Philosophy of Science, 76 (April 2009) pp. 201–224. 0031-8248/2009/7602-0005$10.00
Copyright 2009 by the Philosophy of Science Association. All rights reserved.

201

Selection and Causation*

Mohan Matthen and André Ariew†

We have argued elsewhere that natural selection is not a cause of evolution, and that
a resolution-of-forces (or vector addition) model does not provide us with a proper
understanding of how natural selection combines with other evolutionary influences.
These propositions have come in for criticism recently, and here we clarify and defend
them. We do so within the broad framework of our own ‘hierarchical realization model’
of how evolutionary influences combine.

1. Introduction. In Matthen and Ariew 2002, we argued for the following:

(A) Natural selection is not a cause of evolution. (We are not opposed to
Darwin and the modern synthesis—quite the contrary. Rather, we
argue that the relationship envisaged by these theories is not a causal
one.)

(B) A resolution-of-forces (or vector addition) model does not provide us
with a proper understanding of how natural selection combines with
other evolutionary influences such as drift, mutation, migration, etc.

(C) Our own ‘hierarchical realization model’ offers a better understand-
ing of the interplay of these evolutionary influences.

Propositions (A) and (B) have come in for criticism recently, and our aim
in this article is to respond to these criticisms. We want to do this in a
systematic way, however, not piecemeal. Thus, we structure our replies with
an eye toward our positive view (C), which we adumbrate and extend as
we proceed.

2. Trait Variance and Causation. The first thing to do is mark the dif-
ference between (A)—the claim that natural selection is not a cause of

*Received June 2008; revised May 2009.

†To contact the authors, please write to: Mohan Matthen, Department of Philoso-
phy, University of Toronto, 170 Saint George St., Toronto, ON M5R 2M8, Canada;
e-mail: mohan.matthen@utoronto.ca. André Ariew, Department of Philosophy, 434
Strickland Hall, University of Missouri–Columbia, Columbia, MO 65211; e-mail:
ariewa@missouri.edu.



202 MOHAN MATTHEN AND ANDRÉ ARIEW

evolution—and a different, but superficially similar, proposition. Consider
a common example. A population of moths contains two variants, a dark-
colored kind D and a light-colored kind L. D-type moths are well-cam-
ouflaged in a sooty environment in which the tree trunks on which they
sit are darkened by soot. L-type moths are not well camouflaged in this
environment. Consequently, D-type moths are less subject to predation
in a sooty environment and their frequency increases in the population
compared to L-type moths. In a cleaner environment, L-type moths would
have had the advantage with regard to camouflage and would have in-
creased in frequency.

In this case, it is clear that the variation in camouflage causes evolu-
tionary change in the moth population. This can be seen by appealing to
various tests that philosophers standardly use to identify causal relations.

The probability raiser test (T1) says that

C causes E only if the C raises the probability of E. (An ‘only if ’—
necessary—condition is not a test, but we shall ignore this here, since
our main critical concern is with situations where the condition is
not met; hence something is found not to be a cause.)

Applying this to the case: D-type moths are better camouflaged than
L-type moths in a sooty environment. Since better-camouflaged moths
are more apt to be picked off by predators, this variation in camouflage
raises the probability of D increasing in frequency relative to L. Thus,
this test does not rule against the claim that variation in camouflage causes
the increase in the frequency of the D-type moth—which is an evolutionary
change.

More tellingly, consider the manipulability test (Woodward 2003). (We
use a version of this test that is appropriate to probabilistic causation,
and where cause and effect are variables that take numerical values.)

Manipulate C ‘exogenously’, that is, do not just examine cases where
C takes on a different value in normal contexts where the whole nexus
of surrounding variables also changes. Rather, create such a case by ac-
tively manipulating the value of C while holding everything else the same.1

Now observe what happens to E, a putative effect of C.
The manipulability test (T2) says that

1. Suppose, for example, that you are testing whether falling atmospheric pressure
or falling barometer readings cause wind. According to the proponents of the ma-
nipulability test, you don’t want to examine cases where both the barometer readings
and the atmospheric pressure are (as normal) falling together. Rather you want to
put the barometer in a pressure-controlled box so that its readings can be held at a
low value independently of atmospheric pressure. If, when the barometer reading
has been manipulated in this way, a wind rises up, one may conclude that low
barometer readings cause wind.



SELECTION AND CAUSATION 203

C causes E if and only if we can manipulate the probability-distri-
bution of E by means of some exogenous manipulation of (or ‘in-
tervention’ on) C.

Suppose that we exogenously manipulate the camouflage advantage that
D enjoys by painting all the trees white. Presumably, this intervention
would reduce the probability that Ds increase in proportion. By the ma-
nipulability test, this would imply that variation in camouflage causes the
D-type to increase.

These tests give us excellent reasons for endorsing

(Â) Variation in camouflage causes evolutionary change (of the moth
population).

Nobody today doubts this result, least of all us, though (as we will
show in Sections 5 and 6) there are some puzzles surrounding the exact
nature of this causal relationship, and its proper analysis turns out to be
philosophically interesting.

The reason why we have dwelt on this obvious fact is that the prop-
osition that we have just endorsed is not the same as

(Ā*) Natural selection causes evolutionary change.2

And it is, of course, (Ā*) that is required to show that (A) is false.
The difference between (Â) and (Ā*) is not marked by some of our

critics. Roberta Millstein (2002, 2006), who claims that natural selection
is a population-level cause, contents herself with arguing in support of
propositions like (Â)—which, we repeat, we do not contest. In her article,
Millstein employs tests of causation just like the ones mentioned above.
Her aim is to show that natural selection and drift are causes of evolu-
tionary change. To establish her point, she considers various tests of the
form ‘C causes E if and only if R(C, E)’. But she does not show us how
the term ‘natural selection’ is supposed to take the place of ‘C ’ in these
formulae. Millstein says that she wants to establish a ‘causal basis’ for
evolution. We have no quarrel with this—(Â) is an example of just such
a causal basis. Our claim is that natural selection is the wrong sort of
thing to play a causal role.

