Discussion:
  1. Mohan Matthen & André Ariew (2009). Selection and Causation. Philosophy of Science 76 (2):201-224.
    We have argued elsewhere that: (A) Natural selection is not a cause of evolution. (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. 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.
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2009-09-02
The fate of the received view of natural selection
Received views are an important part of our symbolic order. Once it becomes apparent that they cannot possibly be true, it is sometimes a valuable philosophical task to preserve them, since no rational and educated person could actually believe them. As an example of a critically endangered received view, consider Jerry Coyne's excellent book, Why Evolution Is True:
[T]he process of evolution -- natural selection, the mechanism that drove the first naked, replicating molecule into the diversity of millions of fossil and living forms -- is a mechanism of staggering simplicity and beauty.
The received view is that natural selection is a mechanism or process that shapes all living things, and that the study of natural selection explains a lot about the history of life on Earth. Natural selection makes it possible to treat the billion years of organic evolution as a coherent narrative, making biology an endless reserve of wonder, understanding, and enjoyment.

Matthen and Ariew (20022009), however, have convincingly argued against the view of natural selection as a cause of evolution. Their argument applies as well to other characterizations of natural selection: as a process, as a mechanism, as a force. They maintain that natural selection "is a mathematical aggregate of individual events" (2002), "an abstract phenomenon that obtains in all population histories" (forthcoming). They assert that variation (in a given population, in a given environment) causes evolutionary change, but deny that natural selection causes evolutionary change. Obviously, it is not variation alone that brings about evolutionary change, but once natural selection is understood as the outcome of very many possible interactions amoung traits, individuals, and environments, to be assessed on a case by case basis, the notion of "selection-as-process" becomes untenable and all we are left with is "selection-as-outcome". This sounds like a serious blow to the received view of natural selection. One may wonder whether an alternative account can save it. 


As one of the foremost population geneticists, Coyne cannot ignore the discrepancies between the "vernacular" view of natural selection (as process, mechanism, or cause) and what his science tells him. Here is how he introduces the crucial idea:

The idea of natural selection is not hard to grasp. If individuals within a species differ genetically from one another, and some of those differences affect an individual's ability to survive and reproduce in its environment, then in the next generation the "good" genes that lead to higher survival and reproduction will have relatively more copies than the "not so good" genes. Over time, the population will gradually become more and more suited to its environment as helpful mutations arise and spread through the population, while deleterious ones are weeded out. Ultimately, this process produces organisms that are well adapted to their habitats and way of life.
Thus, Coyne avoids an explicit definition of natural selection: what he describes is an abstract process leading to adaptation. To me, it seems that we all know (well, we may still be a minority since many philosophers appear to think differently) that natural selection cannot be construed as one of the customarily relevant things -- causes, forces, mechanisms, processes -- that can be inserted at the proper place, in a larger account of how things work, in order to do explanatory work.


Since I take Matthen and Ariew's views to be correct, I find it hopeless to insist on natural selection as 'something' behaving like an agent, a designer, a partial optimizer, or even a sieve (as in the rather frequent account of variation followed by selection resulting in evolutionary change). Should this (correct) view become dominant, however, we should face the dire consequences: educated people would have no reason to believe that there is a simple, understandable explanation for the whole of evolution (does anybody know of one such explanation, by the way?), and we should stop praising such excellent books as Coyne's. It could be a philosophically interesting issue (and I'm inviting comments on this as well) to see whether we could maintain the association between natural selection and simplicity, beauty, amazement, or ideas-that-change-everything. Clearly, "selection as outcome" and "variation as cause of evolutionary change" cannot hold to the task.


Whatever the broader philosophical and "political" implications, my interest here is in showing how the received view of natural selection might be preserved. I don't know whether Matthen and Ariew would agree on my interpretation of their work, but I would like to call attention to the fact that although natural selection is indeed a statistical aggregate (a pattern of distribution?) the term alludes to (suggests?, points to?) a causal story about how the aggregate came about (without actually requiring the provision of a causal story). This is my way of seeing the significance of the authors' "hierarchical realization model" of how evolutionary influences combine. 


