Evaluating Dispersion Strategies in Growth Models Subject to Geometric Catastrophes

Extinction time in growth models subject to geometric catastrophes

“…Furthermore, Junior et al [8] showed that the extinction probabilities in the white region of figure 2 satisfies ψ i 2 > ψ A . Thus, in the white region, non-dispersion is a better strategy than independent dispersion.…”

“…Junior et al [8] compute explicitly the extinction probabilities (ψ o 2 , ψ o 3 , ψ i 2 , and ψ i 3 ) as functions of λ and p. In particular, they showed that extinction probabilities for the models C(λ, p) and C o 2 (λ, p) are equal (ψ A = ψ o 2 ). An interesting question is to determine whether, when the models C(λ, p) and C o 2 (λ, p) die out almost surely, dispersion is an advantage or not to extend the population's life span.…”

“…Artalejo et al [1] and Brockwell [2,3] analyzed models for populations that after catastrophes, the survivors individuals remain together in the same colony. Schinazi [15], Machado et al [11] and Junior et al [7,8,10] studied models for populations that after catastrophes, individuals disperse trying to make new colonies to improve the odds of their species survival. In all these works, different types of catastrophes and different dispersion strategies were considered.…”

“…Recently, Junior et al [8] analyzed different dispersion strategies in populations subject to geometric catastrophes, to study how these strategies impact the population viability, comparing them with the strategy where there is no dispersion. Their analysis points to establish which is the best strategy (dispersion or no dispersion), based on the survival probability of the population when some strategy is adopted.…”

“…In section 2 we present the non dispersion model proposed in Artalejo et al [1] and the models with dispersion proposed in Junior et al [8]. Moreover, we added new results for these models.…”