Lande R, Orzack S H
Department of Ecology and Evolution, University of Chicago, IL 60637.
Proc Natl Acad Sci U S A. 1988 Oct;85(19):7418-21. doi: 10.1073/pnas.85.19.7418.
We model density-independent growth of an age- (or stage-) structured population, assuming that mortality and reproductive rates fluctuate as stationary time series. Analytical formulas are derived for the distribution of time to extinction and the cumulative probability of extinction before a certain time, which are determined by the initial age distribution, and by the infinitesimal mean and variance, mu and sigma 2, of a diffusion approximation for the logarithm of total population size. These parameters can be estimated from the average life history and the pattern of environmental fluctuations in the vital rates. We also show that the distribution of time to extinction (conditional on the event) depends on the magnitude but not the sign of mu. When the environmental fluctuations in vital rates are small or moderate, the diffusion approximation gives accurate estimates of cumulative extinction probabilities obtained from computer simulations.
我们对年龄（或阶段）结构种群的密度独立增长进行建模，假设死亡率和繁殖率作为平稳时间序列波动。推导了灭绝时间分布和在特定时间之前灭绝的累积概率的解析公式，它们由初始年龄分布以及总人口规模对数的扩散近似的无穷小均值和方差（μ和σ²）决定。这些参数可以从平均生命史和生命率中的环境波动模式进行估计。我们还表明，灭绝时间的分布（以该事件为条件）取决于μ的大小而非符号。当生命率中的环境波动较小或适中时，扩散近似能准确估计从计算机模拟中获得的累积灭绝概率。
