Wayward Modeling: Population Genetics and Natural Selection

B. Glymour Draft 7/05 Please do not quote or cite 1

Wayward Modeling: Population Genetics and Natural Selection

Abstract: Since the introduction of mathematical population genetics by Fisher, Haldane

and Wright, its machinery has shaped our fundamental understanding of natural selection.

Natural selection is described by, and its consequences found by applications of,

population genetics models. Selection is taken to occur when differential fitnesses

produce differential rates of reproductive success, where fitnesses are understood to be

parameters in a population genetics model. To understand selection is to understand what

these parameter values measure and how differences in them lead to changes in

frequencies in biological populations. I argue here that this way of understanding natural

selection is fundamentally flawed. The descriptions of natural selection rendered by

population genetics models are in general neither predictive nor explanatory, and force

the resolution of a host of questions that turn out to be mere confusions. I conclude that

correct understand of natural selection requires a reconceptualization of the formal

machinery proper for modeling when the resulting models are intended to convey an

understanding of evolutionary processes in biological populations.

1. Introduction. What is natural selection, how do appeals to selection explain

evolutionary events, and how are descriptions of natural selection to be formulated if

such descriptions are to enable reliable forecasts of evolutionary outcomes; in a word,

how is natural selection to be understood? For some seventy years and more biologists

and philosophers alike have taken population genetics to provide the core formal

machinery for describing and understanding natural selection and the evolutionary events

it produces. I will call this assumption the core commitment. The core commitment has a

number of consequences within biology itself. For biologists, selection is understood to

be one among several forces driving deviations from Hardy-Weinberg equilibria. Such

measurable features as selection has are measured using the machinery of population

genetics; for example, the equations of population-genetics provide formulas for

calculating from a model the strength of selection, the opportunity for selection, and the

response to selection. The crucial parameter related to selection in population genetics

models is of course fitness, or its analytical relative, a selection coefficient. These are


written or estimated as some function of the expected reproductive success of classes,

individuated by appeal to phenotypic or genotypic properties. Accordingly, to

understand selection is to understand fitness and the way in which differential fitnesses

cause differential reproductive success.

Philosophers have by and large agreed, more or less uniformly adopting the core

commitment and in practice endorsing its consequences. Those concerned with the

conceptual foundations of evolutionary theory take the core commitment to delimit the

range of philosophical problems demanding investigation, and as well the range of

potential solutions to those problems. For philosophers, the most central of these

problems is to give an interpretation of the fitness parameter in population genetics

models according to which such a model, supplemented with parameter values at some

initial time t, provides an explanation, preferably a causal explanation, of the genotypic or

phenotypic population structure at some latter time t’. That is, the job is to either

describe some variable interpreted-fitness, whose values are a) measured by the fitness

parameters in population genetics models and b) reasonably taken to be properties

causally related to future class frequencies, or to show that no such variable is required to

makes sense of the explanatory import of population genetics models. A showing either

way implicitly or explicitly affords a formulation of the principle of natural selection,

where such a formulation connects differences in values of interpreted-fitness at t to type

frequencies at a later time t’.

So whether one’s attempt to understand selection is itself regarded as a bit of

biology or a bit of philosophy, for most that attempt has been framed by the core

commitment. It has been a presupposition of such endeavors that to understand selection

driven evolution in a population is to have an appropriately detailed population genetics

model of the population. I think the presupposition is in error. The task of interpreting

fitness, philosophers of biology will note, has proved so enormously difficult that despite

thirty years of work by some terrifically able people, we are nowhere near a plausible,

much less demonstrably correct, solution. The limitations of population genetics in

modeling evolutionary phenomenon are also not far to seek: while population genetics

models are often used diagnostically, e.g. to determine whether or not selection has acted

on a particular locus, for a large range of cases population genetics is both explanatorily


and predictively incompetent. More, the descriptive apparatus of population genetics

forces us to address a host of seriously intractable conceptual problems. I think the

reasons for these limitations are simple. Population genetics models evolving

populations with the wrong variables related by the wrong equations employing the

wrong kinds of parameters. I do not mean to impugn population genetics as false, or

even irrelevant. Rather, population genetics is, on its own, inadequate.

2. Predictive Incompetence. Consider a fully specified population genetics model of

some arbitrary population, fitted to data drawn from the population over some initial time

interval. We have a set of variables inducing a partition of the population into exclusive

classes, by genotype or phenotype, and perhaps other demographic features such as age,

geographical location, and so on. We further have a set of outcome variables, the

frequencies of those classes in the nth generation, for arbitrary n. Those outcome

variables are related to one another by some set of equations Oi(t’)=fi(O(t),X(t)), where

Oi(t’) is the value of the ith outcome variable in generation t’, O(t) is the set of values for

all outcome variables in the generation t, and X(t) is a set of values of further variables,

regarded as exogenous with respect to the outcome variables O. The functions fi specify

a functional relation between Oi(t’) and Oi(t), X(t) using various parameters, including

parameters representing mutation rates, migration rates and most importantly either

absolute WC or relative wC class fitnesses. In a fully fitted model, all parameters have

estimated values, and there is some specified joint probability distribution over all

variables without specific values, as for example error terms.

