27

*Received December 2001; revised August 2002.

†To contact the author, please write to Peter Gildenhuys, Department of History and
Philosophy of Science, 1017 CL, University of Pittsburgh, Pittsburgh, PA 15260; e-mail:
peg1@pitt.edu.

‡Thanks to David Hull and two anonymous referees for their helpful comments on
earlier drafts of this paper.

Philosophy of Science, 70 (January 2003) pp. 27–48. 0031-8248/2003/7001-0004$10.00
Copyright 2003 by the Philosophy of Science Association. All rights reserved.

The Evolution of Altruism:
The Sober/Wilson Model*

Peter Gildenhuys †‡

In what follows, I critique the interpretation that Sober and Wilson offer of their group
selection model in Unto Others. Sober and Wilson mistakenly claim that their model
operates as an example of Simpson’s paradox and defend an interpretation of their
model according to which groups are operated upon by natural selection. In the place
of their interpretation, I offer one that parallels the mathematical calculation of the
model’s outcome and does not depend on the postulation of a force of group selection
or a value for group fitness.

1. Introduction. In Unto Others: The Evolution and Psychology of Unselfish
Behavior (1998), Elliot Sober and David Sloan Wilson make some consid-
erable headway in explaining the evolution of altruistic behavior through
the development of a model that specifies circumstances in which there
can be selection for altruism. While this advance is significant, Sober and
Wilson’s definitions both of a “biological group” and of “altruism” remain
inadequate. I will point out these flaws as I go along, but my main critical
focus will be on Sober and Wilson’s interpretation of the mathematical
model they put forward to explain the evolution of altruism. No value is
given for “group fitness” in the mathematical representation of their
model, which leaves their explanation of the evolution of altruism by
group selection questionable. I want to contest Sober and Wilson’s inter-
pretation of the mathematical model they present in their text by present-
ing an alternative causal analysis of what is going on when altruism
evolves in the circumstances hypothesized by Sober and Wilson. First, I



 28

1. Two subgroups, rather than three or more, are easier to deal with mathematically,
but nothing depends on the number of subgroups formed out of the global population.

lay out the general model of group selection from Unto Others, and then
I criticize Sober and Wilson’s interpretation of how it works. Next, I pres-
ent my own version of the situation described by Sober and Wilson. Fi-
nally, I will argue that there is a case for group selection here, or rather
selection operating between individual populations, but there is no case
for group selection occurring between the subgroups on which Sober and
Wilson focus.

2. The General Model of Group Selection. Sober and Wilson eschew the
simple model of altruism according to which altruism is sustained in a
population because everyone is an altruist. In such a situation, reciprocity
is guaranteed straightforwardly among altruists; no one but altruists bene-
fits from altruism. But such models suffer from a couple of familiar ob-
jections. First, they do not explain the evolution of altruism, only its per-
petuation. Second, were a selfish alternative allele to arise within a
population, it would eliminate the altruistic allele by taking advantage of
the altruistic behavior of others without itself paying the costs of altruistic
behavior.

The Sober and Wilson model is more complex than the simple model
and works this way: A population of organisms, only some of which carry
genes that code for altruism, is split into subgroups in which interaction
among organisms takes place, sometimes for only a small portion of the
development of organisms, sometimes for multiple generations. After this,
the organisms congregate into a global population before once more being
distributed into new subgroups with a different assortment of members.
The cycle continues, with new subgroups formed at every cycle. For al-
truism to evolve within the population, everything depends on the char-
acter of the subgroups formed within it. It is only when the subgroups are
uneven in terms of their proportion of altruists and nonaltruists that al-
truists stand a fighting chance.

The most basic version of the model, the one that Sober and Wilson
concentrate upon in their exposition, presents a large population split into
two subgroups, the members of which interact in some fashion relevant
to the fitness of each individual.1 When the large group divides, two sub-
groups that are disproportionate in their constitution are formed: one
subgroup contains 80 percent altruists and 20 percent nonaltruists, the
other contains 80 percent nonaltruists and 20 percent altruists. The altru-
ists acquire an evolutionary edge because, by and large, they help other
altruists while the majority of nonaltruists are segregated into a different
subgroup. Of course, the nonaltruists do capitalize on the altruism of their



  : ⁄  29

fellows, but too few of them turn up in the same group as the majority of
altruists, so they profit less than do other altruists from the altruism of
their conspecifics. Because most of the altruists are in a group together
with only a few nonaltruists, on average the altruists with their altruistic
genes finish ahead by co-operating with one another.

As the number of altruists within the global population grows, it be-
comes more beneficial for the nonaltruists to freeload, so altruism cannot
take over a population. Instead, a polymorphism evolves, kept stable by
frequency-dependent selection. The more altruists there are, the more it
pays to be selfish. The fewer altruists there are, the more it pays to be an
altruist, though it is worth remarking that altruists will gain ground
against nonaltruists beginning at a very low population density only when
such pioneer altruists somehow manage to end up in the same subgroup
so as to take advantage of each other’s altruism. Early on, Sober and
Wilson offer a hypothetical scenario involving the infamous D. dendriti-
cum “brain-worm” parasite that shows how altruism could evolve into a
stable polymorphism with selfishness beginning from a single mutant al-
truistic parasite. Sober and Wilson discuss the formation of biased sub-
groups more generally later on in their work, something I get to below.

