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Selforganizology, 2014, 1(1): 1-7
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Article

The influence of deterministic and stochastic waiting time for triggering mortality and colonization events on the coexistence of cooperators and defectors in an evolutionary game model

YouHua Chen
Department of Zoology, University of British Columbia, Vancouver, V6T 1Z4, Canada

Received 15 May 2013;Accepted 20 June 2013;Published online 1 June 2014
IAEES

Abstract
In the present report, the coexistence of Prisoners' Dilemma game players (cooperators and defectors) were explored in an individual-based framework with the consideration of the impacts of deterministic and stochastic waiting time (WT) for triggering mortality and/or colonization events. For the type of deterministic waiting time, the time step for triggering a mortality and/or colonization event is fixed. For the type of stochastic waiting time, whether a mortality and/or colonization event should be triggered for each time step of a simulation is randomly determined by a given acceptance probability (the event takes place when a variate drawn from a uniform distribution [0,1] is smaller than the acceptance probability). The two strategies of modeling waiting time are considered simultaneously and applied to both quantities (mortality: WTm, colonization: WTc). As such, when WT (WTm and/or WTc) is an integral >=1, it indicated a deterministically triggering strategy. In contrast, when 1>WT>0, it indicated a stochastically triggering strategy and the WT value itself is used as the acceptance probability. The parameter space between the waiting time for mortality (WTm-[0.1,40]) and colonization (WTc-[0.1,40]) was traversed to explore the coexistence and non-coexistence regions. The role of defense award was evaluated. My results showed that, one non-coexistence region is identified consistently, located at the area where 1>=WTm>=0.3 and 40>=WTc>=0.1. As a consequence, it was found that the coexistence of cooperators and defectors in the community is largely dependent on the waiting time of mortality events, regardless of the defense or cooperation rewards. When the mortality events happen in terms of stochastic waiting time (1>=WTm>=0.3), extinction of either cooperators or defectors or both could be very likely, leading to the emergence of non-coexistence scenarios. However, when the mortality events occur in forms of relatively long deterministic waiting time, both defectors and cooperators could coexist, regardless of the types of waiting time for colonization events. Defense (or cooperation) rewards could determine the persistence time of both game players. When the defense reward is low, cooperators could persist better in the simulation. But when the defense reward becomes sufficiently higher, defectors would persist better. Overall, non-coexistence of cooperators and defectors in the present evolutionary game model is dependent on the stochastic mortality events, but not colonization events. In conclusion, my present study quantifies the influence of the temporally fluctuating motility-colonization dynamic on modeling the coexistence of species in the spatial evolutionary game.

Keywords species coexistence;game theory;mortality-colonization dynamic;deterministic versus stochastic mechanisms.

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