Now note that the absolute and releative fitnesses WC and wC are by definition

expectations relative to an environment, and the parameters in the fitted model are

therefore estimates of those expectations conditional on an environment. What exactly is

this ‘environment’? Minimally, specifying an environment amounts to specifying some

set of variables E probabilistically relevant to reproductive success, such that changing

the value of one or more of these variables changes the probability distribution over rates

of reproductive success for some class C in the population. We then have two choices.

We can individuate environments by specific sets of values for variables in E, or by

specific probability distributions over the variables in E. Let us, to avoid confusion, use


the term ‘instantiated environment’ to refer to a set of specific values E for the E

variables, and call a probability distribution over values for the E variables a ‘generalized

environment’.

Suppose we take it that estimates of fitness (i.e. the value of the fitness parameter

used in our fitted model) are estimates of the expected reproductive success relative to a

narrow environment. We fit our favored population genetics model to the measured data

taken from the population over generations 1 to i by using the data to estimate parameter

values and initial variable values. We then generate predictions from our fitted model as

to the behavior of the population over future generations i+1 to n, say. Nearly always our

predictions will be substantively in error, and for non-accidental reasons. Narrow

environments nearly always change over generational time. When they do, the fitnesses

estimated over generations 1 to i+1 will have, conceptually and causally, no connection

whatsoever to the behavior of the population over generations i+1 to n. We have

estimates, perhaps good estimates, of the expected rates of reproductive success given

environment E, a vector of values for the variables in E, whatever they are. But our

population now occupies a different environment E’, and absolutely nothing in or model

tells us how expectations conditional on E relate to those conditional on E’. If our

predictions are right, this is the sheerest accident.

Indeed, if the environment is changing over generations 1 to i, it is hard to make

any sense of what we thought we were estimating when we fit our favored model to the

data—perhaps average expectations over environments E1-Ei. But why should we expect

even a correct estimation of that parameter—the average expectation over E1-Ei—to be

in any way representative of the average expectation over environments Ei+1-En?

Minimally, this would require substantive constraints on the probability distribution over

narrow environments, and, by assumption, nothing in the model implies any such

constraint. Differently, we might make it an explicit constraint on such models that they

are to be used predictively only when environments or fitnesses are constant. But then

we have very good reasons for thinking, before we ever fit model to data, that the fitted

model is flat-out incorrect by our own standards of correctness. The model is correctly

used to generate predictions only when narrow environments or fitnesses are constant,


but we have every reason to think the narrow environment will change over generations,

and with it the fitnesses as well.

Suppose instead we define environments as joint probability distributions over

sets of variables probabilistically relevant to reproductive success, i.e. as generalized

environments. Our problems are now different, but no less severe. Unless i is quite

large, our fitted model is likely to mis-estimate WC, and hence wC, since WC is now a

weighted average over expectations in particular instantiated environments, most of

which will not be instanced over the initial i generations. But never mind, suppose we

have more or less correct estimates of WC for each class in the population. Predictions of

the behavior at generation n are still quite likely to be wrong, unless n-i is extremely

large—behavior at generation n is a consequence of the population structure at generation

i and the instantiated environments from i to n. Since this is a small sample of the space

of alternative instantiated environments over which the probability density is distributed,

the frequency distribution of instantiated environments from i to n is unlikely to be

representative of the generalized environment with respect to which class fitnesses are

calculated. Again, any agreement between prediction and outcome is the sheerest

accident.

There are of course cases in which population genetics models yield lovely

predictions well confirmed by observation. They are revealing. Outside laboratory

settings in which environments are under fairly strict control, predictive success involves

prediction of equilibria. The centrality of equilibria to population genetics is implicit in

every textbook introduction to the subject. In general, one is not interested in predicting

the relative frequency of a type in the nth generation, but rather in the equilibrium

frequency of the type; consequently, equations relating Oi(t’) to fi(O(t),X(t)) are

introduced in order to derive an equation relating Ôi to f’(O(t),X(t)), where Ôi is an

equilibrium value for outcome Oi. And often enough population genetics can predict the

existence of an equilibrium, even if the value of the equilibrium frequencies can not be

predicted with any precision.

The most obvious cases are those of balancing selection. In these cases,

equilibrium results from stable selection against homozygosity: the equilibrium results

from the quantitative balance between selection pressures against each of the


homozygous classes. Such equilibria are, however, only as stable as the selection

pressures in question, and typically population genetics models will not represent the

sources of those selection pressures. That is, the background environmental conditions

against which expected reproductive success is defined are not themselves included in the

model. As they change so too do the expectations for reproductive success estimates of

which appear in the fitted model. Because these background variables are in the

background rather than explicitly included in the model, changes in fitness driven by

changes environments cannot be tracked or predicted by the machinery in the model.