We hope it is clear that we are concerned with an ontological question,
not a scientific one. We do not want to debate whether variation in cam-
ouflage actually caused evolutionary change, or whether differences in
fitness-relevant traits actually played a role in evolution. We are rather
concerned with the meaning and ontological commitments of the claim

2. We mark propositions we contest with an asterisk.



204 MOHAN MATTHEN AND ANDRÉ ARIEW

that natural selection caused evolution. What is natural selection and how
does it influence gene or trait frequencies?3

3. Reifying Natural Selection. In this section, we consider some prelim-
inary reasons for being puzzled by the claim (Ā*), that natural selection
causes evolution. We do this by once again applying the tests mentioned
above, but this time to natural selection. First, the probability raiser test.
Does the operation of natural selection raise the probability that the D-
type moths will increase in frequency? If not, it is not a cause. Second,
is there a way of manipulating the probability that the D-type moths will
increase in frequency by intervening on natural selection? If not, it is,
once again, not a cause.

Before we can tackle these questions we need to address a prior question.
What exactly is natural selection? What entity or process are supporters
of (Ā*) talking about here as a cause of evolution? In this section, we
assume Sober’s fairly orthodox treatment (1984, 21–22): natural selection
is evolution due to heritable variation in fitness.4 To this, we add an
important clarification adapted from Millstein (2002) and Christopher
Stephens (2004).

Millstein and (following her) Stephens make a distinction between drift-
as-process and drift-as-product (or outcome).5 Let us say for present pur-
poses that evolution is a longterm change in gene frequencies in a pop-
ulation.6 For Millstein and Stephens, drift-as-product is the culmination
of a drift-driven evolutionary process, the new gene frequency that results.
Drift-as-product is not a cause of evolution; in this conception, it is the
result of a certain kind of evolutionary process. Drift-as-process, on the
other hand, is supposed to be a causal process that drives a population
to a new gene-frequency level. “It is the process notion of drift that is
needed to understand its role as a cause,” Stephens says (2004, 557).7 He

3. We see our argument as opposing Elliott Sober’s in Chapters 1 and 3 of The
Nature of Selection (1984)—Sober’s argument is ontological in the sense intended
here.

4. Millstein has a related but subtly different account, to which we shall return later.

5. Millstein uses the term ‘outcome’, but we like the resonance of the traditional
process-product distinction.

6. Gene frequencies fluctuate from generation to generation. Our concern is with
the overall trend line: evolution occurs when there is a change in gene frequencies
after short-term fluctuations have been smoothed out.

7. Godfrey-Smith (2007) seems to overlook this distinction. He observes that there
are ways of estimating drift and uses this to admonish us for our skepticism about
drift-as-process. He fails to notice that he is appealing to methods of estimating
drift-as-product.



SELECTION AND CAUSATION 205

goes on to suggest that drift-as-process is a variable-strength force that
drives evolutionary change. According to Millstein in particular, drift-as-
process is something over and above the sequence of births, deaths, and
matings that add up to that new frequency; it is a motor that acts on a
population, driving it to new gene-frequency rates. (Millstein holds that
drift-as-process and selection-as-process are two different motors working
on a population; later we’ll comment on this briefly.)

Sober holds that natural selection is evolution due to heritable variation
in fitness. By analogy with Millstein’s notion of drift-as-process, it is
selection-as-process that he is talking about. Selection-as-process would
be not merely the sequence of events leading from variation in heritable
fitness and culminating in a new gene frequency, but a variable-strength
force that appears or is generated when organisms have heritable differ-
ences that lead to differential reproductive success—a motor that drives
fitter types to greater frequencies within a population. The greater the
variation in these traits, the more powerful the motor.8

Sober appears to take the causal efficacy of this motor quite literally:
“Selection for is the causal concept par excellence. . . . An organism’s
overall fitness does not cause it to live or die, but the fact that [for example]
there is selection against vulnerability to predators may do so” (1984,
100).

Selection for a trait causes animals to die, Sober says.9 (Stephens [2004,
561] endorses the thought.) Since causes and effects are distinct, it follows
that

(1) Selection-for-trait-T ( the death of animals.

Again, fitness (unlike selection-for-trait-T ) does not cause anything to die,
according to Sober, and presumably he thinks that the same is true of
variations in fitness. So,

(2) Selection ( variation in fitness.

8. Robert Brandon (1978) advances a variation on this idea. He thinks that fitness
is a differential strength propensity in individuals, which drives them to reproduce
in different numbers. Population-level changes in frequencies of types result from
the differing fitnesses of individuals, according to Brandon. See also Bouchard and
Rosenberg 2004 and Rosenberg and Bouchard 2005. The argument that we provide
against Sober’s view could be modified to take in Brandon’s view as well.

9. Well, he says that it may do so, but this should be taken in the context of the
emphatic first sentence of the quotation. Actually, we suspect that Sober slipped,
and did not mean to say that selection for caused an animal to die, or even that
the-fact-that-there-is-selection-against-vulnerability-to-predators did this. But since
Stephens takes off from this thought, and since, further, we are not sure what Sober
really meant to say, we will simply let the quotation stand.



206 MOHAN MATTHEN AND ANDRÉ ARIEW

Obviously, also,

(3) The death of animals ( variation in fitness.

These propositions imply that there are three things here. Evolution
does not occur merely because types of organism reproduce and die in
differing amounts. Rather it is driven by natural selection. Natural se-
lection is a tertium quid on Sober’s account,10 an intervening variable that
drives the process. The causal diagram in evolution-by-selection would
go like this, according to his account:

heritable variation in trait T r selection of magnitude proportionate
to variance in heritable fitness due to heritable variation in T r birth
and death of animals r evolution.

If the quote from Sober above is to be taken literally, selection is a Grim
Reaper, killing a weak organism here, preserving a strong one there.11

And Stephens would have drift be its Grimmer Brother, killing at random.
(Of course, selection and drift have a more erotic side also—they cause
animals to mate and reproduce.) Millstein, for her part, believes that
selection is a process by which heritable variation leads to evolution—
heritable variation in fitness is the input to this process—but she believes
that it acts on populations, not individuals.