Since I am not sure I understand the model, I will not elaborate on it. I'll just try to redress the received view of natural selection in a way that can highlight a possible role for the model:

  1. (some) naturally occurring variations improve the organism's ability to survive and reproduce in a given environment; 
  2. these functional improvements (often qualitative) are someway translated into a quantitative, statistically significant difference in reproductive rates;
  3. there is an abstract, mathematical relation between higher reproductive rates and the spread of favorable variations (the outcome).

Here, an analysis of function/causal roles is mainly confined to 1, while the mathematical aggregate we call natural selection is the direct outcome of 3. It is in 2 that the hard work is done, the "work" of converting the interactions among functional variations, other changes in the organism (e.g., changes in fertility or in mating behavior), and environmental changes as well, into quantitative differences in reproductive rates. Whether the hierarchical realization model can accomplish all this work, I don't know, but it seems promising. 
In place of a conclusion, a tendentious question: in view of the symbolic importance of natural selection, why don't they just call it "the hierarchical realization model of natural selection"?





2009-11-09
The fate of the received view of natural selection
Sorry not to have replied to this post earlier -- I somehow failed to see it.

I agree with most of what Marcello says in his post.  I just want to answer the question with which he concludes: "In place of a conclusion, a tendentious question: in view of the symbolic importance of natural selection, why don't they just call it "the hierarchical realization model of natural selection"?"

The force model conceives of natural selection as one influence on evolution, which may be opposed or interfered with by others.  Thus, it takes natural selection to be deterministic Sober (1980), but leading to different results in different domains because of drift (which it sees as a local interference), or interfered with by mutation (which, according to the force model, can amplify or reduce the effects of natural selection) or by migration, etc.  A particle such as an electron may be pulled toward the centre of the Earth by gravity, but kept in place by a positive charge acting on it from the other direction.  Here the force of gravity is added to the force of electrostatic attraction to achieve a net force of zero.  Similarly, natural selection might pull a population toward a certain outcome (eg. 100% well-adapted trait T), but be interfered with by mutation, with the result 70% well-adapted trait T.  The force model sees this as mutation reducing the net force acting on the population.

The hierarchical realization model is an alternative way of understanding the interplay of such influences.  In a model with no constraints -- call it the null model -- all possible evolutionary histories will be considered.  In this model, some histories will give T an advantage, some will not; some will have a high mutation rate toward T', some will not.  In the null model, all outcomes are equally likely.  Now to model the well-adaptedness of T, a subset of the null model will be considered, i.e., the set of all possible histories in which T has the advantage in question.  Call this the T-model.  The T-model is a "realization" of the T-advantage.  The probability of (100% T) given the advantage of T is the proportion of histories within the T-model in (100% T) occurs.  Now, to model the well-adaptedness of T given the advantage of T and a high mutation rate from T to T' we construct the TM-model.  This is the subset of T in which this mutation rate is realized.  The probability of (100% T) given the advantage of T and the high T-T' mutation rate is the proportion within the TM-model of histories with the (100% T) outcome.  And so on.  You get the idea.

The claim is that the algebra of the hierarchical realization model is that of the calculus of probabilities.  The algebra of the force model is that of vector addition.  The former is the required algebra for combining evolutionary influences.  This was the claim in Matthen and Ariew 2002, 2009

That's why the hierarchical realization model is a model of evolution, not of natural selection -- though since natural selection is itself a combination of influences, the hierarchical realization model applies to it as well.  Sober 1984 calls the theory of evolution a theory of forces.  In truth, the theory of evolution is a theory of probabilities.

2009-11-22
The fate of the received view of natural selection

Stephens (2004) and others have identified the conventional Modern Synthesis view of evolution as a "theory of forces".   Evolution is defined as "shifting allele frequencies" in this view, and thus the "forces" of evolution push the frequency of an allele up or down over time.  That is, change in the frequency of an allele over time is the common currency of causation in evolution, just as change in location of an object over time is the common currency of causation in classical physics. Advocates of this view present the Hardy-Weinberg equilibrium as a "zero-force law" defining the state of the system (a reproductive population) at rest, when no forces are present.  

Ariew and Mohan (2009) have identified problems with the conception of selection and drift in this view.  

I realize that their criticisms may make the "theory of forces" view untenable already, but I would like to raise a problem that to me (as an evolutionary geneticist) is more profound. 

