Using ecological niche modelling to infer past, present and future environmental suitability for Leiopelma hochstetteri, an endangered New Zealand native frog

Leiopelma hochstetteri is an endangered New Zealand frog now confined to isolated populations scattered across the North Island. A better understanding of its past, current and predicted future environmental suitability will contribute to its conservation which is in jeopardy due to human activities, feral predators, disease and climate change. Here we use ecological niche modelling with all known occurrence data (N = 1708) and six determinant environmental variables to elucidate current, pre-human and future environmental suitability of this species. Comparison among independent runs, subfossil records and a clamping method allow validation of models. Many areas identified as currently suitable do not host any known populations. This apparent discrepancy could be explained by several non exclusive hypotheses: the areas have not been adequately surveyed and undiscovered populations still remain, the model is over simplistic; the species` sensitivity to fragmentation and small population size; biotic interactions; historical events. An additional outcome is that apparently suitable, but frog-less areas could be targeted for future translocations. Surprisingly, pre-human conditions do not differ markedly highlighting the possibility that the range of the species was broadly fragmented before human arrival. Nevertheless, some populations, particularly on the west of the North Island may have disappeared as a result of human mediated habitat modification. Future conditions are marked with higher temperatures, which are predicted to be favourable to the species. However, such virtual gain in suitable range will probably not benefit the species given the highly fragmented nature of existing habitat and the low dispersal ability of this species. (C) 2010 Elsevier Ltd. All rights reserved.

A new scale-invariant ratio and finite-size scaling for the stochastic susceptible-infected-recovered model

The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered individuals is determined as a function of the infection rate for several values of the system size. The analysis around criticality is obtained by exploring the close relationship between the present model and standard percolation theory. The quantity UP, equal to the ratio U between the second moment and the squared first moment of the size distribution multiplied by the order parameter P, is shown to have, for a square system, a universal value 1.0167(1) that is the same for site and bond percolation, confirming further that the SIR model is also in the percolation class.