Nedorezov L V, Sadykov A M, Sadykova D L
Zh Obshch Biol. 2010 Jan-Feb;71(1):41-51.
Considered is a mathematical model for dynamics of an isolated population with non-overlapping generations. The individuals' birth process (emergence of new-generation individuals) is assumed to have a discrete nature (there exist some fixed time moments at which the new generations emerge), while the death process is assumed to be continuous. In addition, the birth rate is assumed to be a function of the number of individuals survived till the moment of reproduction, the function being non-monotone: there exists an optimal value of the population size at which the birth rate reaches its maximum (Alley principle). Analysis of the discrete-continuous models has revealed that each of the new models has a rich set of dynamical regimes. New models are compared with a number of well-known discrete ones (like Skellam, Moran-Ricker, Hassell, Maynard Smith-Slatkin models, and others) when approximating an empirical time series on fluctuations of a green oak moth population (Korzukhin, Semevsky, 1992). Neither of the models can provide for a satisfactory description of the green oak moth dynamics. It is also shown that usage of the discrete-continuous models for approximation of real datasets enables one to find several important population parameters, which can hardly (or cannot) be found by means of traditional discrete models.
考虑一个具有不重叠世代的孤立种群动态的数学模型。假设个体的出生过程（新一代个体的出现）具有离散性质（存在一些固定的时刻，新一代在这些时刻出现），而死亡过程被假设为连续的。此外，假设出生率是直到繁殖时刻存活个体数量的函数，该函数是非单调的：存在一个种群大小的最优值，此时出生率达到最大值（阿利原理）。对离散 - 连续模型的分析表明，每个新模型都有丰富的动态机制。在逼近绿橡树蛾种群波动的经验时间序列时（科尔祖欣、谢梅夫斯基，1992年），将新模型与一些著名的离散模型（如斯克莱姆模型、莫兰 - 里克模型、哈塞尔模型、梅纳德·史密斯 - 斯莱特金模型等）进行了比较。没有一个模型能够对绿橡树蛾的动态提供令人满意的描述。还表明，使用离散 - 连续模型来逼近真实数据集能够找到几个重要的种群参数，而这些参数很难（或无法）通过传统的离散模型找到。
