Assessment of a Takagi–Sugeno-Kang fuzzy model assembly for examination of polyphasic loglinear allometry

Abstract

Background 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. Methods 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. Results 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 (Uca pugnax), 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. Conclusions 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.

A Generalized Model of Complex Allometry I: Formal Setup, Identification Procedures and Applications to Non-Destructive Estimation of Plant Biomass Units

“…In order to validate the present view, we adopted the MCA model of Equation (2), that assimilates necessary complexity through scaling parameters expressed as functions α(x) and β(x) depending on covariate. A particular form of this paradigm was addressed by Bervian et al [77] and its generalization into the form offered here was suggested by Echavarria Heras et al [132]. A formal exploration established this construct as a source model from which conventional models aimed to address curvature in geometrical space [88] could be derived.…”

“…The extraordinary approximation capabilities of the TSK fuzzy model [133,134] endow H TSK (x) interpolation of allometric patterns in direct scales irrespective of intrinsic complexity. Moreover, the H TSK (x) arrangement makes it possible to detect break points for transition among allometric phases which is unattainable by MCA-DNLR methods [132].…”

“…Nevertheless, it is opportune to emphasize gains derived from adoption of a Ω TSK (u) approach. This construct bears a flexible computational assembly that allows intuitive and interactive integration of previous knowledge into the analysis [132]. This gives Ω TSK (u) a relative advantage over the conventional protocols addressed here.…”

A Revision of the Traditional Analysis Method of Allometry to Allow Extension of the Normality-Borne Complexity of Error Structure: Examining the Adequacy of a Normal-Mixture Distribution-Driven Error Term

“…The idea of a biphasic breakpoint-determined biological scaling conveyed the notion of non-log-linear allometry [ 90 – 95 ]. Extension of Huxley's original idea of a biphasic scaling led to considering multiple breakpoints which in turn spawned the notion of polyphasic log-linear allometry [ 96 – 102 ]. Broken-line regression techniques [ 37 , 103 – 108 ] could deliver identification of breakpoints in polyphasic log-linear allometry schemes.…”

Exceptionally Steep Brain-Body Evolutionary Allometry Underlies the Unique Encephalization of Osteoglossiformes

“…It needs to be augmented by empirical knowledge of the developmental processes that model parameters are supposed to describe. Further research is required to explore alternative models of allometry [Packard, 2009;Echavarria-Heras et al, 2020] in conjunction with additional empirical knowledge of brain development in fish to construct a model of allometry that is biologically more realistic than the standard model of allometry.…”