ANIMAL BEHAVIOUR, 1999, 57, F13–F14Article No. anbe.1998.1073, available online at http://www.idealibrary.com on

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When size is not everything: determining the relative importanceof two asymmetries influencing contest outcome
YONI BRANDTDepartment of Biology and Center for the Integrative Study of Animal Behavior, Indiana University(Received 14 August 1998; initial acceptance 15 September 1998;
final acceptance 19 October 1998; MS. number: SC-1140)

was roughly similar, while the size of their testes was freeto vary. Similarly, the surprisingly low percentage ofpairwise contests won by the larger contestant is simply aconsequence of this aspect of the experimental design. By
contrast, earlier studies consistently revealed effects ofbody size on contest outcome because they were designed
such that body size was the only substantial asymmetry
among contestants. (3) To design experiments that efficiently compare the relative importance of two traits indetermining contest outcome, one should maintain substantial levels of asymmetry in both traits of interest,
thereby ensuring high power to detect the effects of bothtraits. Conversely, when the goal is to establish whether asingle trait may play a role in determining the outcome ofaggressive interactions, it is more efficient to design anexperiment that minimizes asymmetries in all variables
other than the variable of interest.
Neat et al. based their conclusion that relative testes
weight was a good predictor of contest outcome, while
relative body weight was not, upon a multiple logistic
regression analysis (Table 1 in Neat et al. 1998), whichyielded a significant P value (<0.05) for relative testes
weight but not for relative body weight (<0.1). However,the P value is not an appropriate metric for gauging
the magnitude of an effect that an independent variable
has on a dependent variable. The P value quantifies theprobability of obtaining a given regression line assuming
the null hypothesis is correct, that is, assuming thedependent variable varies at random with respect to theindependent variable. It is the regression coefficient thatquantifies the effect of an independent variable on thedependent variable. The regression coefficients of the two
independent variables in Neat et al.’s analysis are strictly
comparable because each is expressed as the log of theratio of the two contestants’ sizes (Enquist & Leimar
1983; Neat et al. 1998).
A comparison of the regression coefficients in Neatet al.’s analysis shows that one cannot exclude thetudies of fighting behaviour in fish have repeatedly
shown that the larger contestant in pairwise contests
is much more likely to win than is the smaller contestant,even when the difference in size is subtle (Turner &Huntingford 1986; Enquist et al. 1990; Ribowski & Franck1993). Body size is an important asymmetry in determining contest outcome across a wide range of taxa, because
larger contestants are physically stronger and thus caninflict more damage upon their opponents (Maynard
Smith 1982; Riechert 1998). Yet in a study of contests
staged between male cichlid fish Tilapia zillii, Neat et al.
(1998) found that larger contestants won only 58% of allcontests. They found a much better predictor of contest
outcome: contestants with relatively larger testes won
88% of all contests. Based on P values obtained from amultiple logistic regression analysis, they concluded thatrelative testes weight was a good predictor of fightoutcome while relative body weight was not.
Here I argue three points. (1) Neat et al. have misinterpreted the results of their experiment, having based theirconclusion upon statistical significance (P values). In
contrast, comparing the regression coefficients reveals
that, compared with testes weight, relative body weight
may be less important, as important, or even many times
more important in predicting contest outcome. Thus,
while Neat et al. have demonstrated that relative testes
weight plays a role in determining contest outcome, theirdata do not support the conclusion that relative bodyweight bears little influence on contest outcome. (2) Neatet al.’s experiment was predisposed to reveal an effect oftestes size, but far less likely to reveal an effect of bodysize, on contest outcome. Their study had very low
statistical power for detecting the effect of body size,
because contestants were paired such that their body size

S

Correspondence: Y. Brandt,
University,
Bloomington,
ybrandt@indiana.edu).

Department ofIN
47405,

0003–3472/99/050F13+02 $30.00/0

Biology,
U.S.A.

Indiana(email:13 1999 The Association for the Study of Animal Behaviour

14

ANIMAL BEHAVIOUR, 57, 5

possibility that relative body weight is important indetermining contest outcome. The regression coefficient
for relative body weight was 22.3312.68, and that for
relative testes weight was 8.693.65 (see Table 1 in Neatet al. 1998). The 95% confidence intervals for the regression coefficients range from 3.41 to +48.07 for relative
body weight and from +1.28 to +16.10 for relative testes
weight. Based on this analysis, one cannot decide
whether relative body weight is less important than, asimportant as or more important than relative testes
weight in predicting contest outcome.
Why were P values significant for relative testes weight
but not for relative body weight in Neat et al.’s study? The
answer to this question lies in the design of their experiment, in which pairs of fish were closely matched forbody weight, but not for relative testes weight. The rangeof variation in body weight in this sample was seven-fold(20–140 g), yet contestants were paired such that thelargest weight advantage was 35%. However, the gonadosomatic index (defined as 100testes weight/bodyweight) of fish in this study varied over 60-fold (0.01–0.61%), and was free to vary within a pair because it was
unknown prior to pairing the contestants. The statisticalpower of a test to detect the effect of an asymmetry is anincreasing function of the magnitude of that asymmetry.
Consequently Neat et al.’s experimental design achieved
high statistical power for detecting the effects of relative
testes weight but low statistical power for detecting theeffects of relative body weight. Thus, their experimental
design stacked the odds in favour of detecting a statistically significant effect of relative testes weight, andagainst detecting an effect of relative body weight.
Why did larger fish win such a small percentage of thecontests in Neat et al.’s study? How could this result beconsistent with the results of some earlier studies, inwhich larger fish won over 90% of the contests, evenwhen contestants were similar in size? The difference
between the experimental designs of Neat et al.’s study
and of earlier studies can easily account for this discrepancy. Earlier studies were designed to eliminate all asymmetries between contestants except the asymmetry inbody size. Such a design maximizes the power of thestatistical test to detect the effect of body size by reducing
the error variance. These earlier studies were not directly
concerned with studying the effects of gonadal state onfighting, nor did they aim to eliminate asymmetries ingonadal state per se. However, by carefully controllingthe subject’s social experience, these earlier studies may
have achieved just that. Subjects in two studies werereared in isolation (Turner & Huntingford 1986; Enquistet al. 1990), while those in a third were matched forsocial status (Ribowski & Franck 1993). By minimizing all
asymmetries other than body size, these earlier studies
demonstrated consistent advantages of larger fish overtheir smaller opponents, even when size differences wereslight. By contrast Neat et al.’s study examined simultaneously the effects of two asymmetries: body size andtestes size, reducing the power of the experiment to detect
the effect of body size. The power of the experiment todetect the effect of body size was further reduced as aconsequence of pairing contestants that were roughly
equal in body size, but were substantially asymmetrical intestes size. Thus it should not be surprising to find theeffect of body size on contest outcome was rather crypticin Neat et al.’s study.
An efficient experimental design for detecting theeffects of two traits and for comparing their relative
importance in determining contest outcome must ensure
substantial levels of asymmetry in both traits of interest.
Such an experimental design maintains adequate powerfor detecting the effects of both traits. An alternative
experimental design is efficient for detecting the effect ofa single trait. In this design, asymmetry in the trait ofinterest is enhanced, while asymmetries in all other traits
are minimized. Clearly, distinct goals are served by eachof these designs. Hence, the goal of a study dictates thechoice between these two experimental designs. Intermediate experimental designs, such as Neat et al.’s, areless efficient for either of these goals. Selecting an efficient experimental design will enhance the quality ofinference that one may draw from an experiment, andcan also be used to reduce the sample size needed toobtain statistically significant results, with favourable
consequences both for economic costs and animal
welfare.
References
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