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

利用近15年的普查资料，分析了不同环境条件下无瓣延龄草和甘草延龄草的流行动态。此外，我们还提出了一种检验密度相关矩阵模型中种群动态指标弹性矩阵可靠性的方法。对于前者，我们估计了重要的生活史参数(存活率和繁殖力等)的均值和方差。并检验了这些参数的时间变化对人口增长率预期的影响。结果表明：(1)无瓣延龄草种群在50年后下降到30%以下的概率为75.6%，而延龄草种群在50年后下降到30%以下的概率为0。(2)在这两个物种中，具有高灵敏度的元素与对种群数量减少贡献更大的元素是不同的，对于后者，我们得到了平衡时的理论弹性矩阵和实际变化动态下的弹性矩阵，并对它们进行了比较。我们发现，它们之间的差异很大程度上取决于生活史模式和密度依赖模式。在Beverton-Holt型密度相关函数的情况下，偏差较小，而在Ricker型密度相关函数的情况下，偏差较大。当所讨论的物种是单果和延迟生长时，弹性矩阵的可靠性变低。

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.