Behavioral Ecology Vol. 12 No. 5: 553-557
© 2001 International Society for Behavioral Ecology
The discrimination of alternative male morphologies
Department of Zoology, University of Western Australia, Nedlands, WA 6907, Australia
Address correspondence to J.S. Kotiaho, who is now at the Department of Biological and Environmental Sciences, University of Jyväskylä, PO Box 35, FIN-40351, Jyväskylä, Finland. E-mail: jkotiaho{at}jyu.fi . J.L. Tomkins is now at the Department of Environmental and Evolutionary Biology, University of St. Andrews, St. Andrews, Fife, Scotland.
Received 10 March 2000; revised 4 August 2000; accepted 5 November 2000.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONREFERENCES |
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Male dimorphisms represent alternative selective regimes within a sex. As such, they can be used as a powerful tool in testing evolutionary theory. However, to realize this potential, we need to be able to accurately discriminate individuals into two separate morphs. In this article we discuss the existing methods and propose a new one. We test our method with data from three dimorphic species and compare these results to results with existing methods. We conclude that existing methods often mis-classify a large proportion of individuals, but applying our method notably reduces these errors.
Key words: male dimorphism, morph discrimination, sexual selection, alternative reproductive strategies.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONREFERENCES |
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Alternative reproductive behaviors are frequently associated with two or more distinct morphologies that occur within a sex (Alcock, 1996b
;
Emlen, 1997; Gross,
1985,
1991). In a few species, the
morphologies associated with the different behavioral tactics are extreme,
such as the order of magnitude difference in body mass of par and anadromous
salmon (Gage et al., 1995;
Gross, 1985). However, in most
species dimorphic variability is limited to specific traits that vary
discontinuously with body size. Discriminating between one morph and another
in these species can be difficult, and this stimulated early researchers to
formulate explicit methods of detecting dimorphisms. The first of these was
the inspection of the modality of the character distribution; bimodality in
character length (e.g., forceps lengths in the earwig Forficula
auricularia) associated with unimodality in a linear measure of body size
was considered indicative of a dimorphism
(Bateson and Brindley, 1892;
Huxley, 1932).
Because male dimorphisms represent alternative selective regimes within a
sex, they can be used as powerful tests of evolutionary theory
(Gage et al., 1995;
Gross, 1996;
Simmons et al., 1999;
Tomkins and Simmons, 1996).
However, in modern evolutionary biology, visual examination of the modality of
character distributions are frequently inadequate and imprecise. This is
because in many cases the character distributions are not strictly
discontinuous, but instead all character sizes are expressed by at least some
individuals (Figures
1,2,3;
see also Eberhard and
Gutiérrez, 1991;
Emlen, 1996;
Simmons et al., 1999;
Tomkins, 1999;
Tomkins and Simmons, 1996).
Thus, to test evolutionary theories with dimorphic species, we need accurate
statistical methods to detect dimorphisms and discriminate between alternative
phenotypes.
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Eberhard and Gutiérrez
(1991) pioneered a method of
statistically detecting and testing for dimorphisms. Before this method only a
handful of studies had attempted any statistical determination between
alternative morphologies (Cook,
1987; Eberhard,
1987; Goldsmith,
1985; Ollason,
1972). Eberhard and Gutiérrez's
(1991) model (which will be
referred to as model 1) is as follows:
 | (1) |
XD; 
is constant; ß is the
regression coefficient, and 
is the error
(Eberhard and
Gutiérrez, 1991).
This model provides a statistical test for the existence of dimorphic
variation in a character associated with body size. First, model 1 tests
whether there is a body size switch point, XD, at which
the distribution of the character size Y becomes discontinuous. This
switch point can be found by first iterating the XD that
gives the best fit (highest R2) for model 1 and then
testing if this XD fitted in model 1 gives a regression
coefficient, ß3, that is significantly different from zero
(Eberhard and
Gutiérrez, 1991).
Second, model 1 tests if there is a body size switch point, XD, at which the linear slope between body size, X, and character length, Y, changes. If the ß3 of the previous test was significant, then the change in the slope at the body size XD may be examined by testing the regression coefficient ß2 against zero. A significant deviation from zero indicates that, in addition to the discontinuity of the character length, there is also a change in the slope. If the ß3 of the previous test was not significant, then the term ß3D in model 1 may be left out, and the change in the slope at the body size XD may be examined with the reduced model by testing the regression coefficient ß2 against zero. The above methods enable the statistical determination of whether a dimorphism exists, and they also establish the exact body size at which individuals are most likely to switch from one morph to the other.