Hence equilibria and the frequencies characterizing them are unstable over generational

time, and that instability can be neither tracked nor predicted by any given population

genetics model.

Equilibria of a second kind are more stable. In these cases equilibria result from

frequency or density dependent selection. Fisher’s explanation of sex-ratios and kin

selection arguments exploit such selection. Suppose, as with sex-ratios, selection works

against the more frequent type, so that WC1>WC2 iff F(C1)<F(C2). Then the qualitative

relations between fitnesses depend on selection pressures which themselves depend on

class frequencies; i.e. class frequencies are the dominant environmental variables

influencing expected reproductive success. Since these class frequencies are represented

in the population genetics model, the model is able to predict the consequences for fitness

of changes in values among causes of reproductive success. Hence the model is able to

reliably predict the existence of an equilibrium in the population over long temporal

spans, and over wide ranges in values for other relevant variables. Moreover, while

changes in other relevant background variables may shift the equilibrium value, they do

so without changing the fact that there is always some equilibrium. Hence the models

provide useful law-like regularities covering those shifts in equilibrium value, e.g. total

investment in each sex should be equal, so as the cost of rearing an offspring of one sex

to adulthood increases, the frequency of that sex at birth should increase as well.

There are lessons here. First, population genetics models are predictively

competent exactly when either parameter values are constant, or the models explicitly

represent the variables upon which qualitative relations between class fitness depend (i.e.

the models explicitly represent the relevant subset of causes of reproductive success).


Second, since parameters in nature are hardly ever constant (which is why equilibria are

so damned rare), predictive success depends essentially on representing the causes of

reproductive success. As it turns out, so too does explanatory success.

3. Explanatory Incompetence. There are two current conceptions of evolutionary

explanations. On one increasingly popular conception, evolutionary explanations are

essentially statistical and largely non-causal (c.f. Walsh, Lewens and Ariew (2002);

Matthen and Ariew (2002)). On this statistical conception evolutionary explanations aim

to explain the ‘central tendencies’ of a population’s trajectory through geno- or pheno-

space by appeal to the statistics describing reproductive rates among classes and the

distribution among types of the offspring produced by matings between parents with

specific genotypes or phenotypes. The only explicitly causal feature of these

explanations is the genetic account of the relations between parental pairing type and the

distribution of genotypes or phenotypes over offspring, and even this is characterized

statistically.

Differently, one can agree that evolutionary explanations take central tendencies

as their explananda, but nonetheless insist that such explanations are essentially causal.

This is, I suppose, the dominant tradition, and so I shall call it. On this view evolutionary

explanations appeal to population level, type causes to explain the central tendencies

exhibited by populations in their trajectories through geno- or pheno- space (Mills and

Beatty (1979); Brandon (1990); Sterelny and Kitcher (1988)). Accordingly, deviations

from expectations are a matter of drift, in one or another sense, and not otherwise

explicable, but the expectations from which these deviations are deviations result from

causal influences summarized by parameters whose values represent fitness, migration,

mutation, assortative mating, and so on. Since actual frequencies are causal

consequences of causes whose net expected effect is represented by the parameters in the

model, population genetic models provide causal explanations of frequencies, at least

when those frequencies reasonably approximate expectations.

The statistical conception of evolutionary explanation has been defended largely

by criticizing the dominant tradition on two grounds. Both lines of criticism challenge

the idea that fitness, understood as a propensity, can underwrite causal explanations. On


the first line of critique, fitnesses are non-causal (as for example Sober (1984)). On the

second, fitnesses are non-existent; there is no underlying fitness property to be measured

by any interpreted-fitness variable. E.g., Ariew and Lewontin (2002) have argued that

there is no hope for a univocal interpretation of fitness, differently measured in different

contexts, which will endow interpreted fitness with the causal potency required by

formulations of the principle of natural selection. Either charge underwrites the further

claim that evolutionary explanations are non-causal, e.g., Walsh, Lewens and Ariew

(2002) and Matten and Ariew (2002) argue that evolutionary explanations, or at least

those generated by population genetics, are essentially non-causal explanations.

I do not think either line of objection is quite right, and in any case both overlook

the really important difficulties facing the dominant perspective. But even were these

objections right, the statistical conception of evolutionary explanation offers little

improvement, unless much, even most, of what population biologists do in their

explanatory practices is simply otiose. Field biologists care about vera causa principles

when generating selection explanations. Consider a pair of particularly well known

cases. Grant and colleagues (1986) are at pains to show that beak morphology in fact

causes mortality—how else to understand the importance of Price’s modeling, of

measures of seed hardness and availability, and so on, in their work? Endler (1980) is at

pains to show that coloration has effects on mate choice and predation frequency in the

lab and in the wild. Why should he care, unless he cares what the facts are about

causation? It is hard to make sense of the effort, time, and money spent to show that

morphological traits thought to be under selection actually do causally influence

components of fitness, and hence reproductive success, except under the assumption that

biologists think causation matters to their explanatory endeavors. But if this is so, the

statistical conception of evolutionary explanations is at best only part of the story, and

simply wrong in claiming that the causal details are irrelevant, only central tendencies

matter.

