Evolutionary Ecology 1998, 12, 59±71
Synergistic selection and graded traits
OLOF LEIMAR1 and JUHA TUOMI2 à
1
2
Department of Zoology, Stockholm University, S-106 91 Stockholm, Sweden
Department of Ecology, Theoretical Ecology, Lund University, Ecology Building, S-223 62 Lund, Sweden
Summary
Fitness interactions where bene®ts are shared only between individuals with similar traits are often referred to
as `synergistic'. Examples include defence characters, like insect warning colouration and plant unpalatability,
and joint activities needing the active participation of all group members, such as cooperative hunting.
Previous analyses, assuming discrete variation in the trait, have shown that synergistic selection can be a
sucient explanation for the evolutionary stability of such traits. Here, we investigate the consequences of
graded variation in the trait responsible for synergistic e€ects. Classifying the synergism as unbiased when an
individual receives maximum associational bene®t by having the same trait value as its neighbours, and letting
a positive (negative) bias represent the maximum above (below) this value, we show that only positively biased
synergistic selection can enhance a graded trait. Thus for graded traits, a synergistic bene®t is not in itself
sucient for evolutionary stability. We study possible reasons for synergistic bias in a simple model of plant
defences against herbivores, and suggest that the processes of herbivore avoidance learning and diet selection
are probable causes of positive bias. We propose that mammalian herbivores exposed to a given level of
toxicity will show stronger feeding aversion to higher toxicity, resulting in positively biased synergistic selection of plant defence traits. Positive bias produced by avoidance learning may, in a similar way, also select
for defence signals.
Keywords: evolutionary stability; mutualistic interactions; plant defences; quantitative traits; synergistic
selection
Introduction
Certain potentially costly traits may bene®t an individual's partner or neighbour. For instance, the
defence traits of a plant could, in addition to protecting the plant itself against attacks by herbivores, also have a protective e€ect on neighbouring conspeci®cs. Our intention here is to clarify
when such ®tness interactions tend to increase the evolutionarily stable level of the trait, and when
they tend to decrease it.
For a costly trait, a relevant distinction is whether neighbours can receive associational bene®ts
without possessing the trait, or if the bene®ts accrue preferentially to those having the trait. The
®rst case can be viewed as a Prisoner's Dilemma game, with the well-known property that, in the
absence of relatedness or repeated interactions between neighbours, expression of the trait cannot
be an evolutionarily stable strategy (ESS). The second is an example of synergistic selection, as
de®ned by Maynard Smith (1982a). Since individuals without the trait do not gain advantages
when associating with others who have it, expression of the trait can be an ESS. Thus synergistic
selection may in itself be a sucient explanation for costly, cooperative or mutualistic traits, the
only proviso being that the trait must become common enough in a population or local group for
synergistic e€ects to begin operating (Maynard Smith, 1989).
*Author to whom all correspondence should be addressed.
à Present address: Department of Biology, University of Oulu, Linnanmaa, FIN-09570 Oulu, Finland.
0269-7653
Ó 1998 Chapman & Hall
60
Leimar and Tuomi
Many defence-related traits show synergism. A property of aposematic colouration is that a
predator, after having attacked one or a few distinctively coloured and distasteful prey, may avoid
attacking potential prey of similar appearance (Matthews, 1977), so synergistic selection may be
important for the evolution of defence signals (Guilford, 1985, 1988; Queller, 1985). Similarly,
Tuomi and Augner (1993) noted that mobile herbivores, by sampling parts of a plant, were able to
use the plant's defence traits to generalize from one plant to the next.
Synergistic e€ects may also be present in social interactions, as when individuals join together for
the purpose of some `project' needing the active participation of all group members for its successful completion. Possible examples of such projects are hunting (Packer and Ruttan, 1988),
mating coalitions in male lions (Packer et al., 1988) and nest defence (Lin and Michener, 1972).
Maynard Smith (1982a, 1989) and others who have analysed synergistic e€ects (e.g. Matessi and
Jayakar, 1976; Queller, 1984, 1985; Guilford, 1985, 1988; Nee, 1989; Tuomi and Augner, 1993;
Maynard Smith and SzathmaÂry, 1995), consider two strategic options: either to have the trait or not.
