Abstract
It has become customary in multilevel selection theory to use the same terms (namely “multilevel selection 1” and “multilevel selection 2”) to denote both two explanatory goals (explaining why certain individual- and, respectively, group-level traits spread) and two explanatory means (namely, two kinds of group selection we may appeal to in such explanations). This paper spells out some of the benefits that derive from avoiding this terminological conflation. I argue that keeping explanatory means and goals well apart allows us to see that, contrary to a popular recent idea, Price’s equation and contextual analysis—the statistical methods most extensively used for measuring the effects of certain evolutionary factors (like individual selection, group selection etc.) on the change in the focal individual trait in multilevel selection scenarios—do not come with built-in notions of group selection and, therefore, the efficacy of these methods at analyzing various kinds of cases does not constitute a basis for deciding how group selection should best be defined. Moreover, contrary to another widely accepted idea, I argue that more than one type of group selection may serve as explanatory means when one’s goal is that of explaining the evolution of individual traits in multilevel selection scenarios and I spell out how this explanatory role should be understood.
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Notes
Throughout this paper, when I say that a group selection process may serve as an ‘explanatory means’ within an MLS1 analysis, what I mean is that one may point to that group selection process in order to provide an explanation—though not necessarily the only or the best explanation—of the evolutionary change of interest (this is similar to pointing to the process of rain when one wants to explain the occurrence of a flood). In other words, when I speak of group selection (or of individual selection, migration, mutation etc.) as an ‘explanatory means,’ I am not referring to the process of group selection insofar as it is taking place in nature, but insofar as it is referred to in an explanation of the evolutionary change of interest.
This assumption is shared by all the above quoted authors who take the MLS1/MLS2 distinction to be a distinction between two kinds of group selection.
Note that what I call here the “units of selection question” refers to particular cases only; it should not be confused with the more general question that asks what kind of biological entities (above or below the organismic level) could, in general, function as units of selection. This more general issue seems to have lead to a large consensus in the field, with many authors agreeing that biological entities ranging from genes to species may be units of selection. However, this consensus often breaks down when one asks what the unit of selection is in particular cases.
A thorny issue—that is beyond the scope of this paper—is that of precisely establishing how group reproduction should be conceived of in cases of this sort (i.e. exactly what type of relations two groups must have with one another in order for them to be considered a “parent group” and, respectively, an “offspring group”). As Wade (1978) has shown, varieties of group reproduction may range from a “propagule pool model” (each offspring group has only one parent group, and this is therefore a kind of equivalent of asexual reproduction) to a “migrant pool model” (which supposes a complete mixing of the individuals of all parent groups before offspring group formation, and consequently each offspring group is likely to have as parents all the groups of the parent generation). Assigning a cut-off point on the continuum between these two extremes may well seem arbitrary in most cases. For the purposes of this paper, we may set the cut-off point very close to the “propagule pool model” and assume that easily manageable forms of G–G group selection are found in cases where offspring groups are likely to have at most two parent groups (this case is therefore similar to sexual reproduction, where the genes of offspring organisms come from just two parent organisms). But the general points about group selection and its explanatory role that I advance here do not hinge on any precise solution to the issue of group reproduction.
Note that I have presented the notions of G–I and G–G group selection in causal terms (i.e. as requiring a causal link between group character and either G–I or G–G group fitness). This accords with the causal theory of natural selection that has been defended or presupposed, in various versions, by certain evolutionary theorists during the past few decades (e.g. Arnold and Fristrup 1982; Sober 1984; Shanahan 1990; Waters 2005; Glymour 2006, 2011; Godfrey-Smith 2007; Otsuka 2016; Jeler 2017).
See, for example, the reference to irreducibility in their ostensive definitions: “Type I group selection occurs when an irreducible group property or process results in group–individual fitness differences among groups” (Mayo and Gilinsky 1987, 518).
The causal chain that links a group character with a change in frequency/average value of the focal individual trait is sometimes called “the process referred to by multilevel selection 1” (e.g. D&H, 412). Consequently, one (but not the only) aim of an MLS1 analysis will be that of determining if, in a given scenario, such a process occurs and what its magnitude is, as acknowledged by D&H (414).
