比较臭鼩雌雄咀嚼肌质量大小的一种数学模型

A Mathematical Model for Comparing Masticatory Muscle Mass Between Males and Females in Suncus murinus

臭鼩(Suncus murinus)雌、雄群体咀嚼肌质量随体质量变化的回归直线不呈平行关系,不符合协方差分析中要求回归直线斜率基本相同的假设。对此,建构了一种新的数学模型,通过体质量即能较准确地比较雌、雄咀嚼肌质量的相对大小。模型原理为通过回归分析建构雌、雄群体中咀嚼肌质量与体质量的数量关系,将雄性样本坐标点沿回归直线等比例放缩,使放缩后雄性群体体质量均值与雌性相同,且前后回归方程不变,然后推导出放缩后的雄性咀嚼肌与雌性差的表达式。经验证,该模型能够根据臭鼩雌、雄体质量正确预测雌、雄间咀嚼肌相对质量的大小关系,利用该模型计算出的结果显示,臭鼩雄性群体具有相对更大的咀嚼肌质量和攻击力。

The regression lines of the masticatory muscle mass of males and females in Suncus murinus do not parallel their body mass,and also does not meet the assumption that the slope of the regression line is essentially the same in covariance analysis.Here,we constructed a new mathematical model that accurately compares relative masticatory muscle mass between males and females in terms of body mass.The quantitative relationships between masticatory muscle mass and body mass in both genders were established by regression analysis.The coor⁃dinate points of the male sample were scaled in equal proportion along the regression line,so that the average weight of the male after scaling was the same as that of the female,and the regression equation before and after scaling was un⁃changed.The expression of the difference between the masticatory muscle masses in males and females was deduced af⁃ter scaling to produce the model.It is verified that the model can correctly predict the relative mass of masticatory muscles between males and females according to their body mass.The model showed that male shrews have relatively greater mas⁃ticatory muscle mass and attack power.