Unfortunately, the causal details of the mechanisms by which differential

reproductive success is produced and equilibria are maintained cannot be represented by

population genetics models. For example, a population genetics model cannot represent

how it is that beak morphology matters to reproductive success, and it cannot represent


the causal basis for the correlation between precipitation and reproductive success that

results, in part, from the causal effects of beak morphology on feeding behavior. A single

population genetics model can at best assume a probability distribution over wet and dry

years, and, given that distribution, employ long run expectations for reproductive success

in predicting evolutionary outcomes among finches (and even here, the assumed

distribution over wet and dry years is entirely implicit). More detail can be captured by

providing different models for different years, depending on rainfall. But again, the

mechanisms by which rainfall is connected to reproductive success are undescribed by

the model itself. Similarly, a population genetics model cannot capture the interplay

between natural and sexual selection affecting guppies. At best, such models can report a

statistical summary of the consequences of that interplay, for particular populations in

particular locations. It cannot, itself, represent the fact that two selection processes are

operating simultaneously, or characterize either process.

These are specific consequences of two general facts. The first is that population

genetics models are non-causal models. By a causal model I mean a model that generates

reliable predictions about the values variables in the model take consequent to ideal

interventions on other variables in the model. Population genetics models simply do not

do this: interventions on class frequencies that set class frequencies to something other

than 0 or 1 will in general modify fitnesses, and those modifications are not predictable

from the model itself, since the fitnesses are parameters, not variables, in the model. For

example, interventions on class frequencies will induce changes in class fitnesses

whenever the population has demographic structure given by values for age, stage or

spatial variables and these variables causally influence survival and reproductive success.

And that occurs almost always. When this is so, interventions produce changes in

fitnesses because the distribution of demographic variable values over the population

after intervention, need not, and typically will not, mirror the distribution of prior to

intervention. The second fact is implicit above: reproductive success and survival are

variables whose values are caused. Hence, population genetics models, being non-

causal, do not explicitly represent the causes of survival and reproductive success, but

instead include parameters representing the net effect of those causes. The parameters in


question are, of course, fitness, and their values are changed by interventions on the

population.

Herein lies one of the several serious difficulties with the dominant view, and the

propensity interpretations of fitness used to buttress it. The causal explanations of

interest in evolutionary biology are not exhausted by those which appeal to type-level

population causes. That, e.g., beak morphology is a type–cause of reproductive success

in the Galopagos environment is relevant, but incomplete, with respect to some of the

questions Grant and Price are trying to answer, viz.: did beak morphology actually cause

reproductive success for individual birds during the study period, did such actual causal

relations occur with sufficient frequency to account for changes in population frequencies

in the study populations, and can these relations of actual causation be expected to recur

in the future at similar frequencies? Those questions, and the explanatory use of their

answers, are sensible only on a conception of evolutionary biology according to which

part of the job is to represent the causes whose effects are summarized by fitness

coefficients, as opposed merely to summarizing the effects of those causes.

The dominant and statistical conceptions are both driven by the core commitment,

by the idea that the formal machinery of population genetics provides relevantly

complete descriptions of selection processes. On both conceptions, it is those equations

and those equations alone that are required for explaining central tendencies. The two

conceptions of explanation differ only over the appropriateness of causal interpretations

of those equations, and hence of the explanations they generate. But population genetics

models cannot describe the causal structure of the mechanisms by which differential

success is produced. Instead, such models can only summarize the net effect of

competing causes of reproductive success. Hence, insofar as such causal structure

matters to explanatory practices in evolutionary biology, both conceptions will fail to

make sense of evolutionary explanation, and they will each do so as a result of the core

commitment.

If to understand selection is to be positioned to describe selection in ways that

causally explain evolutionary outcomes, our understanding of selection cannot rest in our

ability to deploy population genetics models. Similarly, if procedures for describing

natural selection and the populations in which it operates are to generate descriptions


which enable reliable predictions, those procedures must involve more than producing a

population genetics model, and descriptions of natural selection must do more than assign

values to fitness parameters in such a model. It is not that such models and fitness

estimates are unnecessary. It is that they are hardly the beginning of an adequate

explanatory or predictive description. The core commitment is a mistake. Worse, it is a

mistake that engenders conceptual confusions avoidable if one employs alternative

modeling strategies.

4. Alternative Modeling Strategies. There are roughly two ways to produce reliable

predictions for a set of stochastic outcome variables O of interest. The first is to develop

an explicit causal model relating other variables V to O, and to estimate a joint

probability distribution over V∪O from the data. This strategy is employed in much of

statistical social science and epidemiology. Differently, one can attempt to find very

good correlates C of O, and never mind whether the variables in C are causes of the

variables in O, and if so by way of what intermediate variables. In effect, this is the

strategy adopted by population genetics models of evolutionary processes. Fitness is

introduced as a dummy variable which, by the procedures in terms of which it is

introduced, is guaranteed to be strongly correlated with reproductive success so long as

background conditions remain unchanged. There is however nothing essential here about

fitness—any correlate would do, so long as background conditions are stable.