Advocates of the "theory of forces" point to the mutation-selection balance equation from population genetics as a case showing how separate forces combine in a way that is intelligible.  Mutation from allele B to deleterious alternative b pushes up the frequency of b, while natural selection pushes it back down.  Eventually a balance is reached.  In fact there is an exceedingly simple (approximate) expression for the equilibrium frequency, which is f(b) = u/s, where u is the mutation rate from B to b, and s is the selection coefficient against b.  

However, this equation applies to deleterious mutation.  For the case of a mutation event introducing a new neutral or beneficial (i.e., not deleterious) allele-- the kind of mutation underlying most changes in evolution-- the theory of forces breaks down.  When mutation introduces a new allele, acting in the role of an originating process, it does not shift frequencies generally, but specifically shifts the frequency of an allele from 0 to 1/N.  Selection and drift cannot accomplish this result: when mutation is acting in this role, it is acting alone, outside of the range of operation of other "forces".  In other words, the common currency of allele-frequency-shifting forces (mentioned above) is not a common currency.  In its role as the allele-originating process, mutation is a point process and not a mass-action "force"; it opens up dimensions along which selection and drift may act, instead of moving the system along a pre-established dimension.    

Although I accept the arguments of Mohan and Ariew about the weakness of the "force" conception of selection and drift, I am surprised that so much attention is given to relatively subtle arguments about selection and drift when the "theory of forces" view fails so utterly in a rather obvious way.  Why is this?  In one sense, the answer is simple: Stephens, Coyne and others seem to start out by assuming a variable population, so that new mutations are not necessary.  But this just begs a further "why" question. 


2009-11-22
The fate of the received view of natural selection
I don't understand your point, Arlin. 

Stephens claims that if there is a mutation rate of u from B to b, then the proportion of b in the population will increase by u*B/n (where n is the size of the population).  You're right it would only specifically shift the frequency of a single pair of alleles -- not act more widely -- but this is compatible with the forces model.  In other words, though mutation is a point-process, it nonetheless has a population-level effect. 

Secondly, regardless of which direction selection operates in (i.e., regardless of whether or not it is deleterious), the effects of selection will (according to Stephens) be added to that of mutation.  (In the case of beneficial mutation, selection would add to the effects of mutation; in the case of deleterious mutation, it would be negative, but still added -- according to Stephens.)

The objection to this is a. that the additivity of rates depends on the assumption that mutation rate is independent of the composition of the population, and b. that expressing selection in allelic terms disregards that selection is on phenotypes.

What am I missing?

Mohan

2009-11-24
The fate of the received view of natural selection
Reply to Mohan Matthen
Thanks for replying, Mohan.  My point has nothing to do with phenotypes or with the issue of whether or not mutation is independent of demographics.  Its more fundamental than that.  
Lets go back to the analogy with "forces" in classical physics.  In classical physics, forces cause displacement of a particle in space over time.  A force might get its "leverage" from charge or from mass, and its leverage might decrease more or less rapidly with distance, but its effects can be measured in a common currency: displacement in space over time.  This common currency is what allows a common conception of forces, even when the forces have different mechanisms. The forces fit a common pattern.  All "forces" can cause, by continuous motion, displacement of an object in space.  The displacement has a direction and a strength.  If the force is stronger, then the displacement is more powerful.  As an added bonus, some classic forces exert their effects independently, and these effects combine nicely and we can do things like add together vectors of force to get a resultant vector.  

But what if one of the forces did something ELSE that could not be measured in the common currency of causation?  In particular, what if one of the "forces", e.g., gravity, could displace a particle, AND ALSO could cause a new particle to appear?   There is a quite a big difference between causing a particle to exist, and pushing around particles that already exist.   A theory that only included particle-pushing would be insufficient.  

Mutation is such a "force": when it shifts the tally from one pre-existing allele to another, it can be understood as a "force" that pushes around allele frequencies like other forces, but mutation ALSO brings new alleles into existence.  These are not the same.  We might be tempted to think of the process of giving rise to a new allele as just another kind of "shifting allele frequencies", namely a shift from a frequency of 0 to a frequency of 1/N, but that would be cheating, because this is outside the range of the other so-called "forces".  Its not part of the common currency.  Drift can't shift an allele frequency from 0 to 1/N.   Selection can't do this.  If there is to be any "force" theory, then the common currency of forces is limited to shifting alleles frequencies from 1/N to 0 or to 1.  Mutation, drift and selection can do this, in principle.  

