Facet number and genetic growth constants in bar‐eyed stocks of Drosophila

Hersh, A. H.

doi:10.1002/jez.1400600204

Cited by 10 publications

(5 citation statements)

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“…. Similar inverse relationships have been reported by many early workers (e.g., Hersh, 1931;Hamai, 1938;Clark and Hersh, 1939;Anderson and Busch, 1941) so much so that the relationship β = a e −bα (where a and b are constants) has been held to be biologically meaningful. That this is evidently not true is easily seen by asking under what conditions would we…”

Section: The Range Of Applicability Problemsupporting

confidence: 80%

On the Interpretation of the Normalization Constant in the Scaling Equation

Niklas

Hammond

2019

Front. Ecol. Evol.

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The scaling equation, Y 1 = βY α 2 , has been used empirically and explored theoretically primarily to determine the numerical value and meaning of the scaling exponent, α. The mathematical interpretation of α is clear-it is the quotient of the relative rate of change of Y 1 with respect to the rate of change of Y 2 . In contrast, the interpretation of the normalization constant, β, is obscure, so much so that some workers have rejected the idea that it has any biological importance. With the notable exception of Steven J. Gould's early work, Huxley's dismissal of β largely relegated the study of its biological role to that of an academic afterthought. Here, we attempt to clarify the meaning of β by using examples from plant biology to illustrate the four primary difficulties that have obscured its importance: (1) the consistency of the units of measurement and the metric being measured (e.g., meters and body length, respectively), (2) the relationship between β and α, (3) the interpretation of scaling equations, and (4) detecting if the numerical value of β has changed and if the change is biologically meaningful. Using examples, we show that β is biologically interpretable and offers a way to quantitatively consider similarities of biological form if (1) it is expressed in terms of the relative magnitudes of Y 1 or Y 2 for corresponding data points in a set of Y 1 = βY α 2 equations, (2) the units of measurements are in the same scale, and (3) the corresponding dimensionless numbers are established based on the same units of measurement. We provide examples of where the numerical value of β or differences in the values of β are important, and we propose a research agenda examining the meaning of β values in terms of trait-based ecology.

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Section: The Range Of Applicability Problemsupporting

confidence: 80%

On the Interpretation of the Normalization Constant in the Scaling Equation

Niklas

Hammond

2019

Front. Ecol. Evol.

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“…3 is expected for the power model. Going back to Hersh (1931) who established a negative power relationship between the two coefficients in simple allometry, many authors have found this relationship (e.g., Sileshi, 2014;Zianis and Mencuccini, 2004), both for ontogenetic allometry (i.e. size of individuals of the same species at different development stages) and for phylogenetic allometry (i.e.…”

Section: Discussionmentioning

confidence: 98%

Should tree biomass allometry be restricted to power models?

Picard

Rutishauser²,

Ploton

et al. 2015

Forest Ecology and Management

119

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“…) 2 has found that a large number of organs obey this law. Hersh (1928Hersh ( , 1931 has shown that the facet numbers in the dorsal and ventral lobes of bar-eyed Drosophila conform to this equation. Robb (1929) has applied this relation to relative growth of organs in mammals and found it satisfactory.…”

Section: Relative Growth and Variationmentioning

confidence: 85%