Opinion
TRENDS in Ecology and Evolution
Vol.21 No.2 February 2006
Sexually selected signals are not
similar to sports handicaps
Thomas Getty
Department of Zoology & Kellogg Biological Station, Michigan State University, 3700 E Gull Lake Dr, Hickory Corners,
MI 49060-9516, USA
The handicap principle is a simple but powerful
metaphor that has had a major impact on how biologists
study and understand sexual selection. Here, I show that
its application to signalling in sexual selection is not a
valid generalization from its roots in economics.
Although some signalling systems, with additive costs
and benefits, have solutions that resemble sports
handicaps, the signalling in sexual selection has multiplicative costs and benefits, and solutions that do not
resemble sports handicaps. The sports analogy is
technically incorrect, metaphorically misleading and a
poor guide for empirical research on the signalling in
sexual selection. The evolution of sexually selected
signals is not a missing piece of Darwin’s puzzle; it is
an integral piece of the process of evolution by natural
selection, and it should be approached with the same
tools that we bring to bear on the evolution of other
correlated traits involved in social interactions.
Introduction
Research on the evolution of sexually selected signals has
blossomed over the past few decades, stimulated, in part,
by Hamilton and Zuk’s famous paper linking sexual
selection to parasites and health [1–3]. Much of this
research is guided, to some extent, by Zahavi’s simple but
powerful sports analogy, the handicap principle, which
was given credibility by Grafen’s brilliant but arcane
mathematical analysis of biological signalling [4–8]. Few
biologists have taken the time to grasp fully Grafen’s
mathematics. Here, I show that his most well known and
influential result (‘the marginal cost of advertising.
should be greater for worse males’) [6], which is widely
interpreted as a proof of the handicap principle, is based
on a simplifying assumption that does not generalize to
signalling in sexual selection. I show that the general
criterion for reliable signalling can be interpreted to mean
that higher quality signallers must be more efficient at
converting signals into fitness and that, in sexually
selected signalling, higher quality signallers can be more
efficient in spite of higher marginal costs. This increasingefficiency criterion makes it clear that sexual selection on
signals is not a missing piece of Darwin’s puzzle,
characterized by selection for waste and inefficiency, but
Corresponding author: Getty, T. ([email protected]).
Available online 14 November 2005
rather, is an integral piece of the process of evolution by
natural selection, characterized by selection for efficiency.
Signalling
Signalling is a kind of communication that, in biology, is
exemplified by peacocks and peahens. Peacocks vary in
some quality that is of value to peahens, but is not directly
observable by the hens, for instance, resistance to
parasites. The peacocks invest in costly signals, including
eyespots on their tails, that are somehow constrained to be
correlated with the unobservable quality. The correlation
enables peahens to screen for higher quality peacocks by
selecting on the signal. A fundamental question is what
constrains the correlation between the observable signal
and the unobservable quality, for example, keeping
low-quality peacocks from exaggerating their eyespots
(i.e. cheating) and destabilizing the system [7,8].
The handicap principle
In 1975, Zahavi [4] proposed a solution to the stability
(cheating) problem based on signal costs. He argued that
the investments that animals make in signals are similar to
the handicaps imposed on the stronger contestants in a
sporting event. The essential feature of a sports handicapping system is that it reduces disparities in performance
without eliminating them entirely. For instance, faster
racehorses are given bigger handicaps to their speed, in the
form of heaver weights added to the saddle. It was Zahavi’s
great insight that this reduction in disparities in performance requires a correlation across individuals between
unhandicapped performance and the size of the handicap.
Consequently, the handicap signals (or indicates) intrinsic
unhandicapped quality and expected handicapped
performance. Zahavi interpreted this to mean that big
signallers are demonstrating their ability to ‘waste’ more of
the unobservable quality by trading it off for a bigger signal
[5]. For instance, higher quality peacocks with bigger tails
are demonstrating that they can afford to trade off more
viability than can lower quality cocks.
