Quasi-one-dimensional waves in rodent populations in heterogeneous habitats: a consequence of elevational gradients on spatio-temporal dynamics

Extinction transition of hantavirus-infected rodents in a hostile environment

The spatial critical shelter sizes above which populations would survive are investigated for the infection of hantavirus among rodent populations surrounded by a deadly environment. We show that the critical shelter sizes for the infected population and the susceptible population are different due to symmetry breaking in the reproduction and the transmission processes. Therefore, there exists a shelter size gap within which the infected population becomes extinct while only the susceptible population survives. With the field data reported in the literature, we estimate that, if one confines the rodent population within a stripe region surrounded by a deadly environment with the shorter dimension between 335.5±27.2m and 547.9±78.3m, the infected population would become extinct. In addition, we introduce two factors that influence the movement of rodents, namely, the spatial asymmetry of the landscape and the sociality of rodents, to study their effects on the shelter size gap. The effects on the critical size due to environmental bias are twofold: it enhances the overall competition among rodents which increases the critical size, but on the other hand it promotes the spread of the hantavirus which reduces the critical size for the infected population. On the contrary, the sociality of rodents gives rise to a more localized population profile which promotes the spread of the hantavirus and reduces the shelter size gap. The results shed light on a possible strategy of eliminating hantavirus while preserving the integrity of food webs in ecosystems.

Random-walk model to study cycles emerging from the exploration-exploitation trade-off

We present a model for a random walk with memory, phenomenologically inspired in a biological system. The walker has the capacity to remember the time of the last visit to each site and the step taken from there. This memory affects the behavior of the walker each time it reaches an already visited site modulating the probability of repeating previous moves. This probability increases with the time elapsed from the last visit. A biological analog of the walker is a frugivore, with the lattice sites representing plants. The memory effect can be associated with the time needed by plants to recover its fruit load. We propose two different strategies, conservative and explorative, as well as intermediate cases, leading to nonintuitive interesting results, such as the emergence of cycles.

Consequences of animal interactions on their dynamics: emergence of home ranges and territoriality

Animal spacing has important implications for population abundance, species demography and the environment. Mechanisms underlying spatial segregation have their roots in the characteristics of the animals, their mutual interaction and their response, collective as well as individual, to environmental variables. This review describes how the combination of these factors shapes the patterns we observe and presents a practical, usable framework for the analysis of movement data in confined spaces. The basis of the framework is the theory of interacting random walks and the mathematical description of out-of-equilibrium systems. Although our focus is on modelling and interpreting animal home ranges and territories in vertebrates, we believe further studies on invertebrates may also help to answer questions and resolve unanswered puzzles that are still inaccessible to experimental investigation in vertebrate species.