**Marine Biology, in
press**

**Information-theory
approach to allometric growth of marine organisms
**

** Stelios
Katsanevakis**^{1}, Maria Thessalou-Legaki^{1}, Constantina
Karlou-Riga^{2}, Eugenia Lefkaditou^{3}, Evagelos Dimitriou^{4},
George Verriopoulos^{1}**
**

^{1}Department
of Zoology-Marine Biology, Faculty of Biology, University of Athens,
Panepistimioupolis, 15784 Athens, Greece

^{2}Ministry
of Agriculture, Fisheries Laboratory, 15 Karaoli and Demetriou Street, 18531
Piraeus, Greece

^{3}National
Centre for Marine Research, Aghios Kosmas, 16604 Helliniko, Greece

^{4}Prefecture
of Aitoloakarnania, 30200 Messolonghi, Greece

**Abstract**

Allometric growth investigations are usually conducted by fitting the
allometric model (L)
(*y*, *x* are
morphometric characters and *b* the allometric exponent), which is quite
simple both conceptually and mathematically, and its parameters are easy to
estimate by linear regression. However *b *is not necessarily constant and
it may change either continuously or abruptly at specific breakpoints; thus, the
simple L model quite often fails to describe allometric growth successfully. In
the current context, a better alternative is proposed, based on Kullback-Leibler
(K-L) information theory and multi-model inference (MMI). * *Allometric
growth was investigated in eight marine species: the bivalves *Pecten
jacobaeus* and *Pinna nobilis*, the squids *Todarodes sagittatus*
and *Todaropsis eblanae*, the crab *Pachygrapsus marmoratus *(females),
the ghost shrimp *Pestarella tyrrhena *(males),* *and the fishes *Trachurus
trachurus *and *Sparus aurata*. In each of the eight species, a pair of
body parts was measured and the allometric growth of one body part in relation
to the other (reference dimension) was studied, by fitting five different
candidate models including: the simple allometric model, two models assuming
that *b* changed continuously and two other assuming that *b* had a
breakpoint. For each species, the ‘best’ model was selected by
minimizing the small-sample, bias-corrected form of the Akaike Information Criterion. To
quantify the plausibility of each model, given the data and the set of five
models, the ‘Akaike weight’ *w*_{i} of each model was
calculated; based on *w*_{i} the average model was estimated for
each case. MMI is beneficial, more robust, and may reveal more information than
the classical approach. As demonstrated with the given examples, estimation of *b*
from the linear model, when it was not supported by the data, revealed some
characteristic pitfalls, such as concluding positive allometry when there is
actually negative or vice versa, or reporting allometry when the data in reality
support isometric growth or vice versa.