The handicapping analogy is often traced back to
Veblin’s concept of conspicuous consumption: the idea
that rich people who ‘waste’ a lot of money on luxury
goods (the signals) should have more money left in the bank
(the unobservable quality) than do poor people who spend
little on utilitarian goods [9]. However, there is a more
striking and immediate precursor in Vonnegut’s 1961 short
story Harrison Bergeron [10], about a fantasy dystopia
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84
Opinion
TRENDS in Ecology and Evolution
where human performance is equalized by the Handicapper General. Vonnegut appreciated the signalling possibilities of a handicapping system: ‘it was easy to see that she
was the strongest and most graceful of all the dancers, for
her handicap bags were as big as those worn by twohundred-pound men’ [10].
The common interpretation of the handicap principle is
illustrated nicely in the abstract of a recent cover article in
Nature [11]: ‘signals of quality require high and differential
costs to remain honest (1,2).’ The 1 and 2 are the usual
paired references to Zahavi [4] and Grafen [6]. What was
Grafen’s contribution? The handicapping analogy
describes a pattern that is consistent with a signalling
system, but it does not propose a process that would
generate or stabilize that pattern (there is no Handicapper
General in biology). The lack of a plausible evolutionary
process limited the acceptance of the handicap principle
from 1975 to 1990, when Grafen’s paper [6] provided a
credible model for the evolution of biological signals as
handicaps [8].
Absolute and marginal costs
To understand the relationship between Zahavi’s description of a pattern of costs and Grafen’s model of the process
that stabilizes that pattern, one needs to attend to the
distinction between absolute costs and marginal (incremental adjustment) costs. Most people are familiar with
this distinction. For instance, at restaurant near me, a
small soft drink is 0.35l and the absolute cost is US$1.69. A
medium drink is 0.47l and costs US$1.89. Therefore, the
marginal adjustment cost of moving up from small to
medium is US$0.2/0.12lZUS$1.67/l. The marginal adjustment cost is considerably less than the absolute per unit
cost of a small drink (US$4.8/l), which is probably a factor in
the process that leads many people to adjust their order up
to a medium.
Grafen developed a general marginal fitness maximization model of signalling games. A marginal fitness model
examines the incremental effect of a small change in each
independent variable. He was looking for the necessary
conditions to insure a solution with a reliable correlation
between the signal and quality. He found that ‘the marginal
cost of advertising... should be greater for worse males’, and
interpreted this to mean that ‘the signal is acting as a
handicap’ [6]. I refer to this result as the ‘decreasingmarginal-cost criterion’. It implies that a high-quality
peacock with 100 eye spots on its tail should be able to add
one more spot at less viability cost than could a poor-quality
peacock with 100 eye spots.
Grafen’s analysis is similar to an earlier monograph on
market signalling by Spence (Box 1), who found that ‘if
some alterable characteristic is to be an actual signal for
productive capability in a market signalling equilibrium,
then (a) it must be costly to adjust, and (b) the adjustment
costs must be negatively correlated with productive
capability’ [12]. The term ‘adjustment costs’ emphasizes
the important distinction that is often missed by
biologists: the handicap analogy is based on the
assumption that absolute costs increase with signal size
but the decreasing-marginal-cost criterion implies that the
marginal costs decrease with increasing signaller quality.
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Vol.21 No.2 February 2006
Additive and multiplicative costs and benefits
To understand why the handicap principle does not
generalize to sexual selection, one needs to attend to the
distinction between additive and multiplicative models.
Most people are familiar with this distinction. For
instance, if the utility of a room depends on the wall
area (imagine a gallery for photographs), then utility u is
an additive function of the length l and width d of the room
[uZ2$(lCd)] and the marginal utility benefit of an
increase in l is independent of d (the marginal effect of
increasing
l while
holding d constant is a partial derivative
v vu
v: vu vl Z 2; vd
vl Z 0). However, if the utility of the room
depends on the floor area (imagine a gallery for sculpture),
then utility is a multiplicative function of l and d (uZl$d)
and the
in l is not independent
effect
of an increase
vumarginal
v vu
Z
1O
0
:
the
marginal
utility benefit
Z
d;
of d
vl
vl
vd
of increasing the length of a room is greater for wider rooms.