In the analysis performed here, we take into account that a trait with synergistic e€ects may be
expressed to a greater or lesser degree, and show that this could have important consequences. With
graded traits, even strong synergism may fail to cause expression of the trait to be an ESS.
For quantitative characters, it is perhaps not self-evident what should be meant by synergistic
selection. Guilford and Cuthill (1991) described synergistic selection as `the evolution of traits that
bene®t from the interaction of individuals with the same trait more than from interactions between
dissimilar individuals'. Applied to graded traits, we take this to mean that, apart from the direct
e€ects of the trait on its bearer, an individual receives maximum synergistic bene®t by having a trait
value equal to its neighbours' value, and refer to it as unbiased synergism. We will, however, also
view synergism somewhat more generally; an individual may receive maximum synergistic bene®ts
at a trait value either higher (positive bias) or lower (negative bias) than that of its neighbours. In
either case, if neighbours have the trait, an individual should receive few or no synergistic bene®ts
without the trait and more bene®ts at some positive trait value. On the other hand, if neighbours do
not possess the trait, an individual should not receive any synergistic bene®ts.
Previous discussion of synergistic selection has mainly dealt with costly traits lacking nonassociational bene®ts. Nevertheless, it is also of interest to investigate the evolutionary consequences of synergism when it is optimal to express the trait to a certain degree without any
associational e€ects. In fact, most examples of synergistic projects consist of activities performed
by individuals on their own. Similarly, aposematic colouration might bene®t a single individual
(Engen et al., 1986), and the same is certainly true for plant defences (Rhoades, 1979). These types
of interactions have been called `by-product mutualism' (Brown, 1983; Dugatkin et al., 1992;
Mesterton-Gibbons and Dugatkin, 1992). The reason for the terminology is that one can view any
mutual bene®ts from neighbour interactions as incidental consequences of traits that are present
for other reasons. For a two-valued (discrete) trait, this is a natural point of view, since association
with neighbours will not change it, but for graded traits the degree of expression might either
increase or decrease because of associational e€ects.
Our main conclusion will be that only positively biased synergistic selection can cause a graded
trait to be expressed to a greater degree than is the case without associational e€ects. After
establishing this, we look more closely at factors that may produce such bias for defence-related
traits. As an important example, we study plant defences against herbivores, and we consider both
proper defence traits (i.e. those traits primarily responsible for herbivore avoidance behaviour) and
defence signals. Our treatment of defence-related traits is similar to the analysis of aposematic
colouration by Leimar et al. (1986). To focus our presentation, we assume individuals to be
unrelated, although in practice kin selection may often operate in conjunction with synergistic
e€ects (e.g. Queller, 1992a,b).
Synergistic selection
61
Synergistic selection
We will divide a ®tness function into components in a way similar to Maynard Smith (1989) for the
two-strategy case. Let z denote the value of a graded trait, which can be zero or positive. For an
individual alone, or one with neighbours lacking the trait, ®tness is given by w…z†. We are interested
in two cases, illustrated in Fig. 1. If in addition to its cost, the trait confers little or no direct bene®t,
the maximum of w…z† occurs for z ˆ 0, and w…z† is a decreasing function of z (dashed curve in
Fig. 1). Our main question for this case is whether synergistic e€ects can produce an ESS with
positive z. On the other hand, with higher direct bene®ts, the maximum of w…z† might occur for a
positive z ˆ ^z (solid curve in Fig. 1). Here we wish to know whether synergism moves z up or down
from ^z.
For an individual with trait value z, interacting with one or more neighbours each of which has
trait value zn , a synergistic bene®t is added to the direct ®tness component w…z†, resulting in
W …z; zn † ˆ w…z† ‡ s…z; zn †
…1†
Regarding s…z; zn † as a function of z for ®xed zn , Fig. 2 illustrates the kinds of synergistic ®tness
components studied here. When s…z; zn † has a maximum at z ˆ zn , we speak of unbiased synergistic
selection. The maximum for a higher (lower) trait value is referred to as a positive (negative) bias.