Does it make sense to think of selection in this way—that is, as a tertium
quid that drives evolution? The manipulability test of causation employed
above directs us to envisage situations in which we intervene on natural
selection in the above causal diagram, leaving heritable variation in T
and the environment unchanged. The question we are supposed to ask
is, would the probability of evolution in the moth population due to
variation in camouflage change if we changed or eliminated the interven-
ing variable, selection? The answer is surely no. For if the D-type and L-
type moths have differential reproductive success, the probability of evo-
lutionary change will be high even in the absence of any such tertium
quid. This outcome does not depend on the existence or the magnitude
of a tertium quid. Take a coin that is biased towards heads. The bias
implies that it is probable, in a series of tosses of this coin, that heads
will come up more often than tails. No process of ‘toss selection’ is needed
for this result. Similarly, in the presence of heritable variation, it is math-

10. Actually, it is selection for and selection against that are so treated, not selection
as such—we will take this as read.

11. Brandon (see note 5) is, for his part, committed to the causal efficacy of individual
fitnesses. He and Ramsey claim in a current project that, in effect, it is a cause of
births over and above causes such as sexual intercourse, fertilization, etc., and sim-
ilarly a cause of death over and above disease, predation, etc.



SELECTION AND CAUSATION 207

ematically necessary that evolutionary change is probable.12 No interven-
ing variable is required.

For exactly the same reason, the probability raiser test also fails: given
a certain level of heritable variation in fitness, increasing or decreasing
the strength of intervening variables does not change the probability of
evolution taking place. (Shapiro and Sober object to this argument; we’ll
turn to their objection presently.)

It should by now be clear at least that the following inferential slide
by Millstein is problematic: “If . . . we introduced a new beetle genotype
into the population that was able to withstand a greater range of tem-
perature than any of the existing genotypes, we would expect that the
reproductive successes of the other genotypes would decrease. . . . Thus,
selection satisfies a manipulability account of causation” (Millstein 2006,
633; emphasis added). Millstein argues that manipulating variation in
temperature resistance would result in a change of genotype frequencies.
She infers that manipulating selection would result in the change of ge-
notype frequencies. This is precisely the move that we oppose.13

4. The Force-Body Paradigm. Millstein moves from (4) to (5*):

(4) Variation with respect to trait T caused evolutionary change in pop-
ulation P.

(5*) Natural selection caused evolutionary change in population P.

How does she think that this inference is to be justified?
In an earlier article, Millstein says that random drift is “an indiscrim-

inate sampling process in which physical differences between organisms
are causally irrelevant to differences in their reproductive success” (2002,
171). And natural selection, by contrast, is supposed to be a discriminate
process in which physical traits are relevant to differential reproduction
rates. In other words, she holds

12. According to J. H. Bennett, R. A. Fisher wrote to his publisher of his own
“impudence in treating the subject as a branch of mathematics” ([1930] 1999, ix).
Fisher was well aware, in other words, of how he had placed a mathematical theorem
at the heart of his treatment of evolution. Some (e.g., Brandon) think that this
trivializes the subject. We agree with Sober that on the contrary, treatments of
Fisher’s ilk, though mathematical, illuminate an aspect of the causal structure within
which evolution is embedded, and should hence be regarded as explaining evolution.
“Explanation, to be illuminating, need not single out the events that actually did
the causing,” Sober says (1984, 96).

13. In Matthen and Ariew 2002, 62, we say, eyesight leads to differences between
[phenotype fitnesses]—but not drift or ‘neutral’ selection. We meant to be clear
throughout that it is selection that is being denied causal status, not traits such as
good eyesight.



208 MOHAN MATTHEN AND ANDRÉ ARIEW

(6*) Natural selection is the process by which variation in fitness-relevant
traits causes evolutionary change in a population.

(6*), together with the uncontested proposition (4), implies the contested
proposition (5*). Note that there is a certain similarity between the causal
diagram implied by (6*) and the one that we encountered earlier in Sober
and in Stephens. There may be a difference between the two positions,
however, because Millstein believes that selection operates on populations.

One reason for reifying natural selection in this manner lies in a (faulty,
as we shall argue) analogy between equations of population genetics—
such as Fisher’s Theorem—and certain equations of physics. The equa-
tions of population genetics describe the behavior of ensembles of or-
ganisms in terms of ensemble-level parameters.14 For example, Fisher’s
theorem relates the variance of fitness in an ensemble to the rate and
magnitude of increase of its average fitness. Similarly, the equations of
physics describe the behavior of particles in terms of particle-level
parameters.

Think, for example, of Newton’s Law of Gravitation: .2F p G(m*m /r )1 2
This law governs a certain interaction between pairs of massive particles.
But most physicists think that this interaction is mediated by a tertium
quid—the force of gravitational attraction. In other words, they hold that

(7) A massive particle P1 caused another massive particle P2 to move.

is true in virtue of

(8) The gravitational attraction exerted by P1 caused P2 to move.

14. We prefer the term ‘ensemble’ to ‘population’ here. Millstein adopts Futuyma’s
definition of population as “a group of conspecific organisms that occupy a more
or less well-defined geographic region and exhibit reproductive continuity from gen-
eration to generation” (Millstein 2002), and she seems to think that in mathematical
‘population’ genetics, variables such as size, variance, and growth rate are defined
over populations in this sense. This is not exactly correct. A lot of the discussion
within population genetics proceeds in quite abstract terms, and the restriction to
populations is unnecessary. Theorems such as Fisher’s Fundamental Theorem or
Price’s equation apply indiscriminately to any set of organisms, conspecific or not,
connected by region and ancestry or not. Consider a set S consisting of ten organisms
randomly drawn from each mammalian species. S is not a population in Futuyma’s
sense; it fails all of the tests in his definition. Nevertheless, the average fitness of S
will increase, in accordance with Fisher’s Theorem, in proportion to its additive
genetic variance in fitness. Of course, there are some results in population genetics
that apply only to populations in Futuyma’s sense: for instance, the disappearance
of an allele from S does not imply fixation of the alternative allele. Similarly, species
and speciation depend on such populations. All the same, one should not lose sight
of the purely mathematical and abstract side of population genetics.



SELECTION AND CAUSATION 209

Thus, physicists diagnose gravitation in terms of the following causal
diagram:

mass of two particles r gravitational attraction of magnitude pro-
portionate to product of masses r motion.

Let us call this the ‘force-body paradigm’. In physics, this paradigm looks
for forces such as gravitation to mediate the interactions of particles.

This is where the analogy between equations of physics and of popu-
lation genetics comes into the picture. Millstein, in common with many
biologists, seems to apply force-body paradigm to populations. She moves
from variance with respect to some trait T influencing evolutionary change
to a force that mediates the influence that variance with respect to T has
on evolutionary change. This intermediary, she contends, is natural se-
lection. Likely, this kind of reasoning is the ultimate source of the causal
diagram that we attributed to Sober and Stephens in Section 3.

