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1
Expanded Social Fitness and
Hamilton’s Rule for
Kin, Kith, and Kind
DAVID C. QUELLER
Inclusive fitness theory has a combination of simplicity, generality, and
accuracy that has made it an extremely successful way of thinking about
and modeling effects on kin. However, there are types of social interac -
tions that, although covered, are not illuminated. Here, I expand the
inclusive fitness approach and the corresponding neighbor-modulated
approach to specify two other kinds of social selection. Kind selection,
which includes greenbeards and many nonadditive games, is where
selection depends on an actor’s trait having different effects on others
depending on whether they share the trait. Kith selection includes social
effects that do not require either kin or kind, such as mutualism and
manipulation. It involves social effects of a trait that affect a partner, with
feedback to the actor’s fitness. I derive expanded versions of Hamilton’s
rule for kith and kind selection, generalizing Hamilton’s insight that we
can model social selection through a sum of fitness effects, each multi -
plied by an appropriate association coefficient. Kinship is, thus, only one
of the important types of association, but all can be incorporated within
an expanded inclusive fitness.
H
amilton’s rule and the associated concept of inclusive fitness
(Hamilton, 1964a) have provided an extremely successful way of
thinking about and modeling social evolution (West et al., 2007b).
Department of Biology, Washington University, St. Louis, Mo 63130. E-mail: queller@biology2.
wustl.edu.
5
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6 / David C. Queller
There are a number of reasons why this is true. It is simple, and therefore,
users can apply its logic with ease; nevertheless, it is quite general. In
some versions, it is exact, and even less exact versions are not necessar-
ily a strong concern for field or comparative studies, where we can only
measure crudely anyway. Crucially, it is often sufficiently independent of
the genetic details, such as dominance and recessiveness, the number of
genes, and their allele frequencies. This allows it to become an important
tool of the phenotypic gambit (Grafen, 1984) and optimality approaches. It
can be used for traits where we do not understand the underlying genetics,
and, in fact, we never fully understand the genetics. It also conveniently
separates selection into two kinds of summary terms: effects on fitness
(costs and benefits) and population structure (relatedness). This separation
makes the process easy to think about and the equations easy to apply.
Inclusive fitness points to cause-effect relations, specifically to the various
effects caused by the actor’s behavior. This focus on what the actor can
control allows us to tie into the long biological tradition of thinking of
actors, or their genes, as agents. Additionally, it tells us that these agents
should appear to be trying to maximize inclusive fitness.
Inclusive fitness is not perfect. It does not provide the most natural
way to handle explicit dynamics. It usually takes population structure as
a given, and when it does this, it may not yield insight into how popula -
tion structure emerges. Although, in principle, it covers everything, its
summary parameters may sometimes conceal interesting complexity. Even
its treatment of social causation is incomplete. For example, although it
would include any benefits from mutualism in with other effects on the
actor’s direct fitness, it does not usually separate out these effects or pro -
vide a causal treatment of them. Many or all of these deficits are fixable,
although sometimes at the cost of making the models more complex and
therefore, losing some of the advantages of the approach. In this paper, I
will try to expand the types of social causation covered explicitly, while
trying to maintain reasonable simplicity. For example, I will show how
to specify mutualistic social effects in a category that I call kith selection,
named after the largely archaic word for acquaintances, friends, and
neighbors.
I will also argue that it is often worth distinguishing kin and kith
selection from what I call kind selection, partly to properly capture social
causality and partly because these forms of social selection act in very
different ways. Inclusive fitness, developed by Hamilton (1964a), is
closely associated with the process of kin selection, named by Maynard
Smith (1964). However, they are not the same thing. Inclusive fitness is
an accounting method and maximand. Kin selection is a process, and it
can be described by other kinds of accounting. The obvious example is
the neighbor-modulated approach that uses the same fitness partition as
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Expanded Social Fitness and Hamilton’s Rule for Kin, Kith, and Kind / 7
inclusive fitness but groups by effects received rather than effects given
(Taylor and Frank, 1996). However, models with other fitness partitions,
such as multilevel selection models, also often describe kin selection
(Price, 1972; Hamilton, 1975; Wade, 1980; Queller, 1992c). Another reason
is that inclusive fitness includes standard selection where there are no
kin effects at all. Finally, kin selection, when interpreted as resulting from
genomewide genealogical relatedness, does not cover all indirect effects.
The most commonly cited examples are greenbeard genes (Dawkins,
1976b), which act based on their own identities rather than pedigree kin-
ship. These are commonly grouped under kin selection, but I will argue
that greenbeards are one example of the distinct phenomenon that I will
call kind selection.
Specifically, I derive an expanded Hamilton’s rule (1964a) or inclusive
fitness effect (and neighbor-modulated fitness effect) as
– c + ∑ b* r + ∑ d * s + ∑ m* f > 0. (1)
The first two terms look like the standard Hamilton’s rule but are not
exactly the same, because some social effects have been split off into addi-
tional terms. Here, −c is nonsocial direct fitness but does not include some
social components of direct fitness. These fitness effects, m (for mutualism
or manipulation), are multiplied by a feedback coefficient f to give the kith
selection term. Also, kind effects d (deviation from additivity) multiplied
by a kind coefficient s (synergism) are split off. These include greenbeard
effects that are normally in indirect fitness and some frequency-dependent
effects that are usually placed in direct fitness. This is an expanded form
in two senses. First, it covers more kinds of social selection or at least, it
covers more in a causal manner. Second, it expands out into the number of
terms needed to describe this causation with two kinds of distinct terms:
selection terms relating social actions to fitness components and associa -
tion coefficients that essentially describe the relative heritability of those
effects. I continue to call this a version of Hamilton’s rule because of this
key similarity.
