Relative Growth by the Elongated Jaws of Gars: A Perspective on Polyphasic Loglinear Allometry

Packard, Gary C.

doi:10.1002/jez.b.22673

Cited by 20 publications

(11 citation statements)

References 27 publications

(42 reference statements)

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“…Therefore, clinging to Huxley's model, and a non-linear regression protocol in direct scales can at most offer an apparent empirical convenience tied to simplicity, but it may leave behind relevant biological information. This concerns the existence of break points for transition between successive growth phases that are undetected by Huxley's model of simple allometry and are well recognized by the PLA paradigm [91,[93][94][95]. Likewise, identified break point in Zostera marina may perhaps be interpreted as a threshold beyond which the plant promotes generation of a relatively greater amount of tissue in leaves to enhance resistance to drag force effects that induce damage and separation from shoots.…”

Section: Discussionmentioning

confidence: 99%

“…This paradigm is also referred as non-loglinear allometry in Huxley's original interpretation [70,91,92]. Extension of Huxley's break point idea allows consideration of polyphasic loglinear allometry (PLA) [91,[93][94][95]. This approach characterizes heterogeneity of the response in geometrical space by composing the range of covariate into sectors separated by break points.…”

Section: Introductionmentioning

confidence: 99%

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

Echavarría-Heras¹,

Leal-Ramírez²,

Villa-Diharce³

et al. 2019

Applied Sciences

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(1) Background: We previously demonstrated that customary regression protocols for curvature in geometrical space all derive from a generalized model of complex allometry combining scaling parameters expressing as continuous functions of covariate. Results highlighted the relevance of addressing suitable complexity in enhancing the accuracy of allometric surrogates of plant biomass units. Nevertheless, examination was circumscribed to particular characterizations of the generalized model. Here we address the general identification problem. (2) Methods: We first suggest a log-scales protocol composing a mixture of linear models weighted by exponential powers. Alternatively, adopting an operating regime-based modeling slant we offer mixture regression or Takagi–Sugeno–Kang arrangements. This last approach allows polyphasic identification in direct scales. A derived index measures the extent on what complexity in arithmetic space drives curvature in arithmetical space. (3) Results: Fits on real and simulated data produced proxies of outstanding reproducibility strength indistinctly of data scales. (4) Conclusions: Presented analytical constructs are expected to grant efficient allometric projection of plant biomass units and also for the general settings of allometric examination. A traditional perspective deems log-transformation and allometry inseparable. Recent views assert that this leads to biased results. The present examination suggests this controversy can be resolved by addressing adequately the complexity of geometrical space protocols

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Echavarría-Heras¹,

Leal-Ramírez²,

Villa-Diharce³

et al. 2019

Applied Sciences

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“…For example, two-parameter power functions are readily accommodated by dropping Y 0 from the equation, and the fit of equations with a common exponent can be assessed by dropping the parameter d. By moving Y 0 outside the parentheses, the equation estimates a common intercept for both the fitted functions. In addition, different forms for random error can be readily incorporated into the full model (Lolli et al, 2017;Packard, 2016Packard, , 2017a.…”

Section: Methodsmentioning

confidence: 99%

“…The study of allometric relationships by ANCOVA has been severely constrained, however, by the logarithmic transformation, because such analyses require that the distribution for Y and X in each group conforms to that of a two-parameter power equation with lognormal, heteroscedastic error on the original, arithmetic scale (Packard, 2017c). Many distributions follow the paths of threeparameter equations instead of two-parameter equations (Packard, 2015(Packard, , 2016(Packard, , 2017a, and random error may be normal and homoscedastic or normal and heteroscedastic instead of lognormal and heteroscedastic (Packard, 2016). Such distributions are not amenable to analysis by ANCOVA on transformations.…”

Section: Introductionmentioning

confidence: 99%

A new research paradigm for bivariate allometry: combining ANOVA and non-linear regression

Packard

2018

Journal of Experimental Biology

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A novel statistical routine is presented here for exploring and comparing patterns of allometric variation in two or more groups of subjects. The routine combines elements of the analysis of variance (ANOVA) with non-linear regression to achieve the equivalent of an analysis of covariance (ANCOVA) on curvilinear data. The starting point is a three-parameter power equation to which a categorical variable has been added to identify membership by each subject in a specific group or treatment. The protocol differs from earlier ones in that different assumptions can be made about the form for random error in the full statistical model (i.e. normal and homoscedastic, normal and heteroscedastic, lognormal and heteroscedastic). The general equation and several modifications thereof were used to study allometric variation in field metabolic rates of marsupial and placental mammals. The allometric equations for both marsupials and placentals have an explicit, non-zero intercept, but the allometric exponent is higher in the equation for placentals than in that for marsupials. The approach followed here is extraordinarily versatile, and it has wider application in allometry than standard ANCOVA performed on logarithmic transformations.

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“…This suggests a slant aimed at adding complexity in geometrical space while keeping the theoretical essence of traditional allometry in the analytical set up. Is this conception that hosts polyphasic loglinear allometry approaches (PLA afterwards) (Packard, 2016;Gerber, Eble & Neige, 2008;Strauss & Huxley, 1993;Hartnoll, 1978). PLA characterizes heterogeneity of the logtransformmed response by composing covariate range into sectors separated by break points.…”

Section: Introductionmentioning

confidence: 99%

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

Echavarría-Heras

Castro-Rodríguez

Leal-Ramírez

et al. 2020

PeerJ

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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.

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Relative Growth by the Elongated Jaws of Gars: A Perspective on Polyphasic Loglinear Allometry

Cited by 20 publications

References 27 publications

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

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

A new research paradigm for bivariate allometry: combining ANOVA and non-linear regression

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

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