (2010)
Nature, 466 (7308), 861-863
- Stochastic Evolutionary Game Dynamics (2010)
Reviews of Nonlinear Dynamics and Complexity, 2, 25-61
- Evolutionary dynamics on graphs: Efficient method for weak selection (2009)
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 79 (4)
- Exploration dynamics in evolutionary games (2009)
Proceedings of the National Academy of Sciences of the United States of America, 106 (3), 709-712
- Spatial dynamics of ecological public goods (2009)
Proceedings of the National Academy of Sciences of the United States of America, 106 (19), 7910-7914
- Ecological public goods games: Cooperation and bifurcation (2008)
Theoretical Population Biology, 73 (2), 257-263
- Evolutionary dynamics (2008)
NATO Science for Peace and Security Series B: Physics and Biophysics, , 11-44
- Public Goods With Punishment and Abstaining in Finite and Infinite Populations (2008)
Biology Theory, 3 (2), 114-122
- Reputation-based partner choice promotes cooperation in social networks (2008)
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 78 (2)
- Spatial invasion of cooperation (2008)
Journal of Theoretical Biology, 250 (4), 634-641
- Via freedom to coercion: The emergence of costly punishment (2007)
Science, 316 (5833), 1905-1907
- A simple rule for the evolution of cooperation on graphs and social networks (2006)
Nature, 441 (7092), 502-505
- Coevolutionary dynamics in large, but finite populations (2006)
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 74 (1)
- Cooperation, collectives formation and specialization (2006)
Advances in Complex Systems, 9 (4), 315-335
- Erratum: Evolutionary games and population dynamics: Maintenance of cooperation in public goods games (Proceedings of the Royal Society Series B Biological Sciences (2006) DOI: 10.1098/rspb.2006.3600) (2006)
Proceedings of the Royal Society B: Biological Sciences, 273 (1605), 3131-3132
- Evolutionary games and population dynamics: Maintenance of cooperation in public goods games (2006)
Proceedings of the Royal Society B: Biological Sciences, 273 (1600), 2565-2570
- Limits of Hamilton's rule (2006)
Journal of Evolutionary Biology, 19 (5), 1386-1388
- Punishing and abstaining for public goods (2006)
Proceedings of the National Academy of Sciences of the United States of America, 103 (2), 495-497
- Spatial effects in social dilemmas (2006)
Journal of Theoretical Biology, 240 (4), 627-636
- Synergy and discounting of cooperation in social dilemmas (2006)
Journal of Theoretical Biology, 239 (2), 195-202
- Coevolutionary dynamics: From finite to infinite populations (2005)
Physical Review Letters, 95 (23)
- Evolutionary dynamics on graphs (2005)
Nature, 433 (7023), 312-316
- Game theory and physics (2005)
American Journal of Physics, 73 (5), 405-414
- Models of cooperation based on the Prisoner's Dilemma and the Snowdrift game (2005)
Ecology Letters, 8 (7), 748-766
- Of dogs and fleas: The dynamics of N uncoupled two-state systems (2004)
Journal of Statistical Physics, 116 (5-6), 1453-1469
- Spatial structure often inhibits the evolution of cooperation in the snowdrift game (2004)
Nature Materials, 428 (6983), 643-646
- The dynamics of public goods (2004)
Discrete and Continuous Dynamical Systems-Series B, 4 (3), 575-587
- The evolutionary origin of cooperators and defectors (2004)
Science, 306 (5697), 859-862
- Prisoner's dilemma and public goods games in different geometries: Compulsory versus voluntary interactions (2003)
Complexity, 8 (4 SPE), 31-38
- Punishment and reputation in spatial public goods games (2003)
Proceedings of the Royal Society B: Biological Sciences, 270 (1519), 1099-1104
- Altruism (2002)
Current Biology, 12 (8), R270--R272
- Effects of space in 2 × 2 games (2002)
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 12 (7), 1531-1548
- Evolutionary prisoner's dilemma games with voluntary participation (2002)
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 66 (6)
- Phase Transitions and Volunteering in Spatial Public Goods Games (2002)
Phys. Rev. Lett., 89 (11)
- Replicator dynamics for optional public good games (2002)
Journal of Theoretical Biology, 218 (2), 187-194
- Simple adaptive strategy wins the prisoner's dilemma (2002)
Journal of Theoretical Biology, 218 (3), 261-272
- Volunteering as Red Queen mechanism for cooperation in public goods games (2002)
Science, 296 (5570), 1129-1132
- Fundamental clusters in spatial 2 × 2 games (2001)
Proceedings of the Royal Society B: Biological Sciences, 268 (1468), 761-769
- Reward and punishment (2001)
Proceedings of the National Academy of Sciences of the United States of America, 98 (19), 10757-10762
- Self-organized criticality in a nutshell (1999)
Phys. Rev. E, 60 (3), 2706--2709
- Extending the iterated Prisoner's Dilemma without synchrony (1998)
Journal of Theoretical Biology, 192 (2), 155-166
- Effects of increasing the number of players and memory size in the iterated Prisoner's Dilemma: a numerical approach (1997)
Proceedings of the Royal Society B: Biological Sciences, 264 (1381), 513--519
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