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Walsh’s Sure Thing Paper

In Uncategorized on April 16, 2010 by dcmzb8

A bit of a blast from the past here, but…

I agree with Walsh that population genetics doesn’t explain why individual organisms have the traits they do. For that, you’d have to follow the “developmental” history, including giving an account of why the organism’s parents had the genes they did, where the initial mutation came from, etc. However, Walsh is claiming that evolution isn’t providing a causal explanation at all, even at the population level. I disagree, and I think the arguments he has against the two-factor model fail. I would argue that evolutionary theory does provide a causal explanation at the population level, just not the individual level.

His most important argument should work against both the two-factor and single-factor models of natural selection and genetic drift. This is the one involving Simpson’s Paradox and the Sure Thing Principle. I think it does work if what we’re trying to provide a causal explanation about individual organisms. However, his argument fails if the explanadum is about *populations*.

I think the key premise of his argument is this: “Subpopulation size does have an influence on C, but this relation is constitutive, not causal.” (pg 20) This is true if we are talking about populations of individuals. But if we are comparing different sets of populations – populations of populations – then the size of the population does have causal force. I personally think of population size in the context of genetic drift as something like a physical object’s mass. A larger population is more resistant to the spread of “new” genes, just as a large mass is more resistant to a change in momentum from a force. By divying up the overall population into subpopulations, we’re comparing two different populations of populations – a population of large populations (with one member, the overall population) and a population of small populations (the subpopulations). The causal model involved is fairly straightforward, and doesn’t resemble a Simpson case at all.

His other two arguments are more minor. Genetic drift may have been originally intended as an error term, but in quasi-indeterministic causal models, error terms are simply causal factors that the model doesn’t account for. If an error term works in a predictable way, then it should eventually be brought into the model. As for the modularity argument, I think Walsh may be misrepresenting modularity (does it mean you can intervene on one cause without interfering with the other, or that you can intervene on one cause while holding the other *fixed*?), but I can’t be sure without reading Woodward more closely.

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2 Responses to “Walsh’s Sure Thing Paper”

  1. In defense of Walsh:

    Furthermore, understanding drift as analogous to mass seems to misrepresent the situation in important ways. For an object is often thought to have certain causal powers in virtue of its having mass, but dividing a population in different ways doesn’t seem to impose any new causal powers onto it. You simply claim that “if we are comparing different sets of populations then the size of the population does have causal force.” But why? The size of the population tells us (i.e. represents something) about its resilience to the introduction of new variants, but the size of the population surely doesn’t CAUSE that resilience in any way. It is the underlying properties and interactions of indiviudals that cause that resilience. In fact, just intuitively, I don’t see how something like population size ever could CAUSE something to happen.

    In addition, dividing things up into subpopulations leads to a causal model that is not necessarily a case of Simpson’s paradox (or reversal). Walsh certainly doesn’t intend to argue that merely dividing a population into subpopulations and comparing will lead to a Simpson case. However, there are well known cases when it comes to evolutionary biology in which the causal models involved will lead to a Simpson case. There are cases in which trait 1 has higher fitness than trait 2 in a large population (e.g. the overall population), but within smaller populations (e.g. the sufficiently small subpopulations) trait 2 will enjoy higher fitness than trait 1. But if we interpret these models as causal, then we are committed to an inconsistent set of causal claims: natural selection causes an increase in trait 1 in the overall population, but it causes a decrease in trait 2 in each of the subpopulations. The only other options are to say that drift is causing fitness differences (which seems to be mismatch of the terminology) or that the variables are noncausal (in which case the reversal isn’t a problem). In the end, I simply have a difficult time saying anything like the following: well, the way we divide up the population changes the influences of the causal factors that led to its evolution. I’m far more inclined to say: the causal factors remain constant across these cases, but the statistical properties involved can change when we divide up the population in different ways.

    Finally, I don’t see the distinction between your two interpretations of modularity. If you can’t intervene on one cause without changing the other, then you can’t intervene while holding the other fixed. I think Walsh has Woodward’s account correct (and this is a more general requirement for modularity in other contexts as well). Furthermore, it is true that error terms can be taken to represent causal factors left out of the model, but Walsh’s point is that drift (the variable in question here) was never understood as a causal factor. The argument isn’t that error terms in causal models have to be noncausal, but that drift has always been taken to be a noncausal error term since its introduction to evolutionary biology (drift is just sampling error, which is noncausal).

  2. This will be a bit long. Please count this as three separate posts…

    Drift as an error term: In the paper, Walsh does demonstrate that drift was *introduced* as an error term, but is it possible that biologists at some point started talking as if it were causal? Even if not, I suppose it’s possible that they simply got the philosophy wrong, although I would hate to argue that way. To me, it seems that drift works at the *individual* level as a sampling error in reproduction, but it might have a causal effect at the *population* level.

    Woodward: It looks like you can intervene on population size, and then hold Gillespie fitness fixed through a second intervention. For example, you could intervene on variance.

    I’ll admit that I’m not sure we can intervene on Gillespie fitness directly. I think there might be a product/process problem here. It’s not clear to me how to map the product/process distinction onto things like causal DAGs. Maybe manipulable/observable variables are ‘products’, unobservable and non-manipulable causal processes are processes, like the arrows between nodes in a causal DAG. Gillespie fitness might be a non-manipulable process – you can manipulate selection differential (or whatever the term was), variance, population size, but you can’t directly manipulate Gillespie fitness. That might be a problem for the so-called “two-factor” model (which unfortunately ignores the other two inputs to Gillespie fitness). The important bit about the two-factor model is that population size affects trait-change frequency via two causal routes – Gillespie fitness and drift. But if there isn’t a manipulable variable between the three inputs of Gillespie fitness and the trait-change frequency in the actual population….

    Simpson’s Paradox:

    You’re right that I simply claim that population size is causal. I probably need to make the weaker claim that Walsh’s arguments are not enough to demonstrate that population size isn’t causal *at the ensemble level.* I’ll grant that population size isn’t causal at the individual level. I’m just defending that it’s causal at the population level. Which means we have to chuck individuals out of our ontology when we’re looking at evolutionary causation. You say “just intuitively, I don’t see how something like population size ever could CAUSE something to happen.” Could it be the case that you’re just not accepting populations as real in their own right?

    I *am* accepting that drift has a causal effect on trait-change frequency. Same thing with Gillespie fitness (but see my product/process worry). How are we defining ‘fitness’? A selection differential or the expected trait-change frequency? I’m leaning more towards selection differential, while Gillespie fitness looks like it’s talking about expected trait-change frequency. Expected/predicted trait-change frequency looks like the end result, not something even quasi-causal.

    Why is that population more resistant to the spread of a new trait? Because of its large population size. (Sure, the ‘real’ cause is something about individuals, but individuals are not in our ontology right now.) Dicing the population up into sub-population changes an important property of the population. It’d be like doing a drug trial and complaining that the drug has different effects on whole humans verses pieces of chopped-up humans. Granted, there isn’t any *actual* chopping going on, but…

    A question: how are we defining ‘population’ here? Are we dealing with asexual reproduction? Would it matter if we were dealing with sexual reproduction, with mating occurring between sub-populations?

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