Unfortunately, no such strategy is likely to be successful over evolutionary time for most

trait frequencies in most populations, since the relevant background conditions are

unstable exactly in the causal structure relating, and hence the joint probability

distributions over, causes of reproductive success.

This instability is no accident; it is rather a predictable consequence of evolution

itself. To see this consider the way in which phenotypes are influenced by environmental

variables and are themselves influences of reproductive success. Some, perhaps most,

phenotypic traits are sensitive to the (relatively instantaneous) values of local

environmental variables. Even for relatively constrained morphological traits, it often

makes sense to think about norms of reaction; this is especially true when the traits are

behavioral. For example, a prey selection rule is an assignment of probabilities to the


outcome ‘attempt to capture’ conditional on recognition of a prey item of a given kind,

for each kind of prey available in the local environment. For theoretical reasons, it has

been claimed that such rules should be zero-one rules— individual predators should

either always or never attempt capture of prey items of a given kind. As a matter of fact,

predators at least sometimes seem to have partial preferences—they violate the zero-one

rule by taking prey items of a given kind sometimes, but not always. Whether or not prey

selection rules entail partial preferences, such rules ought, and apparently do, change as a

function of prey frequency and the energetic demands of the predator. Indeed, for some

predators at least, individuals will change the selection rules they use as their

environment changes. So which prey selection rule a predator happens to be using at the

moment at least sometimes depends on the current value of a local environmental

variable.

But if individual predators adopt different rules at different times, in response to

local environmental variables, there must be a further feature of these predators—the

choice rule employed by them for choosing one rather than another prey selection rule.

These meta-rules influence reproductive success by influencing prey selection rules. So

meta-rules are themselves potentially evolved responses to environmental circumstances

and ecological demands on organisms. But the environmental variables which make

some meta-rules better than others, as judged by reproductive success, are not local

variables—they are rather statistics characterizing the joint probability distribution over

these local variables, as well as other variables that influence the energetic requirements

of individual predators.

The overall causal structure then is something like this. There are global

environmental variables which, by constraining the joint probability distribution over

some set of local environmental variables, cause over evolutionary time the meta-rules

adopted by predators. The meta-rules themselves, along with instantaneous values of

local environmental rules, cause the prey selection rules adopted by predators. And

which prey selection rule a predator adopts influences its reproductive success.


But as prey selection rules change, so too does the causal structure governing

reproductive success. If items of kind K are omitted from the diets of predators, as a

result of the increase in frequency of items of kind K’, say, the frequency of items of kind

K was, but no longer is, a (direct) causal influence on individual or classwise rates of

reproductive success. Technically, a prey selection rule is an interactive cause of

reproductive success: depending on the rule adopted, different local environmental

variables will influence reproductive success. So changes in prey selection rules change

the causal structure relating environmental variables to reproductive success, and such

changes in causal structure change the correlations between reproductive success and

other variables.

Somewhat differently, if prey selection rules include partial preferences, changes

in the probability that an item of kind K elicits an attempt to capture require a meta-rule.

Given such a meta-rule, it will be possible to change the prey selection rule so that items

of a given kind K are chosen less, or more, frequently. If such changes occur they will

change the degree to which the frequency of K in a local environment affects

reproductive success. So such changes will affect the strength, though not the presence,

of correlations between reproductive success and other variables.

Given environmental variance, dispositional or behavioral meta-properties of

phenotypes therefore entail instability in correlations between reproductive success and

phenotypic and local environmental variables. Further, the presence of such meta-

properties is a predictable result of evolution itself. It is no accident that these meta-

properties are quite common: individuals of given genotypes can exhibit context

dependent variation in morphology, life history strategy, predation behavior, escape


behavior, mating behavior, and so on. Perhaps some of these variations are canalized, so

that there is no selective force operating on meta-properties because there is no variation

in those meta-properties. But, so far as I know, there is no reason to think this is always

or even generally true. As a consequence, correlates of reproductive success will in

general be local, and hence bad predictors of actual rates of reproductive success in the

long run, and bad predictors even in the short run if local environmental variables vary to

any extent in the short run.

If there are good reasons for thinking a search for correlates of reproductive

success will not succeed in finding reliable predictors, the alternative strategy of explicit

causal modeling is the obvious alternative to consider. Unfortunately, such modeling in

evolutionary biology is not so simple as in statistical social science, and that for a number

of reasons.

The range of kinds of variables that influence reproductive success is enormous:

features of genotypes, phenotypes, environments, demographic structure and life history

variables all influence reproductive success. Data sets including measurements on a

suitable range of such variables are rare; they are so because they are both difficult and

expensive to construct. Even when they exist, they present an initial analytic difficulty.

The relevant variables do not obviously measure properties of the same kinds of entities.

