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Register a new userSelf-organization, scaling and collapse in a coupled automaton model of foragers and vegetation resources with seed dispersal
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We introduce a model of traveling agents ({it e.g.} frugivorous animals) who feed on randomly located vegetation patches and disperse their seeds, thus modifying the spatial distribution of resources in the long term. It is assumed that the survival probability of a seed increases with the distance to the parent patch and decreases with the size of the colonized patch. In turn, the foraging agents use a deterministic strategy with memory, that makes them visit the largest possible patches accessible within minimal travelling distances. The combination of these interactions produce complex spatio-temporal patterns. If the patches have a small initial size, the vegetation total mass (biomass) increases with time and reaches a maximum corresponding to a self-organized critical state with power-law distributed patch sizes and Levy-like movement patterns for the foragers. However, this state collapses as the biomass sharply decreases to reach a noisy stationary regime characterized by corrections to scaling. In systems with low plant competition, the efficiency of the foraging rules leads to the formation of heterogeneous vegetation patterns with $1/f^{alpha}$ frequency spectra, and contributes, rather counter-intuitively, to lower the biomass levels.
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In his seminal work in the 1970s Robert May suggested that there was an upper limit to the number of species that could be sustained in stable equilibrium by an ecosystem. This deduction was at odds with both intuition and the observed complexity of many natural ecosystems. The so-called stability-diversity debate ensued, and the discussion about the factors making an ecosystem stable or unstable continues to this day. We show in this work that dispersal can be a destabilising influence. To do this, we combine ideas from Alan Turings work on pattern formation with Mays random-matrix approach. We demonstrate how a stable equilibrium in a complex ecosystem with two trophic levels can become unstable with the introduction of dispersal in space. Conversely, we show that Turing instabilities can occur more easily in complex ecosystems with many species than in the case of only a few species. Our work shows that adding more details to the model of May gives rise to more ways in which an equilibrium can become unstable. Making Mays simple model more realistic is therefore unlikely to remove the upper bound on complexity.
This paper introduces a model of self-organization between communication and topology in social networks, with a feedback between different communication habits and the topology. To study this feedback, we let agents communicate to build a perception of a network and use this information to create strategic links. We observe a narrow distribution of links when the communication is low and a system with a broad distribution of links when the communication is high. We also analyze the outcome of chatting, cheating, and lying, as strategies to get better access to information in the network. Chatting, although only adopted by a few agents, gives a global gain in the system. Contrary, a global loss is inevitable in a system with too many liars
Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment (J. Dockery, V. Hutson, K. Mischaikow, et al., J. Math. Bio. 37, 61 (1998)) of two species which differ only in their dispersal rates the slow species always dominates. We demonstrate that fluctuations can change this conclusion and can lead to dominance by the fast species or to coexistence, depending on parameters. We discuss two different effects of fluctuations, and show that our results are consistent with more complex treatments that find that selected dispersal rates are not monotonic with the cost of migration.
Dispersal-induced growth (DIG) occurs when two populations with time-varying growth rates, each of which, when isolated, would become extinct, are able to persist and grow exponentially when dispersal among the two populations is present. This work provides a mathematical exploration of this surprising phenomenon, in the context of a deterministic model with periodic variation of growth rates, and characterizes the factors which are important in generating the DIG effect and the corresponding conditions on the parameters involved.
The dynamics of populations is frequently subject to intrinsic noise. At the same time unknown interaction networks or rate constants can present quenched uncertainty. Existing approaches often involve repeated sampling of the quenched disorder and then running the stochastic birth-death dynamics on these samples. In this paper we take a different view, and formulate an effective jump process, representative of the ensemble of quenched interactions as a whole. Using evolutionary games with random payoff matrices as an example, we develop an algorithm to simulate this process, and we discuss diffusion approximations in the limit of weak intrinsic noise.
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