Self-Protection and Diversity in Self-Replicating Cellular Automata

Sayama, Hiroki

doi:10.1162/106454604322875922

Cited by 20 publications

(17 citation statements)

References 11 publications

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“…A cellular automaton was designed for a finite number of l × l patches on a two-dimensional homogeneous patchy habitat with synchronous updating. A periodic boundary condition is adopted to avoid the edge effect (Sayama, 2004;Feagin et al, 2007), which is essentially equal to organize the patch on a globe. Simulation will be implemented according to two frameworks: the probability transition model (PTM) and the discrete event model (DEM).…”

Section: Spatially Explicit Modelmentioning

confidence: 99%

Spatiotemporal Dynamics of the Epidemic Transmission in a Predator-Prey System

Hui

Zhang

et al. 2008

Bull. Math. Biol.

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Epidemic transmission is one of the critical density-dependent mechanisms that affect species viability and dynamics. In a predator-prey system, epidemic transmission can strongly affect the success probability of hunting, especially for social animals. Predators, therefore, will suffer from the positive density-dependence, i.e., Allee effect, due to epidemic transmission in the population. The rate of species contacting the epidemic, especially for those endangered or invasive, has largely increased due to the habitat destruction caused by anthropogenic disturbance. Using ordinary differential equations and cellular automata, we here explored the epidemic transmission in a predator-prey system. Results show that a moderate Allee effect will destabilize the dynamics, but it is not true for the extreme Allee effect (weak or strong). The predator-prey dynamics amazingly stabilize by the extreme Allee effect. Predators suffer the most from the epidemic disease at moderate transmission probability. Counter-intuitively, habitat destruction will benefit the control of the epidemic disease. The demographic stochasticity dramatically influences the spatial distribution of the system. The spatial distribution changes from oil-bubble-like (due to local interaction) to aggregated spatially scattered points (due to local interaction and demographic stochasticity). It indicates the possibility of using human disturbance in habitat as a potential epidemic-control method in conservation.

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Section: Spatially Explicit Modelmentioning

confidence: 99%

Spatiotemporal Dynamics of the Epidemic Transmission in a Predator-Prey System

Hui

Zhang

et al. 2008

Bull. Math. Biol.

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“…We construct a lattice model for a finite number of n × n patches on a two-dimensional homogeneous patchy habitat with synchronous updating and a von Neumann (four nearest patches) or Moore (eight nearest patches) neighborhood. We used periodic boundaries, which are often used in theoretical literature (Schonfisch, 1997;Kermer et al, 1998;Sayama, 2004), instead of absorbing boundaries (Huxel and Hastings, 1999). We ignore the time required for movement, which is also the classical assumption in many spatially implicit and explicit models (McGlade, 1999;Dieckmann et al, 2000;Hui and Yue, 2005).…”

Section: Spatial Analysismentioning

confidence: 99%

Spatial Patterns of Prisoner’s Dilemma Game in Metapopulations

Hui

McGeoch

2006

Bull. Math. Biol.

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Because to defect is the evolutionary stable strategy in the prisoner's dilemma game (PDG), understanding the mechanism generating and maintaining cooperation in PDG, i.e. the paradox of cooperation, has intrinsic significance for understanding social altruism behaviors. Spatial structure serves as the key to this dilemma. Here, we build the model of spatial PDG under a metapopulation framework: the sub-populations of cooperators and defectors obey the rules in spatial PDG as well as the colonization-extinction process of metapopulations. Using the mean-field approximation and the pair approximation, we obtain the differential equations for the dynamics of occupancy and spatial correlation. Cellular automaton is also built to simulate the spatiotemporal dynamics of the spatial PDG in metapopulations. Join-count statistics are used to measure the spatial correlation as well as the spatial association of the metapopulation. Simulation results show that the distribution is self-organized and that it converges to a static boundary due to the boycotting of cooperators to defectors. Metapopulations can survive even when the colonization rate is lower than the extinction rate due to the compensation of cooperation rewards for extinction debt. With a change of parameters in the model, a metapopulation can consist of pure cooperators, pure defectors, or cooperator-defector coexistence. The necessary condition of cooperation evolution is the local colonization of a metapopulation. The spatial correlation between the cooperators tends to be weaker with the increase in the temptation to defect and the habitat connectivity; yet the spatial correlation between defectors becomes stronger. The relationship between spatial structure and the colonization rate is complicated, especially for cooperators. The metapopulation may undergo a temporary period of prosperity just before the extinction, even while the colonization rate is declining.

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“…Recently, Sayama independently studied the relationship between a similar set of interaction rules and the diversity of new emergent loops [19]. Using these rules, he investigated aspects of self-protection and robustness in his system of selfreplicating loops.…”

Section: Discussionmentioning

confidence: 99%

Untitled

2006

Artificial Life

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We study a system of self-replicating loops in which interaction rules between individuals allow competition that leads to the formation of a hypercycle-like network. The main feature of the model is the multiple layers of interaction between loops, which lead to both global spatial patterns and local replication. The network of loops manifests itself as a spiral structure from which new kinds of self-replicating loops emerge at the boundaries between different species. In these regions, larger and more complex self-replicating loops live for longer periods of time, managing to self-replicate in spite of their slower replication. Of particular interest is how micro-scale interactions between replicators lead to macro-scale spatial pattern formation, and how these macro-scale patterns in turn perturb the micro-scale replication dynamics.

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Self-Protection and Diversity in Self-Replicating Cellular Automata

Cited by 20 publications

References 11 publications

Spatiotemporal Dynamics of the Epidemic Transmission in a Predator-Prey System

Spatiotemporal Dynamics of the Epidemic Transmission in a Predator-Prey System

Spatial Patterns of Prisoner’s Dilemma Game in Metapopulations

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