From the Force Analogy to the Formal-Pattern Account

Sober (1984) distinguishes four structural similarities between the theory of evolution and the Newtonian theory of force: that the former features some laws or generalisations formally comparable to Newton’s principle of inertia (a zero-force law), to Newton’s second law of motion (a consequence law), to (classical) force laws like the law of gravitation (a source law) and to a principle of force combination. For that very reason he asserts that the theory of evolution is a theory of force. Further, the terms in the theory of evolution that play the similar role to the force term in the Newtonian theory are terms representing the “strength” of migration, mutation and selection. So, by analogy, migration, mutation and selection are forces with respect to evolutionary change. This is the gist of the Soberian force analogy. It obviously rests upon two things:

The two theories are indeed similar and their similarities are sufficient for migration,

mutation and selection to be forces. Most philosophers dissatisfied with it put into doubt some claimed similarities or other between the two theories. For example, Brandon (2006) argues that drift is not a force by demonstrating, amongst other things, that the supposed population-genetic zero-force law (i.e. the Hardy-Weinberg principle) is not a law and there is no zero-force law in the theory of evolution. Attacks by the proponents of the formal-pattern account, on the other hand, are directed mostly towards the (alleged) principle of force combination and the (alleged) consequence laws in population genetics. Matthen and Ariew (2002) contend that there is no principle of force combination in the theory of evolution and those population-genetic counterparts of the Newtonian consequence law are not genuine laws. We begin our discussion by examining their counter-arguments.

Matthen and Ariew hold that there is nothing in population genetics like the principle of force combination. Their main reason is that component selective factors do not combine in a way component forces do. Forces always combine linearly (as well as vectorially). The joint effect of two or more forces upon an object (at a given time and position) is the (vectorial) sum of the individual effect of each of those forces (were they present individually). This is an example of what is known as the superposition principle in physics. By contrast, selective factors do not obey the superposition principle. In statistical terms, this is because causal factors usually have “interactions”.

Since forces cannot interact in this sense, selective factors and their resultant, i.e.

selection, are not forces.

One may think that the above conclusion follows from the requirement that forces be superposing independently. This is not correct. It stands still even if we just demand that individual forces be combined in a universal way, independently or otherwise. And it is plausible to think that there is no universal principle for combining selective factors, as

there is no reason to believe that all selective factors interact with each other in the same way. Thus, the attempt by Stephens (2004) to save the force analogy by stipulating that non-Newtonian forces need not combine additively is in vain. This move is not only ad hoc, but misses the real point of the argument. One may further drop the requirement of

a universal principle of force combination, but then how is the notion of a force supposed to be distinguished from that of a cause? Such a generic, non-physical notion of force is too thin to be significant. It appears that selective factors are called forces merely because they can be conceived as if they pushed, pulled and balanced out. No causal factors cannot be so conceived, however. And we just have to admit that the force talk is, at bottom, a matter of metaphoric use of words.

So, we can accept that this argument successfully establishes that evolutionary factors, or at least selection and selective factors, are not forces. At the very least, the notion of force is superfluous in the theory of evolution. Yet it leaves open the question whether selection is a cause of evolution. This question is addressed, partly and partially, by the argument against there being population-genetic consequence laws. Both Sober and Matthen and Ariew take as relevant in this regard those population-genetic equations between allelic frequencies at the next generation and those at the current generation weighted by coefficients representing the strengths of migration, mutation and selection. For Sober, these are the consequence laws in the theory of evolution. For Matthen and Ariew, however, they are mathematical theorems and ipso facto are not (empirical) laws. And selection is said to be characterised by Li’s growth-rate theorem, which is a population-genetic theorem of that ilk. It is, therefore, a formal pattern, and a formal pattern is not among the right sorts of things that can be causes (e.g. events and property-tokens). Hence, selection is not a cause of evolution. Now, how plausible is this second argument?

I agree that, like Li’s growth-rate theorem, the population-genetic equations containing only frequency variables and coefficients representing the strengths of selection are theorems. They key, of course, lines in the semantic content of those coefficients. They are exactly what are routinely called “fitness coefficients/parameters”

or simply “fitnesses” in population genetics. By both Matthen and Ariew’s interpretation and the standard population-genetic definition (e.g. Futuyma 2009: 306), fitness is basically the cross-generational time rate of change (owing to reproduction) of the frequency or proportion of a (sub-)type of organisms in a population. Population-genetic equations and theorems of the aforementioned family follow solely from the meanings of “fitness”, “(number) frequency” and so on, as well as from the syntax of relevant mathematical operations. They are a priori truths. Since they lack empirical contents, they are not empirical laws. So far, so good.

Yet they go on to claim that selection is characterised by such a theorem. This is where things start going weird. Li’s theorem, which is a simplified version of Fisher’s fundamental theorem of natural selection, states that “in a subdivided population, the rate of change in the overall growth rate is proportional to the variance in growth rates”

(Matthen and Ariew 2002: 72). It surely states a formal pattern. It’s no doubt a truth out of verbal necessity and hence not a law. It definitely cannot be a cause. But, does it represent the notion of selection?

It is the predicament associated with the current debate that there is in fact a plethora of notions of selection among philosophers. When different authors disagree upon the nature of selection, it is likely that they are actually talking about the nature of different things. So, a justification of the adequacy or advantage of a proposed conceptual content of “selection” is no less important than the correct metaphysical categorisation of what a given notion of selection is about. An account of selection as radical as the

formal-pattern one, in contrast to the more conventional ones in which selection is a cause of evolution or a causal process, requires extra efforts to justify. Matthen and Ariew are certainly aware of this. They attempt to justify it along three lines. These are outlined below in the order of increasing importance.