In our opinion, the force-body paradigm is misapplied to natural se-
lection and drift. It is a background assumption of most philosophical
theories of causation that logical or mathematical implications do not fall
under the notion of causation. Manipulate a man’s marital status while
leaving all else the same, and you will change whether he is a bachelor.
(For that matter, manipulate his marital status, and you will change his
marital status.) But surely one does not want to say that being unmarried
causes him to be a bachelor (or that his marital status causes his marital
status). Being unmarried is for him no different from being a bachelor.
Similarly, intervene on the number of items in a collection by adding one
member, leaving all else the same, and you will change whether that
collection is odd- or even-numbered. But surely it would be a mistake to
think that number is a cause of being odd or even. Causes have to be
distinct from their effects.

It is precisely in order to avoid errors of this sort that Hausman and
Woodward say of the manipulability test: “Mechanisms are distinct if and
only if it is in principle possible to interfere to disrupt one while leaving
the other alone. . . . Causation is connected to manipulability and that
connection entails that separate mechanisms are in principle independently
disruptible” (1999, 539–40). In the same vein, Hall says: “I will also take
it for granted that we can adequately discern when two events fail to be
wholly distinct—that is, when they stand in some sort of logical or mereo-
logical relationship that renders them unsuited to stand in causal rela-
tionships” (2004, 226). The force-body paradigm works in physics. Grav-
itation satisfies the tests for causation, and is, moreover, distinct, in the
sense of the two quotes given above, from the interaction of the two
particles. However, natural selection is not in the requisite sense distinct
from heritable variation of fitness.



210 MOHAN MATTHEN AND ANDRÉ ARIEW

Let’s look at the gravity case first. In order to test, for example, whether
the gravitational attraction exerted by the moon is the cause of the motion
of the tides, one must hold the masses of these bodies constant, while
intervening on gravitational attraction between them. At first sight, the
test works. Suppose that we cranked up the gravitational attraction of
the moon while holding its mass and the mass of the oceans constant.
Then the tides would be higher.

Now, it might seem misguided to speak of ‘cranking up’ gravitation in
this way. Since the gravitational attraction between two massive particles
supervenes on their masses, one might think that one cannot manipulate
gravitational attraction in the manner proposed. The only way to ma-
nipulate gravitational attraction is to change the masses that are attracting
one another. Thus, one might want to understand the ‘hold everything
else the same’ or ‘independent disruption’ stipulation of the manipulability
test liberally, in order to permit changes to a supervenience ‘base’ when
one wants to intervene on the supervenient property. This, at any rate, is
how Shapiro and Sober (2007) would have us proceed. So to test whether
the moon’s gravitational force influences the tides, Shapiro and Sober
would presumably have us change gravitational attraction by changing
the masses. They go on to suggest that when we use the manipulability
test to check whether natural selection causes evolutionary change, we
should be permitted to change items in the supervenience base of natural
selection—individual births and deaths, variation in fitness-related traits,
and so on.

We do not agree that loosening the ‘hold everything else the same’
condition is the right way to address the supervenience problem. Let’s
start with the case of gravitation. How would you test whether gravita-
tional attraction is an intervening cause in between mass and motion? If
you intervene on the masses of the moon and the oceans in order to
intervene on gravitational attraction, all that you test is whether these
masses influence the movement of the tides, not whether gravitational
attraction is required as an intermediary. So you have to hold these masses
the same and intervene on gravitation. This does not pose as much of a
problem as Shapiro and Sober suppose—at least not for the philosopher.
For as Woodward argues in effect, it is possible to intervene on gravi-
tation—if you understood ‘intervention’ and ‘manipulation’ properly. He
writes:

Consider, for example, the (presumably true) causal claim (G):

(G) The gravitational attraction of the moon causes the motion of
the tides.

Human beings cannot at present alter the attractive force exerted by



SELECTION AND CAUSATION 211

the moon on the tides (e.g., by altering its orbit). More interestingly,
it may well be that there is no physically possible process that will
meet the conditions for an intervention on the moon’s position with
respect to the tides. . . . It is nonetheless arguable we have a prin-
cipled basis in Newtonian mechanics and gravitational theory them-
selves for answering questions about what would happen if such a
surgical intervention were to occur and that this is enough to vindicate
the causal claim (G). (Woodward 2008)

Woodward proposes, rightly in our view, that “a properly formulated
version of a manipulability theory will thus allow us to talk about causal
relationships in some contexts in which interventions are not physically
possible” (2008).

We believe that it is possible to envisage a ‘surgical intervention’ on
gravitation itself. Accordingly, we would like to say (paraphrasing Wood-
ward) that we have a principled basis in Newtonian mechanics for an-
swering questions about what would happen if we (or God) were to sur-
gically intervene on the relationship between mass and gravitational
attraction. If we made it, for instance, an inverse-cube relation instead of
an inverse-square relation, or changed the gravitational constant, then we
would change the gravitational force exerted by the moon without chang-
ing the mass of the moon or of the ocean. Newtonian mechanics would
lead us to expect that in such a case, the motion of the tides would change.
This is why we say that according to Newtonian mechanics, gravitational
attraction is an intermediary between mass and motion—a tertium quid
as the force-body paradigm urges. Physically impossible intervention is
the proper analytic tool for supervenience cases, not loosening the ‘hold
everything else the same’ clause.

As implied by the earlier discussion, the theory of natural selection is
different from that of gravitation, for natural selection is mathematically
necessary. When there are heritable differences in traits leading to differ-
ential reproduction rates, the probability of the fitter types increasing in
frequency is greater than that of the less-fit types increasing. This is simply
a mathematical truth. Applying the manipulability test, we have to tolerate
hypothetical interventions that are physically impossible, but refuse to
tolerate hypothetical interventions that are mathematically impossible.
This is why the manipulability test cannot properly be applied to

(5*) Natural selection caused evolutionary change in population P.

There is no room for a manipulable intermediary between advantageous
heritable traits and the increase in frequency that results from their being
advantageous. Such an intermediary would not be distinct from the in-
crease in frequency. The analogy with gravitational attraction is flawed.