In introducing kith and kind selection, I am not claiming to have
discovered new forms of social selection. All of the social situations that
I discuss have been explored in other ways. Nor should this treatment be
viewed as invalidating the standard inclusive fitness approach; it can be
viewed as a more detailed version of that approach. My goal here is to
present a useful classification of social behaviors and derive a common
theoretical framework that partakes of the many advantages of the inclu -
sive fitness approach.
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8 / David C. Queller
MODELING SOCIAL EFFECTS
In this section, I illustrate the method I use to partition different kinds
of selection using the methods of Queller (1992a,b). The approach closely
parallels the causal modeling approach pioneered by Lande and Arnold
(1983), which is further developed for social traits in the indirect genetics
effects approach (Moore et al., 1997; Bijma and Wade, 2008; McGlothlin
et al., 2010). I begin with Price’s (1970) equation 9 for the change in the
average of some quantity—here, the average breeding value for a trait,
G , which can be for a single gene or multiple loci affecting a trait. Price’s
(1970) equation is an identity that always holds, but additional assump -
tions are often made. Here, I follow the common practice of ignoring its
second term, which can incorporate effects like meiotic drive or change
in environment, to focus on organismal selection and adaptation. Price’s
(Hamilton, 1964a) equation can then be written as
W∆G = Cov(W,G), (2)
showing that breeding value is expected to increase if it covaries positively
with fitness. Now, consider a social trait where an individual’s fitness is
affected by both his own trait and the trait of a partner. For the moment,
we will assume that we know each individual’s genes for the trait, with a
breeding value of G for the focal individual and G′ for its partner. Fitness
can be written in the form of a regression
W = α + βWG ′⋅GG + βWG ′⋅GG ′ + ε. (3)
The α is the intercept, and it can be conceived of as the base fitness before
any social actions. The β symbols are partial regression coefficients for the
effect of the focal individual’s genes and the partner’s genes on the focal
individual’s fitness, each holding the effect of the other individual con -
stant. The ε is the residual or remainder, including the effects of any other
causes and any truly random effects. The regression equation might make
it seem that we are interested purely in estimation, but it is also gives us a
model of fitness that, depending on the predictors, can be useful, useless,
or even misleading.
Substituting Eq. (2) into expression (1) yields
W∆G= Cov(α ,G) + Cov( βWG⋅G'G,G) + Cov( βWG'⋅GG',G) + Cov( ε ,G).
(4)
The first covariance drops out, because a constant has zero covariance. The
last term drops out, because the residuals of a regression are uncorrelated
with the predictor variables. If we are thinking in terms of a model, we
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Expanded Social Fitness and Hamilton’s Rule for Kin, Kith, and Kind / 9
assume that ε and G are uncorrelated. Next, we can pull the constant β
outside of the covariance terms to give
W∆G= βWG⋅G ′ Cov(G,G) + βWG'⋅G Cov(G,G ′). (5)
Average breeding value DG will increase when βWG∙G′Cov(G,G) +
βWG′∙G′Cov(G′,G) > 0. Dividing through by the first covariance gives
βWG∙G′ + βWG′∙GCov(G′,G)/Cov(G,G) > 0 or
(6)
βWG⋅G' + βWG' ⋅ G βGG' > 0.
This is Hamilton’s rule, with the direct effect on fitness βWG.G′, the indi-
rect effect of a partner βWG′∙G, and a regression coefficient of relatedness
βGG′. It is a neighbor-modulated fitness form of Hamilton’s rule, which
totes up effect on each individual, but it can be rearranged under quite
general conditions to an inclusive fitness form that switches all of the
primes and nonprimes in the second term and thus totes up the effects of
each individual (Frank, 1998).
Because we assumed we knew the genes, this form is extremely gen-
eral. It belies the claim that is occasionally made that inclusive fitness
requires many assumptions (Nowak et al., 2010). Those claims are usually
made about phenotypic versions that are used when we do not assume
that we know the genetic basis of the traits, and the same limitations
would generally apply to alternative models faced with that assumption.
Therefore, proponents of inclusive fitness can rightly refute the claim of
limited generality. However, one of the main appeals of inclusive fitness
is that it can often be used without knowledge of the genes, and therefore,
we will consider the phenotypic gambit shortly.
I have dwelled a bit on already published math (Queller, 1992a,c),
because every subsequent derivation in this paper, for which I will not
show the math, follows an exactly parallel procedure consisting of the
following steps:
(i) Write a regression model for the actor’s fitness.
(ii) Substitute that expression for fitness into the abbreviated Price’s
(1970) equation.
(iii) Divide the covariance into separate terms, one for each term of
the regression.
(iv) Drop out the α (intercept) term.
(v) Drop out the ε (residual) term provided that Cov(G,ε) = 0.
(vi) Extract the regression coefficients from the covariances.
(vii) Ask when D G > 0.
(viii) Divide through by the covariance associated with actor’s fitness.
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10 / David C. Queller
We could stop at step (vi) to preserve a more general equation that
predicts actual change in G, but I will follow the customary step in inclu-
sive fitness analysis of asking the more restricted question of when G
increases. Either way, the crucial step turns out to be step (v). This is the
only step that invokes an assumption, which is Cov(G,ε) = 0. This condi-
tion will, therefore, determine whether an exact Hamilton-type (1964a)
result can legitimately be obtained. When it does drop out, we end up
with an equation with the desired neat separation between fitness and
structure terms, and therefore, I have called this the separation condition
(Queller, 1992c).