Here are the numbers that Sober and Wilson lay out for the simplest
version of their group selection model (1998, 25):

Group 1 Group 2

n 100 100

p 0.2 0.8

Wa 10 � 1 � 5(19)/99 � 9.96 10 � 1 � 5(79)/99 � 12.99

Ws 10 � 5(20)/99 � 11.01 10 � 5(80)/99 � 14.04

n� 1080 1320

p� 0.184 0.787

Global Population

N 100 � 100 � 200

P [0.2(100) � 0.8(100)]/200 � 0.5

N� 1080 � 1320 � 2400

P� [0.184(1080) � 0.787(1320)]/2400 � 0.516

n � number of organisms in a subgroup
p � proportion of subgroup members that are altruistic
Wa � average fitness of altruists
Ws � average fitness of nonaltruists



 30

n� � number of organisms after interaction within subgroups
p� � proportion of subgroup members that are altruistic after subgroup
interaction
N � number of organisms in the global population
P � proportion of the global population that is altruistic
N� � number of organisms in the global population after subgroup in-
teraction
P� � proportion of the global population that is altruistic

I have described Sober and Wilson’s model as one in which altruism is
sustained by a specific sort of group structure allowing altruistic genes to
cause the replication of altruistic genes in other organisms through altru-
istic behavior. The importance of the possibility of altruistic genes causing
their replication in this manner is what explains the requirement that the
subgroups vary in their proportion of altruists. Altruists must be grouped
together such that more altruists benefit from altruistic deeds than do
nonaltruists.

This is not how Sober and Wilson understand their model. They claim
that two sorts of forces are at work in the above scenario, the force of
organismic (they say “individual”) selection and the force of group selec-
tion. The force of group selection promotes altruism within the subgroups,
while the force of organismic selection promotes selfishness. When con-
sidering the evolution of altruism, Sober and Wilson take these forces to
act in opposition to one another:

Between-group selection favors the evolution of altruism; within-
group selection favors the evolution of selfishness. These two pro-
cesses oppose each other. If altruism manages to evolve, this indicates
that the group-selection process has been strong enough to overwhelm
the force pushing in the opposite direction. (1998, 33)

The “force” of group selection acts in opposition to the “force” of organ-
ismic selection in just the same way that Newtonian forces can oppose one
another. The analogy made by Sober and Wilson (1998, 33) is with indi-
viduals pushing upon a billiard ball in different directions. Altruism pro-
motes the “group fitness” of the subgroups, causing them to grow larger
at the expense of the organismic fitness of their members, while selfishness
promotes organismic fitness, the reproduction of organisms within the
subgroup, at the expense of the fitness of the subgroup. When the forces
of group selection for altruism and the force of organismic selection for
selfishness cancel out, the stable polymorphism is reached.

Sober and Wilson’s understanding of their own model suffers from a
serious drawback. Despite their repeated use of “group fitness” to describe
what is going on in their model, there is no value in their mathematical



  : ⁄  31

analysis for the term. Instead, the fitness calculations are done entirely in
terms of the fitness of different trait groups within each subgroup. These
trait groups are the population of altruists in subgroup one, the population
of nonaltruists in subgroup one, the group of altruists in subgroup two,
and the group of nonaltruists in subgroup two.

To show that “group fitness” is never used in Sober and Wilson’s cal-
culations, and that they are made instead using fitness values ascribed to
trait groups, let’s walk through Sober and Wilson’s calculations. The av-
erage fitnesses for the four trait groups (group 1 altruists, group 1 non-
altruists, group 2 altruists, group 2 nonaltruists) appear in lines three and
four. These are calculated by giving everyone a base fitness value of ten
units, subtracting the cost of altruism, if performed, and adding the bene-
fits of altruism received. How much fitness is gained by the members of
each subgroup from others’ altruistic actions is directly proportional to
the constitution of the subgroup. More altruists in a subgroup means more
benefit for everyone in the subgroup.

The next number to appear in Sober and Wilson’s mathematical for-
mulation is n�, reflecting the new size of the subgroups. This figure is
generated (1998, 20–21) for each subgroup by multiplying the average
fitnesses of the altruists by their frequency within the population, perform-
ing the same operation on the nonaltruists, adding the products together,
and multiplying the sum by the number of individuals in each subgroup:
n� � n[pWa � (1-p-Ws)]. Notice how the new size of the subgroup must
be calculated by adding the growth of each of its trait groups, the altruists
and the nonaltruists, separately. The symbol p� represents the percentage
of altruists within the subgroup after interaction among its members. This
value is generated by multiplying the original number of altruists within
the subgroup (np) by their average fitness and dividing this figure by the
total number of members of the subgroup after interaction.

At this point, Sober and Wilson have values for the average fitness of
altruists and nonaltruists within each subgroup, the proportion of altruists
in each subgroup, and the size of each subgroup. In the last two lines of
their mathematical analysis, they use these values to generate a value for
the size of the combined group through simple addition, as well as a value
for the proportion of the global population that is altruistic. Nowhere does
any value for “group fitness” fit into the mathematical representation.
Rather, such a value can at best be abstracted by comparing the growth of
the group with a high proportion of altruists (group two) with the one that
has a low proportion of altruists (group one). The group with more altruists
grows larger and hence is “more fit” (Sober and Wilson 1998, 26).

Sober and Wilson call group selection “the mechanism that we have
proposed to explain the evolution of altruism” (1998, 31; my italics), and
also tell us that “if altruism manages to evolve, this indicates that the



 32

group-selection process has been strong enough to overwhelm the force
pushing in the other direction” (1998, 33; my italics). The use of multiple
terms to capture the role of group selection in the model, along with the
aforementioned force analogy, already indicates some confusion over pre-
cisely what this role is meant to be. The difficulties with their interpretation
become clearer if the parallel they draw between classic formulations of
the theory of natural selection and their own interpretation of their model
are analyzed.

