La Saboteuse: An Ecological Theory of Sexual Dimorphism in Animals

Abstract

Both male ornamentation and male combat result in increased male mortality. Because population sizes are limited by a carrying capacity, increased age-specific adult male mortality will result in decreased age-specific adult female mortality, as well as decreased juvenile mortality. As intersexual competition is one form of intraspecific competition, through choosing to mate with ornamented and/or combative males, females in polygamous systems reduce intraspecific competition. Because average male fitness must exactly equal average female fitness, male fitness will paradoxically rise with increasing male mortality. This theory also offers new perspectives on peripheral problems to sexual theory, such as mate location, resource guarding, leks, harems, and others.

Full text

Abraham: La Saboteuse
La Saboteuse:
An Ecological Theory of Sexual Dimorphism in Animals
[Acta Biotheore tica 1998, 46:23- 35.]
JOSEPH N. ABRAHAM
Department of Biology, University of Mississippi, University MS 38677
and
Health Information Management, University of Southwestern Louisiana, Lafayette LA 705041
ABSTRACT. Both male ornamentation and male combat result in increased male mortality.
Because population sizes are limited by a carrying capacity, increased age-specific adult
male mortality will result in decreased age-specific adult female mortality, as well as
decreased juvenile mortality. As intersexual competition is one form of intraspecific
competition, through choosing to mate with ornamented and/or combative males, females
in polygamous systems reduce intraspecific competition. Because average male fitness
must exactly equal average female fitness, male fitness will paradoxically rise with
increasing male mortality. This theory also offers new perspectives on peripheral
problems to sexual theory, such as mate location, resource guarding, leks, harems, and
others.
In 1871, Charles Darwin published The Descent of Man and Selection in Relation to Sex.
Ironically, the originally inflammatory portions of that work, the origins of humanity, have come
to be well accepted and even viewed as obvious. It is the less offensive portion of the book, the
question about the morphologic divergence of sexes in many species, which has sparked a
fascinating debate that has lived on for over one hundred twenty years.
Darwin himself seemed surprisingly uninterested in the “why” of elaborate sexual
dimorphism. He argued that female choice could produce male elaborations which run counter to
natural selection, but he seemed satisfied with “preference” and “æsthetics” to explain the system.
He stated, “No doubt the perceptive power of man and the lower animals are so constituted that
1 Correspondence should be addressed to: 515 Roosevelt St., Lafayette LA 70503, USA.

Abraham: La Saboteuse
brilliant colours and certain forms, as well as harmonious and rhythmical sounds, give pleasure
and are called beautiful; but why this should be so, we know no more than why certain bodily
sensations are agreeable and others disagreeable,” (Darwin 1871, i. p256).
We now believe that emotions such as “preference”, and sensations which are “agreeable”
or “disagreeable”, are proximate causes (Tinbergen 1963); “beauty” should be a selected
preference, and the “attraction” it invokes should be a utilitarian strategy. Some organisms find
particular food items extremely offensive; others find those same items extremely desirable.
Likewise, beauty as it relates to sexual partners and offspring is equally labile. Beauty, then,
would appear to be arbitrary; it is a product of physiology and fitness. Darwin was not wrong.
Female “preference” does indeed appear to promote elaborations in males. But it seems that he
was incomplete. He did not show a utility, or at least a mechanism which escapes utility, to
explain the ultimate meaning of such a preference by the females.
Several important evolutionary biologists have offered different theories as to the reasons
for sexual dimorphism in animals, and the debate continues. An excellent brief review of the field
is presented by Maynard Smith (1991). Recent additions to the discussion are the theories of
fluctuating asymmetry (Møller 1990) and sensory exploitation (Ryan and Rand 1990, 1993).
Suggested here is an additional proposal, based on competition and carrying capacity.
There are some universally agreed points in this area of research:
1) Darwin (1871) noted that in many animal species, males differ greatly from the
females.
2) Sexually dimorphic species are overwhelmingly polygamous, wherein the males
generally contribute little or no material benefits to the next generation. (Darwin 1871; Huxley
1938; Fisher 1958).