CAUSALITY
There is nothing preordained about the predictors used in the deriva-
tion above. We could attempt to get a result from any equation predicting
or describing fitness. Indeed, it was technically unnecessary to include the
partner’s breeding value. If we use only the focal individual’s breeding
value (W = α + βWGG + ε) and follow steps (ii)–(viii), above, we show that
G > 0 when βWG > 0. This does not take us far from Price’s (1970) equation,
but it has exactly the same level of validity and accuracy as the inclusive
fitness result derived above. Why then do we prefer the inclusive fitness
result? The first reason, to be treated shortly, is that leaving out the part-
ner does not work when we try to play the phenotypic gambit. The other
reason is that including the partner can provide some additional causal
explanation. We are no longer just saying certain genes are associated with
fitness; we are giving a breakdown of how that association is caused. It is
this causal feature that I want to expand to include more than kin effects.
To illustrate the point about causality, consider another model of
fitness based on the individual’s breeding value G and the phase of the
moon, represented by M. If we substitute W = α + βWG∙MG + βWG∙GM +
ε into Price’s (1970) equation, steps (ii)–(viii) lead us to the conclusion that
D G > 0 when βWG∙M + βWM∙G βGM > 0. The first term remains the effect
of the actor’s genes on its fitness, but the second term is now the effect of
the moon phase and is multiplied by βGM, a sort of moony relatedness
linking breeding value and phase of the moon. This model is just as correct
as the first two that we considered (the ε term must drop out, because G
is one of the predictors); however, no one would consider it very useful,
because moon phase is unlikely to have any causality. Even if the phase
of the moon had some effect on fitness (in which case, we would need to
take it into account for a full evolutionary explanation of the trait), the
actor would still be a passive player. There is nothing the actor can do to
alter the phase of the moon, and therefore, for optimality arguments, we
can ignore it.
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Expanded Social Fitness and Hamilton’s Rule for Kin, Kith, and Kind / 11
Any causes can be included (Queller, 1992a; Frank, 1998). In this
respect, my approach is similar to that taken by the indirect genetic effects
(IGE) school of social evolution, which can recover versions of Hamilton’s
rule (1964a) in very similar ways (Moore et al., 1997; Bijma and Wade,
2008; McGlothlin et al., 2010). IGE is an extension of quantitative genet-
ics to social evolution, and quantitative genetics has always engaged in
partitioning evolution into causal components. My interest here is not in
all possible causes but in those that most clarify the role of selection on
an actor’s social behavior. Thus, in the same way that I exclude the moon
phase from the model, I will not generally explore byproduct social effects.
A lion that kills a zebra benefits local vultures, and this can influence
their traits and fitness; therefore, the killing has a social aspect. However,
the vultures do not influence the killing, and the evolution of that killing
behavior (as opposed to the incidental effects on vulture traits) does not
need to take vultures into account. An important exception is when there
are byproducts with feedbacks on the actor’s fitness.
PHENOTYPES AND SOCIAL CAUSES
Much of the value of inclusive fitness stems from its use in the phe -
notypic gambit (Grafen, 1984). If we know costs, benefits, and related-
ness, we can usually make good predictions about what kinds of traits
will be favored, even if we do not understand the underlying genetics.
Such approaches are sometimes denigrated by theoreticians, who prefer
precision and mathematical rigor over all else, but for understanding the
real world, it is essential. To deny this is to deny that Darwin understood
anything about adaptation, because all he had to work with was the fit
of phenotypes to their environments and a knowledge that some form of
heredity exists.
When kin are affected, the phenotypic gambit requires indirect effects.
If we use only the actor’s phenotype P to model its fitness (W = α + βWPP
+ ε) and follow steps (ii)–(viii), we predict that D G > 0 when βWP > 0. This
predicts that altruism cannot evolve, because a cost to self means a nega -
tive βWP. However, we know that altruism can evolve. Mathematically,
the reason that the phenotypic gambit fails here is step (v), the separation
condition (Queller, 1992c). After the effect of the actor’s behavior on its
own fitness is removed, the residual ε is correlated with genotype G if
the interaction involves relatives. The partner’s fitness W is affected by
the partner’s behavior P′, which is correlated with G′, which, in turn, is
correlated with G when the individuals are relatives.
The solution of inclusive fitness theory is to include the partner’s
phenotype in the fitness model: W = α + βWP∙P′P + βWP′∙PP′ + ε. Follow-
ing steps (ii)–(viii) now yields
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12 / David C. Queller
Cov(G, P')
βWP⋅P' + βWP'⋅P > 0.
(7)
Cov(G, P)
Here, the two regression terms represent the cost and benefit like in
(6), except that we now use phenotypes instead of breeding values. The
relatedness coefficient is now a more complicated ratio of covariances
(Michod and Hamilton, 1980). The ratio makes intuitive sense, however,
particularly if we think of phenotype being one for performing the behav -
ior and zero for not performing. Then, relatedness is essentially the ratio
of the actor’s breeding value when the partner performs the behavior to
its breeding value when the actor performs the behavior. Switching this
neighbor-modulated version to inclusive fitness gives
Cov(G, P')
βWP⋅P' + βW'P⋅P > 0. (8)
Cov(G, P)
Seger (1981) discusses the relationship among these regression coefficients.