In a purported analogy with standard formulations of Darwinian nat-
ural selection, Sober and Wilson list the conditions that are necessary to
bring about an increase the number of altruists in the global population
in their model. Three of the conditions are that there be multiple sub-
groups, that these that vary in their proportion of altruists, and that they
periodically subdivide into interacting subgroups before reassembling into
a global population (Sober and Wilson 1998, 26). The first two conditions
correspond to the conditions in the standard formulation of natural se-
lection in which there must be multiple individuals that vary in their char-
acteristics, while the last condition is a special feature of their model. In
an extension of the analogy, they also say that subgroups with more al-
truists must be more fit than subgroups with fewer altruists, where fitness
is understood as the production of more organisms:

There must be a direct relationship between the proportion of altruists
in the group and the group’s output; groups with more altruists must
be more fit (produce more individual offspring) than groups without
altruists. (Sober and Wilson 1998, 26)

As it stands, the formulation of this condition is in need of revision. Quite
simply, the groups do not produce offspring, or at least if they did, they
would produce offspring groups rather than individual organisms. But the
latter possibility is explicitly denied by Sober and Wilson: it is of crucial
importance to the operation of the model that the members of any one set
of subgroups formed by periodic subdivision of the global population
recombine after interaction into a global population from which new sub-
groups are formed with a different assortment of members. The subgroups
in the model do not autonomously or independently go on to produce the
next set of subgroups. Thus, the analogy with Darwinian selection is mis-
placed since, according to Darwin, individuals that are more fit go on to
produce other individuals that are more fit, while in Sober and Wilson’s
model, individual subgroups that are more fit do not go on to produce
individual subgroups that are more fit.

Sober and Wilson cite a final condition for the successful operation of
their model:



  : ⁄  33

To be sufficient, the differential fitness of groups (the force favoring
the altruists) must be strong enough to counter the differential fitness
of individuals within the groups (the force favoring the selfish types).
(1998, 26)

Here confusion has really set in, for it is “fitness,” or rather “differential
fitness,” both of organisms and of groups, that is acting as a force that
affects the resultant distribution of altruists in the global population. If
this last condition is understood as an oblique reference to the fact that,
all things considered, the members of the group with more altruists must
produce more offspring than do the members of the group with fewer
altruists, then the condition is not tendentious or even interesting. How-
ever, the claim that fitness is a causally relevant variable that determines
how many altruists and nonaltruists end up in the global population is
certainly wrongheaded, since the fitness of the organisms and the groups
is calculated in terms of the number of offspring actually produced, as
explained in the prior condition cited above. As it stands, the condition is
a mere tautology: only if members of one subgroup actually go on to
produce more offspring will they produce more offspring. And it would
be of no help for Sober and Wilson to claim that what matters is the
expected fitness of the organisms or groups, rather than their actual fitness,
since we would be left wondering why we should expect the results the
model produces. Sober and Wilson have not offered us, in the form of a
necessary condition, any explanation of why the model produces the re-
sults that it does. The model is abstract, what is expected to happen does
happen. Other factors that could affect the actual reproduction of the
organisms are ruled out of the picture by the authors’ explicit assumption
of genetic determinism (Sober and Wilson 1998, 22).

What Sober and Wilson seem to be getting at with their last necessary
condition for the evolution of altruism in their model is that the fitness
losses accrued from altruists’ altruistic behavior must be somehow com-
pensated for by a fitness benefit to those same organisms. Group selection
is brought into play by Sober and Wilson to fulfill this role. Altruistic
genes benefit the group and group selection favors groups that are more
fit, so it is by being in the faster-growing group that altruists get compen-
sated for their altruism. But Sober and Wilson fail to provide any more
determinate sense of how the force of group selection operates: What does
it do that makes groups grow larger? Nor do Sober and Wilson provide
any explanation of how the alternative force of differential “group fitness”
is detected except through the output of the model itself. While it is clear
from the mathematics that one group does in fact grow larger than the
other, and that this group is the one with more altruists in it, no expla-
nation of how this happens is forthcoming. And, given the manner in



 34

which the mathematical calculations are done, there is good reason to
suspect that the outcome of the model has nothing to do with group fitness
at all. It is worth stressing that in Sober and Wilson’s model it is individual
organisms, not groups or populations, that reproduce and perform altru-
istic acts. So what we need is an explanation of how altruists are compen-
sated adequately enough for their altruism that appeals to factors that are
causally relevant to the reproduction of individual altruists. Group selec-
tion as a force, or a mechanism, or a process affecting or involving groups
and group-level traits is not even a good candidate for fulfilling this ex-
planatory role because the trait in question, altruism, is a trait that belongs
squarely to organisms rather than groups.

So, dispensing with the notion of “group fitness,” which remains con-
spicuously absent from the mathematics, what becomes of Sober and Wil-
son’s interpretation of their model? Are there two distinct forces acting
here, organismic selection and group selection, or group fitness and or-
ganismic fitness, one favoring the evolution of altruism and the other pro-
moting selfishness? No. Actually, the gene for altruism and the gene for
selfishness have different effects depending on the environments in which
the altruistic and selfish organisms find themselves. When surrounded by
other altruists, altruism causes the reproduction of altruists by increasing
the fitness of other altruists who carry the same gene. Surrounded by
nonaltruists, altruism is costly, and causes the spread of selfishness within
the population. Each gene has distinct capacities to affect fitness whose
operations are dependent on the make-up of the surrounding subgroup.

3. Sober and Wilson’s Model Explained. Using their mathematical model,
I will offer my own detailed explanation of the effects of altruistic behavior
on the fitness of each altruist. Altruistic deeds can both cause a net increase
in the fitness of altruists or a net decrease in fitness, depending on the
circumstances in which they are performed. It is because biased subgroups
are formed in Sober and Wilson’s model that conditions are such that
altruism is perpetuated in the population.

