Haccou P, Iwasa Y
Section Theoretical Biology, Leiden University, Leiden, 2300 RA, The Netherlands.
Theor Popul Biol. 1996 Dec;50(3):254-80. doi: 10.1006/tpbi.1996.0031.
We study the establishment probability of invaders in stochastically fluctuating environments and the related issue of extinction probability of small populations in such environments, by means of an inhomogeneous branching process model. In the model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period, individuals have (independent) Poisson distributed numbers of offspring. The expected numbers of offspring per individual are independently identically distributed over the periods. It is shown that the establishment probability of an invader varies over the reproduction periods according to a stable distribution. We give a method for simulating the establishment probabilities and approximations for the expected establishment probability. Furthermore, we show that, due to the stochasticity of the establishment success over different periods, the expected success of sequential invasions is larger then that of simultaneous invasions and we study the effects of environmental fluctuations on the extinction probability of small populations and metapopulations. The results can easily be generalized to other offspring distributions than the Poisson.
我们通过一个非齐次分支过程模型，研究随机波动环境中入侵者的定殖概率以及此类环境中小种群灭绝概率的相关问题。在该模型中，假设个体在离散繁殖期进行无性繁殖。在每个时期内，个体的后代数量服从（独立的）泊松分布。每个个体的期望后代数量在各时期独立同分布。结果表明，入侵者的定殖概率在繁殖期内按照稳定分布变化。我们给出了一种模拟定殖概率的方法以及期望定殖概率的近似值。此外，我们表明，由于不同时期定殖成功的随机性，连续入侵的期望成功率大于同时入侵的期望成功率，并且我们研究了环境波动对小种群和集合种群灭绝概率的影响。这些结果可以很容易地推广到除泊松分布之外的其他后代分布。