Again, the causal chain that links group characters with the change in group character frequencies/average values is sometimes denoted as the process referred to by MLS2 (e.g. D&H, 412). Therefore, one of the aims of an MLS2 analysis will be that of determining whether such a process occurs in the case at hand and what its magnitude is (see D&H, 415–416).
Let me note that, in one place, D&H (410) state that, in the MLS1 approach, “’group selection’ refers to the effects of group membership on individual fitness.” I am not convinced that this statement is meant to provide a definition of group selection (a significantly different one from that discussed in the text). However, some authors claim that this statement (together with a few similar ones from Heisler and Damuth 1987) does outline a notion of group selection that is intrinsic to contextual analysis: I will get back to this issue in Sect. 4.
Though, it should be noted, terminological issues are not altogether insignificant: multilevel selectionist explanations of the evolutionary change in empirical cases are controversial enough as it is and any manner in which we could clarify their terms would, in all probability, be welcome.
Obviously, if one’s goal is that of explaining the transgenerational change in the focal individual trait (and this may often be the case), an additional condition is required, namely that the focal trait be heritable.
I chose to discuss here cases in which the group trait D does not depend on the traits of the individuals contained by the group because the dependency relations are easier to grasp and express in such cases. But the conclusions I will draw about cases where the correlation between z and D is spurious will also apply to the cases that are admittedly more frequent and much more likely to lead to longer-term evolutionary consequences, namely those in which the correlation between z and D is not spurious. Therefore, readers who find Case 1 problematic because D does not depend on the traits of individuals may simply alter the example and imagine that we are dealing with a case in which z-individuals exhibit a behavior that brings a G–I fitness benefit to their group, but z-individuals pay no cost whatsoever for this behavior. In this case, D would simply refer to the proportion of z-individuals in the group.
Of course, given that, by hypothesis, a group’s D is not dependent on the traits of the group’s individual members, the increase in frequency of z due to G–I group selection on D may well be annulled in the next generation. But note that my purpose in this section is that of dispelling some ambiguities that have surfaced in the philosophical literature concerning the main statistical methods for conducting MLS1 analyses, and for this the analysis of evolutionary change over a single generation is enough (this is also why, for my purposes here, it is irrelevant whether groups reform every generation or remain in place for a number of generations). How we should model long-term evolution of traits (which is, of course, a problem of more interest for biologists) is an issue that depends on a much larger array of factors (modes of reproduction of individuals and groups, life-cycle details, migration patterns, mutation etc.) and that does not directly concern us here.
In my toy example, the most convenient way of expressing z as a quantity is to assume that \(z = 1\) for z-individuals and \(z = 0\) for non-z-individuals. I will adopt this notation throughout this paper and \(Z_{j}\) will thus refer to the proportion of z-individuals in the jth group.
Of course, in Case (1), Price’s equation may also be rewritten as \(\Delta \bar{z} = \frac{{\beta_{wD} Cov(z_{ij} ,D_{j} )}}{{\bar{w}}}\), where \(\beta_{wD}\) is the simple linear regression of individual fitness w on D. I only chose the form given in Eq. (1) in order to preserve its similarity with Eq. (4) below.
Alternative explanations might not appeal to “group selection” at all: one could, for example, see the difference in D not as a difference in character between two groups, but as a difference in the environments encountered by the individuals of the given population. But deciding whether this explanation or the explanation appealing to G–I group selection should be viewed as preferable exceeds the scope of this paper, since it pertains to the “units of selection question.”
