菜蚜种群密度简易估计的数学模型

A study of binomial sampling models for estimating aphid population density on crucifer vegeta-bles.

根据田间菜蚜种群的数量消长和空间扩散规律，提出了一个根据有蚜株率Ｐ来估计种群平均密度Ｍ的数学模型，并利用同样数据，对几个常见的Ｐ～Ｍ关系模型进行拟合。根据各个拟合模型的残差平方和分析，新提出的模型对菜蚜种群数据具有较高的拟合能力，该模型适合于田间在一季作物的生长初期菜蚜种群处于定居扩散期间（Ｐ＜１００％）的种群密度简易（二项抽样）估计，可简化田间菜蚜种群的密度调查工作。文中还对该模型的密度估计方差及理论抽样数进行了分析。

Systematic sampling of aphid populations on crucifer vegetables was carried out dur-ing 1990 1992 in Hangzhou,Following an analysis of the patterns of abundance and spatial distri-bution of the aphid population(consisting of Myzus persicae and Lipaphis erysimi),a new binomialsampling model for estimating population density of the two aphids was developed based on theproportion of empty sampling units. The sampling data were also fitted to four other binomial sam-pling models which were derived from either theoretical distribution formulae or empirical relation-ships between mean density and proportion of empty sampling units.Comparison of the goodnessof fit between the different models showed that the new model developed in this paper gave thebest description of the field sampling data. The new model was used successfully to develop bino-mial sampling plans for the aphid populations during the aphid immigration-dispersion phase on anew crop(i.e.,proportion of plants with aphids <100%).The sampling variance and the numberof theoretical sampling units of the new model were also estimated and analyzed in the paper.