Spence’s analysis was based on an explicitly additive
model, whereas Grafen’s was not. However, Grafen’s
decreasing-marginal-cost criterion was predicated on an
arcane simplifying assumption (‘If w23Z0, then.’) that
means that the marginal fitness benefit of increasing
fecundity is independent of signaller quality. This implies
an additive model of fitness benefits and costs (Box 1).
Figure I in Box 1 illustrates an additive signalling system
with decreasing marginal costs and increasing absolute
costs across signallers of increasing quality, which is
consistent with the handicap principle. Because equilibrium signal size increases with signaller quality, selection
on the signal reliably screens for higher quality signallers.
Sexual selection
In the context of sexual selection, signalling is a component
of reproductive effort. The cost of this reproductive effort is
a reduction in survival or viability; the benefit is increased
reproduction or fecundity. Fitness is a multiplicative
function of viability and fecundity (Box 2). The fecundity
benefits of a signal are assumed to be independent of
quality, but the fitness benefits are not. This is because
fitness depends on fecundity multiplied by viability, and at
any given signal size, viability is greater for higher quality
signallers (Box 2). For instance, if a high-quality peacock
and a low-quality peacock each add a spot to their tails, and
that increases their mating rates the same amount, the
expected fitness benefit to the high-quality peacock is
greater because the increment in fecundity is multiplied by
his higher viability (Box 2, Eqn III). This means that he has
a higher probably of surviving long enough to accrue the
fecundity benefit. This fundamental difference between
additive and multiplicative models of fitness raises
questions about the generality of the decreasing-marginal-cost criterion and the sports handicap principle that
it appeared to support.
In fact, neither the criterion nor the principle generalize
to sexual selection that involves multiplicative viability–
fecundity tradeoffs [19,28,29]. A signalling solution with a
reliable correlation between the signal and quality does
require that the signal has marginal costs but, in theory at
least, the absolute costs can be negligible [7] and the
marginal costs can increase with quality (Box 2). In
multiplicative models, higher quality males can have
Opinion
TRENDS in Ecology and Evolution
Vol.21 No.2 February 2006
85
Box 1. Handicapping with additive costs and benefits
Fitness cannot be an additive function of viability and fecundity: the
units do not match.
lower or higher marginal costs and higher or lower absolute
costs (Box 2). High-quality big signallers might or might
not be ‘wasting’ more energy or carotenoids or viability
than are low-quality small signallers. Sexually selected
signals are not similar to sports handicaps (although they
might be in some systems; that would be an empirical fact,
not a general principle).
The general requirement for reliable signalling (Box 2,
Eqn II) can be interpreted to mean that higher quality
signallers must be more efficient at converting advertising
into fitness. I call this the ‘increasing-efficiency criterion’.
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Fitness must be a multiplicative function of viability and fecundity.
For the simple case of semilparity (with probabilistic survival through
one bout of reproduction): wZv$f. In this case v and f interact and the
marginal fitness effect of an increase in fecundity is not independent of
quality (Equation II):
v vw v
Eqn [II]
w Z v$f 0
vf Z vq ½V ða; qÞ s0
vq
Oddly, after deriving a necessary condition for reliable signalling
that is restricted to additive models of fitness, Grafen illustrated a
reliable signalling system with a multiplicative model that violates the
v vw
assumption: w ða; f ; qÞZ f $q a 0 w23 Z vq
vf s0. This might have
contributed to the failure of readers to appreciate the significance of
the assumption ‘w23Z0’.
Additive benefits and costs are impossible for sexual selection with
fecundity benefits and viability costs. However, there are some
biological signalling systems where the fitness costs and benefits
are in the same currency and can be modelled as additive, including
inclusive fitness models of resource allocation among kin [20,21] and
models of altruistic food sharing [22].