For an individual without the trait, the synergistic bene®t s…0; zn † could be zero, or at least smaller
than the maximum.
The synergistic bene®t, of course, also depends on the neighbours' trait value, zn . We must have
s…z; 0† ˆ 0 for all z, implying no synergistic bene®t when neighbours lack the trait. If we focus on
z ˆ zn , we should see the bene®t s…zn ; zn † initially increase with zn , although it might well level o€ or
start to decrease for larger values of zn .
In Equation (1), we could have included an additive associational bene®t depending only on zn
(cf. Maynard Smith, 1989), but for simplicity we regard such a component as part of s. The e€ect of
Figure 1. Two examples of ®tness functions, w…z†, disregarding synergistic bene®ts. For the dashed line, the
trait itself only represents a cost. Without associational e€ects, the optimal trait value is then equal to zero.
The solid line shows a case where it is optimal to express the trait also when there are no synergistic bene®ts,
and the arrow indicates the position, ^z, of the optimum.
62
Leimar and Tuomi
Figure 2. Three examples of synergistic ®tness components. The curves show the synergistic bene®t, s…z; zn †, as
a function of the individual's trait value, z, when the neighbours' trait values are ®xed at zn . The solid curve
illustrates unbiased synergism, where the maximum synergistic bene®t occurs for z ˆ zn , as indicated by the
dotted vertical line. The dashed curve shows synergism with a positive bias, so that maximum synergistic
bene®t occurs for some z > zn . The dash-dotted curve illustrates negatively biased synergism.
such a component is to shift the curve s…z; zn † in Fig. 2 upwards. Synergistic e€ects are present when
s…z; zn † varies with z; that is, when the curves in Fig. 2 are not horizontal lines. The reason for our
choice of ®tness components is to provide a natural extension to graded traits of the kinds of
situations previously studied assuming a two-valued trait.
So, for comparison, let us imagine only two trait values are possible: zero and some positive z1 ,
which could be the level indicated by the dotted vertical line in Fig. 2. Looking at a case with little
or no direct bene®t, it is clear that if the synergistic bene®t s…z1 ; z1 †, given by the height of the
vertical line in Fig. 2, is large enough compared to s…0; z1 †, then expression of the trait will be an
ESS. To see this, note that zero trait level cannot invade when W …0; z1 † < W …z1 ; z1 †, which from
Equation (1) can be written as w…0† ÿ w…z1 † < s…z1 ; z1 † ÿ s…0; z1 †. Of course, zero trait level is also
an ESS, since w…z1 † ‡ s…z1 ; 0† ˆ w…z1 † < w…0†, so that W …z1 ; 0† < W …0; 0†. Thus, we have essentially
the situation considered in many previous investigations of synergistic selection (e.g. Maynard
Smith, 1989).
Returning to graded traits, for a positive z to be an ESS, the ®tness function W in Equation (1),
with zn ˆ z , must have a maximum over z at z ˆ z . A necessary condition for an ESS is then
(Maynard Smith, 1982b):
@W @s
…z ; z † ˆ w0 …z † ‡ …z ; z † ˆ 0
@z
@z
…2†
One should also verify z to be a maximum, and that there is continuous stability (Eshel, 1983;
Taylor, 1989), but our main results follow simply and directly from Equation (2).
First, with little or no direct bene®t from the trait, taken to mean w0 …z† < 0 for all z (dashed curve
in Fig. 1), Equation (2) implies that @s=@z ˆ ÿw0 > 0 at an ESS. Thus, comparing the curves in
Fig. 2, for a positive z to be an ESS, the synergistic bene®t s…z; z † must show a suciently strong
positive bias (i.e. @s=@z at z ˆ z must be suciently positive). On the other hand, zero trait level is
Synergistic selection
63
always an ESS in this case, since for positive z we have W …z; 0† ˆ w…z† < w…0† ˆ W …0; 0†, so zero
trait level is the best response to itself. In conclusion, for synergistic selection without sucient
positive bias, zero trait level will be the only ESS, even if the potential synergistic bene®t is
substantial.
