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The Role of Fluctuations in Cooperation Phenomena

The Role of Fluctuations in Cooperation Phenomena. Supervisor: Prof. Erwin Frey. General motivation, my master thesis and this talk. Main fields of interest and focus of research: Evolutionary dynamics Biodiversity Cooperation phenomena.

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The Role of Fluctuations in Cooperation Phenomena

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  1. The Role of Fluctuations in Cooperation Phenomena Supervisor: Prof. Erwin Frey Johannes Knebel

  2. General motivation, my master thesis and this talk • Main fields of interest and focus of research: • Evolutionary dynamics • Biodiversity • Cooperation phenomena • “Why is there cooperative behavior in nature despite the fact that cooperation is costly and free-riders may receive the benefits without paying any costs?” • My Master thesis… • studies an experimental realization of cooperation • applies and extends a stochastic model developed in the group of E. Frey • examines the occurrence of a life cycle to explain maintenance of cooperation Johannes Knebel

  3. = scope of this talk General motivation, my master thesis and this talk • Main fields of interest and focus of research: • Evolutionary dynamics • Biodiversity • Cooperation phenomena • “Why is there cooperative behavior in nature despite the fact that cooperation is costly and free-riders may receive the benefits without paying any costs?” • My Master thesis… • studies an experimental realization of cooperation • applies and extends a stochastic model developed in the group of E. Frey • examines the occurrence of a life cycle to explain maintenance of cooperation Johannes Knebel

  4. The Rainey & Rainey experiment: success of cooperation • Bacteria and mat growth • Wrinkly spreader (WS) aswild type • WS produce a gluing polymer • (individual cost) • WS = cooperator • Mat formation and colonization of surface • (profit of cooperation) • Emergence and success of cooperation • (profit of cooperation is bigger than costs at individual level) Sketch of bacteria Phenomenology of wrinkly spreader Formation of the mat: success of cooperation (P. Rainey, K. Rainey, Nature 2003) Johannes Knebel

  5. The Rainey & Rainey experiment: dilemma of cooperation • Dilemma of cooperation • WS (“cooperator”) can mutate to “defector” • no production of gluing polymer, • no costs, • no contribution to mat stability, • still benefit from mat • Result • Evolutionary advantage for defectors: • defectors outperform cooperators • Survivability of the whole population is put at risk Number of bacteria at surface Without defectors With defectors The bacteria experiment of Rainey et al. is one example of the emergence, the success, and the dilemma of cooperation Johannes Knebel

  6. Evolutionary game theory in growing populations: A coupled approach • Coupling evolutionary game theory and population dynamics in a stochastic model • System described by two stochastic variables: • Total number of individuals, • Percentage of cooperators • Dynamics described by Master equation • probability distribution • growth advantage • strength of selection • limited resources (A. Melbinger, J. Cremer, E. Frey, PRL 2010) Johannes Knebel

  7. Transient increase of cooperation is a stochastic effect • Deterministic rate equations • (neglecting all fluctuations) • Stochastic simulations reveal transient increase of cooperation (colored lines) • Characterized by cooperation time • Analysis of the regime of transient cooperation • Demographic fluctuations • Probability distr. broadens in the beginning • Van-Kampen expansion (black lines) The role of stochastic fluctuations is crucial to the occurrence of cooperation Johannes Knebel

  8. Outlook: from transient increase to stable cooperation • Occurrence of life-cycles as a possibility to maintain cooperation • Repeated occurrence of cooperation by mutation from defector to cooperator • (P. Rainey, B. Kerr, Wiley 2010) • Next steps of my Master thesis: • establish maintenance of cooperation • Consider an ensemble of mat populations evolving in time • Cooperation becomes stable in the long run if initial conditions are chosen randomly • (A. Melbinger, J. Cremer, E. Frey, to be published 2011) • Goal: Propose an experiment that can be tested by biologist Johannes Knebel

  9. Outlook: from transient increase to stable cooperation • Occurrence of life-cycles as a possibility to maintain cooperation • Repeated occurrence of cooperation by mutation from defector to cooperator • (P. Rainey, B. Kerr, Wiley 2010) • Next steps of my Master thesis: • establish maintenance of cooperation • Consider an ensemble of mat populations evolving in time • Cooperation becomes stable in the long run if initial conditions are chosen randomly • (A. Melbinger, J. Cremer, E. Frey, to be published 2011) • Goal: Propose an experiment that can be tested by biologist Thank you for your attention Johannes Knebel

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