Echavarria-Heras Hector A, Castro-Rodriguez Juan R, Leal-Ramirez Cecilia, Villa-Diharce Enrique
Departamento de Ecología, Centro de Investigación Científica y de Estudios Superiores de Ensenada, Ensenada, Baja California, México.
Facultad de Ciencias Químicas e Ingeniería, Universidad Autónoma de Baja California, Tijuana, Baja California, México.
PeerJ. 2020 Jan 6;8:e8173. doi: 10.7717/peerj.8173. eCollection 2020.
The traditional allometric analysis relies on log- transformation to contemplate linear regression in geometrical space then retransforming to get Huxley's model of simple allometry. Views assert this induces bias endorsing multi-parameter complex allometry forms and nonlinear regression in arithmetical scales. Defenders of traditional approach deem it necessary since generally organismal growth is essentially multiplicative. Then keeping allometry as originally envisioned by Huxley requires a paradigm of polyphasic loglinear allometry. A Takagi-Sugeno-Kang fuzzy model assembles a mixture of weighted sub models. This allows direct identification of break points for transition between phases. Then, this paradigm is seamlessly appropriate for efficient allometric examination of polyphasic loglinear allometry patterns. Here, we explore its suitability.
Present fuzzy model embraces firing strength weights from Gaussian membership functions and linear consequents. Weights are identified by subtractive clustering and consequents through recursive least squares or maximum likelihood. Intersection of firing strength factors set criterion to estimate breakpoints. A multi-parameter complex allometry model follows by adapting firing strengths by composite membership functions and linear consequents in arithmetical space.
Takagi-Sugeno-Kang surrogates adapted complexity depending on analyzed data set. Retransformation results conveyed reproducibility strength of similar proxies identified in arithmetical space. Breakpoints were straightforwardly identified. Retransformed form implies complex allometry as a generalization of Huxley's power model involving covariate depending parameters. Huxley reported a breakpoint in the log-log plot of chela mass vs. body mass of fiddler crabs (), attributed to a sudden change in relative growth of the chela approximately when crabs reach sexual maturity. G.C. Packard implied this breakpoint as putative. However, according to present fuzzy methods existence of a break point in Huxley's data could be validated.
Offered scheme bears reliable analysis of zero intercept allometries based on geometrical space protocols. Endorsed affine structure accommodates either polyphasic or simple allometry if whatever turns required. Interpretation of break points characterizing heterogeneity is intuitive. Analysis can be achieved in an interactive way. This could not have been obtained by relying on customary approaches. Besides, identification of break points in arithmetical scale is straightforward. Present Takagi-Sugeno-Kang arrangement offers a way to overcome the controversy between a school considering a log-transformation necessary and their critics claiming that consistent results can be only obtained through complex allometry models fitted by direct nonlinear regression in the original scales.
传统的异速生长分析依赖对数变换来考虑几何空间中的线性回归，然后再进行逆变换以得到赫胥黎的简单异速生长模型。有观点认为，这会导致偏差，支持多参数复杂异速生长形式以及算术尺度下的非线性回归。传统方法的支持者认为这是必要的，因为一般来说生物体的生长本质上是乘法性的。那么，要保持赫胥黎最初设想的异速生长，就需要一种多相对数线性异速生长范式。高木 - 菅野 - 康模糊模型将加权子模型组合在一起。这允许直接识别各阶段之间转换的断点。因此，这种范式非常适合对多相对数线性异速生长模式进行高效的异速生长分析。在此，我们探讨其适用性。
当前的模糊模型采用高斯隶属函数和线性后件的激发强度权重。权重通过减法聚类确定，后件通过递归最小二乘法或最大似然法确定。激发强度因子的交集设定估计断点的标准。通过在算术空间中使用复合隶属函数和线性后件来调整激发强度，从而得到一个多参数复杂异速生长模型。
高木¬ - 菅野 - 康代理模型根据所分析的数据集调整复杂度。逆变换结果传达了在算术空间中识别出的类似代理的可重复性强度。断点能够直接被识别。逆变换形式意味着复杂异速生长是赫胥黎幂模型的推广，涉及依赖协变量的参数。赫胥黎报道了招潮蟹螯质量与体重的对数 - 对数图中的一个断点（），这归因于大约当螃蟹达到性成熟时螯的相对生长突然变化。G.C. 帕卡德认为这个断点是假定的。然而，根据当前的模糊方法，可以验证赫胥黎数据中存在一个断点。
所提供的方案基于几何空间协议对零截距异速生长进行可靠分析。认可的仿射结构在需要时可适应多相或简单异速生长。对表征异质性的断点的解释很直观。分析可以以交互方式实现。这是依靠传统方法无法获得的。此外，在算术尺度上识别断点很直接。当前的高木¬ - 菅野 - 康方法提供了一种方法来克服一派认为对数变换必要与另一派批评者声称只有通过在原始尺度上进行直接非线性回归拟合的复杂异速生长模型才能获得一致结果之间的争议。