Second, for traits with a positive non-associational optimum ^z (solid curve in Fig. 1), we have
w0 …^z† ˆ 0. Let us also assume w…z† to be unimodal, so that w…z† increases …w0 …z† > 0† for z below ^z,
and decreases …w0 …z† < 0† for z above ^z. With unbiased synergistic selection, where @s=@z ˆ 0 at
z ˆ z , Equation (2) yields w0 …z † ˆ 0. Since the derivative of w…z† is zero only at the non-associational optimum ^z, we ®nd z ˆ ^z to be necessary for the evolutionary stability of a positive z .
With positive bias, where instead @s=@z > 0 at z ˆ z , Equation (2) yields w0 …z † < 0, implying z to
be above ^z. Similarly, with negative bias, z < ^z is necessary for an ESS.
We can thus conclude that synergistic selection with a positive bias may enhance a graded trait,
whereas a negative bias tends to reduce it, and unbiased synergism leaves it unchanged. Finally, we
have only studied necessary conditions for a pure ESS, and there may sometimes be additional
evolutionary outcomes, for instance in the form of a stable polymorphism.
Defence-related traits
It is clearly of interest to investigate possible causes of bias in synergistic selection. Defences against
enemies, such as predators or herbivores, have a synergistic e€ect if an enemy becomes aware of the
defence before in¯icting much damage, and uses information from previous attacks on other
defended individuals to generalize about the likely consequences of carrying out the attack on the
current victim. This psychological process of generalizing may be an important source of bias.
A defence signal like aposematic colouration provides an enemy with a stimulus to generalize
over. The defence itself, which might be the concentration of a chemical substance, may also work
in a similar way. For a plant, in particular, a herbivore could estimate the strength of the defence
by careful sampling of parts of the plant (Tuomi and Augner, 1993). Before analysing the evolutionary consequences of associational e€ects for defences, we introduce a convenient representation of such e€ects.
Generalization gradient
Consider a plant with defence of strength z, surrounded by neighbours with zn . The neighbours
could, in principle, depending on the mobility of herbivores, be all other plants in the population. If
herbivores generalize from previous attacks on neighbours, the intensity of attacks on the plant
depends both on its own and on its neighbours' trait values. For simplicity, we consider neighbour
e€ects only in terms of the number of attacks carried out per unit time, but similar e€ects on the
amount of biomass consumed per attack are quite likely. Figure 3 shows how the attack intensity,
G…z; zn †, might depend on z for a ®xed level of zn . The function G…z; zn †, or rather the shape of its
dependence on z, is called a `generalization gradient'. See Leimar et al. (1986) for a more detailed
account of this concept and its use in learning theory.
We wish to distinguish two situations. For the dash-dotted curve in Fig. 3, a plant achieves
maximum reduction in attack intensity by having the same trait value as its neighbours. We refer to
it as a gradient with a centred minimum; the minimum is centred on the population defence level zn .
An interpretation could be that herbivores are more reluctant to carry out an attack when the plant
is similar to other defended plants.
Herbivores may, however, show a directionality or bias in their generalization, and be even more
reluctant to attack a plant with higher trait level than those previously encountered. The dashed
64
Leimar and Tuomi
Figure 3. Two examples of generalization gradients, G…z; zn †. The curves show the attack intensity, G…z; zn †, as
a function of an individual's trait value, z, when associated with neighbours whose trait values are ®xed at zn .
For the dash-dotted curve, the minimum of the generalization gradient is centred on zn , as indicated by the
dotted vertical line. For the dashed curve, the minimum is shifted to a value greater than zn , which may
produce positively
The curves were obtained by inserting zn ˆ 1 in the formula
biased synergism.
G…z; zn † ˆ 1 ÿ exp ÿ6…z ÿ zn ÿ d†2 z2n =…e ‡ z2n †, where d ˆ 0 and e ˆ 1 for the centred gradient, and d ˆ 0:2
and e ˆ 0:573 for the shifted gradient.
curve in Fig. 3 shows such a case; the minimum of the generalization gradient has been shifted to
above zn . In principle, the gradient could keep on decreasing as z gets larger ± that is, the minimum
could be `at in®nity'. As we will show, a shift of the minimum is needed for synergistic selection to
enhance the trait.