Male dimorphisms (in insects particularly) tend to be conditionally
expressed (Eberhard, 1982), or
what Gross (1996) has
described as "status dependent." The condition for the expression
of alternative behaviors and morphologies is generally body size, which is
linked to the status of the individual. For example, in the dung beetle
Onthophagus acuminatus the unconscious strategy of beetles can be
summarized as two tactics: if small, sneak copulations and do not grow horns,
but if large, grow horns and guard females
(Emlen, 1997). Thus, body size
is usually the variable underlying the expression of many dimorphic traits.
Model 1 therefore provides the important information about where the body size
switch point lies, at which one morph changes to another. The accuracy of this
methodology is, however, dependent on a tight relationship between body size
and the dimorphic trait (Eberhard and
Gutiérrez, 1991;
Tomkins, 1999;
Tomkins and Simmons, 1996).
When there is variance in the switch points of individuals within a
population, either environmental or genetic in origin
(Tomkins, 1999), a large
overlap in body size will exist, and many individuals will be misclassified by
model 1 (Eberhard and
Gutiérrez, 1991;
Tomkins, 1999;
Tomkins and Simmons,
1996).
For example, in Figure 1,
the vertical lines in the graphs indicate the best switch point based on model
1. To the left of the line, individuals are classified as minor morphs, and to
the right of the line as major morphs. It is evident that some of the
individuals even with the longest horns are erroneously classified as minors
(top left of the lines). In addition, some individuals with very small horns
are classified as majors (bottom right of the lines). Similar
misclassification of minors as majors is evident in Figures
2 and
3. Unfortunately, the overlaps
between morphs are very common (Alcock,
1996a; Eberhard and
Gutiérrez, 1991;
Emlen, 1996;
Hunt and Simmons, 1998a;
Moczek and Emlen, 1999;
Simmons et al., 1999;
Tomkins and Simmons, 1999) and
are the reason that further statistical discrimination is needed.
Thus, for establishing the body size switch point for a dimorphic trait,
which is essential for understanding the ontogeny and evolution of
dimorphisms, model 1 is the appropriate model. However, model 1 is not as
effective in identifying individuals as either belonging to one morph or
another. We suggest a modified methodology that specifically aims for the
discrimination of morphs based on the dimorphic character itself, rather than
on body size. By modifying model 1 to substitute Y with X
and X with Y, we find the switch point in the dimorphic
character size that defines the dimorphism, rather than the switch point in
body size that defines the dimorphism. In this model (which will be referred
to as model 2),
 | (2) |
YD. Repeating the calculations discussed with model 1
allows one to statistically test the existence of dimorphism and to find the
best switch point that determines the dimorphism similarly as with the model
1. The only difference between the results is that now the switch point is
found directly for the dimorphic character itself rather than for a correlate
of it—namely, body size.
It may seem inappropriate to use linear regression models and regress
X on Y (i.e., independent body size on dependent character
size). However, because in the majority of morphometric studies, Y is
not strictly dependent on X, and X is not measured without
error (the two basic assumptions of linear regression models;
Sokal and Rohlf, 1981;
Zar, 1996), there is
statistical justification for regressing X on Y as well as
Y on X.
We illustrate the utility of our modification of the model 1 in the
discrimination between morphs by comparing the two models with data from three
species: two species of dung beetles with a horn dimorphism (Onthophagus
taurus [two samples] and Onthophagus binodis) and a species of
earwig with a forceps dimorphism (Forficula auricularia). The first
sample of O. taurus (Figure
1A) consists of individuals from a field population in Margaret
River in southwestern Western Australia. These data were first presented in
Simmons et al. (1999). The
second sample of O. taurus (Figure
1B) consists of second generation, laboratory-reared individuals
also originating from Margaret River. The sample of O. binodis
consists of first-generation laboratory-reared individuals originating from
Walpole in southwestern Western Australia. The F. auricularia were
collected from West Wideopen Island in the Farnes group on the northeastern
coast of England, and the data were presented first in Tomkins and Simmons
(1996).
The best fitting switch point for field-collected O. taurus, using model 1, occurred at the pronotum width of 5.100 mm, and the dimorphism at this point was best characterized as being discontinuous (ß3 significantly different from zero) and having a change in the slope (ß2 significantly different from zero; Tables 1 and 2). Using model 2, the best fitting switch point occurred at the horn length of 0.201 mm, and the dimorphism at this point was best characterized as being discontinuous (ß3 significantly different from zero) and having a change in the slope (ß2 significantly different from zero) (Tables 1 and 2). Using model 1, the best fitting switch point for the laboratory-reared O. taurus occurred at the pronotum width of 5.135 mm, and the dimorphism at this point was best characterized as being discontinuous (ß3 significantly different from zero) and having a change in the slope (ß2 significantly different from zero; Tables 1 and 2). Using model 2, the best fitting switch point occurred at the horn length of 0.310 mm, and the dimorphism at this point was best characterized as being discontinuous (ß3 significantly different from zero) and having a change in the slope (ß2 significantly different from zero; Tables 1 and 2).