C(a,low)
1.0
0.0
0.0
C(a,med)
B(a)
C(a,high)
Benefit, cost, utility
Grafen’s analysis of biological signals as handicaps [6] is similar to a
famous monograph on the economics of market signalling by Nobel
laureate Michael Spence [12,13]. Here, I show that Grafen followed
Spence in assuming that costs and benefits are additive. Consequently, his results do not generalize to the multiplicative viability
costs and fecundity benefits at the heart of sexual selection.
A motivating question for Spence was what conditions are necessary
to make prestigious educational degrees reliable signals of the future
productivity of job applicants. The cost of the signal is tuition; the benefit
is starting salary. Spence explicitly assumed an additive model of
benefits and costs (the net return equals salary minus tuition) and found
that ‘if some alterable characteristic is to be an actual signal for
productive capability in a market signalling equilibrium, then (a) it
must be costly to adjust [tuition], and (b) the adjustment costs must be
negatively correlated with productive capability [more productive
workers get degrees faster and cheaper]’ [12].
In sexual selection, the benefit of a signal is increased reproduction
or fecundity (f ), which is assumed to be an increasing function of
signal size (a); the cost is reduced survival or viability (v), which
decreases with a in a way that depends on signaller quality (q) [14,15].
Grafen represented signaller fitness (w) as a function (W) of signal
size, fecundity and signaller quality: wZW(a,f,q) (I have
changed Grafen’s p for preference to an f for fecundity). Viability
[vZV(a,q)] is implicit in this notation. I prefer to work with viability
explicit {wZW[V(a,q),F(a)]} so that the viability costs can be
addressed explicitly.
The challenge is to determine what conditions are necessary to
insure that optimal signal size a* is an increasing function (A) of
h
i
signaller quality q a Z AðqÞ; dA dq O 0 , so that selection on a*
indirectly selects for high values of q. This kind of analysis is known as
comparative statics [16,17] and a solution where a* increases with q is
known as a separating equilibrium [17,18]. Grafen found that a
separating equilibrium follows if the marginal adjustment cost of
increasing the signal is lower for higher quality signallers. This is
identical to Spence’s result. Figure I illustrates an additive signalling
game that is consistent with the handicapping metaphor: higher
quality signallers pay lower marginal costs at any given signal size and
higher absolute costs at the equilibrium solution.
Grafen was not explicit about assuming additive costs
and benefits,
v vw
but one of his simplifying assumptions was that vq
vf Z 0 (‘w23Z0’
in his notation), which means that the fitness benefit vw of an increase in
fecundity vf does not differ across quality types vq. This implies that
fitness is an additive function of the benefits and costs [19]. This is easier
to see if we express fitness as an explicit function of viability and
fecundity: wZW[V(a,q),F(a)]. If fitness were an additive function of
viability and fecundity, for instance wZvCf, then v and f do not interact
and the marginal fitness effect of an increase in fecundity would be
independent of quality, as Grafen assumed (Equation I):
v vw v
w Z v Cf 0
Eqn [I]
vf Z vq ð1Þ Z 0
vq
0.5
Signal or advertising, a
1.0
TRENDS in Ecology & Evolution
Figure I. Additive signalling consistent with sports handicapping. The green
line B(a) is the benefit returned for a signal of size a. The three blue lines C(a,low),
C(a,med) and C(a,high) show the cost of the signal for low-, medium- and highquality signallers. The marginal cost of a signal at any given signal size is the
slope of the cost line. The optimal signal size (a*) occurs where the marginal cost
equals the marginal benefit (the slopes are equal) and the net benefit of the signal
(BKC) is at a maximum (as shown by the yellow vertical lines). The marginal cost
is lower for higher quality signallers, consistent with the Spence–Grafen
decreasing-marginal-cost criterion. As Zahavi realized, the equilibrium solution
has the structure of a sports handicapping system: the higher quality signallers
pay a higher absolute cost for their bigger signals, thus demonstrating an ability
to ‘waste more’. In this illustration of an additive model, I use the generic
economic variables ‘benefit’ and ‘cost’ rather than the specific life-history
variables ‘fecundity’ and ‘viability’ because viability costs cannot be subtracted
from fecundity benefits. See [7] for an alternative derivation of a similar figure.