212 MOHAN MATTHEN AND ANDRÉ ARIEW

This is the point that Stephens (2004), Kenneth Reisman and Patrick
Forber (2005), and Shapiro and Sober (2007) all miss. Stephens observes
that drift is dependent on population size—that is, that the smaller the
population, the less predictable the result of natural selection. He imagines
the following situation:

Suppose there are two sets of populations, each with two kinds of
otherwise identical individuals. One kind of individual has a trait
(T1) is fitter that the alternative (T2). In one population set, there are
20 (isolated) groups each with 6 individuals, whereas in the other set
there are 20 (isolated) groups each with 1,000 individuals. Suppose
that every group in each population set begins with exactly 50% T1
and 50% T2. Imagine that the population evolves, and, as expected,
the number of groups in which T1 goes to fixation in the second
population set is much higher than in . . . [the first]. . . . Why?
Answer: drift. (Stephens 2004, 564)

Along much the same lines, Reisman and Forber argue that drift is a
cause of evolutionary change because when one manipulates drift by
changing population size one thereby changes the probability value and/
or magnitude of evolutionary change. Finally, Shapiro and Sober say:

Selection and drift are distinct processes whose magnitude gets mea-
sured by different population parameters (fitness on the one hand,
effective population size on the other). And changes in each of these
parameters will be associated with changes in the probabilities of
different outcomes. If you intervene on fitness values while holding
fixed population size, this will be associated with a change in the
probability of different trait frequencies in the next generation. And
the same is true if you intervene on population size and hold fixed
the fitnesses. (2007, 262)

What these critics miss is that the connection between population size/
variation-in-advantageous-traits and drift/selection is purely mathemati-
cal. This connection is the same as that which holds between sample size
and proportional variance from the mean in random sampling. Nobody
would say that the numerical ratio between 4 and 100 is the cause, in any
literal sense of ‘cause’, of there being a higher proportional variance from
the mean when sets of 4 are randomly sampled than when sets of 100 are
so sampled. Sample size and variance under random sampling are con-
nected by a mathematical law, and thus they are not sufficiently distinct
from one another to count as terms in a cause-effect relationship. Cer-
tainly, it is right to say that selection and drift are part of the explanatory
apparatus used to explain evolutionary change. But as Sober says, “Ex-
planation, to be illuminating, need not single out the events that actually



SELECTION AND CAUSATION 213

did the causing” (1984, 96; see our note 9). In other words, selection and
drift can be explanatory (and thus answer Stephens’ ‘Why?’) without being
causes of evolutionary change. This is what Stephens and the others fail
to understand.

5. Causation and Locality. We said earlier that we do not contest on
general principle propositions of the following form:

(4) Variation with respect to trait T causes evolutionary change in
population P.

That some propositions of the form (4) are true and account for evolution
should not be a point of contention between our critics and ourselves.
There is, however, an interesting complication as to the nature of the
causal link asserted by (4), and we shall go into this now.

To appreciate the nature of the complication, let us look first at the
following simple example.

CM Example.

i. Let S be a system consisting of two particles of equal mass. At
time t these particles are moving in exactly opposite directions
at exactly the same speed. At t, therefore, the center of mass
(CM) of S is stationary.

ii. Now, suppose that at time t � d, one of the two particles collides
with a barrier and starts to move in the opposite direction. Since
the particles are now moving in the same direction, the center
of mass (CM) of S begins to move. This change occurs at t �
d; that is, it is simultaneous with the reversal in the particle’s
direction of motion, though the two events are separated in
space.

It seems clear that in the CM example the collision at t � d has two
effects. First, it causes the colliding particle to change its direction of
motion. Second, it also causes the CM to change its direction of motion.
Now, this second causal link seems at first glance to violate a certain
condition on causation, to wit:

Locality Principle. Causal influence is transmitted from one physical
entity to another in a spatiotemporally continuous manner—that is,
by every point in between the two entities being affected.

It seems, that is, that a causal influence was transmitted from the collision
(or from the barrier) to the CM instantaneously, and without any changes
in the medium in between the barrier and the CM. This, moreover, seems



214 MOHAN MATTHEN AND ANDRÉ ARIEW

to violate a fundamental principle of the Special Theory of Relativity—
namely, that causal influence cannot be transmitted from one physical
entity to another at a speed faster than that of light.

It may seem that way on the surface, but in fact the Locality Principle
is not violated. The key to seeing why is to observe that the CM is not
a physical entity—it has no mass, for one thing. It is a derivative entity
that depends, as a matter of mathematical necessity, on other physical
entities—to wit, the two particles that make up system S. To influence
the CM it is (mathematically) necessary and sufficient to influence these
two particles. It is not necessary to transmit causal influence from the
collision site to the CM in order to get the latter to move. (Indeed, it
makes little sense to talk about a physical cause acting on a nonphysical,
or ‘fictional’, entity such as the CM.) One should, therefore, distinguish
between causal transmission, which must respect the Locality Principle,
and a more inclusive sense of causation, which need not do so. In the
more inclusive sense of causation, if x causes y, and y mathematically
implies z, then x inclusively causes z, even though the connection between
x and z is nonlocal.

Now, let us take an example from the theory of natural selection. An
(unfit) animal is caught in a predator’s jaws and killed. The squeezing of
the predator’s jaws causes the death of this organism, and in so doing
immediately affects the mean fitness of a population. There are two causal
connections here: the first between the squeezing of the jaws and the death
of the prey, the second between this same cause and the change of fitness.
The first of these connections respects the Locality Principle. The second,
between the squeezing and the change of mean fitness, however, does not.
This is not an anomaly: it can be accounted for in exactly the same way
as the CM example. Mean fitness is not a physical entity; rather, it is
ontologically dependent on physical entities. Thus, it is not the kind of
change that has to be mediated by causal influence that is transmitted
from one place to another. In fact, it does not even make sense to ask
where the mean fitness of the population is, much less to ask how fast
the influence was transmitted to it from the squeezing of the predator’s
jaws. Along the same lines, suppose that a new mutation occurs that
protects smokers from cancer. This too will affect the mean fitness of the
population instantaneously: the link between these events is not a process
that has to travel from one place to another with finite speed. In each
case, the relation of nonlocal causation is the logical product of the re-
lation of local causation and the relation of mathematical implication.
(See Figure 1.)

