Some Stochastic Versions of the Matrix Model for Population Dynamics
Some Stochastic Versions of the Matrix Model for Population Dynamics
复制标题
种群动态矩阵模型的一些随机版本
DOI：
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发表时间：
1969
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影响因子：
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通讯作者：
Z. Sykes
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作者：
Z. Sykes
为了提供人口预测精度的概率度量，从经典的离散确定性模型出发，定义了人口增长的随机模型，分别假设(1)确定性模型受到加性随机误差；(2)转移矩阵的元素表示概率，而不是速率；(3)转移矩阵是随机变量。每个过程的平均值可以再现确定性过程，而方差可以表示为一步条件方差的加权和。对于第二个模型，这些“创新方差”对于大的总体来说将是很小的，而对于第一个和第三个模型，它们的大小将分别取决于观测到的预测误差和生命率的可变性。由于从经验上知道，后两种模型都具有很大的可变性，因此这些模型可以预期产生相对较高的预测方差，并且这一预期得到了一个数字的证实。
Abstract In an effort to provide probabilistic measures of the accuracy of population projections, stochastic models for population growth are defined from the classical discrete deterministic model by assuming respectively that (1) the deterministic model is subject to additive random errors; (2) the elements of the transition matrix represent probabilities, rather than rates; and (3) the transition matrices are random variables. The mean of each process is shown to reproduce the deterministic process, while the variance can be expressed as the weighted sum of one-step conditional variances. For the second model, these “innovation variances” will be small for large populations, while for the first and third models their size will depend on the observed variability of, respectively, prediction errors and vital rates. Since it is known empirically that both the latter are quite variable, these models could be expected to yield relatively high prediction variances, and this expectation is confirmed by a num...