Sober and Wilson introduce their model with reference to a puzzle for
probabilistic theories of causality known as Simpson’s paradox. This is
the problem of spurious correlation. The classic example of spurious cor-
relation comes from Cartwright (1979). It was thought for a while that
being a woman caused one to be rejected from the graduate school at
Berkeley. But researchers noted that in every department women were no
more likely to be rejected than men, the women simply applied to tougher
departments. Being a woman was correlated with a variable that actually
brought about the effect in question.

Sober and Wilson offer a simplified version of what happened at Berke-
ley as an analogy to what is going on in their model. They have us imagine



  : ⁄  35

that a hundred individuals, ten men and ninety women apply to a tough
department with a thirty percent acceptance rate, while another hundred
individuals, this time ten of them women and ninety of them men apply
to an easier department with a sixty percent acceptance rate. Neither de-
partment discriminates, so thirty-three women are accepted to the gradu-
ate school along with sixty men. Sober and Wilson write:

A bias exists in the two departments combined, despite the fact that
it does not exist in any single department, because the departments
contribute unequally to the total number of applicants who are ac-
cepted. In just the same way, altruists can increase in frequency in the
two groups [in their model] combined, despite the fact that they de-
crease in frequency within each group, because the groups contribute
unequally to the total number of offspring.

Sober and Wilson’s analogy is misplaced, and to see why, we need to
flesh out the supposed parallel in more detail. Sober and Wilson tell us
that the bias in the two groups of applicants combined is owing to the fact
that each group contributes unequally to the total number of applicants
who are accepted. This explanation fits with their explanation of what’s
going on in their biological model: altruists can survive and reproduce
because the subgroup of altruists grows larger faster than thus contributes
more members to the global population. But it is easy to offer a different
set of numbers that shows a supposed bias in the total number of appli-
cants accepted to Berkeley despite the fact that each department contrib-
utes the same number of applicants to the total. Consider the following
hypothetical situation in which a hundred people are accepted at Berkeley,
fifty-six men and forty-four women. Each department contributes fifty
applicants to this total. The English department is tough, with a forty
percent acceptance rate, while the physics department, having a sixty per-
cent acceptance rate, is relatively easy to get into. All that is left is to
gerrymander the remaining numbers. To make things work out, let’s say
that there are eighty-three applicants to the physics department and a
hundred and twenty-five applicants to the English department. Of the ap-
plicants to the physics department, seventy-two are men and eleven are
women; of the applicants to the English department, thirty-two are men
and ninety-three are women. That makes a hundred and four applicants
of each gender. The physics department accepts forty-three men and seven
women. The English department accepts thirteen men and thirty-seven
women. Each department contributes an equal number of individuals to
the total number of acceptances, fifty people each. But the total number
of acceptances still looks biased, despite the fact that the same number of
women applied as men, a hundred and four each. Fifty-six men, and only
forty-four women, are accepted to Berkeley.



 36

2. In order to avoid Simpson’s paradox, advocates of probabilistic theories of causality,
such as Cartwright (1979) whom Sober and Wilson cite as the source of the Berkeley
example, adopt the contextual unanimity clause, stating that causal relations can be
inferred from correlations only for those situations that are homogenous with respect
to other causes of the effect in question.

Whether or not each department contributes unequally to the total
number of acceptances is irrelevant to the operation of Simpson’s para-
dox, as the above hypothetical scenario shows. On the above numbers,
the graduate school looks biased, despite the fact that neither department
is biased, and also despite the fact that each department contributes an
equal number of applicants to the overall total of acceptances. Sober and
Wilson have misunderstood how Simpson’s paradox operates, and it is
worthwhile spending some time to clarify just that.

Simpson’s paradox is not really a paradox since there is a clear expla-
nation for what is going on in such scenarios. A purported cause, being a
man, does not lead to its purported effect, getting accepted at Berkeley,
because of the operation of another cause that works to skew the numbers.
In the Berkeley case, the alternate cause in operation is applying to easy
departments. It turns out that being a man is correlated with applying to
easy departments and being a woman is correlated with applying to tough
departments. That is what explains the overall bias in the acceptance of
candidates to the graduate school. Sober and Wilson explicitly assume
genetic determinism in their model (1998, 22), so the only traits that make
a difference to the evolution of altruism in their model are the genes for
altruism and selfishness along with the two traits, being among mostly
nonaltruists, and being grouped with the majority of altruists, that are
acquired when the population divides into subgroups. The distribution of
these last two traits is what is responsible for the success of the altruists
over the nonaltruists. Being surrounded by altruists increases fitness, and
altruism is correlated with being surrounded by altruists while selfishness
is correlated with being surrounded by nonaltruists.

