Data from: Assessing the influence of temporal autocorrelations on the population dynamics of a disturbance specialist plant population in a random environment

Biological populations are strongly influenced by random variations in their environment, which are often autocorrelated in time. For disturbance specialist plant populations, the frequency and intensity of environmental stochasticity (via disturbances) can drive the qualitative nature of their population dynamics. In this article, we extended our earlier model to explore the effect of temporally autocorrelated disturbances on population persistence. In our earlier work, we only assumed disturbances were independent and identically distributed in time. We proved that the plant seed bank population converges in distribution, and we showed that the mean and variance in seed bank population size were both increasing functions of the autocorrelation coefficient for all parameter values considered, but the interplay between increasing population size and increasing variability caused interesting relationships between quasi-extinction probability and autocorrelation. For example, for populations with low seed survival, fecundity, and disturbance frequency, increasingly positive autocorrelated disturbances decreased quasi-extinction probability. Higher disturbance frequency coupled with low seed survival and fecundity caused a nonmontone relationship between autocorrelation and quasi-extinction, where increasingly positive autocorrelations eventually caused an increase in quasi-extinction probability. For higher seed survival, fecundity, and/or disturbance frequency, quasi-extinction probability was generally a monotonically increasing function of the autocorrelation coefficient.生物种群 (Biological populations) 强烈受到其生存环境中随机波动的影响，这类波动往往在时间上呈现自相关特性。对于干扰专性植物种群 (disturbance specialist plant populations) 而言，环境随机性 (environmental stochasticity，通过干扰作用得以体现) 的发生频率与强度，能够决定其种群动态的定性特征。在本文中，我们拓展了此前的研究模型，以探究时间自相关干扰 (temporally autocorrelated disturbances) 对种群存续 (population persistence) 的影响。在先前的研究中，我们仅假设干扰在时间上服从独立同分布 (independent and identically distributed)。我们证明了植物种子库 (seed bank) 种群依分布收敛 (converges in distribution)，同时发现：在所考量的全部参数取值下，种子库种群规模的均值与方差均为自相关系数的递增函数；但种群规模扩张与变异程度提升之间的相互作用，使得准灭绝概率 (quasi-extinction probability) 与自相关系数之间呈现出颇具趣味的关联。例如，对于种子存活率、繁殖力 (fecundity) 与干扰频率均较低的种群而言，愈发呈正相关的干扰会降低准灭绝概率；而当干扰频率较高且伴随低种子存活率与低繁殖力时，自相关系数与准灭绝概率之间呈现非单调关系：随着自相关系数愈发趋近于正相关，准灭绝概率最终会上升。对于种子存活率、繁殖力和/或干扰频率较高的种群而言，准灭绝概率通常随自相关系数的增大呈单调递增趋势。