We study both analytically and numerically the model of biological evolution with coherent noise. We establish the conditions for the mean-field approximation applicability. We note the inaccuracy of some results of the model's analysis that is caused by violation of these conditions. We show the power law statistics of extinctions for a wide class of stress distributions. We found for power laws stresses the connection between the exponents of initial and final distributions and we demonstrate for non-power law stresses the appearance of logarithmical correction to power density with fixed exponent. We perform finite-size scaling for simulated densities that confirms the accuracy of theoretical calculations.

biological evolution, extinctions, coherent noise, stress model, power laws

Mathematical modelling in actual problems of science and technics