Meerson Baruch, Sasorov Pavel V, Kaplan Yitzhak
Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jul;84(1 Pt 1):011147. doi: 10.1103/PhysRevE.84.011147. Epub 2011 Jul 28.
The position of propagating population fronts fluctuates because of the discreteness of the individuals and stochastic character of processes of birth, death, and migration. Here we consider a Markov model of a population front propagating into a metastable state, and focus on the weak noise limit. For typical, small fluctuations the front motion is diffusive, and we calculate the front diffusion coefficient. We also determine the probability distribution of rare, large fluctuations of the front position and, for a given average front velocity, find the most likely population density profile of the front. Implications of the theory for population extinction risk are briefly considered.
由于个体的离散性以及出生、死亡和迁移过程的随机性，繁殖种群前沿的位置会发生波动。在此，我们考虑一个种群前沿传播到亚稳态的马尔可夫模型，并关注弱噪声极限。对于典型的小波动，前沿运动是扩散性的，我们计算前沿扩散系数。我们还确定了前沿位置罕见的大波动的概率分布，并且对于给定的平均前沿速度，找出前沿最可能的种群密度分布。简要考虑了该理论对种群灭绝风险的影响。