The amount of reduction in attack intensity naturally depends on the strength of the neighbours'
defence. When neighbours are undefended, there should be no reduction and G…z; 0† ought to be
constant. As zn increases, there will be more reduction, so G…zn ; zn † should decrease with zn .
E€ect on plant defences
A synergistic bene®t for plant defences comes about by way of the generalization gradient. To
determine the type of synergism, we need also to take into account that a reduction in attack
intensity is of higher value for a less defended plant than for a more defended plant. This last
relationship is very general and can be viewed as the de®ning characteristic of a proper defence
trait: when an attack is carried out, it must be less costly for a better defended plant.
If the generalization gradient has a centred minimum (Fig. 3), there are trait values slightly
below and slightly above the neighbours' value, both of which achieve the same reduction in attack
intensity. Since the reduction is more bene®cial when the trait value is slightly below, the synergistic
bene®t must be negatively biased. A suciently steep decrease in the gradient at z ˆ zn , implying a
shift of the minimum, can compensate for this and produce a positive bias.
Although the argument above is conclusive, we also give a more concrete example, illustrating
that a shifted gradient is needed for positively biased synergism. Equating plant ®tness with the
rate of biomass growth, an allocation z to defence is assumed to reduce growth rate by an amount
Synergistic selection
65
C…z†, where C…z† increases with z. If a herbivore attack is carried out, the loss of plant matter is
H …z†. The loss should be smaller for a better defended plant, so H …z† must be decreasing. With
attacks per unit time given by G…z; zn †, the ®tness function can then be written as:
W …z; zn † ˆ W0 ÿ H …z†G…z; zn † ÿ C…z†
…3†
This formulation combines aspects of models used in plant optimal defence theory (e.g. FagerstroÈm et al., 1987) with associational e€ects of the kind studied by Tuomi and Augner (1993).
For a numerical example, we use W0 ˆ 1:5, H …z† ˆ eÿz , and C…z† ˆ 0:5z. Assuming G…z; 0† ˆ 1,
the non-associational ®tness component is:
w…z† ˆ W …z; 0† ˆ 1:5 ÿ eÿz ÿ 0:5z
…4†
shown as the solid curve in Fig. 1. The synergistic ®tness component must then, according to
Equation (1), be given by:
s…z; zn † ˆ W …z; zn † ÿ W …z; 0† ˆ eÿz …1 ÿ G…z; zn ††
…5†
Using the centred gradient in Fig. 3, this becomes the negatively biased synergistic bene®t shown in
Fig. 2. If instead the shifted gradient in Fig. 3 is used, the positively biased component in Fig. 2 is
obtained. To determine an ESS for each of these two cases, we should, according to Equation (2),
solve the equation:
w0 …zn † ˆ ÿ
@s
…zn ; zn †
@z
…6†
Figure 4. The e€ect of synergism on plant defences. First, the solid curve is the derivative w0 , which is zero at
the non-associational optimum ^z ˆ 0:693 (middle arrow). The ESS-solution to Equation (6) is then illustrated
for two cases: negative bias and positive bias. The dash-dotted curve shows ÿ@s=@z at z ˆ zn when the
synergistic bene®t, s…z; zn †, derives from the centred generalization gradient in Fig. 3. This gradient produces
negatively biased synergism, making ÿ@s=@z positive. The leftmost arrow indicates the ESS solution,
z ˆ 0:483, to the equation w0 ˆ ÿ@s=@z; because of negative bias, we have z < ^z. Similarly, the dashed curve
shows ÿ@s=@z at z ˆ zn when there is synergism with positive bias, derived from the shifted gradient in Fig. 3.
The ESS, z ˆ 1:292 (rightmost arrow), has a higher level of defence than the non-associational optimum ^z.
66
Leimar and Tuomi
The equation is illustrated graphically in Fig. 4. With the centred gradient, the solution is below
the non-associational optimum ^z, whereas the shifted gradient leads to a solution above ^z. With
some additional computations, which we leave out, it is straightforward to verify that the solutions
in Fig. 4 are continuously stable ESSs.