But only mutation can shift a frequency from 0 to 1/N, or from 1 to 1 - 1/N.  We can't combine the allele-originating effects of selection, drift and mutation, because only mutation has this effect. For instance,  you said that "regardless of which direction selection operates in (i.e., regardless of whether or not [the mutation] is deleterious), the effects of selection will (according to Stephens) be added to that of mutation."  Actually, no, that is not correct.  There is no allele-creating effect of selection that can "be added to that of mutation".  Once an allele is present, we could think of ways that both mutation and selection could increase the frequency of the allele, but mutation and selection did not combine in the origination of the allele.  Selection did not help to bring the allele into existence.  Mutation did it alone.   

Arlin

2009-11-24
The fate of the received view of natural selection
MM: "The claim is that the algebra of the hierarchical realization model is that of the calculus of probabilities. The algebra of the force model is that of vector addition." 

I think the distinction is clear, especially given Mohan's example. On the other hand, in this very condensed form it could appear as a more or less metaphysical issue, which I believe is the main reason why Arlin is not so happy with (at least some) philosophers. The problem is that both kinds of model can (in principle) be translated into similar mathematical, population-genetics models. That would mean that science has nothing to offer in order to adjudicate between the two claims; philosophy, on the other hand, could go on discussing the issue without caring too much for what scientists are actually doing with their models. So I'm going to dig a bit deeper into the models.

Any mathematical (population biology) model would attempt to capture the rate of change of a quantity over time. Let's say that the quantity is the frequency of an allele in a population. We might write (just for illustration):
(1) dx/dt = aS + bM + cG + ...
The only purpose of this equation is to show how one could decompose a change in frequency into distinct "forces" (Selection, Mutation, miGration, ...). Given appropriate parameters a, b, c, these forces can be added, subtracted, and compared. One might even add drift to the equation (though I find the idea of a "force of drift" offensive). Now, the important point Matthen and Ariew are making is not that, instead of adding quantities, one should multiply them. In their model, the right-hand side of the equation would contain no S because selection is itself the outcome of other processes (/"influences").

Just to avoid confusion, there is no reason to deny that natural selection plays a prominent role (is explicitly factored) in a large class of models in population genetics, and that these models give important results. There are many ways to realize a pattern of natural selection, but once it is established other properties follow, generalizations can be made, deviations from the norm can be detected.  One should however resist the temptation of "reifying" selection. That is, even if a "model" such as (1), where selection is explicitly factored, can give useful results, S has no independent existence outside concrete conditions which may include ecological or demographic factors (in the spirit of, e.g., Ariew and Lewontin 2004). The temptation is strong because the idea of selection is so powerful: it suggest an account of evolution that follows a familiar causal path, and the same account can serve to explain the presence of a trait as well as its shape, size, or function.

Arlin's objection, as I understand it, is that you can indeed represent the interplay between mutation and selection in a single equation; that equation, however, reflects a sort of "reified" idea of the process: it is a process of sorting out variants that already exist in the population, whose stock is replenished by mutation -- a sampling process, which may be good for most research purposes but not for cases where you are dealing with the intricacies of novelty, especially at the molecular level. Suppose one wants to address the infamous case of the bacterial flagellum: I assume that in that case most mutations would be neutral, and that the goal would be to give both a plausible reconstruction of the chain of mutations, a plausible estimate of their cumulative probability, and hints about the emergence of novel functions.

More generally, I take Arlin's objection as a basic demand on philosophers: "unless you are dealing with metaphysical issues, ask the scientists as well". In the end, the purpose of a model is to get a grip on a reality that can be addressed with different research goals in mind. If, as in Coyne's popular book, the main focus is on the evolution of adaptations, it is reasonable to concentrate on natural selection. If the focus is on molecular evolution, mutation and drift deserve equal consideration. I'm not a biologist, but I see the abandonment of the force model as an essential step towards a more cohesive population biology; or, perhaps, towards a better philosophical understanding of population biology. Both ways, I hope that someone in that field will take notice of it.


2009-11-24
The fate of the received view of natural selection
Ah, I see (better) now what you are getting at, Arlin.  (Thanks Marcello.)

