Crossover in spreading behavior due to memory in population dynamics.

The reaction-diffusion equation is one of the possible ways for modeling animal movement, where the reactive part stands for the population growth and the diffusive part for random dispersal of the population. However, a reaction-diffusion model may not represent all aspects of the spatial dynamics, because of the existence of distinct mechanisms that can affect the movement, such as spatial memory, which results in a bias for one direction of dispersal. This bias is modeled through an advective term on an advection-reaction-diffusion equation. Thus, considering the effects of memory on the population spread, we propose a model composed of a coupled partial differential equation system with two equations: one for the population dynamics and the other for the memory density distribution. For the population growth, we use either the exponential or logistic growth function. The analytic approach shows that for the exponential and logistic growth, the minimum traveling wave speeds are the same with or without memory dynamics in which the variation of memory is infinitesimal. From the numerical analysis, we explore how our parameters, memory, growth rate, and carrying capacity, affect the population redistribution. The combinations of these parameters result in a redistribution pattern of the population associated with either diffusive or superdiffusive and imply the dispersal is faster than the diffusion. Further, in the parameter-space defined by memory and growth rate, we have shown that memory is a factor that switches the dynamics between two spreading behaviors, one faster than the other.

The world's biogeographical regions revisited: global patterns of endemism in Tipulidae (Diptera).

This paper explores the distributional data of 4,224 Tipulidae (Insecta: Diptera) species to search for endemism patterns in a worldwide scale and to test the extent to which the global patterns of endemism of the group fit into previously proposed regionalization schemes, particularly Wallace's system and recent revisions of it. Large scale areas of endemism are assessed using the grid-based method implemented in VNDM. VNDM depends on the prior definition of the grid size for analysis, but a criterion for choosing beforehand a particular grid size is not clear. The same holds for the choice of the level of similarity in species composition selected for the calculation of consensus areas. In our study, we developed a methodological approach that helped defining objective criteria for choosing suitable values for these critical variables. Large-scale areas of endemism around the globe are identified and ranked according to endemicity levels: 1--West Palaearctic, 2--Nearctic, 3--East Palaearctic-Oriental, 4--West North America, 5--Australia, 6--Neotropical, 7--Sub-Saharan Africa, 8--Palaearctic, and 9--Middle East. Our main conclusion is that there are still some limitations in applying biogeographical classifications proposed mostly on the basis of vertebrate distribution to other taxonomic groups, such as the Tipulidae. While there is a general congruence of the broad-scale areas of endemism of tipulids with previously proposed regionalization schemes, for some areas, the sharpness of boundaries between traditional regions is not so acute, due to a great level of overlap of part of its biotic elements.

Ergodic crossover in partially self-avoiding stochastic walks.

Consider a one-dimensional environment with N randomly distributed sites. An agent explores this random medium moving deterministically with a spatial memory µ. A crossover from local to global exploration occurs in one dimension at a well-defined memory value µ_{1}=log_{2}N. In its stochastic version, the dynamics is ruled by the memory and by temperature T, which affects the hopping displacement. This dynamics also shows a crossover in one dimension, obtained computationally, between exploration schemes, characterized yet by the trajectory size (N_{p}) (aging effect). In this paper we provide an analytical approach considering the modified stochastic version where the parameter T plays the role of a maximum hopping distance. This modification allows us to obtain a general analytical expression for the crossover, as a function of the parameters µ, T, and N_{p}. Differently from what has been proposed by previous studies, we find that the crossover occurs in any dimension d. These results have been validated by numerical experiments and may be of great value for fixing optimal parameters in search algorithms.

Modeling habitat split: landscape and life history traits determine amphibian extinction thresholds.

Habitat split is a major force behind the worldwide decline of amphibian populations, causing community change in richness and species composition. In fragmented landscapes, natural remnants, the terrestrial habitat of the adults, are frequently separated from streams, the aquatic habitat of the larvae. An important question is how this landscape configuration affects population levels and if it can drive species to extinction locally. Here, we put forward the first theoretical model on habitat split which is particularly concerned on how split distance - the distance between the two required habitats - affects population size and persistence in isolated fragments. Our diffusive model shows that habitat split alone is able to generate extinction thresholds. Fragments occurring between the aquatic habitat and a given critical split distance are expected to hold viable populations, while fragments located farther away are expected to be unoccupied. Species with higher reproductive success and higher diffusion rate of post-metamorphic youngs are expected to have farther critical split distances. Furthermore, the model indicates that negative effects of habitat split are poorly compensated by positive effects of fragment size. The habitat split model improves our understanding about spatially structured populations and has relevant implications for landscape design for conservation. It puts on a firm theoretical basis the relation between habitat split and the decline of amphibian populations.