Abstract
Felsenstein’s method of independent contrasts (FIC) is one of the most widely used approaches to the study of correlated evolution. However, it is also quite controversial: numerous researchers have called various aspects of the method into question. Among these objections, there is one that, for two reasons, stands out from the rest: first, it is rather philosophical in nature; and second, it has received very little attention in the literature thus far. This objection concerns Sober’s charge that the FIC is methodologically flawed due to its (seemingly) resting on the assumption that the traits it studies evolved by drift—and thus ruling out selective hypotheses from the start. In this article, I try to rebut this charge. To do this, I first consider a preliminary conceptual worry—the question of how it is even possible for two drift-driven traits to be evolutionarily correlated—and show that it can be answered by noting that the FIC can be seen as being concerned with the investigation of the modularity of the relevant traits. Given this, I then show that Sober’s methodological charge can at least be mitigated by noting that the assumptions behind the FIC do not in fact preclude it from investigating selective hypotheses. I end by pointing out that making this clearer is not just relevant for defending the cogency of the FIC, but also for developing a deeper understanding of correlated evolution in general.
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Notes
Recently, a different type of method, Phylogenetic Generalized Least Squares (e.g., Bulmer 1991), has become popular as well; however, it remains true that the FIC occupies a central position in this area.
A somewhat related worry could also be raised for many methods of phylogenetic inference. For example, maximum likelihood methods typically assume that the relevant characters evolved by drift (e.g., Harvey and Pagel 1991; Felsenstein 2004), even though the results of this analysis are often used to test the claim that these characters have evolved by natural selection (e.g., through doing comparative studies). However, to make the discussion more tractable, I will restrict myself to discussing only the FIC here.
As we will see momentarily, though, there might also be other reasons for the existence of the correlation.
Note that the reason why we need to calculate the values of the interior nodes is that what we are interested in (at least in most cases) is establishing a correlation in the evolution of traits X and Y in general—not just in that of X and Y in the tip taxa (see also Westoby et al. 1995a, b; Felsenstein 1985, pp. 5–6). For details of the calculations—which are not so important here—see, e.g., Felsenstein (1985) and Harvey and Pagel (1991, Chap. 5). Note also that there is scope for debate about how precise these calculations need to be; see, e.g., Martins et al. (2002); this point will be addressed again below.
Technically, the contrast-based approach is not the only way of interpreting the FIC. Mathematically, all the method does is calculate covariances (and variances) of an evolutionary process, which is made possible by the Brownian motion assumption. For present purposes, though, the formulation in the text is sufficient. I thank Joe Felsenstein for useful discussion of this point.
Alternatively, one might say that trying to determine the absolute values of the relevant traits or the possibility of evolutionary stasis concerning them is answering a different question from the one that motivates the FIC (and which needs different kinds of data to be answered).
In fact, these worries speak to all kinds of comparative methods. See also Sober (2000, Chap. 6).
Instead of talking of modularity, some writers prefer to speak of the existence of genetic constraints or additive genetic covariances (e.g., Felsenstein 1988, 2002, 2004, Chap. 25). I favor the terminology of "modularity," as it makes clearer that the source of the connection between the traits in question need not be genetic, but can lie elsewhere as well.
This does not appear as plausible when it comes to the present example, though.
Of course, it might be claimed that investigating the degree of modularity is not normally what the FIC is in fact used for. However, this is not a problem for the present defense of the method: on the one hand, as made clearer below, the FIC can also be seen to have other aims, and on the other, the present point is merely that the FIC can be given a coherent aim even if it is assumed to be based on drift. See also Felsenstein (1988, 2004, Chap. 25).
Note that, as such, trait modularity need not be a symmetric relation: it may be possible that one trait can vary quasi-independently of another, but not vice versa. If so, then the direction (including bi-directionality) of the modularity needs to be established separately, after a correlation in independent contrast has been found for correlations are symmetric (see also note 24 below).
Note that this argument depends essentially on the assumption that the two traits evolved by drift. If this assumption is dropped (as is done below), the issues get more complex.
Note that the dialectic here is a bit complex. On the most straightforward reading of Sober’s worry, he merely requires logical independence between the assumptions of a method and the hypotheses under study. This, though, is consistent with the assumptions and hypotheses being probabilistically highly non-independent (e.g., there might be exactly one very far-fetched scenario of selection that is consistent with the Brownian motion assumption, with all the other scenarios featuring drift only). As I try to make clearer below, though, I think that the solution defended here can apply to both readings of independence.
Moreover, these three scenarios can be combined with the scenario of traits that have a low degree of modularity with respect to each other. See, e.g., Felsenstein (2002) for a model of this kind of case.
In fact, the same is true for all idealizations.
I thank David Baum for some useful remarks about this point.
It is also interesting to note that precisely this is sometimes assumed in methods based on phylogenetic least squares (see also note 1).
It seems that Sober (2008) wants to exclude this scenario from consideration by his insistence that we investigate "stable optima" only. However, it is not clear why he would do this, given the importance of moving optima.
We might also consider the possibility of "internal selection" in this context—see below for more on this.
Note that "internal" here merely means that the trait in question is an adaptation to features that are somehow part of the organism. It does not mean that these features must be on the "inside" of the organism (whatever exactly this may be taken to mean); in fact, in the example to follow, both leaves and fruit are not internal in this latter sense.
Another good example for this sort of scenario might be camouflaging coloration in various animals. In order for such a coloration to be successful in hiding the animal, it might matter that the patterns it involves stand in the right relationships to each other; however, it might otherwise be irrelevant what size the individual patterns are.
Figure 2 assumes that all combinations of leaf and fruit size that are non-optimal have the same level of fitness; however, this can be changed at the cost of further complications (essentially, one can make the fitness landscape three-dimensional, and let fitness drop off non-uniformly and continuously as one moves away from the line in Fig. 2).
It does need to be noted, though, that the FIC cannot establish which of the two traits is the adaptation and which is the "internal environment," or if both traits are adaptations to each other. In order to establish this, another method is needed—for example, increases in one trait must be brought about artificially in the lab, and the fitness of organisms that differ in the second trait must be measured. However, this issue can be tackled separately from the one at stake here, and does not invalidate the present conclusion in any way. See also above in note 11.
This is also important in the context of the point raised in note 13 above.
In fact, both of these could be true at the same time: for example, it might be adaptive for two traits to stand in a certain ratio with respect to each other, but certain instances of this ratio might also be physiologically determined (e.g., if fruit become sufficiently large, larger leaves might be a physical necessity; at any point, though, only a certain ratio of fruit and leaf size is adaptive).
Note that what the FIC, specifically, can add to this study is to provide (a) a quick check to see whether there are any linkages among the relevant traits that it would be useful to investigate further, and (b) partial evidence of the degree of modularity and evolutionary history of the relevant traits (using further experimental data to supply the relevant missing premises—see also notes 12 and 24). Neither of these contributions should be underrated. Finally, note that this issue is neutral concerning the debate whether natural selection can also have effects in individual organisms; for more on this debate, see, e.g., Neander 1995; Sober 1995; Bouchard and Rosenberg 2004; Forber 2005; Millstein 2006.
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Acknowledgments
I would like to thank Elliott Sober, David Baum, Joseph Felsenstein, and audiences at the University of Bristol, Exeter University, and the London School of Economics and Political Science for useful remarks on previous versions of this article.
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Schulz, A.W. Selection, Drift, and Independent Contrasts: Defending the Methodological Foundations of the FIC. Biol Theory 7, 38–47 (2013). https://doi.org/10.1007/s13752-012-0070-2
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DOI: https://doi.org/10.1007/s13752-012-0070-2