Species survival and scaling laws in hostile and disordered environments.

نویسندگان

Rodrigo P Rocha

Wagner Figueiredo

Samir Suweis

Amos Maritan

چکیده

In this work we study the likelihood of survival of single-species in the context of hostile and disordered environments. Population dynamics in this environment, as modeled by the Fisher equation, is characterized by negative average growth rate, except in some random spatially distributed patches that may support life. In particular, we are interested in the phase diagram of the survival probability and in the critical size problem, i.e., the minimum patch size required for surviving in the long-time dynamics. We propose a measure for the critical patch size as being proportional to the participation ratio of the eigenvector corresponding to the largest eigenvalue of the linearized Fisher dynamics. We obtain the (extinction-survival) phase diagram and the probability distribution function (PDF) of the critical patch sizes for two topologies, namely, the one-dimensional system and the fractal Peano basin. We show that both topologies share the same qualitative features, but the fractal topology requires higher spatial fluctuations to guarantee species survival. We perform a finite-size scaling and we obtain the associated scaling exponents. In addition, we show that the PDF of the critical patch sizes has an universal shape for the 1D case in terms of the model parameters (diffusion, growth rate, etc.). In contrast, the diffusion coefficient has a drastic effect on the PDF of the critical patch sizes of the fractal Peano basin, and it does not obey the same scaling law of the 1D case.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Survival in hostile environments: strategies of renal medullary cells.

Cells in the renal medulla exist in a hostile milieu characterized by wide variations in extracellular solute concentrations, low oxygen tensions, and abundant reactive oxygen species. This article reviews the strategies adopted by these cells to allow them to survive and fulfill their functions under these extreme conditions.

متن کامل

The effects of Geno hot spring cyanobacteria on growth, survival and morphology of gill tissue in killifish Aphanius dispar in normal and long term thermal stress environments

A killifish species Aphanius ginaonis occurs in Geno hot spring is one of the unique fish species that could successfully survive and acclimated to the high temperature of hot springs. In this study, we investigated the effects of Geno's cyanobacteria extracts on growth, survival and morphology of gill tissue in Aphanius dispar exposed to normal temperature and long-term thermal stress. For thi...

متن کامل

Walking on fractals: diffusion and self-avoiding walks on percolation clusters

We consider random walks (RWs) and self-avoiding walks (SAWs) on disordered lattices directly at the percolation threshold. Applying numerical simulations, we study the scaling behavior of the models on the incipient percolation cluster in space dimensions d = 2, 3, 4. Our analysis yields estimates of universal exponents, governing the scaling laws for configurational properties of RWs and SAWs...

متن کامل

Flux front penetration in disordered superconductors.

We investigate flux front penetration in a disordered type-II superconductor by molecular dynamics simulations of interacting vortices and find scaling laws for the front position and the density profile. The scaling can be understood by performing a coarse graining of the system and writing a disordered nonlinear diffusion equation. Integrating numerically the equation, we observe a crossover ...

متن کامل