Statistical Mechanics of Population: The Lattice Lotka-Volterra Model

Matsuda, Hirotsugu; Ogita, N.; Sasaki, Akira; Satō, Kazunori

doi:10.1143/ptp/88.6.1035

Cited by 366 publications

(351 citation statements)

References 7 publications

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“…To model colonization and facilitation we also need a way to represent local densities: following Matsuda et al (1992) we represent these by the probabilities of finding a neighbor of a given site i in state j, in mathematical form q j|i (where i and j are either +, 0 or À). In what follows, all symbols stand for parameters and variables that have nonnegative values (Appendix A).…”

Section: Basic Events and Their Associated Ratesmentioning

confidence: 99%

Local facilitation, bistability and transitions in arid ecosystems

Kéfi

Rietkerk

Baalen³

et al. 2007

Theoretical Population Biology

173

221

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Arid ecosystems are liable to undergo sudden discontinuous transitions from a vegetated to a desert state as a result of human pressure and climate change. A predictive framework about the conditions under which such transitions occur is lacking. Here, we derive and analyze a general model describing the spatial dynamics of vegetation in arid ecosystems considering local facilitation as an essential process. We investigate the conditions under which continuous or discontinuous transitions from a vegetated to a desert state are likely to occur. We focus on arid ecosystems but our approach is sufficiently general to be applied to other ecosystems with severe environmental conditions. The model exhibits bistability and vegetation patchiness. High local facilitation decreases the risk of discontinuous transitions. Moreover, for arid ecosystems where local facilitation is a driving process, vegetation patchiness indicates proximity to a transition point, but does not allow distinguishing between continuous and discontinuous transitions. r

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Section: Basic Events and Their Associated Ratesmentioning

confidence: 99%

Local facilitation, bistability and transitions in arid ecosystems

Kéfi

Rietkerk

Baalen³

et al. 2007

Theoretical Population Biology

173

221

View full text Add to dashboard Cite

show abstract

“…This behavior can be linked to zealots in social dilemmas and has been shown to change the evolutionary outcome to some extent (e.g. Masuda, 2012;Mobilia, 2012;Liu et al, 2012). In this paper, we used a simple framework to study deterministic evolutionary dynamics in conjunction with external enforcement.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Similarly, one can imagine local frequencies such as q ijjl which represent the conditional probability that the focal player uses strategy i, given that an adjacent player uses strategy j and that a two-step adjacent player uses strategy l (Ohtsuki and Nowak, 2006b). For analytical tractability, we adopt the pair approximation method of Matsuda et al (1987Matsuda et al ( , 1992 and van Baalen (2000), which assumes q ijjl ¼ q ijj . The key assumption is that a two-step adjacent player does not directly affect the focal site.…”

Section: Pair Approximationmentioning

confidence: 99%

“…However, in real-life social evolutionary dynamics, there may be zealous players who stick to one option according to their idiosyncratic preferences, independent of the payoff to them or their peers (Nakajima and Masuda, 2013). Typically, zealous cooperators in social dilemmas are observed in military services and team sports (Coleman, 1988), and occasionally in charity campaigns (Masuda, 2012). In non-game situations, collective social dynamics in the presence of zealots has been examined, for instance, competition between two equally strong opinions in the voter model (Mobilia, 2003;Mobilia et al, 2007;Galam and Jacobs, 2007;Xie et al, 2011;Singh et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

“…Masuda (2012) proposes an evolutionary dynamical model that links these experimental findings to the evolution of cooperation. By assuming a small fraction of (imperfect) zealous cooperators, he shows that zealous cooperators can transform the population to be fully cooperative under standard evolutionary dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Evolutionary prisoner׳s dilemma game on graphs and social networks with external constraint

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Wang

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Ecosystem Analysis and the Governance of Natural Resources

McGlade

1999

Advanced Ecological Theory

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IntroductionDespite the growing hegemony of the environment, many of the earth's living resources are in decline or under serious threat of collapse. Such changes are occurring everywhere as a result of human population growth, alterations to the biosphere, via long-term trends in the climate, and increased levels of exploitation.Given that it is impractical to control the dynamics of most natural ecosystems, the current emphasis in many resource management systems on determinism, stability and optimization is clearly inappropriate. Instead, resource governance requires a new theoretical basis upon which to create management tools that will mitigate against the effects of change and cope with increasing levels of conflict over use demands.In previous chapters, new concepts and theoretical approaches have been presented to address the impacts of stochasticity, biological variation and external forcing functions on resource exploitation and ecosystem functioning. These have included different types of spatial models, individualbased models, pairwise correlations, trophic interactions, life-history dynamics and ecological economics. In this chapter I explore how these and other approaches can be integrated over a range of physical, biological and socioeconomic scales to respond to the problems of resource governance that now face us.System description is still one of the least resolved aspects of ecology. There are numerous approaches available, each using different criteria and operating over different space and time scales. They include biogeography, habitat delimitation, population and metapopulation dynamics, trophodynamics, etc. Once an approach and numeraire (e.g. numbers of species, units of carbon flow between trophic levels, etc.) has been adopted, the boundaries of an ecosystem need to be determined and the groupings within it established. But the problem is that ecosystems, by their very nature, are continuously changing, and the elements within them shifting between groups (e.g. age classes). Fuzzy logic (Zadeh 1965) provides a tool to address this problem and later in the chapter I explore its use and suggest why it is

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Statistical Mechanics of Population: The Lattice Lotka-Volterra Model

Cited by 366 publications

References 7 publications

Local facilitation, bistability and transitions in arid ecosystems

Local facilitation, bistability and transitions in arid ecosystems

Evolutionary prisoner׳s dilemma game on graphs and social networks with external constraint

Ecosystem Analysis and the Governance of Natural Resources

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