KITH SELECTION
Hamilton’s rule (Wade, 1980) is normally applied to kin selection,
with the relatedness covariances arising from common descent (Hamilton,
1964a). However, there is nothing in the derivations that limits it to this
case. The primary limitation, as I will show, is additivity of the two fit -
ness components βWP∙P′ and βWP′∙P . Within that constraint, the gene-
phenotype associations represented in the covariance ratio could have
any cause. Queller (1985) pointed out that the phenotypic covariance ratio
could also be used to describe reciprocity. Frank (1994, 1998) argued that
mutualism or indeed, any correlated interaction could be described by a
version of Hamilton’s rule, and argued for a general informational view
of relatedness coefficients. Fletcher and Doebeli (2009) further developed
these themes and argued for abandoning genetic relatedness as the main
key to cooperation in favor of correlated interactions. I will develop those
themes here, grouping the mechanisms under the heading of kith selec -
tion—selection involving neighbors who need not be kin or similar in
kind.
Fig. 1.1 illustrates the connections. Under kin selection, an arrow
would connect G and G′. However, even if there is no kinship, P′ and P
can still be used to model or predict the focal individual’s fitness W, result-
ing in expression (7) or (8). If the actor’s phenotype predicts its partner’s
phenotype P′ (heavy arrow), this generates a covariance between G and
P′ (or G′ and P), making the relatedness coefficient in expressions (7) and
(8) nonzero. However, we now allow P′ to represent an entirely differ-
ent behavior than P, coded for by different kinds of genes that possibly
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Expanded Social Fitness and Hamilton’s Rule for Kin, Kith, and Kind / 13
FIGURE 1.1 Kith selection. An actor’s phenotype P
can influence P′, its partner’s phenotype (often for a
different trait), by manipulation, partner choice, and
partner fidelity feedback (heavy arrow). These com-
ponents create an association between phenotypes P
and P′ and therefore, also between P′ and G required
in Eq. (7) [or P and G′ in Eq. (8)].
belong to different species. P could be carbon production by an alga in a
lichen, and P′ could be nitrogen production by its fungal partner. The link
between P and P′ could come through several means, including the two
kinds of mechanisms that can be involved in reciprocity and mutualism:
partner choice and partner fidelity feedback (Sachs et al., 2004). If coop -
erators choose to associate with cooperators and reject noncooperators,
this situation will generate a correlation between P and P′. The same will
be true if individuals join at random, but those who give larger benefits
induce their partners to return larger benefits. Finally, the actor could
influence the partner’s phenotype through pure manipulation.
Kin selection occurs through genetic identity, and can occur even if
the partner does not express the behavior. Indeed, conditional helping of
partners who do not help underlies some of the most important manifesta-
tions of kin selection, such as social insect workers helping queens. Kith
selection, in contrast, requires phenotypic expression by the partner. The
focal individual can affect its own fitness in kith interactions only through
feedbacks. It affects the phenotype of the partner—whether by manipula -
tion, partner fidelity, or partner choice—and the partner’s phenotype feeds
back on the actor’s fitness. The essential role of phenotypes is brought out
by modeling the partner’s phenotype as P′ = α + βP′PP + ε and substituting
it into the covariance ratio of expression (7):
Cov(G, α + β P'⋅P P + ε )
(9)
βWP⋅P' + βWP'⋅P > 0.
Cov(G, P)
Splitting the covariance, dropping the α and ε terms, and extracting the
β coefficient yields
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14 / David C. Queller
βWP⋅P' + βWP'⋅P β P'⋅P > 0.
(10)
We now have Hamilton’s rule with the usual effect on fitness of self
(βWP∙P′) and partner (βWP′∙P), but instead of genetic relatedness, there
is a structural feedback coefficient βP′P that tells how much the actor’s
behavior influences or is correlated with the relevant behavior of its part -
ner. Remember that the phenotypes may be entirely different things (per-
haps cooperative carbon production by an alga and cooperative nitrogen
production by a fungus) but that a correlation can still exist between the
two forms of cooperation. The actor’s cooperation can pay, even if it pays
a cost (βWP∙P′ 0)
partner behaviors with positive benefits (βWP′∙P > 0).
If the partner is unrelated or in a different species, the standard
Hamilton’s rule (1964a) would simply require βWP > 0, where βWP
includes any effects of the actor’s behavior that operate by feedback
through partners. That result is perfectly correct and does not need to be
altered, but it does not capture the social causation. With expression (10)
we can see that the actor increases its own fitness by a pathway that, like
kin selection, involves social benefits and some kind of association.
Expression (10) is an expanded version of Hamilton’s rule that cap-
tures kith selection, but it is a neighbor-modulated form, with effects on
a focal actor rather than an inclusive fitness form that attributes all effects
to a focal actor. Neighbor-modulated forms are often better for modeling
(Taylor and Frank, 1996), whereas inclusive fitness forms are often better
for intuition and insight. To obtain an inclusive fitness form that tells how
actors value a partner’s fitness, we need to include the partner’s fitness.
I distinguish two cases. In the first case, the partner’s fitness is inci -
dental for the actor, affected only as a side effect of the actor’s effect on the
partner’s phenotype (dashed arrow in Fig. 1.1). The effect of the actor’s
behavior on partner fitness is the product of its effect on the partner’s
phenotype βP′∙P and the effect of the partner’s phenotype on the partner’s
fitness βW′∙P = βP′∙P βW′∙P’. Therefore, βP′∙P = βW′∙P/βW′∙P. which can be
substituted into expression (10) to give
βW'P
βWP⋅P' + βWP'⋅P >0
βW'P'
or, shifting the denominator,
βWP'⋅P
βWP⋅P' + βW'P > 0.
