基于Carter-Morley Jones蛋形模型的参数估计新方法  

A new parameter estimation method based on the Carter-Morley Jones eggshape model

作　　者：王林 尹梓杨 黄慧芳 王静 Lin Wang;Ziyang Yin;Huifang Huang;Jing Wang(College of Life Sciences,Sichuan University,Chengdu 610064,China;Faculty of Science and Technology,University of Macao,Macao 999078,China;College of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China;College of Life Sciences,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]四川大学生命科学学院,成都610064 [2]澳门大学科技学院,中国澳门999078 [3]华中科技大学数学与统计学院,武汉430074 [4]郑州大学生命科学学院,郑州450001

出　　处：《生物多样性》2025年第1期119-127,共9页Biodiversity Science

基　　金：郑州大学科研启动基金和河南省高等学校重点科研项目(24B220007)。

摘　　要：作为鸟类对多样化生存环境适应的一种解释,鸟蛋的形状长期以来受到生物学家和数学家的关注。Carter-Morley Jones方程是一种描述鸟蛋二维投影形状的极坐标方程,通常应用多元线性回归方法估计其模型参数。然而,多元线性回归方法可能因其前提假设不成立而导致拟合较差。本研究提出了一种基于非线性最优化理论的Carter-MorleyJones蛋形模型的参数估计方法,并使用多元线性回归和非线性最优化两种方法对51个物种共416组实际蛋形数据进行了拟合。应用均方根误差和非线性曲率度量分别评价两种方法的拟合优度和线性近似行为。同时,本研究还比较了基于Carter-Morley Jones蛋形模型预测的鸟蛋体积和使用排水法测量的实际体积。结果表明:(1)相较于多元线性回归参数估计方法,非线性最优化方法能够获得更好的拟合优度;(2)在蛋形方程的线性近似行为表现方面,多元线性回归和非线性最优化两种参数估计方法之间并无显著差异;(3)基于Carter-MorleyJones蛋形模型预测的鸟蛋体积和使用排水法测量的实际体积之间并无显著差异。本研究为蛋形方程的实际应用提供了数学工具。同时,非线性曲率度量也为将来评估蛋形模型提供了一个新的视角。Aim:The shape of eggs is a subject of considerable interest among biologists and mathematicians,particularly regarding avian adaptation to diverse environments.The Carter-Morley Jones equation is a polar coordinate equation that describes the two-dimensional projection shape of bird eggs,typically with its model parameters estimated using multiple linear regression.However,multiple linear regression may result in poor fits due to the failure of its underlying assumptions.This study proposes a novel parameter estimation method for the Carter-Morley Jones equation based on nonlinear optimization theory.Methods:We employed both multiple linear regression and nonlinear optimization techniques to fit actual egg-shape data obtained from 416 eggs spanning 51 species.The performance of each fitting method was assessed by evaluating the goodness of fit through root-mean-square error and analyzing the linear approximation behavior through nonlinear curvature measures.Additionally,we compared the egg volumes predicted by the Carter-Morley Jones equation with actual volumes measured using a graduated cylinder.Results:The findings indicated that:(1)The nonlinear optimization method provided a superior goodness of fit compared to the multiple linear regression method;(2)No significant difference was observed in the linear approximation behavior between the two parameter estimation methods;and(3)There was no significant difference between the predicted egg volumes from the Carter-Morley Jones model and the actual volumes measured via the graduated cylinder.Conclusion:This study offers a robust mathematical tool for applying the egg-shape equation in ecological research.Furthermore,the use of nonlinear curvature measures presents a fresh perspective for evaluating egg shape models in future investigations.

关 键 词：鸟蛋 Carter-Morley Jones方程 非线性最优化 蛋形建模 生态适应 

分 类 号：Q959.7[生物学—动物学]