Stephens contests the account just given: “It is far from clear that [the
Locality Principle and other such conditions] are requirements on fun-
damental physical processes. My contention is that these are ad hoc re-



SELECTION AND CAUSATION 215

Figure 1.

quirements. What if one of our fundamental physical theories turns out
not to meet these criteria? . . . Quantum mechanics throws doubt on
[such criteria], since there are important senses in which quantum phe-
nomena is [sic] discontinuous” (Stephens 2004, 567–568; Millstein en-
dorses and relies on this argument as well).

This strikes us as completely unmotivated. Perhaps quantum processes
do, as Stephens claims, violate the Locality Principle and other classical
principles of causation. But is he really suggesting that the CM example
and the changes of mean fitness discussed above involve fundamental
physical processes that violate the Locality Principle and other such prin-
ciples? Here, we recall Hall’s witty remark: “Is this all it takes to achieve



216 MOHAN MATTHEN AND ANDRÉ ARIEW

nonlocality? (And to think that philosophers have been fussing over Bell’s
Inequalities!)” (2004, 236).15

The account that we have just offered—that CM and mean fitness are
nonphysical derivative entities, affected by nonfundamental causal con-
nections—is not only cribbed from treatments in classical statistical theory
of gases (Matthen and Ariew 2002, 79–80) but completely conforms with
biological orthodoxy. Natural selection is ontologically derivative on in-
dividual-level events such as births, deaths, and mutations—even Shapiro
and Sober are committed to this by their supervenience claim. It occurs
in ensembles as a mathematical consequence of events that involve mem-
bers of those ensembles. The latter events are brute physical occurrences—
they occur by the transmission of physical influence from one place to
another.

6. Why Selection Is Not a Force. Once the force-body paradigm has been
applied to natural selection, another idea follows rather naturally. It is a
commonplace idea of evolutionary theory that evolutionary change is
caused not only by differences of heritable fitness, but also by drift, mu-
tation, genetic constraints, and migration. If you think that natural se-
lection is a force that mediates differences of heritable fitness, then you
might think that drift, etc., are forces that act in different directions,
thereby opposing or assisting natural selection, or taking evolution in
different directions.

Elliott Sober is one person who has developed this idea in some detail.
The opening chapter of his classic book The Nature of Selection (1984)
is entitled “Evolutionary Theory as a Theory of Forces.” We have criti-
cized this conception in some detail (Matthen and Ariew 2002). We assume
that forces are vectors—entities that have magnitude and direction
(though the direction does not have to be spatial in a literal sense). A
theory of forces is, in essence, theory of how these vectors combine when
several of them are acting together. We argued that evolutionary theory
has no zero force law, no singleton force models, and most importantly,
no law of resolution of forces. We will not repeat these arguments here,

15. Stephens is not the only one of our critics who posits entirely new and mystical
forces of nature. Brandon and Ramsey (2007) say, “The propensity interpretation
of fitness is committed to the fundamental indeterminacy of the lives, deaths, and
ultimately reproductive successes of individual organisms.” The term ‘fundamental’
suggests that the indeterminacy of these events is like the indeterminacy of quantum
processes—no hidden variables will explain them. Along the same lines, it has some-
times been remarked to us that in General Relativity, there are causal influences that
fail the Locality Principle. The question, once again, is: do we really need these
exotic kinds of causation just to understand what is happening in the simple cases
we are describing?



SELECTION AND CAUSATION 217

but we do want to reply briefly to some criticisms, and then to conclude
by restating our alternative.

Our basic reason for denying the ‘resolution of forces’ model was this.
We have no way of estimating from the theory of evolution how two
factors combine. We said, “Suppose a certain species undertakes parental
care, is resistant to malaria, and is somewhat weak but very quick. How
do these fitness factors add up? We have no idea at all. The theory of
probability has no general way to deal with such questions? (Matthen
and Ariew 2002, 67). Stephens has two objections to this line of thought.
The first is the following: “Empirical observation is how one determines
how these factors ‘add up’. If we sample the members of the population,
the estimated fitnesses may tell us that the traits interact—the relationship
between these various possible traits may be additive or nonadditive”
(2004, 553). Actually, Stephens is simply rephrasing our own point.16 Sup-
pose that a force of one dyne is acting eastward from a point, and a force
of two dynes northward. The magnitude and direction of the resultant
force is determinate. (By the ‘parallelogram of forces’, the resultant acts
in a roughly north, north-easterly direction with a magnitude of �5 dynes.)
The resultant force is a mathematical function of the components. But
suppose that two organisms of species S that differ by x in strength will
differ by y in fitness. Suppose further that if they differ by a in speed,
they differ by b in fitness. Now suppose that two organisms differ by x
in strength and a in speed. By how much will they differ in fitness? This
is the kind of question that probability theory and population genetics
cannot answer.17 It isn’t that there is no answer in particular cases—rather,
it is that there is no general way of combining probabilities, unless the
occurrences are independent of one another. The joint fitness is simply
not a function of the separate fitnesses. Just as the probability of p & q
depends not just on the probability of p and the probability of q, but also
on the probability of p given q, so also the joint fitness of two traits
depends not just on the individual probabilities, but on a variety of in-
teraction factors at both the genic and the phenotypic levels. This is why
one has to resort to ‘empirical observation’ as Stephens puts it: one has
to estimate the interaction factors independently. The first disanalogy with
force, then, is that forces combine in a predictable way across the board,

16. Cf. Matthen and Ariew 2002, 67: “The overall fitness values . . . must be es-
timated statistically, that is, by looking at actual values for number of offspring,
and using these actual values to estimate expected values and other statistical
quantities.”

17. What is the relevance of probability theory here? Population genetics is a calculus
of frequencies, which interact in ways formally isomorphic to probabilities.



218 MOHAN MATTHEN AND ANDRÉ ARIEW

while distinct evolutionary influences combine case by case. We shall re-
turn to the consequences of this point in the following section.