Defence signals
Consider a population of defended individuals and de®ne a defence signal, z, as a trait which an
enemy can generalize over, but having no protective value if an attack is carried out. Since there
may be costs involved in producing the signal, and a possible disadvantage from increased conspicuousness, the non-associational ®tness component should decrease with the level of the trait
(dashed line in Fig. 1). Furthermore, for a positive z to be an ESS, the cost accompanying a slight
increase of z from z must be balanced by an equal bene®t, and the only possible bene®t is a
reduced attack intensity, implying a suciently steep decrease in the generalization gradient at
z ˆ zn (dashed curve in Fig. 3). We conclude that a shift of the minimum of the gradient is
necessary for expression of the signal to be an ESS.
As a concrete example, which may be thought of as a plant defence signal, let us modify the
®tness function in Equation (3) to:
W …z; zn † ˆ W0 ÿ H0 G…z; zn † ÿ C…z†
…7†
Since H0 is independent of z, the trait does not reduce the amount of damage if an attack is carried
out; the only possible value of the trait derives from the generalization gradient. The reason for a
reduced attack intensity for z close to zn would be that the plants have other traits with a harmful
e€ect on herbivores, and the herbivores learn to associate the signal with these harmful e€ects.
With a centred gradient G…z; zn †, Equation (7) results in unbiased synergistic selection. As illustrated in Fig. 5, the only ESS in this case is not to express the signal. In general, when unbiased
synergistic selection acts on a trait with no direct bene®ts, an individual with neighbours expressing
the trait might do best by having the trait, but to a lesser degree than its neighbours (cf. Fig. 5),
which may be regarded as `subtle cheating'. A positive bias is needed to prevent destabilization
from such subtle cheating, and can produce an ESS with a positive value of the signal (Fig. 5).
Relatedness and synergistic selection
The situation becomes more complex when nearby individuals are related to each other, or if they
are otherwise associated in such a way that neighbours tend to have similar traits (Eshel and
Cavalli-Sforza, 1982; Tuomi and Augner, 1993). For instance, in contrast with the situation illustrated in Fig. 5, relatedness may lead to evolutionarily stable expression of a defence signal even
with a centred generalization gradient (for an example, see Leimar et al., 1986). Since relatedness
produces a positive correlation between the traits of nearby individuals, the dependence of the
synergistic component s…z; zn † on the second variable, zn , enters into the condition for evolutionary
equilibrium. If s…z; zn † for z ˆ zn increases with zn , neighbour relatedness would tend to enhance the
trait. This is most easily seen when there is complete genetic identity of nearby individuals (e.g. a
clonal plant), in which case the ®tness function in Equation (1) becomes w…z† ‡ s…z; z†.
Thus, when considering the evolution of graded defence-related traits, both relatedness and
synergism need to be taken into account. This holds for the question of whether the trait will be
expressed at all and also for the degree to which it will be expressed. On the other hand, for a
discrete, two-level trait with a synergistic e€ect, relatedness plays a somewhat more limited role. As
argued by Guilford (1985, 1988), relatedness can be important in destabilizing a situation where the
trait is absent from a population, but once the trait is common, it is `uncheatable' because of the
Synergistic selection
67
Figure 5. The e€ect of synergism on defence signals. The solid curve shows the optimal trait level z as a
function of the neighbours' level zn for a case with centred generalization gradient. This best response curve
intersects the line z ˆ zn only at zn ˆ 0, which is then the only ESS. For the dashed curve, the minimum of the
gradient is shifted, and there are three intersections with the line z ˆ zn . Both zn ˆ 0 and the other intersection
indicated by a ®lled dot are continuously stable ESSs, but the intersection (from below) between these two is
continuously unstable (open dot). To compute these curves,
the ®tness function
in Equation (7) was used, with
H0 ˆ 1, C…z† ˆ 0:05z ‡ 0:075z2 , and G…z; zn † ˆ 1 ÿ exp ÿ0:5…z ÿ zn ÿ d†2 z2n =…1 ‡ z2n †, where d ˆ 0 for the
solid curve (centred gradient) and d ˆ 0:5 for the dashed curve (shifted gradient).
synergistic e€ect, and relatedness has no in¯uence on the evolutionary stability. For graded traits
this is no longer true, since one has to take into account the possibility of subtle cheating, and
relatedness also plays a role when most members of the population express the trait to a certain
degree.