3) In those polygamous systems, a few males copulate with the majority of the females
(Bateman 1948: Kruijt and Hogan, 1967; LeBoeuf 1972, 1974; Mackenzie et al. 1995). Many
males do not copulate at all, and therefore contribute nothing to the fitness of themselves, to their
relatives, nor to the available females.
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4) Darwin (1871) also noted that in sexually dimorphic species, one of two systems
generally occur. Either males enter into physical combat with one another, with the victor
“winning” the right to mate with the female(s); or, males elaborate visually attractive
exaggerations, which the females seem to prefer in mates.
5) Finally, Darwin (1871) recognized that in either of these situations, the males’ traits
seemed to run counter to natural selection. The males’ size, weapons, behaviors, or ornaments,
were obstacles to survival. This has been well documented in many different animals (Haskins et
al. 1961; Selander 1965, 1972;. LeBoeuf 1972, 1974; Endler 1978, 1980, 1982, 1983; Froehlich
et al. 1981; Lloyd and Wing 1983).
Why the peacock’s feathers? Why should females prefer males with characters which
make it hard for the males to survive? Perhaps the answer to that question is the question itself:
to make it hard for them to survive. Females may be “deliberately” sabotaging males, to increase
adult male mortality, and thereby decrease intraspecific competition.
One of the insights which led Darwin (1859) to his theory of natural selection was the
principle of limited populations, which Malthus (1798) previously had applied to humans. This
concept led Darwin to realize that the struggle for life is not only interspecific, but also
intraspecific; and that an important clue to understanding organic evolution lay in examining
competition among conspecifics.
Another important insight here was offered by Trivers (1972), that females are generally
the “limiting resource”. Krebs and Davies (1992) state: “A male can increase its reproductive
success by finding and fertilizing many different females, but a female can only increase her
success by turning food into . . . offspring at a faster rate.” If some way could be found to
increase the “limiting resource” (females), then the end product— fitness— would likewise
increase.
This is the crux of this paper, that by sabotaging males, females reduce intraspecific
competition, and correspondingly increase the “limiting resource”. Before discussing this further,
it should be noted that this theory immediately offers two very important benefits. First, it
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reunites male elaborations and male combat. Since both traits result in increased male mortality,
they are equal in relieving females and juveniles of intraspecific competition, a point to which I
will return later.
But the larger appeal of this theory is a more parsimonious evolutionary theory; this
solution folds sexual selection back into fundamental framework of natural selection. Intraspecific
competition is the keystone of evolutionary reasoning, and intraspecific competition is the
centrum of this paper. As noted in statement 5) above, Darwin proposed sexual selection in
response to male characters which seemed to defy natural selection. By showing that those male
characters do not defy natural selection, this paper refutes Darwin while supporting him, i.e., I
argue that his original theory of evolution is sufficient in itself, and his secondary theory of sexual
selection may have been unnecessary. This paper seeks to fully restore Darwinian selection to its
original pristine, minimalist strength. This is no small point: Darwinian selection was the
philosopher’s stone which transmuted our discipline into a science, and sexual selection has
proven a controversial, problematic exception to Darwinian selection.
This theory of female “sabotage” is not entirely new. Seger and Trivers (1986) showed
that under certain conditions, females could benefit by hampering males. This paper differs from
theirs in three important ways. First, they saw increased mortality of sons as a possible obstacle
to success of female sabotage. I will show that the sons’ fitness paradoxically rises with
increasing male mortality. Second, they suggested only a few limited applications for their model.
This paper hypothesizes that most of what has been called “sexual selection” can be explained
under a model of female sabotage. Third, their model was a complex, multi-variable system
analyzing the spread of such a strategy, the mathematics of which is largely inaccessible to most
biologists. What follows is a much simpler game theory approach, where only resource
distribution is considered, and where the conclusion is in terms of ultimate payoff, i.e. fitness.
Consider the figure. In a polygamous system, males are expending most of their resources
in nothing more than mating. Actually, this diagram is probably generous in its estimate of male
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nurturing; in many polygamous systems, male contribution to nurturing amounts to no more than
a complement of DNA, suggesting an energetic input of zero.
A mathematical argument can be constructed of this system.