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The best fitting switch point for O. binodis using model 1 occurred at the pronotum width of 5.565 mm, and the dimorphism at this point was best characterized as being continuous (ß3 not significantly different from zero) but having a change in the slope (ß2 significantly different from zero) (Tables 3 and 4). Using model 2, the best fitting switch point occurred at the horn length of 0.48 mm, and the dimorphism at this point was best characterized as being continuous (ß3 not significantly different from zero) but having a change in the slope (ß2 significantly different from zero; Tables 3 and 4).
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The best fitting switch point for F. auricularia, based on model 1, occurred at the pronotum width of 1.959 mm, and the dimorphism at this point was best characterized as being discontinuous (ß3 significantly different from zero) and having a change in the slope (ß2 significantly different from zero; Tables 5 and 6). Using model 2, the best fitting switch point occurred at the forceps length of 4.50 mm, and the dimorphism at this point was best characterized as being discontinuous (ß3 significantly different from zero) and having a change in the slope (ß2 significantly different from zero; Tables 5 and 6).
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In Figures 1,2,3, we have plotted the horn lengths of O. taurus and O. binodis and the forceps length of F. auricularia on their respective pronotum widths. As pointed out earlier, it is immediately clear from the figures that the switch points calculated by using model 1 misclassify a substantial proportion of the males. However, by using our model 2, misclassification is notably reduced.
As morphological dimorphisms are frequently associated with alternative
reproductive behaviors (Alcock et al.,
1977; Cook, 1990;
Emlen, 1997;
Goldsmith, 1987; Hunt and
Simmons, 1998b,
2000;
Hunt et al., 1999), only a
combination of behavioral and morphological studies can ultimately confirm the
correct position of a switch point. In dung beetles, the dimorphism in horn
lengths has been shown to be associated with different behaviors. In O.
acuminatus, major morphs with large horns defend the tunnels in which a
female constructs a brood mass, while minor morphs try to sneak copulations
(Emlen, 1997). In O.
taurus and O. binodis, major and minor morphs use different
tactics in helping the female in brood mass construction; major males help
females, whereas minor males do not help
(Cook, 1990;
Hunt and Simmons, 1998b).
However, only one study has examined whether the change in male morphology
from one morph to another coincides with the change from one behavior to
another. Hunt and Simmons
(2000) showed that in O.
taurus the start of horn development coincided with a behavioral change
from a nonhelping minor to a helping major morph; furthermore, the change in
helping was not continuous but showed an abrupt discontinuity. This abrupt
change in behavior accompanied with much less abrupt change in horn lengths
(Figure 1) suggests that the
biologically correct switch point from minor to major morph in O.
taurus occurs immediately at the start of horn development and not across
a body size threshold per se.
From Hunt and Simmons's study
(2000), it is obvious that
model 1 sometimes misclassifies many males of O. taurus
(Figure 1). However, our model
2 performs better and provides us with a horn length switch point that
coincides well with the behavioral switch described by Hunt and Simmons
(2000).
Other methods of describing dimorphisms in Onthophagus have been
used. For example, Emlen
(1996) modified logistic
regressions and nonlinear regressions to determine a switch point for both the
pronotum width and the horn length (inflection point and curve height,
respectively, in Emlen, 1996).
However, in these models the switch point is located at the inflection point
of the sigmoidal distribution of horn lengths plotted on pronotum width
(Emlen, 1996). Although this
model is useful for calculating relative horn size, it may be unsuitable for
finding the correct switch point. It is likely that the positions of
behavioral and morphological switch points in O. taurus are also
applicable to other Onthophagus species with approximately similar
sigmoidal relationships between horn length and pronotum width. Hence, the
determination of switch points based on inflection of the sigmoid
(Emlen, 1996) is likely to
overstimate the position of the real switch point and misclassify a proportion
of small majors as minors.
Eberhard and Gutiérrez's
(1991) model (model 1) is based
on the notion of conditional expression determined by body size. This model is
not redundant because it determines the lateral position of the point across
which most individuals are likely to change phenotypes, providing a vital
component of understanding the evolution and ontogeny of dimorphisms. Our
modification (model 2) is not based on body size but rather directly on the
dimorphic character of interest and thus is not affected by overlaps in body
size between morphs. In all of the four data sets that we analyzed, our
modification (model 2) performed better in classifying the morphs than the
original model. Our modification provides additional information about the
dimorphism and has its primary advantage in discriminating accurately between
the alternative phenotypes.
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ACKNOWLEDGEMENTS |
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We thank John Hunt and Leigh W. Simmons for comments on the manuscript. J.S.K. was funded by the Academy of Finland and J.L.T. was funded by a University Postdoctoral Research Fellowship from the University of Western Australia.
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