One may also object to the fact that I speak of G–I group selection on Z here, even though, in this case, there are arguably no fitness-affecting interactions with respect to trait z by the members of each group, i.e. even though the fitness-affecting interactions criterion to identifying groups is not satisfied (see Okasha 2006 for more extensive discussion). However, there are three interconnected problems with the idea that group selection for a given trait requires fitness-affecting interactions between individuals with respect to that trait. First, there are serious difficulties with regards to our ability to test when the fitness-affecting interactions criterion is actually satisfied by the groupings of a given population (see Glymour 2017). Second, often empirical studies of group selection do not identify groups on the basis of fitness-affecting interactions (again, see Glymour 2017). Finally, the fitness-affecting interactions criterion seems too restrictive: two groups may well vary in G–I fitness because they vary in initial size (as per the Allee effect), and yet it would be difficult to claim that the individuals of each group “interact” with respect to group size—would we have to conclude that there is no “group selection” here and thus define out of multilevel selection theory many if not most cases involving group traits that are not directly measurable at the level of individuals? That being said, footnotes 12, 19 and 20 briefly indicate that the points I make in this section also apply to cases in which there are fitness-affecting interactions between individuals with respect to the relevant trait.
Equation (2) may be easily derived from Price’s (1972) hierarchical equation, i.e. \(\Delta \bar{z} = \;\frac{{E\left[ {Cov(z_{ij} ,w_{ij} )} \right]}}{{\bar{w}}} + \frac{{Cov(Z_{j} ,W_{j} )}}{{\bar{w}}}\). First, we write (following Heisler and Damuth’s 1987 application of multiple regression analysis to multilevel selection) the fitness w of each individual i from group j as \(w_{ij} = \alpha + \beta_{wz} z_{i} + \beta_{wD} D_{j} + \varepsilon_{i}\) (where \(\alpha\) is the intercept and \(\varepsilon_{i}\) is the residual whose variance is to be minimized). Equation (2) is then obtained by substituting this expression into the term \(W_{j}\) of the second term on the right hand side of Price’s hierarchical equation (recall that \(W_{j} = \frac{1}{n}\sum\limits_{i = 1}^{n} {w_{ij} }\), where n is the number of individuals in the group). Note that, by the construction of Case 2, I assumed that individual fitness w does not depend on Z: this is why Z does not figure among the independent variables that wij depends on and this is also why, in deriving Eq. (2), I assumed that there is no correlation between Zj and \(\varepsilon_{i}\). (Let me also note that the first term on the right-hand side of Eq. (2) should normally be weighted by initial group size. However, because I assumed that groups are of the same initial size, the weighting can be dropped.).
Again, for readers that find it odd that, in Case 2, D does not depend on the traits of the individuals of the group, we may replace some of the elements of the scenario to obtain a more common sort of case. Imagine that z-individuals exhibit a behavior that boosts the fitness of all the members of their group (and thus increases the G–I fitness of the group); but let us suppose that, because they possess trait z, the z-individuals are also more fertile than the non-z ones. In such a case, the proportion of z-individuals contained by a group affects the group’s G–I fitness via two causal pathways (i.e. directly, via the extra fertility of each z-individual, and indirectly, via the fitness benefit that all individuals of the group receive from z-individuals); but note, also, that here an individual’s fitness is not affected at all by the extra fertility of the z-individuals in its group, but its fitness is affected by the fitness benefit z-individuals bring to the group. In such a case, it is reasonable to claim that there is a single group selection process (namely group selection on the proportion of z-individuals contained), but that only a fraction of this group selection affects the metapopulation change in z, namely the fraction that refers to the indirect effects of the proportion of z-individuals on the group’s G–I fitness. This means that the partition from Eq. (2) remains accurate, but the variables Z and D become here one and the same variable denoting the proportion of z-individuals contained by the group. The only difference such a case brings with respect to my analysis of Case 2 is that, instead of stating that not all G–I group selection processes we may identify are useful for explaining the metapopulation change in z, we would have to state that only a fraction of a G–I group selection process identified in a case may be useful when we aim to explain the change in z. Let me stress that this also refers to most cases involving altruistic traits discussed in the literature, with the sole difference that, instead of receiving a fertility boost, the altruists incur a fitness deficit because of their behavior.