Let: p = male percentage of population biomass
q = female percentage of population biomass
M = male resources dedicated to mating effort
m = female resources dedicated to mating effort
N = male resources dedicated to nurturing effort
n = female resources dedicated to nurturing effort
K = carrying capacity, i.e., the total resources available to the population
ω = pN + qn = offspring investment, one aspect of fitness.
Assume that M + N = m + n = 1. If,
K = pK(M + N) + qK(m + n),
then it follows,
1 - pM - qm = ω.
But since often N = 0, then M = 1 and the equation simplifies to,
(1) q(1 - m) = ω.
Several topics are addressed in this model. First, offspring investment should increase
with q, female biomass. If the carrying capacity is limiting, the only way to increase female
biomass is to decrease male biomass. Under this model, as age-specific male mortality increases,
more resources become available for the females and their offspring; age-specific female mortality
and juvenile mortality will therefore decrease.
Intersexual competition is a subset of intraspecific competition. Normally one thinks of
males and females as reproductive collaborators, but as soon as their strategies diverge— as soon
as polygamy “invades” (Emlen and Oring 1977)— then males and females become competitors
for resources. The above equation states that as long as females are contributing more resources
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to the next generation than males are, then theoretically the fewer the males, the more offspring
can be produced.
Such a model does not violate Fisherian investment (Fisher 1958) which says that parental
resources should be equally distributed between the sexes. Darwin (1871) at great length pointed
out that females and juveniles tend to resemble one another, and that production of weapons and
elaborations occur only at maturation, after parental investment. Therefore, increased male
mortality which results from adult secondary sexual characters is in line with investment theory.
Some workers have suggested that this model requires group selection (John Maynard
Smith, Mark Kirkpatrick, pers. comms.) and therefore cannot work. Group selection requires
that unrelated conspecifics benefit from a trait more than the individuals expressing the trait
(Williams 1966). At first consideration, all local females would benefit from decreased
competition, while sabotaging females would presumably suffer a loss of fitness through increased
mortality of their sons. As noted above, this was one of Seger and Trivers (1986) concerns.
But neither the sabotaging females nor their sons are losing fitness in this system. To the
contrary: in a system beginning at Fisherian sex ratios (Fisher 1958), average male fitness must
exactly equal average female fitness. If fewer sons survive, and therefore more daughters do, the
daughters will produce more offspring, and increase the mother’s fitness. But since each of the
offspring must have one mother and one father, given assortative mating, increase in the number
of offspring demands that the sons’ average fitness increase, despite the increased mortality.
Consider that matings approximately equal fitness. If the number of matings increase, then
the average fitness of both females and males have likewise increased. Given that total matings
can only increase when the number of females— again, the limiting resource— also increases,
then male numbers are immaterial. This point cannot be overstated. Average survivorship does
not equal average fitness, and fitness is only a question of which strategy produces the greatest
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number of offspring. No matter how catastrophic the mortality of the sons, given assortative
mating, if enough sons remain to carry out the required matings, the average fitness of the sons
absolutely must increase with the average fitness of the daughters. For this reason, in a
polygamous system male fitness paradoxically increases with increasing male mortality. And
because of this, females do not lose fitness through their sons.
One might point out monomorphic conspecifics in such a system are equally benefited by
the death of the dimorphic males. This is true, but they will never benefit more than the females in
a dimorphic system: given that increased sons’ mortality is not an obstacle, the benefits of
sabotage are never visited upon nearby non-participants more than upon the saboteuse. There is
no penalty to the dimorphs, except in relation to populations which contain an even larger
percentage of sabotaging females.
Consider that in a population of mixed dimorphs and monomorphs, offspring will be
produced at a faster rate— correlative with the percentage of dimorphs in the population— than
in any population of pure monomorphs.
For that reason, the mixed population will enjoy increased relative fitness, and their
offspring will emigrate and spread. But the benefit of increased offspring production is linked
only with dimorphism. As the offspring emigrate, when monomorphs leave the vicinity of
dimorphs, the monomorphs’ fitness will again return to previous levels. Some fitness benefit,
however, is always visited upon the dimorphs themselves.
