Echavarría-Heras Héctor, Villa-Diharce Enrique, Montesinos-López Abelardo, Leal-Ramírez Cecilia
Centro de Investigación Científica y de Estudios Superiores de Ensenada, Carretera Ensenada-Tijuana No. 3918, Zona Playitas, Ensenada, B.C., México.
Centro de Investigación en Matemáticas, A.C. Jalisco s/n, Mineral Valenciana, Guanajuato Gto., 36240, México.
Biol Methods Protoc. 2024 Apr 18;9(1):bpae024. doi: 10.1093/biomethods/bpae024. eCollection 2024.
Allometry refers to the relationship between the size of a trait and that of the whole body of an organism. Pioneering observations by Otto Snell and further elucidation by D'Arcy Thompson set the stage for its integration into Huxley's explanation of constant relative growth that epitomizes through the formula of simple allometry. The traditional method to identify such a model conforms to a regression protocol fitted in the direct scales of data. It involves Huxley's formula-systematic part and a lognormally distributed multiplicative error term. In many instances of allometric examination, the predictive strength of this paradigm is unsuitable. Established approaches to improve fit enhance the complexity of the systematic relationship while keeping the go-along normality-borne error. These extensions followed Huxley's idea that considering a biphasic allometric pattern could be necessary. However, for present data composing 10 410 pairs of measurements of individual eelgrass leaf dry weight and area, a fit relying on a biphasic systematic term and multiplicative lognormal errors barely improved correspondence measure values while maintaining a heavy tails problem. Moreover, the biphasic form and multiplicative-lognormal-mixture errors did not provide complete fit dependability either. However, updating the outline of such an error term to allow heteroscedasticity to occur in a piecewise-like mode finally produced overall fit consistency. Our results demonstrate that when attempting to achieve fit quality improvement in a Huxley's model-based multiplicative error scheme, allowing for a complex allometry form for the systematic part, a non-normal distribution-driven error term and a composite of uneven patterns to describe the heteroscedastic outline could be essential.
异速生长指的是生物体某一性状的大小与整个身体大小之间的关系。奥托·斯内尔的开创性观察以及达西·汤普森的进一步阐释为将其整合到赫胥黎对恒定相对生长的解释中奠定了基础，这种解释通过简单异速生长公式得以体现。识别此类模型的传统方法符合在数据的直接尺度上拟合的回归协议。它涉及赫胥黎公式的系统部分和一个对数正态分布的乘法误差项。在许多异速生长检验实例中，这种范式的预测强度并不合适。既定的提高拟合度的方法在保持伴随正态性误差的同时，增加了系统关系的复杂性。这些扩展遵循了赫胥黎的观点，即考虑双相异速生长模式可能是必要的。然而，对于目前由10410对鳗草叶片干重和面积测量值组成的数据，依赖双相系统项和乘法对数正态误差的拟合在保持重尾问题的同时，几乎没有提高对应测量值。此外，双相形式和乘法对数正态混合误差也没有提供完全的拟合可靠性。然而，更新此类误差项的轮廓，使其以分段式模式出现异方差性，最终产生了整体拟合一致性。我们的结果表明，当试图在基于赫胥黎模型的乘法误差方案中提高拟合质量时，允许系统部分采用复杂的异速生长形式、非正态分布驱动的误差项以及用不均匀模式的组合来描述异方差轮廓可能是至关重要的。