Stephen's point is independent of yours, I think.  Let's say that mutation creates an entirely new allele -- which, as you say, selection cannot do.  Then there is one copy of this new allele in the population -- and mutation brought about this result.  Now, suppose that after selection -- i.e., after several generations of births, deaths, and matings -- there are thirty copies of the new allele in the population.  Stephens wants to say that the thirty copies are the result of mutation plus selection.

As you observed in your original post, I don't agree with this way of looking at the matter, but it does seem that the "creativity" of mutation is something Stephens could concede.

Is that right?

Mohan

2009-12-04
The fate of the received view of natural selection
Thanks for replying.  Generally, I think we understand each other, but I wanted to clarify that I am not trying to chide philosophers for failing to consult with scientists.  The "forces" view of Sober and or of Stephens reflects how most evolutionary biologists talk and (apparently) think about causal processes in evolution. To the extent that the "forces" view is flawed, evolutionary biologists have been living with its flaws for a long time.  

This raises a question about why the "forces" view has persisted.  I do not believe that a scientific theory can have a significant "metaphysical" flaw that has no practical implications for scientists (this would be like believing that a car could have a design flaw that has no implications for how well the car drives).  I also don't believe that scientists will hang on to a flawed view without reasons.  If it were simply a matter of translating "force" language into something more probabilistic, without any more fundamental change in how we think about evolution, then scientists would have made this shift a long time ago.  Its not as though the concept of "probability" were new.  The probability of fixation of a new mutation (by selection or by drift) is a concept that has existed in population genetics for over 70 years, and can be found in the foundational works of Fisher, Haldane, and Wright.  


There are wider issues at work here.  I agree with Marcello that "abandonment of the force model is an essential step towards a more cohesive population biology", but this goes further than just population biology.  I've been trying to understand and to address this as a theoretical evolutionary biologist for 10 years.  My colleague Lev Yampolsky and I have argued that the "forces" view, because it fails to represent the novelty-introducing role of mutation, encourages incorrect reasoning about population-genetic causes, and closes off known phenomena from our understanding.  In particular, this view makes it impossible to understand how one could get mutation-biased adaptation.  Mutation-biased adaptation is not a complex or speculative idea. Its just a matter of "first come, first served" (or in the language that I prefer: "a bias on the introduction of variants is a prior bias on the course of evolution").  If there is the potential for "adaptive" evolution via fixation of several different beneficial alleles, each of may be introduced into the population by mutation at a different rate, then evolution will tend to go in the direction of the mutationally favored allele-- the probability of mutational origination is higher, therefore (other things being equal) the joint probability of origination-and-fixation (i.e., completing an evolutionary step) is higher.   This effect can be demonstrated in a theoretical model (2001) and has been seen in laboratory evolution experiments (2005). Presumably its a general feature of evolution (2009).  





From my experience, I sense a major roadblock to reforming how evolutionary biologists think about causes.  Moving away from the "forces" view to a more probabilistic view is not just a translation in language, but represents a shift away from a historic "neo-Darwinian" or "Modern Synthesis" theory of evolution viewed as Darwin's legacy, toward an alternative "mutationist" or "new mutations" view that used to be treated as a heresy but which now underlies much of the thinking of molecular evolutionists (2006).   In the view called the "Modern Synthesis" or "neo-Darwinism" and associated historically with Mayr, Simpson, Ayala, Fisher, etc, evolution really is nothing more than shifting the frequencies of genes in the "gene pool", and this process is understood to be largely deterministic, though highly contingent, i.e., once we know what alleles are in the "gene pool" (which is based on the previous history of the population), the adaptation to an environmental change-- and in this view, evolution is predominantly a matter of adaptation-- is a relatively deterministic matter of shifting relative frequencies in the gene pool.  In the "new mutations" or mutationist view, evolution is not such a smooth process.  Instead, it is a series of episodes in which a new mutation occurs, and then, whether through selection or drift, its descendants reach fixation in the population.  These views differ in a variety of ways, e.g., in the first view, evolutionary change is initiated by a change in the environment that brings on selection of available variation, whereas in the second view, change is initiated by a new mutation.  