Discussion
It is possible to use the concept of synergistic selection more generally than we have done here. Any
®tness component that is not a sum of e€ects, where each e€ect depends only on the phenotype of a
single individual, could be called synergistic (Maynard Smith, 1982a; Queller, 1984, 1985). For
graded traits, such an interpretation is somewhat too general to allow any strong conclusions to be
drawn. Our aim is to shed some light on the consequences of graded variation for a number of
situations previously studied mainly with two-strategy models, and we have restricted ourselves to
simple, non-additive ®tness e€ects resulting from mutualistic neighbour interactions.
As we have shown, the evolutionary consequences of such associational e€ects vary depending
on whether an individual achieves maximal synergistic bene®ts at a trait value equal to the population level (unbiased synergism), or at a lower (negative bias) or a higher (positive bias) value.
For synergistic selection to enhance a graded trait, a positive bias is required. This result shows that
synergistic bias can be an important mechanism for the evolution of mutually bene®cial traits, in
addition to the mechanisms discussed by Mesterton-Gibbons and Dugatkin (1992) and Dugatkin
et al. (1992).
68
Leimar and Tuomi
For graded defence-related traits, synergism in the form of bene®ts shared only between individuals with similar traits does not in itself select for increased expression of these traits, in contrast
with the situation for discrete, two-level traits. Instead, a positive bias, resulting from a directionality in the generalization of the enemy against which the defence is directed, is needed to
enhance the trait. A shift of the minimum of the generalization gradient has been suggested as one
of the main factors responsible for the evolutionary stability of aposematic colouration (Leimar
et al., 1986), and there is also experimental evidence for such a shift (Gamberale and Tullberg,
1996).
For costly defence traits showing strong synergism, a negative bias is very likely. If the joint
e€ect of the population defence level means a radical decrease in the risk of attack, an individual
can gain little additional protection by increasing its investment in defence, but at an evolutionary equilibrium the marginal cost of increased investment must be exactly compensated by
additional protection (Leimar et al., 1986; Guilford, 1994; Tuomi et al., 1994). In general, when
costs vary gradually with investment in a defence trait, evolutionary stability requires that each
individual's level of defence has a suciently high probability of being tested by an attempted
attack. This is most likely to be the case if the total attack rate on the population of victims is not
very much decreased by the defence. Selection for increased investment in defence will be particularly intense when the defence mainly serves to redistribute attacks from more to less defended individuals.
The potential importance of interspeci®c associational e€ects for plant defences has been recognized, particularly in relation to plant mimicry (Rhoades, 1979; Eisner and Grant, 1981;
Launchbaugh and Provenza, 1993; Augner, 1994) and associational refuges (McNaughton, 1978;
Hay, 1986; P®ster and Hay, 1988). Less attention has been directed towards the possible selective
e€ects of herbivore learning and generalization together with quantitative variation in defence
within a plant population.
Many animals, including herbivores, learn to avoid harmful foods by associating primarily the
taste of food with its post-ingestive consequences (Garcia, 1989; Provenza et al., 1990, 1992; Bryant
et al., 1991). There is also evidence that herbivores generalize conditioned ¯avour aversion from
one type of food to another (Launchbaugh and Provenza, 1993). However, there appears to have
been no attempt at direct estimation of a generalization gradient in relation to quantitative variation in plant palatability traits. We suggest that such experiments, of a kind similar to the many
studies of intra-dimensional discrimination learning in animal psychology (reviewed by Purtle,
1973; for taste generalization in rats, see Tapper and Halpern, 1968; Nowlis, 1974), would be of
interest. The presence of a shift of the minimum of the generalization gradient, referred to as a
`negative peak shift' in the psychological literature (Purtle, 1973), could be of relevance for the
evolution of plant defence traits.
