Modelling allometry: statistical and biological considerations – a reply to Packard

Pélabon, Christophe; Tidière, Morgane; Lemaître, Jean‐François; Gaillard, Jean‐Michel

doi:10.1093/biolinnean/bly141

Cited by 18 publications

(22 citation statements)

References 42 publications

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“…S1). This is relevant to ongoing debates on whether allometries are best studied on arithmetic or logarithmic scales (see Lemaître et al 2015;Packard 2015;Pélabon et al 2018 for a manifestation in relation to horns and antlers). It has been argued that biological deviations from the statistical model tend to be multiplicative and thus homoscedastic on a proportional (e.g.…”

Section: Discussionmentioning

confidence: 99%

Measuring Complex Morphological Traits with 3D Photogrammetry: A Case Study with Deer Antlers

et al. 2020

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The increasing availability of 3D-imaging technology provides new opportunities for measuring morphology. Photogrammetry enables easy 3D-data acquisition compared to conventional methods and here we assess its accuracy for measuring the size of deer antlers, a complex morphological structure. Using a proprietary photogrammetry software, we generated 3D images of antlers for 92 individuals from 29 species of cervids that vary widely in antler size and shape and used these to measure antler volume. By repeating the process, we found that the relative error averaged 8.5% of object size. Errors in converting arbitrary voxel units into real volumetric units accounted for 70% of the measurement variance and can therefore be reduced by replicating the conversion. We applied the method to clay models of known volume and found no indication of bias. The estimation was robust against variation in imaging device, distance and operator, but approximately 40 images per specimen were necessary to achieve good precision. We used the method to show that conventional measures of main-beam length are relatively poor estimators of antler volume. Using loose antlers of known weight, we also showed that the volume may be a relatively poor predictor of antler weight due to variation in bone density across species. We conclude that photogrammetry can be an efficient and accurate tool for measuring antlers, and likely many other complex morphological traits.

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Section: Discussionmentioning

confidence: 99%

Measuring Complex Morphological Traits with 3D Photogrammetry: A Case Study with Deer Antlers

et al. 2020

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“…Again, for promoters of the traditional approach this viewpoint sacrifices appreciation of biological theory in order to privilege statistical correctness (Houle et al 2011;Lemaître et al 2015;Pélabon et al 2018). The approach underwent here demonstrates that a merging of points above can be achieved by evoking Huxley's report on the existence of a breakpoint in the loglog plot of chela mass vs body mass of fiddler crabs (Uca pugnax) (Huxley, 1924;Huxley, 1927;Huxley, 1932 (Julious, 2001;Muggeo, 2003).…”

Section: Discussionmentioning

confidence: 88%

“…On Huxley's elucidation (Huxley, 1932) the intercept of TAMA's line was of no specific biological importance, but the slope was significant enough as to mean allometry itself. This interpretation has permeated contemporary research to such an extent that many practitioners still consider it to be the valid theoretical perspective for static and ontogenetic allometry (Eberhard, 2009;Houle et al 2011;Pélabon et al 2018). But, there are views that assert that a TAMA approach produces inconsistent results, thereby recommending allometric examination by relying instead on nonlinear regression of in the direct scales of data (Packard, 2017a;Packard, 2013;Packard, 2009;Packard & Birchard, 2008).…”

Section: Introductionmentioning

confidence: 99%

“…But, there are views that assert that a TAMA approach produces inconsistent results, thereby recommending allometric examination by relying instead on nonlinear regression of in the direct scales of data (Packard, 2017a;Packard, 2013;Packard, 2009;Packard & Birchard, 2008). This is, debatable for defenders of the traditional approach that claim that, as it is conceived in the original theoretical context of allometry, a logarithmic transformation deems necessary in the analysis (Lai et al 2013, Klingenberg, 1998Nevill et al 2005;Kerkhoff & Enquist, 2009;Xiao et al 2011;White et al 2012;Ballantyne, 2013;Glazier, 2013;Niklas & Hammond, 2014;Lemaître et al 2015;Pélabon et al 2018). Yet steering further away from Huxley's perspective on covariation among different traits, other views conceive allometry centered on the covariation between size and shape (Mosimann, 1970;Klingenberg, 2016).…”

Section: Introductionmentioning

confidence: 99%

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Peer Review #1 of "Assessment of a Takagi–Sugeno-Kang fuzzy model assembly for examination of polyphasic loglinear allometry (v0.1)"

Packard¹

2020

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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 multiparameter 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

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“…Moreover, in Huxley's rationale the intercept lnβ of TAMA's line was of no explicit biological relevance, but the slope α was significant enough as to mean allometry itself. This interpretation maintains nowadays as the only valid theoretical perspective for many practitioners of allometry [57][58][59]. However, in spite of TAMA's prevalence, there are views asserting this scheme produces biased results [60][61][62][63][64].…”

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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(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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Modelling allometry: statistical and biological considerations – a reply to Packard

Cited by 18 publications

References 42 publications

Measuring Complex Morphological Traits with 3D Photogrammetry: A Case Study with Deer Antlers

Measuring Complex Morphological Traits with 3D Photogrammetry: A Case Study with Deer Antlers

Peer Review #1 of "Assessment of a Takagi–Sugeno-Kang fuzzy model assembly for examination of polyphasic loglinear allometry (v0.1)"

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

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