Another evolutionary biologist who has been publishing in this area is molecular evolutionist Masatoshi Nei.  A few years ago, Nei (2007) wrote that "Natural selection occurs as a consequence of mutational production of different genotypes, and therefore it is not the fundamental cause of evolution."  This sounds very similar to what Mohan is saying.  It also echoes things that mutationists and other critics of Darwinism have been saying for 150 years.   So, this is not just about developing a language of probabilities.  To shift away from the view that natural selection is creative and is a fundamental cause is to shift away from Darwinism.  This shift is not going to happen easily, given how much the dominant culture of English-speaking evolutionists has invested in "Darwin", "Darwinism" and "neo-Darwinism".  




2010-04-25
The fate of the received view of natural selection
Let me go back to Darwinian selection. My intention would be to defend Darwinian selection while rejecting the force model of natural selection. Well, I can't do that, but here is a sketch of an argument that looks promising to me:
  1. In population genetics terms, Darwinian selection can be seen as a special, "boring" case of natural selection.
  2. Darwinian selection is about the origin of adaptations.
  3. There are models, other than usual population genetics models, for the study of adaptations.
  4. The force view of natural selection does not account for the intricacies of these models of adaptation.
  5. Darwinian selection can still be valued as a first step in the study of the relations (less obvious than often expected) between adaptation and natural selection.

1. The Darwinian, or "vernacular" view of natural selection can be translated into a (sort-of) elementary model of population biology. The only parameters in such model would be the reproductive rates of two variants. The model would constrain the population to be fixed in size, or limited in growth, and assume non-blending inheritance and asexual reproduction. It would be a rather boring model, with a predictable behavior for any choice of parameter values, but a legitimate model of natural selection. This is an indication that Darwinian selection can be construed as a special case of natural selection.

What I find interesting in the poverty of this model is that it is not just a poor representation of the world, but a poor representation of the (Darwinian) theory as well. The model is pretty useless as a tool to study evolution, but it also fails to capture many essential parts of the Darwinian view, including the asserted relation between function (new or improved) and fitness. (I use "function" loosely, as the effect of a part on the survival and reproduction of an organism in a certain environment.) 

2. As Coyne says, a better title for Darwin's treatise would have been "The Origin of Adaptations". One may also say that in devising a theory about the origin of adaptations Darwin provided the first insight into the fundamental concept of fitness, although his concept of fitness ("vernacular fitness") was fairly rudimentary.

3. As far as I can tell, the relation between function and fitness is not captured by population genetic models. There are good reasons for that: function would be, at best, an accessory to fitness, and it would introduce many complications since it is often difficult to define and measure. But even though we can study natural selection using models that do not represent function, it doesn't follow that the theory at large can dispense with function.

According to Orr 2005, modeling efforts in the study of adaptation follow the lines of either Fisher's geometric model, adaptive landscapes, or (perhaps more promisingly) mutational landscapes. I say "more promising" from the point of view of its integration with population genetic models. As I understand it, in Gillespie's mutational landscape model the effect of a mutation alter the contours of the adaptive landscape, thus changing the path (and probabilities) towards a fixed optimum. 

4. The force model sees the integration of variation and selection in terms of composition of forces (I'm ignoring drift and other population genetic processes since they are at least homogeneous with natural selection in modeling terms). Given the limited degree of integration in the models of adaptation and population genetics, however, the model of vector addition is arbitrary so say the least. In order to accommodate the mutational landscape model, the force view should include a dampening mechanism to the effect that the current application of a force reduces the effects of the future applications of another force.

5. The vernacular view is the idea that natural selection "selects" variable traits according to their differences in function. But the whole vernacular story does not discount the role of variation. We can have a vernacular view where variation "causes" natural selection to occur by providing it with the raw material on which selection "acts". Though philosophically objectionable, such view does not preclude seeing variation, and population genetic processes such as natural selection, as requiring different models, with the study of adaptations as the proper place to attempt an integration. The vernacular view could then be maintained as a first approximation to the scientific view(s), but not rejected as necessarily leading to false or inappropriate models.


2010-04-28
The fate of the received view of natural selection
I'm sorry to bog down this discussion with another long post, but I think there is an enormous potential benefit if philosophers actually understood more about how the theoretical apparatus of evolutionary genetics is brought into play, because my fellow evolutionary biologists don't seem to care very much if their understanding of causation makes any sense at all, whereas you folks do care about such things.  