The first has its roots in the view that population genetics is the theory of natural selection. Population genetics is concerned with mathematically representing all sorts of (biological) evolutionary phenomena and exploring possible as well as ruling out impossible evolutionary consequences with the aid of involved mathematical/statistical techniques. It is held to be different from, albeit complementary to, field/lab studies of evolution: It is said to give explanations of evolution in terms of fitness whereas the latter provide explanations of evolution in terms of traits and environmental conditions.

In other words, it yields “explanation by fitness” but doesn’t offer “explanation of fitness” (Byerly and Michod 1991a); that is, it doesn’t address why a given type of organisms of a certain population in a given environment has the fitness (i.e.

reproductive growth rate) it does. Since population genetics is the theory of selection, what it says most generally about selection (i.e. Li’s theorem or Fisher’s theorem, together with the equations containing only fitness parameters and frequency variables), and nothing else, are about selection proper.

The second centres upon the universal applicability of the notion of selection. The fact that the general statements about selection in population genetics are mathematical theorems, and the interpretation that “fitness” means, and can only mean, “reproductive growth rate” in population genetics, are two sides of the same coin. And both of these are further connected to the idea that the notion of selection applies to populations of all sorts of organisms. If “fitness” meant anything else, the notion of selection would not be applicable to all types of organisms across the board. Nevertheless, Matthen and Ariew

do recognise an alternative notion of fitness which they call “vernacular fitness”. The latter is precisely the Darwinian notion of fitness which appears in the cliché “the survival of the fittest”. They accept that it expresses an organismal property that is tightly connected to traits, and Walsh, Lewens and Ariew (2002) even conceded that that property is a causal property in regard to an individual organism’s reproductive success. Yet, they all insist, the Darwinian notion of fitness does not enter into the population-genetic theory of evolution. Consequently, it is not part of the notion of selection.

Now, Matthen and Ariew carry further the generality of selection, for the growth-rate theorem applies not only to populations of organisms. It applies to any sub-typed ensemble regardless of what sort of things/events constitutes it or whether, and how tightly, its constituents are spatially or causally bound together. Also, the constituents of an ensemble need not literally reproduce; all that matters is that the number proportions of the different types of its constituents can change over time for whatever reason. Thus, what enters into the growth-rate theorem is neither the Darwinian fitness nor the population-genetic fitness; it is the more general notion of “time rate of change in number proportion”, a.k.a. “growth rate”. This generic notion as well as the growth-rate theorem itself is required to characterise selection proper, because “[s]election also occurs in nonbiological realms: in the economic domain, for example, as well as in

“clonal selection” in the mammalian immune system, in classical conditioning, and, according to some, in the propagation of theories and other cultural artifacts” (Matthen and Ariew 2002: 71). For that matter, selection is said to have “multirealizability” and is

“realized in many substrates”. It is itself “not even a biological phenomenon as such”

(Matthen and Ariew 2009: 222). It 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” (loc. cit.). Matthen and Ariew consider this characterisation of selection better than its competitors for the reason that it has universal applicability and covers whatever is called selection, especially those outside the domain of biological evolution.

The third line of justification is their direct rebuttal of the traditional claim that selection is a cause of evolution. At the heart of this rebuttal is the “constitution thesis”:

“Ensemble-level selection events are constituted without remainder by individual-level selection events; consequently, the causes of ELSEs are the causes of the ILSEs that constitute them. Thus, ELSEs are wholly caused by [the causes of] ILSEs.” (Matthen 2010: 2) In the domain of biological evolution, an ELSE is just an evolutionary change, whereas an ILSE is the birth or death of an individual organism. This thesis is plausible.

Yet it entails that there is no population-level cause of evolution that is to be identified with selection. Colloquially, one may say that the causes of births and deaths of individual organisms, e.g. predations and matings, are causes of evolution. But this is not metaphysically adequate. The correct way is to say that they (severally) cause those births and deaths, and the latter (collectively) constitute an evolutionary change. That is, there is no cause of evolution: It is an epiphenomenon. There are certainly causal processes that are explanatorily relevant to evolution, but they are to be identified only with those processes involving individual organisms.

But what about statements such as “variation in wing darkness caused the evolution of the moth population”? While Matthen and Ariew (2009) admit that it is a statement about a causal relation in the sense of cause as probability raiser, they refuse to acknowledge that it means that selection caused the evolution of the moth population, for “variation in wing darkness” doesn’t mean the same thing as “selection” does.

According to them, saying that selection is a cause of evolution is reifying selection. It

amounts to positing a tertium quid called “selection” over and above, say, variation in wing darkness and evolutionary change, such that it (arises from the former variation and) acts upon the moth population to produce the latter change. Evidently this tertium quid is explanatorily redundant. Therefore, they claim, from the ontological

consideration there is no selection as a cause of evolution.

Thus are their justifications of the formal-pattern account of selection. Even though there are many insights in them (which will be picked up in due courses), they have serious problems that they fail to justify it after all. The first line, in itself, manifests an unduly preoccupation with mathematical representations and statistical reasonings to the exclusion of empirical studies. Moreover, there are population-genetic equations that are by no means mathematical theorems but nevertheless are thought to model selection.

There are no convincing reasons why they are not about selection. So, the first line of justification is very flimsy by itself. It has to be backed up by the other two in order to maintain that those fitness-free equations are not about selection proper and that they cannot be taken to mean that selection causes evolution. This suggests that what really do the supposed justificatory work are the concern about generality and the argument against the existence of selection as a cause of evolution. These latter two, on the contrary, are more substantial and demand more elaborated treatments to show that they are mistaken. To these we now turn.