Matis James H, Kiffe Thomas R
Department of Statistics, Texas A&M University, 3143 TAMU, College Station, TX 77843-3143, USA.
Theor Popul Biol. 2004 Feb;65(1):89-104. doi: 10.1016/j.tpb.2003.08.003.
This paper develops a stochastic logistic population growth model with immigration and multiple births. The differential equations for the low-order cumulant functions (i.e., mean, variance, and skewness) of the single birth model are reviewed, and the corresponding equations for the multiple birth model are derived. Accurate approximate solutions for the cumulant functions are obtained using moment closure methods for two families of model parameterizations, one for badger and the other for fox population growth. For both model families, the equilibrium size distribution may be approximated well using the Normal approximation, and even more accurately using the saddlepoint approximation. It is shown that in comparison with the corresponding single birth model, the multiple birth mechanism increases the skewness and the variance of the equilibrium distribution, but slightly reduces its mean. Moreover, the type of density-dependent population control is shown to influence the sign of the skewness and the size of the variance.
本文建立了一个具有移民和多胎生育的随机逻辑斯谛种群增长模型。回顾了单胎生育模型低阶累积量函数（即均值、方差和偏度）的微分方程，并推导了多胎生育模型的相应方程。针对两类模型参数化，使用矩封闭方法获得了累积量函数的精确近似解，一类用于獾种群增长，另一类用于狐狸种群增长。对于这两类模型，平衡规模分布可以用正态近似很好地逼近，用鞍点近似则更精确。结果表明，与相应的单胎生育模型相比，多胎生育机制增加了平衡分布的偏度和方差，但略微降低了其均值。此外，密度依赖型种群控制的类型被证明会影响偏度的符号和方差的大小。