Darwin's original theory has no explicit formalization and is incompatible with genetics as we know it, though it persists as a folk theory. Thus, its a bit absurd to talk about a "population genetics" of "Darwinian selection".  The Duke of Argyll said, in an 1864 speech, that "Strictly speaking, therefore, Mr. Darwin’s theory is not a theory of the Origin of Species at all, but only a theory on the causes which lead to the relative success and failure of such new forms as may be born into the world", and Darwin responded in a letter to Lyell saying "That may be a very good theory, but it is not mine" (this exchange is related by Poulton, 1909).  

To understand Darwin's view, one must think of heredity and variation as processes mediated by *fluids*, not discrete particles.  The Duke and others mistakenly try to discretize Darwin's world, but Darwin was deeply committed to a doctrine of natura non facit salta, and this was entangled in his view of heredity and variation.  In Darwin's view, the variations manifested in an individual emerge because the underlying hereditary substances FLUCTUATE continuously in potency on the scale of one or a few generations.  Due to the fluidity of inheritance, these fluctuations BLEND during reproduction.  Infinitesimal fluctuations emerge (roughly) in every character in every generation, especially under altered "conditions of life".  It is these relative fluctuations, NOT mutant particles, that provide the leverage for selection in Darwin's view. 

The idea that a single variant individual (a "mutant" we would say) could be the start of something new in evolution is our view today, and it is a view suggested by many of Darwin's critics, and quite a few of his friends (e.g., Galton, Huxley), but it was NOT Darwin's view.  

Thus, "Darwinian selection" is alien to population genetics.  One may attach a selection coefficient to a Mendelian allele, but in Darwin's theory, there is NO constant informational or hereditary unit to which one may attach a selection coefficient. 

Instead, a properly constructed Darwinian theory for the movement of an evolving system in morphospace would yield an equation for the instantaneous rate of flow as a function of direction (in morphospace), conditioned on the underlying flow of variation and the selection differential.  A key problem with this view is that the evolving system has no inertia-- given the high rate of fluctuation, it would flow all over the place if it were not for selection keeping it in place.  Its no wonder that Darwin and his advocates placed so much faith in selection.  In their view, the evolving system was like a ball placed on an uneven surface, ready to roll in any direction and come to rest in a local minimum.

I wish that some theoretician or philosopher would develop a formalism for this. Perhaps it corresponds to the quantitative evolutionary genetics, a formalism that does not address genes explicitly, but simply allows for some heritability of the variation in a quantitative trait. The master equation (2002) is
 
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where delta z, the "response to selection", is the change in values for a vector of trait-values z (and G/P is a heritability matrix, and S is selection differentials).  This framework corresponds most closely to the folk theory of Darwinism, because it assumes abundant infinitesimal variation.  However, it can be justified under Mendelian inheritance given extreme assumptions (no drift, infinitely many loci each with alleles with infinitesimal effects on the trait, and no linkage, etc).  Steppan, et al. say, in regard to this "quantitative genetics" framework,
"If stochastic events, such as genetic drift, fluctuating adaptive landscapes and rare mutations, are more important, then quantitative genetics might not be informative and macroevolution might be decoupled from microevolution.  Resolution of this issue is crucial to evolutionary biology as a whole" (p. 322)
Once we take an explicitly genetic view, everything changes.  Historically, there are two Mendelian views (2006).  For some purposes, its convenient to think of them as extremes on a continuum defined by the availability of variation, from low to high.  

1. At one extreme, there is the "neo-Darwinian" or "Modern Synthesis" view that allelic variation is always abundantly available, "selection" (reified) never waits for a new mutation, and evolution consists of shifting the relative frequencies of Mendelian alleles so that the multi-locus frequency distribution collectively reaches an optimum.  This view re-defines "evolution" as "shifting gene frequencies".  This view is easy to fit with the "forces" concept, so long as we make it deterministic.  But we could make it probabilistic and then it doesn't fit as well.

2. The other extreme is the canonical "mutationist" view in which evolution is a two-step process of mutation and acceptance. That is, a mutation arises, and its subject to acceptance or rejection. This view does *not* fit the force model in any way at all.   The probability of acceptance reflects any effects on fitness, i.e., what we might call "selection", although its a different kind of thing.  It corresponds roughly to the folk theory of causes used in molecular evolution, where evolutionists tend to think of evolutionary changes as "mutations" that have been "accepted" either by "drift" or by "selection". 