In a multiplicative model, higher quality signallers can
have higher marginal viability and fitness costs and still
be more efficient because of their higher marginal fitness
benefits (Box 2, Eqn III). It is the lower conversion
efficiency for lower quality signallers that selects against
exaggeration (i.e. cheating).
The increasing-efficiency criterion can be transformed
to say that higher quality signallers must have lower
proportional marginal viability (and fitness) costs (Box 2,
Eqn IV). Unfortunately, the meaning and measurement of
proportional marginal costs are difficult to fathom.
Opinion
86
TRENDS in Ecology and Evolution
Vol.21 No.2 February 2006
Box 2. Sexual selection with multiplicative costs and benefits
Here, I derive the general criterion for reliable signalling and show
that, for the multiplicative viability costs and fecundity benefits at the
heart of sexual selection, higher quality signallers might have lower or
higher marginal costs and higher or lower absolute costs (Figure I).
In the context of sexual selection, signalling is a component of
reproductive effort [15]. The cost of this reproductive effort is a
reduction in survival or viability (v), which is a function (V) of both
signal size (a) and signaller quality (q): vZV(a,q). The benefit is
increased reproduction or fecundity (f), which is a function (F) of signal
size (a) but is independent of signaller quality: fZF(a). Fitness (w) is a
multiplicative function of viability and fecundity [14,15]. In the simple
case of semilparity (with probabilistic survival through one bout of
reproduction): wZW[V(a,q),F(a)]Zv$f.
We want to find the conditions that insure a signalling (separating)
equilibrium, corresponding to an optimal signal size (a*) that
is an
increasing function (A) of signaller quality (q): a Z AðqÞ;dA dq O 0.
Implicit differentiation shows that [19] (Equation I):
v vw
vq
0! dA dq ZK va
v vw
va
va
Eqn [I]
The denominator is negative at the fitness maximum, so the general
requirement for a reliable signalling solution is that the numerator
must be positive (Equation II):
v vw Eqn [II]
va O 0
vq
This general condition can be interpreted to mean that higher
quality signallers must be more efficient at converting advertising into
fitness. I call this the ‘increasing-efficiency criterion’. Grafen
derived
v vw
this in passing but then went on to assume that vq
vf Z 0.
Bondurianski and Day [23] derived the same criterion for positive
allometries, which are correlated morphometric traits.
We can use the chain rule to decompose the criterion in equation II
(Equation III)
v vw v vw vv vw vf
v
vv
vf
0!
$
C
$
Z
f
$
C
v$
Z
va
vq
vq vv va
vf va
vq
va
va
Eqn [III]
vv
vv
va represents marginal viability costs and f $ va represents
marginal
fitness costs. If costs and benefits are additive, then
v vw
vq
vf Z 0 and the increasing-efficiency criterion collapses to
the decreasing marginal-cost criterion.
Fecundity, viability, fitness
1.0
V(a,high)
F (a )
V(a,med)
V(a,low)
0.0
0.0
In a multiplicative model, reliable signalling requires that the
proportional marginal viability (or fitness) costs decrease with
increasing signaller quality (there is a confusing double negative
here; costs are decreases in v and w). This has been discovered
independently by several authors [24–26]. This decreasing-proportional-marginal-cost criterion is potentially powerful. However, I
think most biologists will find it more useful to adopt the increasingefficiency perspective (Eqns II and III), measuring fecundity and fitness
as well as viability, because in sexual selection, signaller fecundity and
fitness are important components of the receivers’ half of the
signalling game. We have been focusing on the signallers’ half of
the game, just assuming that receivers return increasing fecundity
benefits. This might be taking too much for granted. We cannot know
whether receivers should be, or even are returning increasing
fecundity benefits without measuring signaller fecundity.