The upshot of the Berkeley case and other situations in which Simp-
son’s paradox is at work is that a purported cause, a characteristic that
looks to be causally connected to another characteristic based on statistical
evidence, turns out not to be a cause of the effect at all. Instead, it turns
out to be a characteristic that is correlated with another characteristic that
is the real cause of the effect.2 This is not the moral that Sober and Wilson
want to draw with respect to their model. The upshot of Sober and Wil-
son’s model is not that altruism does not cause the reproduction of altru-
ists or the replication of altruistic genes. Sober and Wilson’s model is like
the Berkeley case insofar as there is another cause other than altruism
relevant to the effect in question that is at work in their model, namely



  : ⁄  37

Figure 1. Here is the diagram used by Cartwright (1989, 99) to illustrate the paradoxical
effects of taking birth control pills (C) on thrombosis (T). The path of arrows on the left
illustrates the positive causal connection between the pills and thrombosis. The pills alter
their takers’ blood chemistry, here illustrated as the production of a fictional chemical (C�),
and this causes thrombosis. The pills also prevent pregnancy (�P) which leads to a decrease
in the likelihood of thrombosis ( � T), as illustrated by the causal chain on the right.

the characteristic of being grouped mainly with nonaltruists in subgroup
one versus being grouped mainly with altruists in subgroup two. It is also
similar insofar as being in group two, a trait that is beneficial to fitness, is
correlated with being an altruist, and it is this correlation that explains
why altruists outcompete nonaltruists. But Sober and Wilson’s model is
different from the situation at Berkeley, since it turned out that being a
man had no effect at all on the probability of one’s being accepted, while
altruism does have an effect on the probability of reproduction of altruists.
Altruism and selfishness remain variables causally relevant to the repro-
duction of the organisms that bear the genes that code for these activities.
The trick, then, is to handle each of the four populations that are distinct
in terms of the variables that are causally relevant to fitness separately,
and Sober and Wilson do just that by using the average fitnesses of the
altruists and the nonaltruists in each subgroup (Wa and Ws) separately in
their calculations.

Sober and Wilson’s model has more to do with another puzzle, Hes-
slow’s (1976) purported counter-example to probabilistic theories of cau-
sality, subsequently discussed in a slightly modified form by Cartwright
(1989) and Eells (1991). Figure One represents the standard causal path-
analysis for the notorious pills/thrombosis case and Figure Two represents
what I take to be going on in Sober and Wilson’s model:

In both cases, two causal paths, one whose net effect is positive and the



 38

Figure 2. Constructed to resemble Cartwright’s illustration of the effects of birth control
pills on pregnancy, this diagram shows the effects of altruism (A) on the reproduction of
nonaltruists and altruists. As illustrated by the left-hand causal chain, altruism increases the
fitness of nonaltruists (FFs) when they benefit from altruistic deeds, and thus increases the
likelihood of their reproduction (FRs). Because the nonaltruists and the altruists are in com-
petition, anything that causes an increase in the likelihood of reproduction of the nonaltruists
causes a decrease in likelihood of reproduction to the altruists (fRa), as shown by the last
link in the chain. The middle causal chain shows how altruism decreases the likelihood of
reproduction of the altruists in a second fashion: altruistic deeds decrease the fitness of the
agents that perform them(fFa), thereby decreasing their likelihood of reproduction (fRa).
Altruism, when it benefits other altruists, increases their fitness (FFa) leading to an increase
in their likelihood of reproduction (FRa), as illustrated by the right-hand causal chain. Al-
truism acts both to bring about and inhibit the reproduction of altruists simultaneously, just
as birth control pills simultaneously bring about and inhibit thrombosis.

other negative, link the causes (taking the pills or behaving altruistically)
to their effects upon fitness or the probability of acquiring thrombosis.
Whether or not birth control pills increase the likelihood of thrombosis
or decrease it is obviously dependent on a number of factors, most obvi-
ously the pill taker’s chance of getting pregnant if she does not take the
pills. For instance, if an individual is incapable of getting pregnant, then
in her case the preventative causal chain linking the pills to thrombosis is
made inoperative and the pills will cause thrombosis. Similarly, the causal
effects of an altruistic gene on making copies of itself are dependent on
the circumstances in which altruistic deeds are committed. Altruistic
genes cause the replication of other altruistic genes when they affect other
altruists and fail to do so when the altruism they induce benefits nonal-
truists. Indeed, Sober and Wilson’s model is not even identical to the



  : ⁄  39

3. These numbers look different from Sober and Wilson’s because I am considering
only the causal effects of altruism in each of the two groups, that is, what difference
altruism makes to the fitnesses of altruists and nonaltruists. To get back to Sober and
Wilson’s calculations simply average out the net change to the fitness of the nonaltruists
and altruists in each subgroup (net change/number of altruist subgroup members) and
add it to ten, the base fitness that Sober and Wilson give to each individual. This will
yield Sober and Wilson’s values Wa and Ws, the average fitness value for altruists and
nonaltruists in each subgroup. Wa in group one: 10 � �1/20 � 9.95. Wa in group
two: 10 � (239)/80 � 12.99. Ws in group one: 10 � 81/80 � 11.01. Ws in group two:
10 � 81/20 � 14.05. Some of the numbers are a hair off because I have rounded off my
calculations at different points.

pills/thrombosis case because altruism has three causal consequences, not
just two. The altruism of the members of each subgroup produces a fitness
increase for altruists when altruists benefit, a fitness loss for altruists when
nonaltruists benefit (or conversely, a fitness benefit to nonaltruists who
freeload), and a fitness loss to the altruistic agent no matter who benefits
from the altruism. Thus, the positive causal path linking altruism to the
reproduction of altruists must predominate over both negative causal
chains. Selection for altruism can occur only if altruists are grouped to-
gether and receive the bulk of each other’s altruism. The variable of being
grouped with most of the altruists, a characteristic that causes reproduc-
tion, must be correlated with being an altruist, a characteristic that inhibits
reproduction.