βW'P'
(11)
Now, we have the actor’s nonsocial effect on its own fitness and its kith
effect on its partner’s fitness βW′∙P through its effect on the partner phe-
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Expanded Social Fitness and Hamilton’s Rule for Kin, Kith, and Kind / 15
notype. The latter is multiplied by a regression ratio that tells how the
actor values those fitness effects on the partner. This kith or feedback
coefficient shows that the actor values effects on its partner’s fitness (by
P and P′) only to the degree that they are associated with fitness returns
to itself. This makes sense as a scaling factor for the actor, when it acts
through affecting the partner’s phenotype. The effect on the partner’s fit-
ness is incidental, but when the feedback coefficient is positive, the actor
gets a positive feedback by aiding its partner. The feedback need not be
positive. We could use the equation to describe manipulation that harms
the partner but benefits the actor.
A second possibility is that the actor gains not so much by affecting
some particular cooperative trait of the partner but by affecting its fitness
in general. That is, effects on the partner’s fitness are necessary for the
feedback to the actor, not just an incidental effect. In a lichen, an alga that
produces more carbon may make its fungal partner fitter, and fitter fungi
may make more nitrogen that benefit the alga. Here, we write fitness as W
= α + βWP∙W′P + βWW′∙PP′ + ε and follow steps (ii)–(viii) to get a simpler
result (12):
βWP⋅W' + βW'P βWW'⋅P > 0.
(12)
Here, the actor affects its own fitness (βWP∙W′) and the fitness of its partner
(βW′P), with the latter multiplied by a feedback coefficient of βWW′∙P that
describes how much partner’s fitness affects the actor’s fitness, partial-
ing out the nonsocial effects of the actor’s behavior (which are included
in the first term). This is a more intuitive result than expression (11), but
it is really just a special case of it, where P′ = W′. In both cases, the actor
values its partner’s fitness according to how it affects its own fitness, but
in one case, it is mediated through some intermediate trait. The difference
may be important for the evolution of complex mutualisms, which may
be much easier to evolve when any benefits to partner’s fitness feed back
to the actor than if it occurs through only one or a few traits.
Expressions (10)–(12) provide Hamilton’s rule forms to handle kith
selection. As suggested previously, both reciprocity (Queller, 1985; Fletcher
and Zwick, 2006) and mutualism (Frank, 1994, 1998; Fletcher and Zwick,
2006; Foster and Wenseleers, 2006) can be addressed using such results.
The analysis here adds at least three features. First, manipulation can
be added to the kinds of interactions treated. Second, the results can be
expressed not just in terms of neighbor-modulated fitness but also in
terms of inclusive fitness. Third, I have put these kinds of results into the
common language of regressions and covariances used by quantitative
geneticists. The regressions of phenotype on fitness are selection differ-
entials. The coefficient that scales the second regression has to do with
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16 / David C. Queller
heritability; it is actually a ratio of the heritability of the nonsocial effect on
self and the heritability of the social effect of, or on, one’s partner. This has
been shown previously for relatedness in the kin selection form, where the
heritability of the indirect selection effect is lowered, because the partner
is less likely to pass on the trait (Queller, 1992c). For kith selection, the
heritability through social effects is lowered by the fact that the actor’s
phenotype does not perfectly predict the partner’s phenotype.
KIND SELECTION
Another type of selection that is usefully considered separately from
the other two is what I call kind selection (Strassmann et al., 2011a). The
first example is the greenbeard gene, which has three effects: It produces
a cue (like a greenbeard), perceives that cue in others, and directs some
special action to those cue bearers (Hamilton, 1964a). Once viewed more
as a thought experiment than as a real possibility (Dawkins, 1976b), real
greenbeards are being identified with increasing frequency (Keller and
Ross, 1998; Queller et al., 2003; Sinervo et al., 2006; Smukalla et al., 2008;
Strassmann et al., 2011a). There are greenbeards that help others with the
same trait, and there are greenbeards that harm others with different traits.
There are both facultative greenbeards that take special actions to like or
unlike interactants and obligate greenbeards that perform a general action
that has different effects on like and unlike (Gardner and West, 2010).
Table 1.1 shows many differences between greenbeard or kind selec-
tion relative to kin selection (and also, for completeness, to kith selection).
I will focus on greenbeards for the moment and come to other forms of
kind selection later. The key difference is that, where kin selection works
through genealogical kin of the actor, kind selection operates on those
who specifically possess the same trait as the actor. Those two features
can be correlated of course; kin tend to have similar genes that will tend
to produce similar traits. However, in one case kinship is fundamental,
and in the other case, phenotypic similarity is fundamental. Greenbeards
can be favored even among nonkin. Conversely, kin selection can operate
even in the absence of having actual traits in common; often, one kind of
individual will express the trait, such as a worker bee’s behavior, to benefit
others who specifically do not express the trait (queens and males) but
are nevertheless kin.
Where kin selection operates through cues that correlate with identity
by descent, kind selection operates based on all identities (both by descent
and by state). Indeed, identity by trait might be a better description; two
separate loci producing the same greenbeard trait could work just as
well as one. Because identity by descent is normally the same across the
genome, kin-selected genes across the genome agree, and complex coop-
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TABLE 1.1 Kin and Kind Discrimination
Kin Kind Kith
Behavior Action with Interaction with Feedback from
partner partner partner
Key partner Possession of Expression of Expression of other
feature same allele same trait trait
Beneficiaries Genealogical kin Same trait or Any
kind
Role of genetic By descent only All identities None
identity (but really trait
identity)
Kinship required Yes No No
Genes Often multigenic Often one or Often multigenic
linked complex
Relatedness Same across Higher at kind None
or genetic genome locus
correlation
Complex Possible Unlikely Possible
cooperation
Additive fitness Yes Usually no Possible
effects
Frequency Usually no Usually yes Possible
dependence
eration can easily be built. The situation with greenbeards is more com -
plex. An altruistic greenbeard allele is related by r = 1 to its beneficiaries
and therefore may give more aid compared with what would be favored
at other loci not related to that degree. There has been some debate over
whether greenbeards are outlaws with respect to the rest of the genome
(Alexander and Borgia, 1978; Gardner and West, 2010). However, the
important point here is that no other locus, unless very closely linked,
would build on a greenbeard’s identification of beneficiaries. More pre-
cisely, if it did build on this identification, it would only be to the extent
that the greenbeard cue identified kin. As a result, we do not expect a lot of
complexity from greenbeards—they are generally limited to simple traits.