Stephens attempts a second point against us. He says that mutation
and selection can add up in the way that forces do: “We can talk about
cases where the force of mutation more or less strongly opposes selection,
and cases where mutation operates in the same direction as selection. It
makes perfect sense to say that as the force of selection gets stronger
relative to an opposing mutation rate . . . the equilibrium frequency . . .
gets smaller” (2004, 554–555)

Robert Brandon echoes the point:

Consider mutation and migration. Both are similar in that they are
already net forces that could be broken down into their components.
Migration consists of immigration into a population and emigration
from it. Both can have effects on gene frequencies, which can then
be added together to get the force of migration; similarly for mu-
tation. In a simple system with one locus and two alleles, A1 and
A2, there is an actual number of mutations from A1 to A2, and an
actual number from A2 to A1. The change in A1 is simply the second
number minus the first. There is no problem in conceiving of these
as forces. (2006, 322)

Brandon and Ramsey (2007) extend the point. Suppose that we have
two alleles A and a. There is a net mutation rate of A to a of m and a
net migration rate of A-type organisms of n. Surely we can add mutation
to migration in such a case. Stephens and Brandon and Ramsey seem to
be giving us a general purpose method for compounding distinct evolu-
tionary influences. Thus, Brandon (2006, 334) concludes: “What I have
found surprising is how useful is the comparison” between evolutionary
theory and a Newtonian theory of forces.18

Stephens and Brandon are wrong about this. Once again, they are
overlooking interdependencies. Suppose that the rates of mutation, mi-
gration, and selection were dependent on one another. Then we couldn’t
calculate net change in the simple way that these authors suggest. That
is, we could not simply add mutation to migration, or to selection, and
assume that we have calculated net change. For as migration occurred,
the mutation rate would also be changing. To calculate net change, there-
fore, we would need to know how mutation varied as a function of mi-

18. Brandon agrees with (but, unfortunately, has never acknowledged) our conten-
tion that “drift should not be regarded as a force that can be added to others acting
on a population” (Matthen and Ariew 2002, 61). He thinks, as we do, that drift
ensues even when there are no differences of heritable fitness, no mutation, migration,
etc. Brandon calls this ‘Biology’s First Law’.



SELECTION AND CAUSATION 219

gration, and vice versa—and of course we would need the same quantities
for selection as well. Here too, combined change under selection, migra-
tion, and mutation is not a function of change under selection alone,
migration alone, and mutation alone. Additional independent variables
have to be specified.19

There is another problem in the Stephens-Brandon approach. In order
for the simple additive process they conceive of to work, selection, mu-
tation, and migration have to be cited in terms of genes. If these rates
are cited in genic terms, and if they are independent of one another, we
can add selection rates to one another and solve the above-mentioned
problem of combining strength and quickness.20 Or we can just count net
changes in gene numbers after the evolutionary influences have operated.
The problem, however, is that the theory of evolution does not always
specify selection and migration rates in terms of net results on allelic
frequencies. For the theory of evolution is not just interested in alleles:
it is also interested in adaptation and trait-selection (Lewontin 1974, in-
troduction; Walsh 1998). Differences of trait fitness are responsible for
changes in gene frequency: differences with respect to these traits are
responsible for differential reproduction rates, and the latter account for
changes of gene frequency. As well, phenotypes are at issue in discussions
of selection for, frequency-dependent selection, assortative mating, repro-
ductive strategies, body plans, and so on—and even migration. What
would it mean, then, for only gene frequencies and not trait frequencies
to be at issue? We would have to ignore trait interactions and look directly
at genes. Goodbye, Darwin. So long, Modern Synthesis.

If you base your theory of forces simply on the addition of gene fre-
quencies, you ignore the trait-based or phenotypic factors that are at the
heart of evolutionary theory. Evolutionary theory is a two-level theory—
it deals with both genotypes and phenotypes. The moment phenotypic
properties enter the picture, the resolution of forces becomes problematic.
We concede to Stephens and Brandon the important qualification that
gene additions and deletions can be handled in the manner of forces, when
these additions are specified in a manner that makes them independent

19. Our critics persistently ignore the problem of interdependencies. Brandon and
Ramsey, for instance, elaborate a number of different ways of estimating total evo-
lutionary change under multiple causes—methods that detect selection in terms of
its effects, methods that detect selection in terms of its causes, etc.—but fail to notice
that they are all subject to this same difficulty.

20. Other philosophers seem uncritically to accept the Stephens-Brandon approach.
We find instances in Godfrey-Smith 2007 and in Depew 2008.



220 MOHAN MATTHEN AND ANDRÉ ARIEW

of one another.21 But evolutionary theory ubiquitously deals with phe-
notypes. Fisher’s Fundamental Theorem is extremely difficult to state and
to prove for precisely this reason—it deals with the fitness of traits, not
genotypes and so he has to deal with dominance. The same holds true
for Price’s equation. Both theorems would have been much easier to state
if gene-frequencies and their rates of change were all that were at issue.22

7. Hierarchical Realization. Take a nexus of factors at work in some
evolutionary situation. Suppose that (i) tall people tend to mate with other
tall people, and (ii) dark-skinned people with other dark-skinned people.
Suppose that (iii) dark-skinned people tend at a higher rate than others
to migrate to a certain location, L, where (iv) relatively speaking, there
is selection in their favor, but (v) tall people are neutral with respect to
L, where (vi) their fitness is neither enhanced nor reduced. Suppose finally
that (vii) tall people tend overall to have more short offspring by reason
of mutation and dominance than vice versa. Suppose that each of these
tendencies is quantifiable in terms of the effect that each has on the rate
at which tall/short/dark/light people occur in future generations, relative
to the rate they occur in earlier generations. Suppose that these numbers
are known. Can their joint effect be calculated? Is it determinate?

As we said earlier, it is a fundamental principle of probability/frequency
theory that the rates of increase associated with each of these conditions
are insufficient to determine the joint effect of the suppositions offered
above. Consider tall people. The probability of their increasing in fre-
quency is influenced by the rates of increase associated with (i), (v), (vi),
and (vii). Correspondingly, the probability of dark-skinned people in-
creasing in numbers is influenced by (ii), (iii), and (iv). Note, however,
that the rate of increase in a certain subclass of dark-skinned people is
influenced by (i), (v), (vi), and (vii)—namely, that of tall dark-skinned
people; correspondingly, the rate of increase of a certain subclass of tall
people is also influenced by (ii), (iii), and (iv). Moreover, these rates are
influenced by dominance—how often tall/dark-skinned people have short/

21. Gene frequencies can be specified independently even when they are interdepen-
dent. If allelic additions and deletions are specified in brute numerical terms—and
this, pretty much, is the trick that Stephens and Brandon rely on—rather than as
functions of various other parameters, then they can be added. These brute numerical
additions and deletions are not, of course, how population genetics or field evolu-
tionists specify conditions. They don’t go around counting alleles. They are interested
in interconnections.