Analytic techniques for causal discovery from statistical data require a uniform unit of

analysis, and the appropriate unit is entirely unclear. Should variables be taken to

measure properties of alleles, genotypes, phenotypes, individual organisms, or sets of

such, delimited demographically, phenotypically, or genetically?

Further, the causal systems driving reproductive success are nearly always

represented by cyclic rather than acyclic graphs. Recruitment rates for genotypic classes

depend on the rates on the frequency distribution of mating types (or other varieties of

genetic transfer), and rates of reproductive success for pairing types. Both statistics

depend on the phenotypic features of individual organisms, their environments, their

demographic properties and the demographic structure of the population as a whole.

Environmental variables and genotype influence phenotype. Phenotype and demography

influence environmental variables directly, by causing changes in the values of those

variables, and indirectly, by producing migration. Rates of reproductive success, along


with survivorship and recruitment, influence demographic structure. So unless variables

are time indexed, the causal structure governing evolutionary outcomes will be cyclical.

Relatively little is known about reliable inference to cyclic causal structures from time

series data. So here we find another set of analytic problems.

So if there is a clear modeling strategy, it is tremendously unclear just how to

implement the strategy. Finding procedures by which to produce good causal models of

evolutionary phenomena will require conceptual innovation, in both data collection and

analytic methods. The innovations present a plethora of challenges both philosophic and

biological. It is unclear whether or not those challenges can be met. But some biologists

are beginning to develop models that recognize the chore and offer some promise.

The relevance of causal models to evolutionary biology has been recognized, at

least in passing, ever since Sewall Wright’s introduction of path analysis. While the

regressions methods implicit in path analysis have been the target of objections from

Fisher and his followers since their introduction, biologists have never wholly refrained

from their use or from causal interpretations of the resulting models. A different, but

equally causal, use of graphical machinery, loop analysis, was introduced into

demographic studies by Levins (1973) and can be nicely adapted by quantitative methods

developed by a variety of others, beginning with Lande (1982). I’ll describe the basic

idea not to endorse it as the correct modeling procedure, but rather by way of a proof-of-

concept showing that sufficiently detailed causal models are in principle possible, and

subject to empirical test.

The basic idea is relatively straightforward. Induce a demographic structure by

dividing a population into demographic groups defined by spatial location and stage (life-

history) or age. Data on transition rates between classes and on reproductive rates can be

used to build a projection matrix model of the population. The structure of causal

influences between demographic groups can be represented by a directed graph over

variables. The edges can then be associated with a parameter representing the degree of

influence between distinct demographic groups directly connected in the graph. One can

then use loop analysis to find a parameter, most commonly a sensitivity or elasticity,

representing the influence of a demographic group, a particular group-to-group transition,

or a particular life-history pathway, on population growth.


Because the average fitness in a population is typically related in straightforward

fashion to changes in population size, such models offer the opportunity to measure

quantitatively the effect of particular components of fitness on group-to-group transition

rates, and hence on overall reproductive rates. One can then build a causal model of the

effect of phenotypic or environmental variables on components of fitness. Introduced by

van Teinderen (see van Teinderen (2000) for an elegant introduction, Coulson et al.

(2003) for an extension to environmental variables), such ‘heirarchical models’ are

essentially causal models representing the ways in which phenotypic and environmental

variables influence reproductive success. A graph representing such a model, taken from

van Teinderen (2000) is reproduced below.

Again, I do not mean here to endorse the particular procedures employed or

recommended by van Teinderen or Coulson et al. There are difficulties, or at least

questions, about the adequacy of the methods: it is not clear how the choice of

demographic variables is best constrained, whether elasticities or sensitivities or

something else are the right statistics for edge loadings, and there are substantive

questions about model selection for every independent piece of the model. But I

From van Tienderen (2000), pg. 674.


do want here to recommend the general strategy. If a predictive evolutionary biology is

possible, it will require models that, like hierarchical models, explicitly represent the

phenotypic and/or genotypic causes and environmental causes of reproductive success;

such models will also have to represent explicitly the demographic variables that mediate

the causal influence of these distal causes, and will need to represent as well causal

interactions between these distal causes themselves. Such models further provide richer

causal explanations both of particular evolutionary phenomena and the general role of

selection in the production of evolutionary change.

5. Conceptual Confusions Avoided. If, in contrast to the core commitment, causal

models are taken to provide the core formal machinery for describing processes of natural

selection, a number of longstanding conceptual worries disappear, and others at least

seem to be susceptible of solution. Rather than attempting an exhaustive list, I’ll treat

briefly two conceptual problems in the philosophy of biology, namely those of

interpreting fitness and discriminating between the effects of drift and of selection.

