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

In this work we study the effect of two different ecological mechanisms on the desertification transition in arid or semi-arid ecosystems, modeled by a stochastic cellular automaton. Namely we consider the role of the facilitation mechanism, i.e. the local positive effects of plants on their neighborhood and of colonization factors, such as seed production, survival and germination probabilities. Within the model, the strength of these two mechanisms is determined by the parameters f and b, respectively controlling the rates of the recovery and colonization processes. In particular we focus on the full desertification transition occurring at increasing value of the mortality rate m and we discuss how the values of f and b affect the critical mortality mc, the critical exponents β and γσ′, determining the power-law scaling of the average vegetation density and of the root-mean-square deviation of the density fluctuations, and the character of the transition: continuous or abrupt. We show that mc strongly depends on both f and b, a dependence which accounts for the higher resilience of the ecosystems to external stresses as a consequence of an increased effectiveness of positive feedback effects. On the other hand, concerning the value of the exponents and the character of the transition, our results point out that both these features are unaffected by changes in the strength of the local facilitation. Viceversa, we show that an increase of the colonization factor b significantly modifies the values of the exponents and the order of the transition, changing a continuous transition into an abrupt one. We explain these results in terms of the different range of the interactions characterizing facilitation and colonization mechanisms.