Imagine, for example, that the density of a group determines the number of attacks that that group will sustain from a given predator (the denser the group, the less it will be attacked); but, at the same time, imagine that for each attack that the group does sustain, the casualties are as follows: 2 small individuals and 1 large individual. Therefore, how many attacks a group will sustain (and thus what its G–I fitness will eventually be) only depends on the group’s density. But the total losses of the group to predation are unevenly shared by the individual types (with small individuals being twice as affected by each attack). Thus, even though a group’s G–I fitness is not determined by the proportions of individual types it contains, this G–I fitness is unevenly shared by the individual types within each group. This is, obviously, a hypothetical example. Identifying empirical populations in which G–I group selection operates and the proportions of types contained have no bearing on the difference in output between groups might not be easy (the only potential populations of this sort tentatively indicated by Okasha 2016 are eusocial insect colonies). But, again, for readers who find it problematic that here D does not depend on individual traits, what I will say about Case 3 holds equally well if we assume that trait D is a group property that results from complex interactions between multiple individual traits; being very difficult (if not impossible) to reduce this property to the proportion of individual types contained by the groups, we may thus presuppose that researchers simply resort to measuring trait D and determining to what extent it affects G–I fitness.
Okasha (2006) argues that one disadvantage of the Price equation partition is that it is applicable only to cases in which the relevant group trait is defined as the average individual character within that group. This, Okasha argues, is a limitation of the Price equation partition, a limitation that is not shared by the contextual analysis partition, and thus constitutes one of the reasons why the latter is preferable. However, as I did here in deriving Eqs. (1) and (4), there is nothing that stops us from rewriting the second term of the canonical form of Price’s hierarchical equation with the help of simple regression analysis: in this way the Price partition may accommodate any group-level trait and its apparent limitation vanishes.
Let me add that Cases 1–3 are not meant to provide an exhaustive list of the types of cases involving G–I group selection.
Here is one of the forms taken by this suggestion: “Which equation [between the contextual and Price partitions] we favor depends on whether we think ‘individual selection’ and ‘group selection’ should be understood as within-group and between-group selection, or as selection on the component of individual fitness that is due to differences in individual p-score, and to differences in group p-score” (Okasha and Paternotte 2012, 1134).
Similarly, if we are dealing with a case like the one from footnote 19 in which the behavior of z-individuals affects the G–I fitness of their group both on a direct and on an indirect path, applying contextual analysis does not lead to the conclusion that the direct path is not a component of the process of group selection on Z; it only leads to the conclusion that the fraction of the group selection process corresponding to the direct path may not be said to be a cause of the metapopulation change in z.
Goodnight’s (2013) discussion of “soft selection” seems to point in this direction too.
Indeed, in a case of that sort, contextual analysis would wrongly identify two sources of the difference in G–I fitness of the two groups. To put it otherwise, the inappropriateness of contextual analysis for such a case would stem from the fact that the second term on the right hand side of Eq. (2) would be non-zero.
Let me note that, in this paper, I have not adopted the notion of group selection attributed by some authors to contextual analysis for two reasons. First, in order to get my points across easier, I preferred to adopt the notion of G–I group selection that is more common among the authors in the field. Second, because there are serious reasons to believe that “group selection sensu contextual analysis” should not be called selection at all (see Jeler 2020).
To put it otherwise, Eq. (4) is preferable when the proportion of individual types contained affects the total output of the groups only indirectly (i.e. by giving rise to other group-level traits that do affect the output of groups directly) or when it does not affect at all the total output of groups.
To take just one example here, cases involving species selection may, in theory, be of this sort. However, there are some insurmountable-looking practical difficulties that stand in the way of conducting MLS1 analyses on such cases (see D&H, 424).
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Acknowledgements
I am very grateful to Lorraine Heisler for her detailed feedback on the manuscript. I would also like to thank Samir Okasha, Michael J. Wade, four anonymous reviewers for this journal and three anonymous reviewers for another journal for their comments on various drafts of this paper.
Funding
This work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS—UEFISCDI, Project No. PN-II-RU-TE-2014-4-2653.
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Jeler, C. Explanatory goals and explanatory means in multilevel selection theory. HPLS 42, 36 (2020). https://doi.org/10.1007/s40656-020-00333-y
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DOI: https://doi.org/10.1007/s40656-020-00333-y