To begin, we must have a clear view of what selection processes are. How, given

such a model, should one think about selection in terms of it? The answer is, I think,

straightforward. A model is correct, but possibly incomplete, if the model omits no edges

between included variables when one causally influences the other, and includes no edges

between included variables when neither causally influences the others, and the estimates

of the parameters in the model are reasonably close to the true parameter values. There is

selection on a population just in case in some correct causal model of the population there

is at least one directed path from a phenotypic or genotypic variable to population size (or

growth). In hierarchical models, any such path will include some component of fitness

and some transition matrix element as intermediaries, but this is a local feature of

hierarchical models. There is selection on a particular trait variable, phenotypic or

genotypic, just in case there is a path in some correct model from that trait to population

growth. Each such path is a partially characterized selection process. There is selection

on a particular trait, i.e. a particular value for a trait variable, just in case an intervention

changing the frequency of that trait value, but holding constant all and only other

variables that are exogenous with respect to the trait variable in question, would change


the probability distribution over population growth. The extensions required to make

sense of ‘selection for’ and ‘selection against’ relative to some identified alternative value

of any trait variable are then obvious.

Given this understanding of selection, what should we say about fitness? Recall

that the philosophical worry about fitness within the dominant tradition is that selection is

defined as differential fitnesses causing differential reproductive success. Fitnesses must

therefore be causal if evolutionary selection explanations are to be causal. But fitness is

measured in quite different ways in various contexts, and this issues in a difficulty: what

is the shared causal basis for differently measured fitnesses in virtue of which appeals to

differential fitnesses endow selection explanations with causal content? From our new

perspective, the philosophic worry about fitnesses disappears. Selection is not defined in

terms of fitness, so fitnesses need not be causes of anything for selection explanations to

be causal. A fitness is just a parameter in a population genetics model; however

estimated, the model in which such a fitness occurs is satisfactory just in case it fits the

data. Allowing the model to fit the data is all that the fitness estimate need do, so no

more need be said about the thing, whatever it is, which is estimated by the parameter in

a fitted model. All that is possible because population genetics models are now used

neither to generate predictions nor to convey understanding, but for different epistemic

ends.1

What of drift? Beatty (1984) notes that on the propensity interpretation of fitness

there is an intractable difficulty in sorting the effect of selection from that of drift. The

difficulty, I claim, results entirely from the core commitment: it is engendered by

thinking about selection in terms of population genetical models, and largely evaporates

once causal models are employed. There are classically three kinds of drift. First, if

selection is conceived of as a sampling process, selection, as any sampling process, will

be accompanied by sampling error, i.e. uncaused non-representative sample statistics (if

the non-representativeness of a statistic is caused, we have a case of sampling bias rather

1 The machinery of population genetics is not dispensable. Minimally it is correctly and ineliminably used to estimate important parameter values, e.g. allelic frequencies and heterozygousity; arguably population genetics provides for a set of hypothesis testing procedures useful for determining whether selection is acting on a population; and clearly it provides a set of qualitative explanations about population behavior given qualitative assumptions about the direction and relative magnitudes of selection pressures, as well as explanations of equilibria in a non-trivial range of cases.


than error). Second, no model is likely to capture all causes of reproductive success, so

any data set will exhibit noise, some of which is due not to sampling error or intrinsic

stochasticity, but to omitted causes. Third, particular individuals in a population may

have their reproductive fates determined by phenotypic variables that are themselves

causally irrelevant to reproductive success in that population, in the sense that such

phenotypic causes as there are of the reproductive fate are constant in value over the

population. The lightning-struck twin is an exemplar.

What should we say about sorting the effect of drift from that of selection in each

of these three cases? In the first we should simply point out that there is no such sorting

to do. In the first sense of drift, drift is not a force or a cause, and perforce is not a force

or cause in contrast to selection. To see this, imagine a correlative question asked of an

epidemiologist. “Look, Igor”, we say, “we have a very good causal model of cancer rates

in the US, with very reliable estimates of parameters and initial values. But it happens

that significantly more smokers died from cancer last year than we expected. How much

of that is the result of smoking, and how much is just an accident of chance?” Igor can

only respond by pointing out that we don’t know what we are talking about; the question

presupposes a category mistake. Actual cancer deaths, according to the model, are a

sample according to a distribution. What we actually get when we sample is a matter of

chance, according to the model. The causal model tells us what the distribution of

chances is, and what interventions on which variables will change that distribution. To

put a question which contrasts chance with causes represented in the model is a category

mistake. Similarly, to put a question that contrasts selection with drift, in the first sense,

as different explanatory sources for a difference between expected and actual sample

frequencies is to engage in a category mistake.

We should give much the same answer to the same question about the second

sense of drift, on which drift is noise in the data produced by unmeasured causes not

represented in our model. Of course, it makes perfect sense to ask whether deviations

from expectations are large enough to count as evidence that the model is incomplete. If

so, it makes perfect sense to ask, of candidate causes not in the model, whether they are

in fact causes and if so how much of the deviation can be rectified by including each

candidate in a new model. It may even make sense to ask, for a particular outcome


variable F whose value is a frequency for some property P, what percentage of the cases

of P were caused by a variable omitted from the model, though this depends on what

account of actual causation we give. But it makes no sense at all to think of such an

unmeasured and unrepresented cause as something opposed to selection, on the present

understanding of selection. If U is an unmeasured, unrepresented cause of reproductive

success, and hence of population growth, then there is some correct model, including U,

on which there is at least one path from U to population growth, every such path

represents a selection process, and whatever effect U has on reproductive success is

selection, albeit selection not represented by our current model.

