Abstract:

The effects of noise and nonuniformity on dynamics of populations are relevant and timely subjects of investigation. One form of variation is the time dependence of the reproduction rate (fitness), referred to as ?seascape? noise; another is time-independent intrinsic dependencies of fitness on location (in the parlance of statistical physics, corresponding to annealed and quenched disorder, respectively). The former was studied recently and demonstrated to lead to novel universality classes for extinction and growth. To reduce the gap between this theoretical model and reality, we develop a new formalism for seascape noise where growth and migration parameters are inhomogeneous. In this formalism, we consider several subpopulation classes: each class consists of patches with similar properties, but patches for different classes are different. Employing a generalized mean-field approach, we self-consistently find distributions for numbers of each subpopulation in steady-state. Interestingly, we find that extinction is characterized by a critical exponent which depends on the characteristics of the subpopulation with the largest noise-to-migration ratio, regardless of the relative size of this subpopulation. Growth is now governed by a generalized Richards law, with an effective exponent varying with population size.

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