Growth models and the expected distribution of fluctuating asymmetry

被引:70
作者
Graham, JH [1 ]
Shimizu, K
Emlen, JM
Freeman, DC
Merkel, J
机构
[1] Berry Coll, Dept Biol, Mt Berry, GA 30149 USA
[2] Keio Univ, Dept Math, Yokohama, Kanagawa 2238522, Japan
[3] NW Biol Sci Ctr, Biol Resources Div, Seattle, WA 98115 USA
[4] Wayne State Univ, Dept Biol Sci, Detroit, MI 48202 USA
[5] Berry Coll, Dept Math & Comp Sci, Mt Berry, GA 30149 USA
关键词
developmental instability; gamma distribution; leptokutosis; lognormal distribution; measurement error; multiplicative error; size-scaling;
D O I
10.1046/j.1095-8312.2003.00220.x
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
Multiplicative error accounts for much of the size-scaling and leptokurtosis in fluctuating asymmetry. It arises when growth involves the addition of tissue to that which is already present. Such errors are lognormally distributed. The distribution of the difference between two lognormal variates is leptokurtic. If those two variates are correlated, then the asymmetry variance will scale with size. Inert tissues typically exhibit additive error and have a gamma distribution. Although their asymmetry variance does not exhibit size-scaling, the distribution of the difference between two gamma variates is nevertheless leptokurtic. Measurement error is also additive, but has a normal distribution. Thus, the measurement of fluctuating asymmetry may involve the mixing of additive and multiplicative error. When errors are multiplicative, we recommend computing log E(l) - log E(r), the difference between the logarithms of the expected values of left and right sides, even when size-scaling is not obvious. If I and r are lognormally distributed, and measurement error is nil, the resulting distribution will be normal, and multiplicative error will not confound size-related changes in asymmetry. When errors are additive, such a transformation to remove size-scaling is unnecessary. Nevertheless, the distribution of l - r may still be leptokurtic. (C) 2003 The Linnean Society of London.
引用
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页码:57 / 65
页数:9
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