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Bivariate versus multivariate allometry: A note on a paper by Jungers and German

✍ Scribed by M. Hills

Publisher
John Wiley and Sons
Year
1982
Tongue
English
Weight
149 KB
Volume
59
Category
Article
ISSN
0002-9483

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✦ Synopsis

Abstract

Jungers and German (1981) found differences when they compared 1) coefficients of allometry from bivariate plots of log measurements versus log body weight with 2) those coefficients from the first principal component of the log measurements excluding body weight. It is argued here that an arbitrary choice of unit for β€œinternal size” is all that separates these coefficients. When the unit is chosen to make internal size isometric with body weight the coefficients agree rather well.

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Let c E IN. For d E Z with gcd (d, c) = 1 let 6(d, c) be defined by d . 6 ( d , c) I 1 mod c, 1 5 6(d, c) 5 c. Let s, t E IN with 1 5 s 5 c, 1 5 t 5 c. The main result is that for arbitrary fixed E > 0, but uniformly over c, s and t, # { d E I N : ( ~, d ) = l , I 5 d S S and 1 < 6 ( d , c ) < t } =