Heyde C C, Cohen J E
Theor Popul Biol. 1985 Apr;27(2):120-53. doi: 10.1016/0040-5809(85)90007-3.
This work is concerned with the growth of age-structured populations whose vital rates vary stochastically in time and with the provision of confidence intervals. In this paper a model Yt + 1(omega) = Xt + 1(omega) Yt(omega) is considered, where Yt is the (column) vector of the numbers of individuals in each age class at time t, X is a matrix of vital rates, and omega refers to a particular realization of the process that produces the vital rates. It is assumed that (Xi) is a stationary sequence of random matrices with nonnegative elements and that there is an integer n0 such that any product Xj + n0...Xj + 1Xj has all its elements positive with probability one. Then, under mild additional conditions, strong laws of large numbers and central limit results are obtained for the logarithms of the components of Yt. Large-sample estimators of the parameters in these limit results are derived. From these, confidence intervals on population growth and growth rates can be constructed. Various finite-sample estimators are studied numerically. The estimators are then used to study the growth of the striped bass population breeding in the Potomac River of the eastern United States.
这项工作关注的是年龄结构种群的增长，其生命率随时间随机变化，并涉及置信区间的提供。本文考虑了一个模型(Y_{t + 1}(\omega) = X_{t + 1}(\omega)Y_t(\omega))，其中(Y_t)是时刻(t)各年龄组个体数量的（列）向量，(X)是生命率矩阵，(\omega)指产生生命率的过程的一个特定实现。假设((X_i))是具有非负元素的随机矩阵的平稳序列，并且存在一个整数(n_0)，使得任何乘积(X_{j + n_0}\cdots X_{j + 1}X_j)的所有元素以概率(1)为正。然后，在适度的附加条件下，得到了(Y_t)各分量对数的强大数定律和中心极限结果。推导了这些极限结果中参数的大样本估计量。由此，可以构建关于种群增长和增长率的置信区间。对各种有限样本估计量进行了数值研究。然后，这些估计量被用于研究在美国东部波托马克河繁殖的条纹鲈种群的增长情况。
