A stochastic model for the evolution of species with random fitness

Electronic Communications in Probability

Daniela Bertacchi¹ 

关键词: generalized GMS model;    birth and death process;    survival;    fitness;    queuing process;    limit distribution;   

DOI  :  10.1214/18-ECP190

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

We generalize the evolution model introduced by Guiol, Machado and Schinazi (2010). In our model at odd times a random number $X$ of species is created. Each species is endowed with a random fitness with arbitrary distribution on $[0,1]$. At even times a random number $Y$ of species is removed, killing the species with lower fitness. We show that there is a critical fitness $f_c$ below which the number of species hits zero i.o. and above of which this number goes to infinity. We prove uniform convergence for the fitness distribution of surviving species and describe the phenomena which could not be observed in previous works with uniformly distributed fitness.

【 授权许可】

CC BY