The last two rows in Table 1.1 require a bit more explanation.
Greenbeard traits depend on all identities, not just identity by descent,
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18 / David C. Queller
and therefore, they usually depend on the frequency of the trait in the
population (facultative helping greenbeards can be an exception) (Gardner
and West, 2010). Kin selection is typically frequency independent; the
condition −c + rb > 0 includes no allele frequencies, because the fraction
of alleles identical by descent is independent of gene frequency. However,
kin selection models with costs and benefits that are nonadditive typically
show frequency dependence. I will argue below that this is because these
nonadditive models include a form of kind selection.
I will begin by comparing facultative and obligate greenbeards and
then build an argument (Queller, 1984) that obligate greenbeards are
insensibly different from more general forms of kind selection. In faculta-
tive greenbeards, the actor first classifies its partners and then performs
the appropriate behavior. Fire ant workers identify queens lacking their
greenbeard allele and then attack them (Keller and Ross, 1998). Obligate
greenbeards, in contrast, perform a behavior to all interactants without
prior identification, but the behavior has different effects on partners
who are greenbeards versus those who are not. Bacteriocins provide
many examples of obligate harming greenbeards (Riley and Wertz, 2002;
Gardner and West, 2010). Many bacteria have several tightly linked genes
that make a poison, which some cells release at times of stress, and also
make an antidote to the poison, which they keep private (Riley and Wertz,
2002). Cells lacking the complex are killed by the poison, freeing up
resources for those who have it. This greenbeard is obligate, because the
cells produce the poison and antidote independently of who their partners
are; however, the poison adversely affects only those that lack the gene
complex (Gardner and West, 2010).
The key feature of a greenbeard is that it gives some fitness benefit to
partners who share the trait that it does not give to partners who lack the
trait. In a two-interactant payoff matrix, this can be represented as in Fig.
1.2. The simplest greenbeard effect does not require this full complexity. It
could be represented with the d parameter alone; d is what a greenbeard
cooperator gets when playing another greenbeard cooperator, and it is
generally the sum of the cost of greenbeard cooperation and the benefit
of being helped. These are not the c and b variables in the matrix, which
instead represent any general costs and benefits, not specific greenbeard
ones. Consider the Ti plasmid of Agrobacterium tumefaciens, an obligate
helping greenbeard (Gardner and West, 2010). It harbors a number of
genes that induce its plant host to produce a tumor and produce a food
source in the form of opines (White and Winans, 2007; Platt and Bever,
2009). The costs of these behaviors are represented by c in Fig. 1.2—they
apply whether there are nonbearers present or not. Any benefits that are
public goods benefiting bearers and nonbearers alike—perhaps tumor
production—are represented by b. However, the gains from opine pro-
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Expanded Social Fitness and Hamilton’s Rule for Kin, Kith, and Kind / 19
FIGURE 1.2 General payoff matrix for the two persons expressed in terms of
general effects on self (c), general effects on partner (b), and an extra effect (d) that
applies only when both partners perform the behavior.
duction are a greenbeard effect, because opine catabolism is also coded
on the Ti plasmid; nonbearers do not benefit. This targeted benefit must
be represented by d. Thus, greenbeard effects may be superimposed on
nongreenbeard effects, and they can be viewed as nonadditive fitness
parts. When you are both an actor and a recipient, the payoff is not the
−c + b that would come from adding the separate effects, but −c + b + d.
The payoff matrix in Fig. 1.2, required to represent greenbeard effects,
is actually the general payoff matrix for two interactants (Queller, 1984).
With three parameters plus zero, it covers exactly the same ground as any
four-parameter matrix. Every such game can be expressed as a general
effect on self c, a general effect on partners b, and a specific effect that
applies only when both actor and partner perform the behavior d. That
means that any nonadditive two-person game, one that requires the com -
plexity of a d parameter, has the greenbeard-like character of giving some
fitness gain (or loss) to those who share the trait but not to others (Queller,
1984). Additionally, most of the games that have occupied the interests of
evolutionary theorists over the years are nonadditive. Long ago, I noted
this similarity and toyed with the idea that all these games represent
forms of greenbeard selection (Queller, 1984). That had the problem of
subsuming the larger familiar category under the smaller—then nearly
nonexistent—category of greenbeard. It might be more palatable to do
the opposite (subsume greenbeard effects under the other type), but the
problem here is that there really is no name for the process that underlies
selection in these games. They are frequency dependent and nonadditive,
but those terms do not capture the reason why the process works (the way
kin selection does for affecting relatives). Kind selection does capture the
feature, common with greenbeards, that an actor has different effects on
its own kind than on different kinds.
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20 / David C. Queller
Although I motivated this kind selection grouping using nonadditiv -
ity and frequency dependence, the similarities extend throughout Table
1.1. Most notably, the fitness increment (or decrement) represented by d
depends on expression of the trait by one’s partner. This involves all iden -
tities rather than just identity by descent, and kinship is not required. The
similarity between partners receiving the d effect is generally higher than
genealogical relatedness at the loci causing the behavior, but not at the rest
of the genome. Cooperation that results from this single-trait similarity is
expected to be relatively simple cooperation and not the highly complex
cooperation that can lead to major transitions.