4. How the Model Works. I want to offer another representation of the
causal effects of altruism, one that breaks it down into its parts in order
to add up the effects of altruism on the fitness of altruists and the effects
of altruism on the fitness of nonaltruists. Because altruists are grouped
mainly with other altruists in group two, the bulk of the fitness benefits
produced by altruists is directed toward other altruists. Even when we
factor in the cost of altruism performed, altruists still finish ahead. The
net effect of altruism in the Sober and Wilson model is to promote the
relative fitness of altruists. Figure Three and Figure Four show the causal
effects of altruism in each subgroup in Sober and Wilson’s model along
with a mathematical representation of the quantity of fitness benefits and
costs incurred by altruists and nonaltruists.3

In Sober and Wilson’s model, altruistic genes indirectly cause the rep-
lication of altruistic genes because by and large altruists are grouped with
other altruists. Altruism, which decreases the fitness of the agent, is cor-
related with being in the same group as the majority of altruists, a trait
that increases fitness by allowing altruists to take advantage of their fel-
lows’ altruism. In the conditions stipulated in Sober and Wilson’s model,
altruism is ultimately beneficial to the altruists, as is shown by Figure Five
representing the effects of altruism in both groups combined.



 40

Figure 3. This figure shows the causal effects of altruism in group one on the fitness of
altruists and nonaltruists separately. The pool of a hundred units of fitness produced by the
altruistic behavior of the twenty altruists in the group is divided up evenly among the other
group members. The altruists receive just less than a fifth of the benefits of the altruism (since
they cannot benefit from their own altruism) and also suffer a penalty of a single fitness
point each for their altruistic sacrifice. In this group, altruism leads to the reproduction of
nonaltruists who reap the lion’s share of the benefits from the altruistic deeds.

5. Altruism Defined. Once we recognize that altruistic genes must replicate
themselves indirectly by benefiting other altruists, Sober and Wilson’s def-
inition of altruism comes into question. According to Sober and Wilson
altruistic behavior, “increases the [relative] fitness of others and decreases
the [relative] fitness of the agent” (1998, 17). I twice added in “relative”
because of what Sober and Wilson say later on (1998, 33; italics in origi-
nal): “In general, evolutionary success depends on relative fitness (Wil-
liams 1966). It doesn’t matter how many offspring you have; it only mat-
ters that you have more than anyone else.” According to this definition,
any gene that causes fitness-reducing behavior will count as altruistic, de-



  : ⁄  41

Figure 4. This figure shows the causal effects of altruism on the fitness of altruists and
nonaltruists of group two separately. In this group, where altruists predominate, they receive
the bulk of the altruism produced by the group’s eighty altruists. Even when the fitness loss
brought about by their altruistic behavior is factored in, the altruists still fare far better than
their nonaltruistic counterparts. Not only is this a group in which the altruists receive the
bulk of the fitness benefits from their altruism, this group also produces four times as much
fitness benefit to be divided up among the members.

spite the fact that genes that do no more than cause a loss in fitness simply
cannot last in the gene pool except by luck. Biting off one’s leg is an
altruistic behavior, according to Sober and Wilson’s definition, because
the behavior lowers the relative fitness of the organism that does it and
thus increases the relative fitness of other conspecific competitors. But to
construe this as biological altruism is a mistake, because such behavior
could not evolve even in the situation postulated by Sober and Wilson’s
model, since nothing is to be gained when a group of organisms all get
together and mutilate themselves. Contrary to Sober and Wilson’s defi-
nition, to count as altruistic an action must do more than simply alter the
relative fitness of two agents. It must also be the sort of behavior whose
net benefit to other altruists must be greater than its cost to the agent.
This condition is satisfied by Sober and Wilson’s model because altruistic



 42

Figure 5. This figure shows the effects of altruism in groups one and two combined. Overall,
the altruists gain two hundred and thirty-eight units of fitness from each other’s altruism
while the nonaltruists gain one hundred and sixty-two fitness units by freeloading (these
values are just summed from those in Figures 3 and 4). All other things being equal, the
global population, which began with the same number of altruists as nonaltruists, will have
become disproportionately altruistic before it subdivides once again. Thus, in the scenario
hypothesized by Sober and Wilson, altruism causes the reproduction of altruists by increasing
their fitness and hence their probability of reproduction.

genes cause a five point increase in fitness to others, and it is mostly al-
truists that receive the fitness boost, while costing only a single fitness point
deficit to the agent (1998, 25). For altruism to maintain a foothold within
a population of organisms, it is enough that on average an altruist is just
as likely to gain, in terms of relative fitness to altruists and nonaltruists,
from the altruism of other altruists as it is to suffer from its own altruistic
actions.



  : ⁄  43

6. Altruism and Averaging. By paying attention to the causal chains linking
altruistic behavior with fitness values we can see why Sober and Wilson
do their calculations using fitness values ascribed to the trait groups (the
altruists and the nonaltruists in each subgroup) in place of the subgroups
in their model. Members of the trait groups are all affected in the same
manner by the altruistic actions of their counterparts, and they all affect
the other members of their subgroup in an identical fashion. In short, the
members of each trait group are all exposed to the same set of causally
relevant factors and can be treated as a group when calculating fitness
values. But this is not the case with the subgroups in Sober and Wilson’s
model. Here, the groups represent members of the population that interact
in ways relevant to organismic fitness, not members of the population that
share a common set of factors causally relevant to their reproduction. It
is the absence of an overlap between these two sorts of groups that indi-
cates that no “force” of group selection operating between the subgroups
is responsible for the evolution of altruism in Sober and Wilson’s model.
The subgroups are not groups with which one can do causal reasoning;
they cannot be treated as a homogenous unit since their members vary in
terms of those characteristics that are causally relevant to the probability
of their reproduction.