The third sense of drift is more tricky, and the present account of selection does

not so easily resolve the question. But it does add clarity to what exactly we are asking

when we ask how much of a given value, change in value, or deviation in value from

expectation is owed to selection and how much to drift. The question must be about

actual causation. There are various accounts to give of what actual causation amounts to,

and how statistical data and causal models can be used to answer them (see, e.g., Pearl,

2000). Here I just presume a commonsensical interpretation, but nothing important

hinges on this. Consider again the correlative question asked of an epidemiologist.

“Igor”, we say, “we have a very good causal model for cancer frequencies in the US, and

very good estimates of parameters for the model and of initial variable values.

Nonetheless, we have significantly more cases of cancer among smokers than we

expected. What proportion of those cases were actually caused by smoking, and what

proportion were actually caused by some other variable whose value is more or less

constant across the whole of the US population?” Igor may have no answer, but it is

clear at least what an answer would look like, and what kind of information would be

required to give it. Similarly one may ask, over the period observed by the Grants and

colleagues, what proportion of finch deaths were actually caused, directly or indirectly,

by beak morphology, and what proportion were not caused by any phenotypic feature

over which finches vary, e.g. deaths from lightning strikes. The Grants and colleagues

are unlikely to be in a position to answer, but it is clear what an answer would look like,

and what sort of information would be required to provide it. Count up the cases of finch

deaths in which some phenotypic trait that varies over the population is an actual cause,


according to your favorite account of actual causation. Whatever is left is the effect of

drift, and whatever the number of deaths in which beak morphology is an actual cause,

that number is an effect of selection on beak morphology.

6. Conclusion. Population genetics gives us a set of extraordinarily useful devices for

representing frequency changes in natural populations, and for describing selection

processes. Those uses remain important, even essential, in much of evolutionary and

population biology. But, largely as an historical accident, many biologists and nearly all

philosophers have over invested in population genetics by taking it to provide the core

formal machinery for describing selection processes. This assumption has lead to a

conception of evolutionary modeling on which evolutionary biology cannot predict many

phenomena of interest, and can predict others only under special conditions or with much

unnecessary effort. It has lead biologists and philosophers alike to mis-represent the

structure and aim of evolutionary explanations, reading them as causal explanations of

the wrong explananda, or worse as non-causal descriptions of evolutionary trajectories.

And finally, it has lead to avoidable conceptual confusion, at least among philosophers.

Better representations of evolutionary phenomena and their causes are, in principle, to be

had by appeal to explicit causal models and parameterizations of them. Such models

ought to permit better predictions; they will make sense of explanatory demands and

explanatory practices in biology; and they offer conceptual resources to resolve a number

of longstanding philosophic puzzles, not least those of defining selection, interpreting

‘fitness’, and distinguishing the effects of selection from those of drift.

Replacing population genetics models with causal models as our core machinery

for describing and understanding selection invites other concerns, in particular

epistemological problems regarding model discovery, selection and specification. If

these problems are difficult, they at least have an advantage over those we inherit from

the last three decades of work in philosophy of biology. Being epistemological rather

than metaphysical or interpretative, one can at least hope for a definitive resolution of

them. I recommend them to your attention.

References.


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for the Philosophy of Science, 55: 347-363.

Beatty, John (2004): ‘Chance and Natural Selection’, Philosophy of Science, 51: 183-211.

Brandon, Robert (1990): Adaptation and Environment. Princeton University Press,

Princeton NJ.

Coulson, T., L. Kruuk, G. Tavacchia, J. Pemberton, and T. Clutton-Brock, (2003):

‘Estimating Selection on Neonatal Traits in Red Deer Using Elasticity Path

Analysis’, Evolution, 57: 2879-2892.

Endler, John (1980): ‘Natural Selection on Color Patters in Poecilia Reticulata.’

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Grant, Peter (1986): Ecology and Evolution of Darwin’s Finches. Princeton University

Press, Princeton NJ.

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Natural Selection.’ Journal of Philosophy, 99: 55-83.

Mills, Susan and John Beatty (1979): ‘The Propensity Interpretation of Fitness’,

Philosophy of Science, 46:263-288.

Pearl, Judea(2000): Causation. Cambridge University Press, Cambridge UK.

Sober, Elliott (1984): The Nature of Selection, MIT Press, Cambridge Mass.

Sterelny, Kim and Philip Kitcher (1988): ‘The Return of the Gene’, Journal of

Philosophy, 87:151-158.

van Tienderen, Peter (2000): ‘Elasticities and the Link Between Demographic and

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Walsh, Dennis, Tim Lewens and Andre’ Ariew (2002): ‘The Trials of Life: Natural

Selection and Random Drift.’ Philosophy of Science, 69: 452-473.

Wayward Modeling: Population Genetics and Natural Selection

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