Given random emigration of the dimorphs, “clumping” will eventually occur (if herd
behavior, contiguous population spread, or preferential association of dimorphs do not cluster
them first). Such clumping will produce populations which contain higher percentages of
dimorphs than the natal population. The larger the percentage of dimorphs in a population, the
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greater the overall advantage and benefit for all individuals in the population, monormorphic and
dimorphic.
But for any population which contains monomorphs, a population with fewer
monomorphs will always be able to “invade”— i.e., populations which contain more dimorphs
will always enjoy increased fitness over neighboring population containing fewer dimorphs.
Eventually, pure populations of dimorphs will appear, and they will enjoy higher fitness than any
mixed population.
Once a dimorphic population of saboteuses have established an area of geographic
continuity (or again, physical continuity, as with a herd), the benefits of increased male mortality
will be visited more upon the interior of that group, than on peripheral non-sabotaging neighbors.
The interior of the geographic area will produce offspring at a faster rate, and will tend to expand.
It should be noted that this theory of female sabotage does not immediately exclude other
theories of sexual dimorphism, and could conceivably work in tandem with one or more of them.
But whether this theory alone generates the level of sexual dimorphism we see in animals, or
whether another theory is primarily responsible, once dimorphism is established, females and
juveniles derive a material benefit from increased male mortality.
Consider that many models for “runaway” have suggested that females can push males to
increased mortality on mere whim, i.e. “preference” (O’Donald 1962, 1977; Lande 1980, 1981;
Lande and Arnold 1985; Kirkpatrick 1982; Heisler 1985; Seger 1985; Pomiankowski et al. 1991;
Pomiankowski and Iwasa 1993). “Preference” is apparently an entity without properties, as
evidenced by the fact that none of these authors has ever supplied the variable “trait”—
ostensibly a vector (longer, broader, brighter)— with any dimensions whatsoever. If runaway
can predict the increase of an entirely undefined variable, and in so doing produce a maternal
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increase in sons’ mortality, without any stronger impetus than “preference”, then how much
stronger must those theories be when a clear material advantage can be shown?
Nevertheless, whatever theoretical objections one may offer, they are moot. We do not
use theory to test the facts: females in dimorphic systems have already saddled males with traits
which result in increased male mortality. And if increased male mortality does not leave more
resources for females and offspring, then all of Darwinian evolution is in jeopardy. When
theoreticians suggest that a situation cannot exist, and it already does, then we have an important
caution about investing too much confidence in untested theory.
Therefore, in a polygamous system female preference for costly male traits produces
sabotage, regardless of whatever mechanism is hypothesized to be driving the system. However,
it must be noted— and this is no small point— that this is the only theory of sexual dimorphism
to date in which any advantage to female preference can be directly measured.
Let us return to male combat. As noted above, Darwin (1871) suggested that there were
two mechanisms involved in sexual dimorphism: female “preference” for some males types; and
male competition for “possession” of females. Poulton (1890) defined the first of these as
“epigamic”, after which Huxley (1938) discussed them as “intersexual” and “intrasexual”
selection. This tradition continues as a tension between “female choice” (intersexual selection)
and “male competition” (intrasexual selection), and a debate over who “controls” mating (Trivers
1972; Parker 1979, 1983; Andersson 1982; Halliday 1983; Hammerstein and Parker 1987;
Bradbury and Davies 1987; Ryan and Rand 1990; Maynard Smith 1991; Droney 1992). We have
generally assumed that the winner of an arbitrary contest also “wins” the female. But no less an
authority than Darwin (1871 ii. p269) himself points out, “The female could in most cases escape,
if wooed by a male that did not please or excite her; and when pursued, as so incessantly occurs,
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by several males, she would often have the opportunity, whilst they were fighting together, of
escaping with, or at least of temporarily pairing with, some one male.”
It is therefore not apparent why victory of one animal over a second animal provides de
facto access to a third animal: despite the widespread acceptance of the theory, no one has ever
explained how this might work. However, fighting of males, particularly with weapons, often
leads to heavy male mortality (Gorsuch 1934; McHugh 1958; Bannikov et al 1967; Schaller 1972;
Geist 1966, 1971, 1974; Sorenson 1974; Sussman and Richard 1974; Wilkinson and Shank 1976;
Clutton-Brock et al. 1979; Silverman and Dunbar 1980). The theory of “intrasexual” competition
portrays females as hapless victims, when it is clear that they are equally capable of every
ruthlessness which have been traditionally assigned to males.