We can see that the decreasing-marginal-cost criterion for additive
models (Box 1) does not generalize to multiplicative models by taking
the derivatives in Equation III and rearranging terms (Equation V)
0!
v vw v
vv
v
vf
f
$
C
v$
Z
va
vq
vq
va
vq
va
Zf$
v vv vv vf
v vv K1 vv vf
$ 0
$
$
C
O
va
va
vq
vq va vq
f
vq va
0.5
Signal or advertising, a
1.0
Eqn [V]
The marginal viability cost vv va can increase with quality [18], up
h
i
vf
vv
to: Kf1 $ vv
vq $ va . If viability is sensitive to quality ( vq is large) and
vf
is large), then higher quality
fecundity is sensitive to signal size ( va
signallers can be more efficient even if they have to pay much higher
marginal costs. Hausken and Hirshleifer [27] came to the same
conclusion independently, using an approach they call ‘the
Malthusian equi-marginal principle.’
In multiplicative models of sexual selection, higher quality
signallers can be more efficient with lower or higher marginal costs
and higher or lower absolute costs (Figure I).
(b)
1.0 V(a,high)
Fecundity, viability, fitness
(a)
Rearranging terms so that fecundity falls out yields a simple
relationship (Equation IV)
" " #
#
v vv va vf va
v vv va
C
Z
C0
Eqn [IV]
0!
v
f
v
vq
vq
F (a )
V(a,low)
0.0
0.0
0.5
Signal or advertising, a
1.0
Figure I. Mutiplicative signalling inconsistent with the handicap principle. (a) Multiplicative signalling inconsistent with the decreasing-marginal-cost criterion. The green
line F(a) is the fecundity benefit returned for a signal of size a. The three blue lines V(a,low), V(a,med) and V(a,high) show the residual viability for low-, medium- and highquality signallers. The cost of the signal is the drop in residual viability. The marginal viability cost is the negative slope vv=va. In this example, the marginal viability cost is
higher for higher quality signallers, which is inconsistent with the Spence–Grafen criterion. This seems unlikely, but could happen if there were a power-efficiency
(intercept–slope) tradeoff. Fitness is the product of viability and fecundity, represented by the humped yellow lines. The optimal signal size (a*) occurs at the fitness peak
(yellow diamonds), and it increases with signaller quality despite the violation of the Spence–Grafen criterion. (b) Multiplicative signalling inconsistent with sports
handicapping. The symbols are as in (a) but in this example the marginal viability costs are lower for higher quality signallers, consistent with the Spence-Grafen
criterion. The optimal signal size (a*) increases with signaller quality. However, at the equilibrium, high-quality big-signallers do not demonstrate an ability to ‘waste’
more viability; they ‘waste’ less than do low-quality small signallers. Inspired by [15] and adapted with permission from [28].
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TRENDS in Ecology and Evolution
I suggest that we stick with the traditional life-history
variables, viability, fecundity and fitness, and focus on
selection for efficient tradeoffs, rather than trying to
build a research program around proportional
marginal costs.
Why does the validity of a metaphor matter?
The fundamental difference between sexually selected
signals and sports handicaps matters because the
metaphor guides empirical studies, which are often
designed to measure absolute costs (handicaps). Absolute
costs are not sufficient for understanding how differences
in viability–fecundity tradeoffs stabilize the signalling in
sexual selection. Currently, this misunderstanding gets
played out most often in the realm of the Hamilton–Zuk
hypothesis that, within a species, big signallers are
advertising fewer parasites [1]. Because the common
assumptions of decreasing marginal costs and increasing
absolute costs are not (yet) justified for multiplicative
sexual selection, neither (yet) are predictions about
parasite loads. Positive and negative correlations are
both consistent with current theory. Perhaps this is why
approximately half of the reported comparative studies
find that individuals with big signals have more parasites
than do individuals with small signals [29].
