关键词:  大优角蚱, 卵块, 数据拟合, 数学模型, 生态学意义

Abstract: 【Aim】 To explore the ecological implications of the unique merogony morphology of Eucriotettix grandis. 【Methods】 Based on a large number of field investigations on the ecological characteristics of egg mass of E. grandis, we got the fitted equation of merogony cross section curve through extracting section line in the three dimensional data point from the photos of egg mass of E. grandis, built the corresponding mathematic model by means of line fitting process, and analyzed the geometrical features of data fitted curve from the aspects of fitted curve curvature and second derivative value map. 【Results】 E. grandis often lays intact egg mass which is near-hexagonal orange segment, with an obvious hemispheric groove on the top and a slightly apophysis in the middle part of the bottom. By using line fitting theory, the kernel function with both the goodness of fit and the smoothness was constructed, and the model curve obtained from the function value fitted quite well with the curve of true value. 【Conclusion】 The groove is probably for water preservation to keep the egg mass moist and make the egg more likely to survive and incubate. The edges and corners are conducive to relieve the long distance rolling and breaking for egg mass, and the tight coupling of egg mass is beneficial to moisturizing the egg.

Key words: Eucriotettix grandis, egg mass, data fitting, mathematical model, ecological implication