Arlin 

Poulton, E. B. 1909. Fifty Years of Darwinism. Pp. 8-56. Fifty Years of Darwinism: Modern Aspects of Evolution. Henry Holt and Company, New York.

2010-04-30
The fate of the received view of natural selection
Thank you Arlin, I have to admit that I am actually more interested in your argument than in my own. I understand that I often express myself quite loosely. Unfortunately there are a lot of "Darwinian" ideas around that are not Darwin's but are part of the "received view" I wish to defend. So I did take some liberty in my inclusion of non-blending inheritance in the "boring model", because the received view happily admits that Darwin was wrong on inheritance, and wasn't right about variation. I also spoke of "variants" because the received view knows about mutations but does not make any difference between "new" mutations and standing genetic variation. The received view is also agnostic, or just confused, about the levels of selection.

I'm afraid this will be a longish reply. Before I proceed, I don't know for sure why I wish to defend a view which I don't believe is true. It has something to do with the difference between narrative and scientific explanation: most laypeople will accept as explanatory a narrative account of the "mechanisms" of evolution, while many scientists (especially molecular biologists) strongly reject the idea that scientific explanations of evolutionary processes can be rendered in narrative form. As I said, I don't know for sure, they may be right, but I believe that a narrative account of evolutionary processes may serve important purposes outside of science, and while I don't expect it to have much value as scientific explanation I wouldn't want it to be just a myth.

The starting point of my defense of the received view is, of course, to maintain that the received view is not true. If we go deeper into theoretical details we may well realize that it is just false. Still, we may hope to put it to some good use along the lines of "false models as means to truer theories" (Wimsatt).

The abstract form of mathematical models allows us to dispense with the theory at large and with some probematic constructs. My "boring model" captures a basic idea about fitness: different reproductive rates bring about different frequencies. Having the model, we can look at it and ask "fitness/frequencies of what?" and once we start adding entities and mechanisms such as genes and sexual reproduction we can throw it away. 

Darwin's theory, however, and the received view, are about adaptation by natural selection. I'm not a fan of adaptation, but if a relation between adaptation and natural selection exists it could be a point in favor of preserving something of the received view (i.e., the idea that such relation exists, though not necessarily a cause-effect relation). Apparently, this part of Darwin's theory (quite obvious from a folk-theoretical point of view) is difficult to formalize and model in population genetics terms, and the few models around show that the relations between adaptation and natural selection are less straightforward than imagined. So the received view is most likely wrong, again, but can we put it to some good use? 

Since we don't have a simple, "boring" mathematical model for the relations between adaptation and natural selection in folk-theoretical terms, let's take Arlin's geometrical model of "a ball placed on an uneven surface, ready to roll in any direction and come to rest in a local minimum". Adaptation in this model is the movement of the ball, while natural selection is the force causing the ball to roll (gravity). One thing that the model gets almost right (since in this first approximation we are not interested in drift) is that the ball cannot move against gravity. But the interesting thing in this model is that there is no force that can displace the ball once it has reached the local minimum, so adaptation requires a change in the landscape. 

If we take this as an assertion, or a scientific hypothesis about the need of environmental changes to start the process of adaptation, then it is most likely wrong (though it might be close to Darwin's own views). But if we take it as the result of a simplifying assumption of our initial model ("let's ignore the force altering the landscape, let's concentrate on the path of adaptation"), then we can take the model as a starting point to test the effects of changes in our other simplyfing assumptions. We can model different shapes of the ball and see how the adaptive path is changed (similar to Galton's polyhedron analogy); or the effects of a change in shape or weight of the ball along the path (a mutation?); or let the ball change the underlying surface while rolling upon it. Admittedly, all these geometrical models rely on selection as a force, and are thus incompatible with a statistical view of natural selection.  But as "means to truer theories" they may serve an exploratory purpose, allowing us to insert real entities and mechanisms. Real entities can in turn provide indications about the appropriate mathematical, population genetics models, and are the best safeguard against reification.


My point is that the received view (not the Modern Synthesis view, but a folk-theoretical view built upon various narratives, many inspired by the Modern Synthesis) can indeed accommodate these models in its account of evolutionary processes. We (laypeople) should try to understand which accounts are just simplifications and which are hopelessly (i.e., uselessly) wrong.