Nedorezov L V
Zh Obshch Biol. 2011 Mar-Apr;72(2):83-92.
Analysed are the data of larch bud moth (Zeiraphera diniana Gn.) fluctuations in Swiss Alps. The analysis applies simplest mathematical models of isolated population dynamics (in particular, Kostitzin model, Skellam model, the discrete logistic model, and some other ones), which include the minimal number of unknown parameters. The parameters have been estimated, for all the models in hand, by the least-squares method, to fit certain data from the Global Population Dynamics Database (N 1407 and N 6195), the sequences of the data deviations from the model trajectories being treated as well. The best approximations are shown to be achieved with Moran-Ricker model and the discrete logistic model. Statistical criteria (Kolmogorov-Smirnov and Shapiro-Wilk tests) reveal that the hypotheses of normal distribution of residuals must be rejected for one of the time series (N 1407); some models demonstrate serial correlations in the sequence of residuals (according to Durbin-Watson test). This leads to the conclusion that periodic fluctuations in the larch bud moth population (N 1407) can hardly be explained by self-regulation mechanisms alone. For another time series (N 6195), the modified discrete logistic model has appeared to be acceptable as a mode of fluctuations.
分析了瑞士阿尔卑斯山落叶松芽蛾（Zeiraphera diniana Gn.）数量波动的数据。分析采用了孤立种群动态的最简单数学模型（特别是科斯季茨因模型、斯克莱姆模型、离散逻辑斯蒂模型以及其他一些模型），这些模型包含的未知参数数量最少。对于手头的所有模型，已通过最小二乘法估计参数，以拟合全球种群动态数据库中的某些数据（N 1407和N 6195），同时也处理了数据与模型轨迹的偏差序列。结果表明，莫兰 - 里克模型和离散逻辑斯蒂模型能实现最佳近似。统计标准（柯尔莫哥洛夫 - 斯米尔诺夫检验和夏皮罗 - 威尔克检验）显示，对于其中一个时间序列（N 1407），必须拒绝残差正态分布的假设；根据杜宾 - 沃森检验，一些模型在残差序列中表现出序列相关性。由此得出结论，落叶松芽蛾种群（N 1407）的周期性波动很难仅由自我调节机制来解释。对于另一个时间序列（N 6195），修正后的离散逻辑斯蒂模型似乎可作为波动模式接受。
