Critical desertification transition in semi-arid ecosystems: The role of local facilitation and colonization rate

Corrado, Raffaele; Cherubini, Anna Maria; Pennetta, C.

doi:10.1016/j.cnsns.2014.08.041

Cited by 20 publications

(7 citation statements)

References 44 publications

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“…In the present case, the values of β and γ σ significantly differ from the values reported in the literature for the corresponding exponents of the DP class in two-dimensional systems: β = 0.583 ÷ 0.584 and γ σ = 0.15-0.18 [47][48][49][50][51]. Moreover the critical exponents are found dependent on the model parameters [46]. As a general conclusion concerning this point, we can say that the SCA model provides nonuniversal exponents.…”

Section: A Full Desertification Transitioncontrasting

confidence: 67%

“…As a general conclusion concerning this point, we can say that the SCA model provides nonuniversal exponents. The reasons of this nonuniversality and the connection with DP will be investigated elsewhere [46]. The critical character of the full desertification transition is also confirmed by considering the fluctuation distribution of the size of the biggest cluster of vegetated cells.…”

Section: A Full Desertification Transitionmentioning

confidence: 84%

“…For this last we found a continuous power-law decrease of the average living cell density ρ + which approaches the extinction threshold and a power-law increase of the root-mean-square deviation of the ρ + fluctuations, σ ρ + . Both power laws are associated with nonuniversal critical exponents β and γ σ [46]. Since the model leads to different kinds of transitions in different regions of the parameter space [9], the continuous character of the transition discussed here depends on the choice of the parameters.…”

Section: Discussionmentioning

confidence: 99%

“…We call this transition at m c full desertification transition. The value of m c depends on the system size and on the values of the other parameters[46]: for the set of parameters adopted here the m c values are reported in…”

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Early warning signals of desertification transitions in semiarid ecosystems

2014

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The identification of early warning signals for regime shifts in ecosystems is of crucial importance given their impact in terms of economic and social effects. We present here the results of a theoretical study on the desertification transition in semiarid ecosystems under external stress. We performed numerical simulations based on a stochastic cellular automaton model, and we studied the dynamics of the vegetation clusters in terms of percolation theory, assumed as an effective tool for analyzing the geometrical properties of the clusters. Focusing on the role played by the strength of external stresses, measured by the mortality rate m, we followed the progressive degradation of the ecosystem for increasing m, identifying different stages: first, the fragmentation transition occurring at relatively low values of m, then the desertification transition at higher mortality rates, and finally the full desertification transition corresponding to the extinction of the vegetation and the almost complete degradation of the soil, attained at the maximum value of m. For each transition we calculated the spanning probabilities as functions of m and the percolation thresholds according to different spanning criteria. The identification of the different thresholds is proposed as an useful tool for monitoring the increasing degradation of real-world finite-size systems. Moreover, we studied the time fluctuations of the sizes of the biggest clusters of vegetated and nonvegetated cells over the entire range of mortality values. The change of sign in the skewness of the size distributions, occurring at the fragmentation threshold for the biggest vegetation cluster and at the desertification threshold for the nonvegetated cluster, offers new early warning signals for desertification. Other new and robust indicators are given by the maxima of the root-mean-square deviation of the distributions, which are attained respectively inside the fragmentation interval, for the vegetated biggest cluster, and inside the desertification interval, for the nonvegetated cluster.

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Section: A Full Desertification Transitioncontrasting

confidence: 67%

Section: A Full Desertification Transitionmentioning

confidence: 84%

Section: Discussionmentioning

confidence: 99%

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confidence: 99%

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Early warning signals of desertification transitions in semiarid ecosystems

2014

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We propose a simple theoretical model for desertification processes based on three actors (soil, seeds, and plants) on a two-dimensional lattice. In recent works [19,22,23,24], one of the authors of this paper (A.M.C.) We show that even taking into account only a few parameters, accounting for external actions on the ecosystem or the response to positive feedbacks, the model provides a plausible description of the desertification process, and can be adapted to different ecological landscapes.

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confidence: 78%

An Operatorial Description of Desertification

Багарелло

Cherubini

Oliveri

2016

SIAM J. Appl. Math.

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We propose a simple theoretical model for desertification processes based on three actors (soil, seeds, and plants) on a two-dimensional lattice. Each actor is described by a time dependent fermionic operator, and the dynamics is ruled by a self-adjoint Hamilton-like operator. We show that even taking into account only a few parameters, accounting for external actions on the ecosystem or the response to positive feedbacks, the model provides a plausible description of the desertification process, and can be adapted to different ecological landscapes. We first describe the simplified model in one cell. Then, we define the full model on a two-dimensional region, taking into account additional factors such as nonhomogeneities, the competition for resources between plants, and the spread of seeds due to the action of wind or animals. This allows us to explore the effects of positive feedback on slowing down, stopping, or reversing the desertification process.great part of the work on desertification follows a statistical approach, analyzing time series of simulated or empirical spatial data typical of an area at risk of imminent desertification. In [17,21] the authors proposed a stochastic cellular automaton on a lattice to model semi-arid regions subjected to external stress, such as grazing. In recent works [19,22,23,24], one of the authors of this paper (A.M.C.) applied percolation theory to analyze time series of data generated by the cellular automaton. This theoretical approach allows us to follow the degradation of an ecosystem through different stages, characterized by the increasing loss of connectivity in the vegetation and identified by several indicators, which are early warning signals of desertification.In these studies, the variables in the models are vegetation densities and the ecological factors at play, such as seed dispersal and overall quality of the soil, facilitation and competition between plants. In order to understand the interactions between some of these factors, we apply here a completely different theoretical approach: we use operators to model the ecosystem, while vegetation, quality of soil, and presence of seeds are the variables of the system. The dynamics is driven by a Hamiltonian on a lattice and the parameters in the Hamiltonian are local, i.e., relative to each cell of the lattice, in order to model environments where there are local ecological differences, e.g., in the distribution of water. We can construct in this way a model which is flexible enough to describe different ecological landscapes and which provides useful insights, not only on the desertification process but also on possible ways to stop or reverse it. The study of the process opposite to desertification, i.e., colonization of bare ground by vegetation, is a relatively unexplored area (see [25] for a model of vegetation pattern formation by colonization), though projects to fight desertification often go in this direction.To the best of our knowledge, this is the first time that the deterioration of an ecosystem...

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