I have focused on the details of the causal chains that link altruistic
genes to the perpetuation of altruism because I do not want to be accused
of adopting what Sober and Wilson dub “the averaging fallacy” (1998,
31). Sober and Wilson point out that if we simply look at the output of
their model, it looks as though altruistic genes are “really” selfish, since
they manage to outcompete the nonaltruistic ones (1998, 31). But careful
attention to exactly how altruistic genes accomplish their replication
shows that they are truly altruistic, at least insofar as this means that they
must bring about the reproduction of another altruistic organism in order
to cause their replication. Sober and Wilson also write that “another rea-
son to reject the averaging approach is that it fails to identify the separate
causal processes that contribute to the evolutionary outcome” (1998, 32).
While I disagree with their gloss on what these processes are, I have dis-
cussed in detail my alternative representation of their model. Only one
feature of the model has been left out of my analysis. The positive causal
chain that links altruistic action with increased fitness for altruists domi-
nates over the negative causal chain because the subgroups are dispro-
portionate in terms of the number of altruists in each. What we want to
know, then, is how the subgroups become biased in that fashion.

7. How Subgroups Are Formed. Sober and Wilson write: “A group is de-
fined as a set of individuals that influence each other’s fitness with respect
to a certain trait but not the fitness of those outside the group” (1998, 92).
This definition is inadequate for two reasons. First of all, it encompasses



 44

far too much. The biological world is way too complicated for such loosely
defined groups to have any discernible role. Just imagine the group of
aquatic organisms that influence one another with respect to swimming
ability. But this is not the main difficulty with their definition. The definition
is misleading because it makes it seem as though the subgroups in the model
consist of those organisms that actually do interact with one another. This
leaves out exactly why the organisms interact with one another. The point
is that the groups are not composed simply out of interacting organisms,
but rather composed out of organisms that, for some other reason, are
constrained such that they must interact (in some important fashion) only
with one another. The bias in the proportion of altruists in each subgroup
only matters because interaction must occur within the boundaries of the
subgroups.

Sober and Wilson focus on three explanations for the bias in group
constitution so essential to their model. Subgroups may be formed ran-
domly, out of kin relations, or out of mutual recognition among altruists.
I’ll deal with each of these cases in turn, but much here is left to the
imagination of the reader. What matters is that groups assort themselves
in a biased fashion, not exactly how they do so. I briefly consider, however,
one interesting question: To what entity does one ascribe responsibility
for this vital characteristic of subgroup formation? There may just be a
case for “group selection” here, but it is not to be found where Sober and
Wilson are looking for it.

In the case of random group formation, the mechanism by which al-
truists are grouped with altruists, and hence disproportionately affect
other altruists with their altruism, is not, as one might be tempted to
suppose, no mechanism at all. Rather, the mechanism is simply a tendency
among members of the global population to sort themselves randomly
into subgroups. After all, there are lots of ways they could form subgroups
and doing so randomly is only one available option. If subgroups are
formed randomly, then altruism will be sustained within the population
only if the benefits caused by altruists are high relative to their cost, since
it is unlikely that, in general, the groups will vary greatly in terms of the
proportions of altruistic members. The more egalitarian the constitution
of the subgroups, the more altruism must be beneficial to the fitness of the
recipient relative to its cost for the agent, for altruism to remain viable
within the population. One of Sober and Wilson’s examples of a popula-
tion in which random group formation promotes the evolution of altruism
is the population of various strains of the mixoma virus developed to
control the rabbit population in Australia (1998, 46). The virus, designed
to kill, began to reproduce less quickly after infesting rabbits in the wild
and so became less virulent a few weeks after its release into the rabbit
population. The decrease in virulence occurred because the virus is spread



  : ⁄  45

by mosquitoes that bite only live rabbits. Viral strains that reproduce less
quickly and hence do not kill the rabbits they inhabit as quickly will be
more likely to make it into another rabbit. Mosquitoes spread the virus
from rabbit to rabbit and the mixture of different strains transmitted to any
given rabbit ( � subgroup), some more and some less virulent ( � selfish),
is likely to be random.

Subgroups that are formed out of kin provide the most plausible ac-
count of how altruism might evolve according to Sober and Wilson’s
model. Here, altruists manage to disproportionately affect other altruists
by interacting with their relatives who, because of shared heredity, are
more likely to be altruists than are unrelated individuals. The formation
of subgroups of kin, then, can be used to explain how altruism could
evolve within a population by natural selection beginning at very low levels
within the population. One of the examples here is the Dicroelium dentri-
ticum parasite. Some members of the species invade the brains of ants and
cause them to hang about on top of grass blades, where they (and their
hosts) are eaten by cattle. This act of suicidal altruism benefits their fellow
parasites holed up in the ants’ digestive system waiting to continue their
lifecycle within the ungulate’s digestive system (Sober and Wilson 1998,
18). The parasites reproduce asexually before entering the ant so, as in the
case of the wasp discussed above, many of the parasites within the ant
carry the same genes.

Finally, the subgroups could be formed by reciprocal recognition
among altruists. This is often called the “green beard” effect, so named
because, according to a popular hypothetical example, the gene for altru-
ism also allows altruists to recognize each other by some obvious marking,
the “green beard.” But altruists could perhaps more easily recognize each
other as altruists simply by attending to whether or not another organism
acts altruistically. Sober and Wilson refer to experimental work on guppies
(1998, 46) that shows that guppies choose their associates on the basis of
their fellows’ previous behavior, though it remains unclear to me why all
guppies, not just altruistic ones, do not share the same tendency to group
themselves with other guppies who are willing to risk their lives checking
predators.

