Model for clustering of living species

Bazeia, D.; Moraes, M. V.; Oliveira, B. F. de

doi:10.1209/0295-5075/129/28002

Cited by 9 publications

(9 citation statements)

References 26 publications

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“…Importantly, the new individual is settled only if the total number of individuals in the neighborhood (within a distance R = 0.1) does not exceed a threshold value M . This local constraint of maximum number of individuals is a significant difference from our previous model where only a global constraint for the maximum number of total population was assumed [14]. Another important change comparing to our previous model is mov and rep could be different.…”

Section: The Modelmentioning

confidence: 78%

“…In a previous paper we studied a simple model of clustering in which female and male individuals followed a basic rule of reproduction, die and movement and demonstrated that a uniformly distributed population can transform into a state where species form a huge single cluster [14]. While the centre of this aggregation moves randomly its size follows a power law behavior in terms of the number of individuals in the whole population.…”

Section: Introductionmentioning

confidence: 99%

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Mobility driven coexistence of living organisms

de Oliveira,

de Moraes,

Bazeia

et al. 2021

Preprint

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We propose a minimal off-lattice model of living organisms where just a very few dynamical rules of growth are assumed. The stable coexistence of many clusters is detected when we replace the global restriction rule by a locally applied one. A rich variety of evolving patterns is revealed where players movement has a decisive role on the evolutionary outcome. For example, intensive individual mobility may jeopardize the survival of the population, but if we increase players movement further then it can save the population. Notably, the collective drive of population members is capable to compensate the negative consequence of intensive movement and keeps the system alive. When the drive becomes biased then the resulting unidirectional flow alters the stable pattern and produce a stripe-like state instead of the previously observed hexagonal arrangement of clusters. Interestingly, the rotation of stripes can be flipped if the individual movement exceeds a threshold value.

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Section: The Modelmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Mobility driven coexistence of living organisms

de Oliveira,

de Moraes,

Bazeia

et al. 2021

Preprint

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“…But there are cases where off-lattice simulations seem to be more appropriate, hence we can not avoid the numerical difficulties of the latter models. We just quote here some microbiological systems, but other situations, like collective movement or floating may also require off-lattice modeling [52,53,54,55].…”

Section: Discussionmentioning

confidence: 99%

Social dilemmas in off-lattice populations

Oliveira

Szolnoki

2021

Chaos, Solitons & Fractals

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Exploring the possible consequences of spatial reciprocity on the evolution of cooperation is an intensively studied research avenue. Related works assumed a certain interaction graph of competing players and studied how particular topologies may influence the dynamical behavior. In this paper we apply a numerically more demanding off-lattice population approach which could be potentially relevant especially in microbiological environments. As expected, results are conceptually similar to those which were obtained for lattice-type interaction graphs, but some spectacular differences can also be revealed. On one hand, in off-lattice populations spatial reciprocity may work more efficiently than for a lattice-based system. On the other hand, competing strategies may separate from each other in the continuous space concept, which gives a chance for cooperators to survive even at relatively high temptation values. Furthermore, the lack of strict neighborhood results in soft borders between competing patches which jeopardizes the long term stability of homogeneous domains. We survey the major social dilemma games based on pair interactions of players and reveal all analogies and differences compared to on-lattice simulations.

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“…Indeed, the latter technique is more demanding and requires larger numerical efforts, but in certain cases we cannot avoid this difficulty. For example this is the proper way to study certain phenomena, like clustering 61 , 64 .…”

Section: Introductionmentioning

confidence: 99%

Environment driven oscillation in an off-lattice May–Leonard model

Bazeia

Ferreira

Oliveira

et al. 2021

Sci Rep

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Cyclic dominance of competing species is an intensively used working hypothesis to explain biodiversity in certain living systems, where the evolutionary selection principle would dictate a single victor otherwise. Technically the May–Leonard models offer a mathematical framework to describe the mentioned non-transitive interaction of competing species when individual movement is also considered in a spatial system. Emerging rotating spirals composed by the competing species are frequently observed character of the resulting patterns. But how do these spiraling patterns change when we vary the external environment which affects the general vitality of individuals? Motivated by this question we suggest an off-lattice version of the tradition May–Leonard model which allows us to change the actual state of the environment gradually. This can be done by introducing a local carrying capacity parameter which value can be varied gently in an off-lattice environment. Our results support a previous analysis obtained in a more intricate metapopulation model and we show that the well-known rotating spirals become evident in a benign environment when the general density of the population is high. The accompanying time-dependent oscillation of competing species can also be detected where the amplitude and the frequency show a scaling law of the parameter that characterizes the state of the environment. These observations highlight that the assumed non-transitive interaction alone is insufficient condition to maintain biodiversity safely, but the actual state of the environment, which characterizes the general living conditions, also plays a decisive role on the evolution of related systems.

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Model for clustering of living species

Cited by 9 publications

References 26 publications

Mobility driven coexistence of living organisms

Mobility driven coexistence of living organisms

Social dilemmas in off-lattice populations

Environment driven oscillation in an off-lattice May–Leonard model

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