In addition, if victory over other males led irrevocably to possession of females, then we
might ask why the strategy of male combat has not invaded the arena of male elaborations: a
“less stimulating” but more pugilistic male should quickly appear, who would fight with the object
of the female’s fancy, and thereby acquire mating rights by superior force. Therefore we might
ask which is more reasonable, do males exploit females by fighting with other males (and if so,
how?), or do females exploit males by exclusively mating with males who fight and win?
Male elaborations and combat produce another benefit for females. An important cause of
animal mortality is predation, and predators are also held at a carrying capacity. Male
elaborations/traits often result in increased predation (Endler 1978, 1980, 1982, 1983; Haas 1976;
Ryan 1985; Breden and Stoner 1987). If ornaments and battle wounds more readily attract
predators, create obstacles to swift escape, and/or physiologically weaken males so that they are
more easily captured, then predation load will shift away from females, and onto males. If so,
through their preference for costly male traits, females are getting more “bang for their buck”:
they are being relieved of both interspecific and intraspecific competition.
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Likewise, this model of sexual dimorphism addresses the “bright male” situation.
Hamilton and Zuk (1982) suggested that male elaborations can serve as indicators of health. That
being so, we should expect that the larger the elaboration, the further away an accurate health
assessment can be made. If ornamentation loudly broadcasts “health” or the lack thereof, as has
been postulated for “stotting” or “spronking” in gazelles (Estes and Goddard 1967; Walther 1969;
Zahavi in Dawkins 1976), then large male ornaments will aid predators in assessing prey health
and in identifying the easier prey (Endler 1978, 1980, 1982, 1983; Haas 1976; Breden and Stoner
1987).
Another point offered by equation (1) is that offspring investment decreases as m, female
mating investment, increases. This suggests an explanation as to the relative roles of males and
females in mate location (Trivers 1972; Parker 1978; Alexander and Borgia 1979; Hammerstein
and Parker 1987; Kirkpatrick 1987; Real 1990). When there is a cost or risk to attracting a mate,
e.g., acoustics or bioluminescence, it is generally the males who take the risk (Parker 1978; Arak
1983; Lloyd and Wing, 1983; Ryan 1985). When the greater cost or risk is not in attracting a
mate, but in locating one— as in pheromonal systems— then the males tend to take that risk
(Beer et al. 1958; deVos et al. 1967; Wood 1970; Kaissling 1971; Myers and Krebs 1971; Parker
1978). Females should assume whichever is the less costly role in mate location.
Many authors have addressed the tension between “natural selection” and “sexual
selection”, and the limits they impose on male characters (Fisher 1915; Arnold and Wade 1984;
Breden and Stoner 1987; Endler 1980, 1982, 1983). The above equation offers an alternate
hypothesis for the upper and lower limits on male characters: maximization of female biomass,
and minimization of female mating costs. This model suggests that male elaborations and fighting
should increase male mortality just to the point that males cease to become readily available for
mating, i.e., the point at which m becomes too large.
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This model also offers a different perspective to some other aspects of mating behavior.
Many authors have studied systems in which one male reportedly “controls” a group of females
(Hrdy 1977; Clutton-Brock et al. 1977; LeBoeuf 1972, 1974; Dunbar 1984). Despite the
apparent similarities between human and animal harems, it is not at all clear the methods by which
one or a few males physically restrain and dominate a female biomass many times their own. The
concept that males can “dominate” females would seem to stem from the Victorian mores of
Darwin and his contemporaries. Again, females are not hapless victims, and they are capable of
every ruthlessness. If females who live in harems only allow one male into their territory, and he
excludes all other males, then there will be an increase in material benefits for females and their
young, when compared to a system with equal numbers of adult sexes. If that one male is also
primarily responsible for physically protecting the harem from competitors and predators, then
females are also relieved of that cost.
Similarly, resource defense polygyny has often been seen as male exploitation of females
(Verner and Willson 1966; Orians 1969; Emlen and Oring 1977; Borgia 1979). But if one male
denies all other males access to vital resources, he is in fact aiding the females in concentrating
those resources into offspring investment. Females who prefer to mate with males who exclude
other males from limited but vital resources will experience increased fitness.