As an example, consider the Hawk–Dove game (Fig. 1.3A) (Maynard
Smith and Price, 1973). There is some contested resource worth V fitness
units at stake. Hawks fight, gaining all of the fitness units against doves,
whereas two doves divide them peaceably. Two hawks will fight each
other; a random one of them gets the resource, and the other gets injured,
suffering fitness loss I. We can convert to the form of Fig. 1.3B by subtract-
ing V/2 from all entries to get Fig. 1.3B. We can now see that being a hawk
adds V/2 to your own fitness, subtracts V/2 from your partner’s fitness,
and subtracts an additional I/2 only when both partners are hawks. Thus,
the d term here is negative, representing an antigreenbeard effect of harm -
ing one’s own type. A negative d means negative frequency dependence,
with strategies being more favored when rare, leading to the possibility
of polymorphism.
An example of a positive d would be two ant foundresses cooperat-
ing in colony establishment. Groupers pay a cost of searching for other
groupers (c term in Fig. 1.2) and may also impose a general cost on all
potential partners as they negotiate or figure out who is a grouper and
who is a loner (the b term, likely negative in this case). However, there
are also synergisms that can apply to two groupers that associate. For
example, if one dies before the first workers hatch out, the other inherits
those workers, getting a double brood, an advantage that loners never get.
Many such group effects, such as selfish-herd defense (Hamilton, 1971),
can be viewed in this way.
Warning coloration in distasteful insects provides a more elaborate
example (Queller, 1984; Guilford, 1985). A bright individual is more likely
to be seen by a predator (c term). If eaten, it will teach the predator that
insects like this taste bad. That might provide some general benefit b to
both bright and dull forms, but warning coloration will not evolve for that
reason. It is favored if an eaten bright bug teaches the predator specifically
about bright bugs being bad. This is a positive d, a benefit that bright bugs
confer only on other bright bugs.
I do not include all game theory under kind selection, only games
between individuals with the same trait options, with nonadditive effects.
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Expanded Social Fitness and Hamilton’s Rule for Kin, Kith, and Kind / 21
FIGURE 1.3 Payoffs for the Hawk–Dove game in (A) conventional form and (B)
the form of Fig. 1.2, emphasizing that there is a nonadditive effect of both partners
performing the behavior, d = I/2.
Games between individuals with different roles, such as male and female,
that express different traits are better considered as kith selection. Also
excluded from kind selection are some frequency-dependent effects in
multi-interactant games if the effects of an individual’s behavior are the
same on both like and unlike partners (Smith et al., 2010a).
How should we model kind effects? There are many ways, with game
theory having been the most popular. Even within the inclusive fitness
approach, there are multiple options. Frequency-dependent effects are
often incorporated into direct fitness. Greenbeard effects, in contrast, are
usually attributed to indirect fitness through the partner. This is odd given
that these two kinds of effects are so similar, but it is because d effects are
really joint effects of the pair, and the two different historical traditions
that attributed them to one partner happened to choose differently. A third
alternative is often better. If the effect comes from the joint behavior of
both partners, the best causal representation would be joint one (Queller,
1984, 1985).
This can be accomplished, for the two-person game, by adding the
joint phenotype P × P′ as a part in the model (Queller, 1985, 1992b). This
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has a particularly clear interpretation when the trait is dichotomous and
assigned values of 1 and 0. P × P′ then equals zero unless both partners
express the trait, and therefore, it becomes a variable indicating when
that happens. Specifically, let W = α + βWPP + βWP′P′ + βWPP′PP′ + ε
(here, I omit the extra regression subscripts showing the partialed-out
variables, but let it be understood that these are still partial regression
coefficients). Now, follow steps (ii)–(viii) from earlier in the paper to find
that DG increases when
Cov(G, P') Cov(G, PP')
βWP + βWP' + βWPP' >0 (13)
Cov(G, P) Cov(G, P)
from the neighbor-modulated point of view or
Cov(G', P) Cov(G', PP')
βWP + βW'P + βW'PP' >0 (14)
Cov(G, P) Cov(G, P)
for inclusive fitness with indirect effects on partners (Queller, 1992c). I
have termed the second covariance ratio, which depends on when both
partners perform the behavior, a synergism coefficient (Queller, 1984,
1985, 1992b).
There are two reasons for preferring these forms to simpler versions
of Hamilton’s rule (1964a) that bundle nonadditive effects into one of
the other terms. The main reason is the same one that applies to the
kith selection forms: It captures the social causality better. Instead of an
undifferentiated average direct fitness that implicitly combines two kinds
of direct fitness (some individuals get −c and some get −c + d), the new
forms split out those two effects and make the frequency dependence
more explicit. It distinguishes true kin effects from effects that result from
being similar in kind.
A secondary reason for preferring these forms is that they are some-
times more accurate than the simpler Hamilton’s rule. As noted above, the
strictly genetic version of Hamilton’s rule (6) is always valid, but much
of the value of Hamilton’s rule lies in being able to apply the phenotypic
gambit. The two phenotypic predictors in expressions (7) and (8) success-
fully capture the complexity of an additive game. Together, the two predic-
tors define a plane as do the four fitness values in the two-person additive
game. However, a plane cannot fit four nonadditive points. Adding P × P′
as a predictor allows us to fit those points and explain more of the vari -
ance. However, more importantly, the simpler versions can sometimes be
incorrect, biased in the same way that caused us to reject the simple direct
fitness model in favor of inclusive fitness. Specifically, the crucial step ( v)
of our derivation procedure, dropping Cov(G, ε), is not always possible
for a model with only P and P′. Suppose, for example, that cooperation
is multigenic. Cooperators all perform the behavior, but they can vary in
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Expanded Social Fitness and Hamilton’s Rule for Kin, Kith, and Kind / 23
their breeding values for the trait. Then, if partners are at least sometimes
related, those actors with the highest breeding values will be more likely to
have partners who also perform the behavior and therefore are more likely
to get the d effect. Thus, the average G differs for actors who get −c + b +
d and those who get −c + b. One cannot simply average the two types any
more than one could average eight fitness units given to a sibling and one
unit given to a third cousin. In short, there are cases in phenotypic models
where we cannot get away with two predictors. Synergism can be more
complex than in the simple two-person game. When interactions occur in
larger groups, additional terms may be needed to capture higher-order
interactions (Smith et al., 2010a).