I suggest that we think of costly signals as investments
instead of handicaps. This would at least reduce the risk of
researchers jumping to the conclusion that a healthy
peacock that has invested in a bigger tail must have
‘wasted’ more viability on his investment than has another
less-healthy peacock with a smaller tail.
What next?
The signalling that I am considering here is a component
of sexual selection. Zahavi and Zahavi [5] suggest that we
reverse the nesting and view sexual selection as a specific
type of a more general process that they call ‘signal
selection’, which they say is counterutilitarian, selecting
for waste and inefficiency. Miller [30] interprets this to
mean that ‘Waste is Good’ [30], because signals can only
work if they are inefficient. This is what supposedly
distinguishes wasteful signal (and hence sexual) selection
from efficient natural selection. This distinction apparently justifies the subtitle of Zahavi and Zahavi’s book [5]
A Missing Piece of Darwin’s Puzzle.
There is no grandeur in this view of life, with its endless
forms most wasteful and inefficient. The increasing
efficiency perspective that I am advocating here contrasts
sharply with the idea of selection for ‘waste’ and it has the
benefit of being consistent with our understanding of
natural selection.
Sexual selection is a nested type of natural selection,
mediated by social interactions and involving access to
mates. Because access to mates requires that one be alive
and perhaps more healthy than the competition, it is
harder to separate sexual selection from the rest of
natural selection than most people acknowledge. I
advocate keeping signalling and sexual selection well
integrated into the overarching framework of natural
selection. The signal is a target of selection by receivers
and the signalled quality is a correlated trait under
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Vol.21 No.2 February 2006
87
indirect selection by receivers. Signaller fitness depends
on the interaction between the signal trait and the
quality-dependent viability tradeoff, which are, therefore,
under correlational selection [30–32]. In this framework,
reliable signalling can be visualized as a diagonally rising
ridge on the three-dimensional fitness surface for the
signal and quality traits [28,33].
The Fisherian runaway process [2], resulting from
genetic correlations between signals and preferences, is
often presented as an alternative to the kind of signalling
model that I have addressed here, which is sometimes
referred to as the Zahavian good-genes model [2,8]. Recent
theoretical work suggests to some that the runaway and
good-genes processes are extremes of a continuum and that
we should adopt a combined ‘Fisher–Zahavi model’ for the
evolution of traits that are correlated with a high breeding
value for fitness [24,34–36]. This seems promising,
especially if we can figure out how to bring this perspective
to bear on the challenge of understanding assortative
mating markets and systems where offspring fitness and
breeding value depend on mate compatibility [37–40].
Of course, the ‘Zahavi’ part of this unified perspective
should not be confused with sports handicaps, given that
selection for good genes (or possibly direct benefits) is not
similar to sports handicapping.
Conclusions
The handicap principle does not provide a reliable
foundation for empirical research on the signalling in
sexual selection because multiplicative sexual selection is
not similar to additive sports handicapping. The handicap
principle has had an important role in stimulating theory
development and empirical research, but it has outlived
its usefulness and become an impediment to progress. It is
time to usher the handicap principle off to an honourable
retirement. The evolution of sexually selected signals is
not a missing piece of Darwin’s puzzle, involving selection
for waste, it is an integral piece of the process of evolution
by natural selection, involving selection for efficiency, and
it should be approached with the same tools that we bring
to bear on the evolution of other correlated traits involved
in social interactions.
Acknowledgements
I thank Carl Bergstrom, Chad Brassil, Jeff Conner and Stefan Lüpold for
helpful comments on the article. I thank Brian Hazlett for getting me
started along this path, and Amotz Zahavi and Alan Grafen for making
the trip so interesting. This work was supported, in part, by the US
National Science Foundation grants DGE 0114378 and IBN 998220. This
is Kellogg Biological Station contribution number 1182.
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