Leks are a prominent polygamous behaviour, and are very expensive metabolically for
males, sometimes exhaustingly so (Ryan 1985; Gibson 1990; Hausfater et al. 1990; Höglund et al.
1992). And yet, some lekking species are dimorphic, while others are monomorphic. Female
sabotage offers a different explanation for lekking, particularly in monomorphic species. In a brief
period sheer exhaustion from lek displays can insure as much male mortality as taxing elaborations
may require months to do. By protracting the rendezvous between the sexes over several days,
and preferring to mate with males who repeatedly perform athletic activities, females can push
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males to extreme fatigue and a loss of metabolic reserves. Males who perform for only a limited
period during lekking may be spared some of the mortality, but they should also experience
proportionately fewer matings (Mackenzie et al. 1995). And since position within the lek is
important (Gibson 1990, Droney 1992) males who do not stay the duration will lose access to
prime display areas.
It is interesting that lekking, and the exhaustion it exacts, are not explained by any of the
other theories of sexual dimorphism. Runaway (Fisher 1915, 1958), sensory exploitation (Ryan
and Rand 1990, 1993), and fluctuating asymmetry (Møller 1990b) do not explain nor predict such
behavior. Handicap (Zahavi 1975, 1977), and bright male (Hamilton and Zuk 1982) predict it,
but only if females wait until the end of a lekking period before choosing a mate; the females who
arrive early should not be able to make a reliable evaluation of mate quality.
One final problem that this theory addresses, and one which provides an interesting “test
case” for the various theories of sexual dimorphism, is the frequent appearance of non-mimetic
males in Batesian mimic butterflies (Turner 1978). The hypotheses of runaway, bright male,
fluctuating asymmetry, and sensory exploitation all predict that males should be brightly colored,
as do revealing handicap (Hamilton and Zuk 1982; Iwasa et al. 1991; Maynard Smith 1991) and
conditional handicap (Zahavi 1977, West-Eberhard 1979; Andersson 1986; Iwasa et al. 1991;
Maynard Smith 1991). Only pure epistasis (Zahavi 1975, Maynard Smith 1985, 1991) predicts
that males should be dull (or perhaps that males should be brightly colored in a different pattern)
thereby proving that they can survive without subterfuge; but pure epistasis is the portion of the
handicap principle which the theoretical models do not support (Maynard Smith 1976, 1978,
1985; Heisler 1985; Davis and O’Donald 1976, Kirkpatrick 1986).
The sabotage hypothesis predicts that Batesian mimic males should be dull. If predators
avoid butterflies with certain bright coloration, and there is an advantage to maximizing the ratio
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of mimics to models, then female mimics should seek to minimize the numbers of mimetic males,
and thereby preserve the females’ advantage. If females can force males to be either bright
mimetics or dull non-mimetics, the females should prefer disadvantaged non-mimetics, and
thereby reduce the females’ predation load.
Finally, just as Darwin (1859) used artificial selection to illustrate natural selection, so
artificial population maximization (specifically, game management) can be used to illustrate female
sabotage as a method of natural population maximization: preferential hunting and fishing of
males is a long-established cornerstone of wildlife preservation and renewal.
To conclude, Fisher (1958, p155) asserted, “To judge, however, of the relative efficacy of
the different possible situations in which sexual preference may confer a reproductive advantage,
detailed ecological knowledge is required.” His comment is certainly supported by this paper.
Just as Fisher used the advances in genetic theory of his day to propose an explanation of sexual
dimorphism, so this paper is an attempt to use the ecological theory of our day to propose a
different explanation of that same dimorphism.
This paper is being submitted in partial fulfillment of the Doctor of Philosophy in Biology,
University of Mississippi, Oxford. Special thanks to Gary Miller, Robert Jaeger, Andrew
Pomiankowski, and two referees who provided valuable comments.
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Figure. Resources allocated to nurturing and mating. Light areas reflect nurturing effort, dark
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Borgia (1979).
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Male /Polygam ous
Male /M onogam ou s
Fem ale/Polygam ous
Fem ale/M onog amo us
Figure.