The development of estimation method of extinction probability in population under varying environment

本文利用近15年的普查资料，分析了不同环境下无柄万里草（Trillium apetalon）和苦参（T. camschatcense）的流行动态。此外，我们还开发了一种在密度依赖矩阵模型中检验种群动态指标弹性矩阵可靠性的方法。对于前者，我们估计了重要生活史参数（存活率和繁殖力等）的均值和方差，并考察了这些参数的时间变化对种群增长率预期的影响。结果得出了人口增长和减少的概率，并阐明了几点；(1)无瓣草种群在50年后减少到30%以下的概率为75.6%，而苦仙子种群在50年后减少到30%以下的概率为0%。(2)在两个物种中，敏感性较高的元素与对种群大小减小贡献较大的元素不同。对于后者，我们得到了理论的平衡弹性矩阵和实际变化动力下的弹性矩阵，并进行了比较。研究发现，二者之间的差异主要取决于生活史模式和密度依赖模式。对于beverton - holt型密度相关函数，差异相对较小，而对于ricker型密度相关函数，差异较大。当所讨论的物种是单性和延迟生长时，弹性矩阵的可靠性变得越来越低。

We analyzed the popular dynamics of Trillium apetalon and T. camschatcense under varying environment, using the census data during about 15 years. Moreover, we developed a method to check the reliability of elasticity matrix, which is an index of population dynamics, in density-dependent matrix model.As for the former, we estimated the mean and variance of important life-history parameters (survival rate and fecundity etc.) and examined the effect of temporal variation of those parameters on the expectation of population growth rate. As the result, we obtained the probabilities of increase and decrease of the population and clarified several points; (1) The probability that the population of Trillium apetalon decreases under 30% after 50 years is 75.6%, while the probability that the population of Trillium camschatcense decreases under 30% after 50 years is 0%. (2) In both species, elements with high sensitivity are different from elements that contribute more to the decrease of the population size.As for the latter, we obtained the theoretical elasticity matrix at equilibrium and the elasticity matrix under actually varying dynamics, and compared them. We found that the discrepancy between them depend largely on the life history pattern and the pattern of density-dependence. In the case of Beverton-Holt-type density dependent function, the discrepancy is relatively small, while in the case of Ricker-type density dependent function, the discrepancy is large. The reliability of elasticity matrix is becoming low when the species in question is monocarpic and delayed growth.