8. Group Selection After All? Sober and Wilson’s model for the evolution
of altruism requires some mechanism for the periodic assortment of the
majority of altruists into the same group as one another. As stressed
above, this is necessary because altruists must receive the lion’s share of
the fitness benefits produced by altruistic deeds. Anything that disturbs
the operation of the mechanism by which altruists are grouped together
will lead to the disappearance of altruism from the group. So the perpet-
uation of altruism in the conditions hypothesized by Sober and Wilson is



 46

contingent upon a population-level process that causes the periodic for-
mation of interactive subgroups that are unequal in terms of the number
of altruists in each. Thus, my rendition of Sober and Wilson’s model is
not in any sense reductionist, since it must be acknowledged that group-
level processes form a necessary condition for the evolution of altruism.
However, the fact that a population-level trait must be in place for the
model to work does not mean that altruism itself arises as a result of group
selection. There may, however, be a case for population-level selection
here, but for the group-level property of biased subgroup formation, not
for the individual-level property of altruism.

To see this, we must switch the roles played by altruism and biased
subgroup formation such that the latter is a cause and the former a mech-
anism. Viewed in this way, group selection is established between individ-
ual populations of organisms, not for altruism, but instead for periodic
biased subgroup formation. Selection will favor those populations of or-
ganisms that contain altruists and periodically divide into biased sub-
groups over populations of organisms that do not contain altruists as well
as those that do contain altruists but do not divide into biased subgroups.
Take for example some population with the characteristic of periodically
fragmenting into kin groups. A population that contains a substantial
number of altruists that periodically fragments itself in this fashion
would prosper at the expense of populations that are also partially com-
posed of altruists, but which do not fragment themselves in this way.
Such a population would also be selected over populations that contain
no altruists at all.

The key question to ask, then, is whether the tendency of a population
to sort itself into biased subgroups is a characteristic of the population as
a whole or a characteristic of individual organisms. This is not always an
easy question to answer. When subgroups are biased in their proportion
of altruists owing to each altruist’s ability to recognize other altruists, it
seems pretty clear that the bias is owing to a characteristic of individual
organisms. When subgroups are biased in their proportion of altruists
because of random subgroup formation processes within the population,
we have a clear example of a group-level characteristic that is responsible
for the bias. When the bias is owing to kin-group formation, the case seems
more ambiguous and one would need detailed examples in order to decide.
But if it is a population-level property that is responsible for the formation
of biased subgroups, then altruism at the organismic level could count as
a condition that must be in place in order for the group-level property of
biased subgroup formation to perpetuate itself. So perhaps Sober and
Wilson’s model is a model of population selection after all, but not a model
of group selection for altruism. Instead, Sober and Wilson’s model can be



  : ⁄  47

construed as a model showing how a population-level property of biased
subgroup formation can be selected for when as least some members of
the population are altruists.

Altruism itself is not favored by population-level selection; Sober and
Wilson’s groups, after all, are not properly speaking altruistic. But group
structures are at work in the evolution of altruism, since a peculiar group-
level property, biased subgroup formation, is a necessary condition for
the perpetuation and spread of altruism within the population. And con-
versely, the peculiar property of biological altruism among members of a
population is a necessary condition for the selection of populations that
assort themselves into subgroups made up of unequal numbers of altruists,
over populations that lack at least one of these characteristics. Sober and
Wilson have simply confused the importance of a group-level property for
the evolution of altruism with the group selection for altruism.

It is no surprise that Sober and Wilson’s model should turn out to be
one that shows the possibility of group selection, since it relies on such a
peculiar group-level trait, namely the periodic assortment of population
members into biased subgroups. In calling their model one that shows the
possibility of group selection, I mean to say that they have shown how
some irreducibly population-level property, such as periodic random sub-
group formation, could be selected over an alternative irreducibly popu-
lation-level property, such as not forming temporary subgroups at all.
Group selection, as I understand it, is a process by which groups with one
property outcompete groups with a different property, by increasing the
number of groups with the superior trait at the expense of the groups with
its inferior alternative. Group selection on my understanding is a matter
of the selection of some group-traits over others; what makes it group
selection rather than organismic selection is a matter of which sort of entity
has the trait.

9. Conclusion. To sum up, I have argued the following. First, what counts
as altruistic behavior, at least of the sort that stands a fighting chance of
evolving by natural selection, is not merely behavior that is detrimental
to the fitness of the agent. To evolve by natural selection, altruistic be-
havior must benefit others above and beyond the benefits that they accrue
from the corresponding fitness loss on the part of the altruist. Second,
when altruism does evolve it evolves because, on average, altruistic genes
indirectly benefit other altruistic genes more than they benefit nonaltruistic
genes. Altruistic behaviors are ones that increase fitness indirectly, through
benefiting other individuals within a population who share an altruistic
disposition. Third, group selection is not implicated in the evolution of
altruism on Sober and Wilson’s model. But, though they did not realize



 48

it, Sober and Wilson’s model does show how selection could favor some
individual populations of organisms that contain altruists and periodically
divide into biased subgroups over other populations that contain altruists
but do not divide into biased subgroups. Such a process can legitimately
be called group selection. It is worth remarking, however, that none of the
criticisms I have made of Sober and Wilson’s model is aimed at refuting
it. The model stands as a powerful instrument for explaining the evolution
of altruism. Instead of refuting the model, I have shown that group selec-
tion is not implicated in its workings in the manner that Sober and Wilson
suggest.

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Cartwright, Nancy (1979), “Causal Laws and Effective Strategies”, Nous 13: 419–437.
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Hesslow, Germund (1976), “Discussion: Two Notes on the Probabilistic Approach to Cau-

sality”, Philosophy of Science 43: 290–292.
Sober, Elliott, and David Sloan Wilson (1998), Unto Others: The Evolution and Psychology

of Unselfish Behavior. Cambridge: Harvard University Press.
Williams, George (1966), Adaptation and Natural Selection: A Critique of Some Current

Evolutionary Thought. Princeton: Princeton University Press.