22. In Matthen and Ariew 2002, we discussed Li’s Theorem, which is essentially a
restriction of Fisher’s Theorem to allele addition alone and on the assumption that
growth rates are constant, hence independent. This theorem is very easy to state and
understand, because dominance relations, etc., do not enter the picture.



SELECTION AND CAUSATION 221

light-skinned offspring without mutation—and the interaction of the var-
ious genes that make up each complex. Inter-trait connections of this sort
are essential to the outcome, but their magnitude and influence are neither
implied nor counterimplied by conditions such as (i)–(vii). In probability/
frequency theory, the probability of conjunctions is not determined by
the probability of the conjuncts alone: the interdependence relations
among conjuncts, the relevant conditional probabilities or conjunctive
frequencies, have to be specified in addition. The same holds here.

It is by contrast a fundamental principle of Newtonian force-theory
that forces are vectors and combine by vector addition—the resultant
force of two forces is wholly determined by the magnitude and direction
of each force. Thus, forces have one kind of calculus of combination, and
probabilities another. It is our contention (Matthen and Ariew 2002) that
evolutionary influences such as migration, mutation, and selection com-
bine in the manner of propositional conjuncts in probability/frequency
theory, and not in the manner of forces combining by vector addition.
These algebras are quite different from one another. Hence proposition
(B) stated at the start of this paper: the resolution-of-forces model does
not provide us with a proper understanding of how natural selection
combines with other evolutionary influences, or for that matter how dis-
tinct selective influences combine with one another.

We offer Hierarchical Realization as a model of propositional con-
junction in probability/frequency theory? Consider the set of all possible
population histories, N. N assumes no facts about types of organisms, no
fact of the type exampled by (i)–(vii) above: each such possibility con-
cerning types is true in a subset of population histories, but since N
includes all of the histories that conform to these conditions as well as
all of the histories that violate them, N is neutral with respect to them.
Call it, therefore, the ‘neutral model’. Because the Laws of Natural Se-
lection (Fisher’s theorem, etc.) are mathematically true, we need no more
than the neutral model to understand them.

Now, each condition among (i)–(vii) corresponds to a subset of N, the
set of histories in which these conditions is satisfied. Each member of
such a subset is a realization of the corresponding history. Further, the
realization of the conjunction of conditions is the intersection of the sub-
sets that realize each condition taken separately. The point that we have
been emphasizing is that the frequencies that prevail in a realization of
component conditions are not the same as those that prevail in the set
out of which the realization is carved. Thus, the frequencies that prevail
in N do not predict the frequencies that prevail in any condition-defined
subset of N. And frequencies in the intersection of two conditions are not
mathematical functions of the frequencies in the sets that intersect.

The frequencies that prevail in the realization set corresponding to any



222 MOHAN MATTHEN AND ANDRÉ ARIEW

condition can be ascribed to the effects of that condition. For example,
if it turns out that the reproductive success of tall people depends on how
many other such people are around, it is plausible to cite condition (i)—
the assortative mating condition for tall people as a cause of the frequency
dependency of the success of tall people. Now, (ii), the assortative mating
condition for dark-skinned people, will combine with (i) in the intersection
of the realization sets of (i) and (ii). But note that (i) and (ii) give us no
reason to assume any particular pattern of assortative mating for tall
dark-skinned people—the strength of their preference for one another
might be quite different from that of dark-skinned people generally, or
tall people generally. Further, these conditions may combine in a quite
different way than other pairs of conditions—(iii) and (iv), for example.
The upshot is that there is no shared underpinning for conjunctions. In
Newtonian force-theory, the combination of forces is handed off to a
shared mathematical operation, the parallelogram of forces. In frequency
theory, the combination of conditions has to proceed case-by-case. Com-
bination depends on local conditions, as it were—on the causal influences
that operate with the particular traits or conditions that are thus com-
bining.

The theory of natural selection—mathematical population genetics—
is not as such concerned with added conditions such as (i)–(vii). Natural
selection is an abstract phenomenon that obtains in all possible population
histories. Natural selection is not even a biological phenomenon as such.
It holds in any history in which the terms of the theory can be jointly
interpreted in a way that accords with the abstract requirements of the
theory. Suppose that you have two bank accounts, one yielding 5% interest
and the other yielding 3%. One can treat units of money in each account
as the members of a population, and the interest rate as an analogue of
fitness. Provided that no money is transferred from one account to another,
one can treat these ‘fitness’ values as heritable—that is, the fitness of any
particular (nonoriginal) piece or unit of money can be ascribed to the
‘reproductive’ rate (i.e., interest) on preexisting units of money. Thus you
would have, as between the monies resident in the two accounts, variation
in heritable fitness. On this interpretation, Fisher’s Fundamental Theorem
of Natural Selection applies to your bank accounts: it predicts (correctly)
that the average interest earned by the two bank accounts taken together
will increase in proportion to the variance of interest rates earned by your
money in the two accounts.

Natural selection is wholly abstract, then, but its realizations are shaped
by concrete relations—these concrete relations are what determine the
value of the abstract parameters of natural selection. This is why, as we
have argued, variation with respect to a particular trait (such as cam-
ouflage) can be said to cause evolutionary change, but natural selection



SELECTION AND CAUSATION 223

cannot. This abstractness of natural selection is what our critics miss.
Brandon, Millstein, and Stephens are interested in selection as a causal
process. But they look for the causes in the wrong place—in the empirically
vacuous conditions that determine the set of all possible population his-
tories, rather than in the causally potent conditions that correspond to
specific biological traits and conditions.

Mathematical population genetics is, in large measure, an application
of probability/frequency theory. It is only with the concrete realization of
abstract quantities such as growth rates that biology enters the picture.
Once the hierarchical nature of realization is properly appreciated, it will
also be seen that there is no one causal process that different realizations
share. Bank accounts are not subject to the same causal processes as
populations of moths. Yet both instantiate Fisher’s Fundamental Theo-
rem. This is why it is a mistake to think that Fisher’s Theorem (or any
other theorem of population genetics) describes a unitary causal process.

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