CONCLUSIONS
Although I have worked through kin, kith, and kind selection sepa-
rately, the results can be combined in the expanded version of Hamilton’s
rule in expression (1). It covers more kinds of social selection in a causal
manner. The inclusive fitness form would use terms from expression (8)
for kin, expressions (11) or (12) for kith, and expression (14) for kind,
whereas the neighbor-modulated form would use expressions (7), (10),
and (13), respectively. These expanded social fitness results, like the tradi -
tional ones, separate out two kinds of distinct terms: selection terms relat -
ing social phenotype to fitness components and relative heritability terms
that derive from associations of genes and phenotypes, or just phenotypes.
The model suggested here stakes out a middle position between stan-
dard inclusive fitness theory and more complex models (e.g., from popula-
tion genetics). The goal has been to extend the advantages of inclusive fit -
ness theory to a more explicitly causal analysis of social effects other than
kin selection. I have chosen to still call the result Hamilton’s rule because
of the way both separate fitness terms from association or currency trans-
lation terms that measure relative heritability. This approach makes the
phenotypic gambit a plausible strategy; we can ask how phenotypes affect
fitness and then separately assess or measure the associations implied by
relatedness, synergism, or feedback coefficients. Like standard inclusive
fitness, these high-level summary variables can cut through much of the
complexity of population genetic models, where often, a new model must
be constructed and solved for a small change in assumptions. The result
is, like standard inclusive fitness, an individual-centered analysis that
allows us to use the intuition that comes from a simple model and view -
ing individuals as agents.
This model probably does not much change the view that standard
inclusive fitness is maximized, although it does change it to some extent.
Kith effects are simply cleaved off of the standard direct fitness term, and
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therefore, they do not alter total inclusive fitness. Kind effects are a bit
more complex. The strictly genetic form of standard inclusive fitness (6)
is always valid. However, the phenotypic form (8), which is often more
useful in practice, is not always exactly valid under kind selection, and
therefore, the expanded inclusive fitness with kind selection can differ
somewhat from standard inclusive fitness. More work needs to be done on
when these two forms differ and by how much, but I suspect that standard
inclusive fitness will usually be a good approximation.
I have framed this paper largely in terms of the problem of coopera-
tion, with positive costs to the actor and positive benefits to partners, that
has intrigued biologists for the last several decades. However, of course,
as with inclusive fitness, the equations here also apply when they have
fitness terms of the opposite sign. If c is negative, we have selfish effects.
If b is negative, harm falls on relatives. If d is negative, two actors together
have more negative effects than one acting alone. If m is negative, the actor
is harming its partner, which can be favored if it is coupled with a nega -
tive feedback coefficient—if negative effects on partners generate positive
effects back to the actor. Predation is an extreme example.
One complication that I have not treated explicitly is kith selection
with multiple partners. For example, mutualisms often involve a large
partner of one species and many smaller (often microbial) partners in
another species. Actions of one of the smaller partners may then feed
back onto kin, so extra terms, with both feedback and relatedness, may
be required (Frank, 1994, 1998; Fletcher and Zwick, 2006; Foster and
Wenseleers, 2006). There could also be an interaction with kind selection if
the fitness feedbacks affect actors and nonactors differently. For example,
the A. tumefaciens Ti plasmid works this way, with the opine greenbeard
effects operating through influence on the host plant.
No social model will perform all possible functions. There are trade-
offs in precision, realism, and generality (Levins, 1966) as well as in sim -
plicity and elegance. Inclusive fitness does pretty well on most of these
scores, but it does not tell us everything in either the standard or expanded
forms. There is, for example, an increasing interest in how genetic relat -
edness patterns are generated in the course of selection, migration, and
drift. Inclusive fitness typically (although not always) takes the relatedness
pattern as given. This is true as well for the associations that underlie kith
and kin selection. It is certainly useful to have more detailed models of
how these associations are built up, and the paths may sometimes be too
complex for such simple models to fully illuminate. However, the his -
tory of inclusive fitness suggests that it is also extremely useful to have
summary models that cut through much of the complexity to illuminate
crucial similarities and differences. Such models are especially useful to
empiricists who do not usually know the genetics underlying their trait
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Expanded Social Fitness and Hamilton’s Rule for Kin, Kith, and Kind / 25
and prefer to work with a small number of parameters rather than many.
These advantages should apply to the expanded social fitness model that
includes and distinguishes kin, kith, and kind.
ACKNOWLEDGMENTS
I thank Francisco Ayala and John Avise for helping to organize the
National Academy of Sciences Sackler symposium on cooperation and
conflict. For comments on the manuscript, I thank two anonymous ref-
erees, Joan Strassmann, Michael Whitlock, Stuart West, Kevin Foster,
Claire El Mouden, and the Oxford Social Evolution Group. Our research
is supported by U.S. National Science Foundation Grants DEB 0816690
and DEB 0918931.
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