Diet selection by herbivores is sometimes a more complex process than simply learned avoidance
of unsuitable food. Mammal grazers regularly feed on plants containing toxins, but avoid harmful
e€ects by regulating intake in accordance with the toxicity (Bryant et al., 1991; Launchbaugh and
Provenza, 1993). A likely consequence is a concentration of herbivory to the least defended
members of a plant population. Thus the `grazing intensity gradient' would show a shift of the
minimum, resulting in a selection pressure for increased investment in defence. The phenomenon
might apply quite generally to mammalian herbivores in relation to the concentrations of toxic
secondary metabolites in food plants. If this is indeed the case, plant defences against mammalian
herbivores may partly have evolved by synergistic selection.
We conclude that synergistic selection may well have an important in¯uence on the evolutionarily stable level of graded plant defence traits. The general tendency ought to be that a strong
mutualistic bene®t causes a negative bias, which then results in low defence investment, whereas a
Synergistic selection
69
redistribution of herbivores to the least defended plants may produce a positive bias and thus could
lead to high investment.
Our analysis can also be applied to certain social interactions where synergistic selection has
been suggested to be important (Maynard Smith, 1989). An individual's decision of whether or not
to join in a `synergistic project' is perhaps best viewed as a discrete trait, and both theory and data
point to synergistic selection as the evolutionary force behind the formation of groups of many
kinds. The thing to look for is an increased survival or reproduction for group members as
compared to singletons. Examples include joint parental care (Houston and Davies, 1985), joint
colony-founding (pleometrosis) in ants (Bartz and HoÈlldobler, 1982), mating coalitions in male
lions (Packer et al., 1988) and ¯ocking to reduce predation risk (Lima and Dill, 1990). It is another
matter altogether whether the activities performed in synergistic projects can be explained by, or
are at least enhanced by, synergistic selection. Such activities or behavioural tendencies are often
best viewed as graded traits. Typically, singletons also perform these activities and, as far as is
known, tend to invest more than group members. For instance, a single female shows a higher rate
of brood provisioning than one working together with a mate (Houston and Davies, 1985), and
lone individuals devote more time to vigilance than ¯ock members (Lima and Dill, 1990). This
suggests a negative bias, and there are reasons to expect it. A group member must bear the full cost
of its e€ort, but gains from the e€orts of others, which tends to reduce the marginal bene®t of an
increased investment. However, we do not claim that there cannot be a positive bias for activities
making up synergistic projects, but only that we are not aware of any documented examples.
To gain some perspective, it is worthwhile noting that interspeci®c mutualisms often entail
activities shown only in the context of an interaction or traits having no value outside the interaction. Apart from being asymmetric, with each partner performing a di€erent type of activity,
interspeci®c mutualism shows much similarity with the kind of synergistic projects we have discussed. With regard to the (discrete) decision of whether or not to enter into a mutualistic relationship, synergistic e€ects will operate, in the sense that the bene®ts can only be gained by joining
with a partner. We must, however, also ask ourselves whether synergism can be responsible for
maintaining positive values of the (graded) investments of the partners. As far as the basic principle
of interspeci®c mutualism is the trade of one service for another, the ®tness components are, at
least to a ®rst approximation, additive: a bene®t depending on the partner's trait minus a cost
depending on the individual's own trait. This makes synergistic selection less likely as a primary
explanation for the evolutionary stability of such traits. The alternative would be that individuals
regulate their mutualistic investments in relation to information obtained about the partner's
investment. Such a situation must then be analysed as a game with a time structure (cf. Axelrod
and Hamilton, 1981; Bull and Rice, 1991).
In conclusion, although synergistic selection is likely to act in many contexts, there are few cases
where a positive synergistic bias has been clearly identi®ed. However, for defence-related traits, the
process of predator/herbivore generalization may be important in producing a positive bias.
Acknowledgements
We thank M. Augner for valuable comments and G. Gamberale for help in locating discrimination
learning studies. This work was supported by the Swedish Natural Science Research Council.
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