Abstract
Evolutionary transitions in individuality (ETIs) are events during which individuals at a given level of organization (particles) interact to form higher-level entities (collectives) which are then recognized as new individuals at that level. ETIs are intimately related to levels of selection, which, following Okasha, can be approached from two different perspectives. One, referred to as ‘synchronic’, asks whether selection occurs at the collective level while the partitioning of particles into collectives is taken for granted. The other, referred to as ‘diachronic’, asks about the origins of the partitioning of particles into collectives. After having presented the two perspectives and a classical formalism used to deal with the levels-of-selection question in the literature, namely the multilevel version of the Price equation, I show that because this formalism treats the levels-of-selection question from a synchronic perspective, it is inadequate to explain ETIs. This is because a fundamental aspect of ETIs is the origin of collectives. From there, I develop a framework for levels of selection compatible with the diachronic perspective. This framework relies on the distinction between what I call, on the one hand, a ‘functional aggregative collective trait’, and on the other hand, a ‘functional non-aggregative collective trait’. After having presented this distinction, I implement it in the Price equation, leading to a new statistical partitioning of this equation which, I argue, represents a causal decomposition more relevant for ETIs. Finally, I exploit this partitioning to explain the critical stages of an ETI. In addition to its explanatory power, a measure of the degree of functional non-aggregativity could be used as a proxy for the degree of individuality of a collective.
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Notes
The distinction between the synchronic and diachronic perspectives on the levels of selection was first drawn by Okasha (2006, pp. 220–225).
Note that evolutionary biologists typically do not make the distinction between the synchronic and the diachronic approach. Rather, it is often implicit in the type of questions they ask.
Okasha (2006, 2018) argues that the move from asking the levels-of-selection question from a synchronic to a diachronic perspective is a special case of a more general strategy in evolutionary biology which he calls the ‘strategy of endogenization,’ in which the values of variables that were initially taken for granted in a model (exogenous to the model), become progressively explained (endogenized) by other variables in the model. In the case of levels of selection, the ‘variable’ which is endogenized is the existence of collectives.
The term ‘event’ should be understood here loosely in the sense that ETIs need not occur abruptly at a point in time. They might rather occur as a result of processes over a long period of time.
There is a parallel here between the last of the six transitions and the literature on the holobiont—a macrobe and its microbial symbionts. Some have put forward the idea that the holobiont as opposed to the traditional organism—the macrobe without its symbionts—is the unit ‘seen’ by selection. Although in some specific cases holobionts might be regarded as units of selection, there are important problems with this idea. For an analysis see Bourrat and Griffiths (2018).
Although I will sometimes refer to w and \(\omega \) as fitness, they are, strictly speaking, not ‘fitness,’ but absolute and relative reproductive output which, as such, are proxies for or measures of fitness.
‘Statistical aggregate’ simply means that a collective property is defined as a mean of the properties of its constituent particles.
The character is attributed, rather than intrinsic, here, because nothing guarantees that in a non-collective context, the same particle-level character would be observed.
For details see Frank (1998, pp. 13–15).
Okasha (2006, p. 107) defends the idea that the collective level can be an autonomous level of selection and that this is consistent with the supervenience of the collective level on the particle level. The problem with this argument is that the expected fitness of a collective, following my assumptions, depends on the fitness of its particles, so that there exists a relation of dependence between collective and particle fitness. Similarly, Okasha (2016) discusses the problem of intervening on collective characters when they supervene on particle characters: intervening on one is impossible without, at the same time, intervening on the other, because they are two descriptions of the same material substrate. Such interventions as noted by Okasha (2016), are known in the literature as ‘fat-hand’ interventions (Scheines 2005). Okasha (2016, p. 450) proposes to solve this problem by the following convention: “when we consider hypothetically intervening on the supervenient variable we do not hold fixed the variables on which it supervenes, but rather alter them to preserve consistency.” This convention, although mathematically sound, is however inconsistent with the idea of supervenience. Unless there are good reasons to reject the supervenience of collective characters on particle characters, and I believe there are not, this convention cannot be justified. For other problems related to this convention see Birch (2017, pp. 92–93).
Note, furthermore, that Damuth and Heisler (1988) are very explicit that MLS1 and MLS2 represent two perspectives on a given evolutionary process, not a factual distinction. When referring to the two approaches they claim (1988, pp. 410–411): “our point of view is that neither approach represents the multilevel selection process. Rather, both are aspects of any multilevel selection situation. Once one has decided to analyze a given situation in terms of multilevel selection processes both approaches are legitimate within that context and a choice has to be made depending upon what questions are of interest.” Additionally, the definition of fitness as number of particles (MLS1) and number of collectives (MLS2) produced after one generation does not correlate perfectly with selection. As is well known in life-history theory, number of offspring is not the only measure of fitness. The size of offspring, for instance, is often correlated to long term evolutionary success. Once these other factors are taken into consideration, the MLS1 and MLS2 distinction collapses. For more details see Bourrat (2016).
Of course, taking a single collective character, there is no guarantee that it will depend on a single character of particles. It might depend on more than one particle character(s).
Note that in real situations the two components might not occur temporally when generations are not discrete, and there might be some interaction between them.
I will only consider the reproductive mode of multiplication in the reminder of the article. Note also that the notion of ‘phase’ I use here should not be understood temporally. They are conceptual phases so that the selection and response phases can occur at the same time, consistently with the point made in Footnote 13.
The clause that the parts are taken independently is important. If they are not, then because of the existence of a relationship of mereological supervenience between the system and the properties of its parts, a system would always be aggregative. As we will see in the next section, this subtlety is at the heart of what distinguishes a functional aggregate from a statistical aggregate.
Even this is controversial since some mass is transformed into energy during exothermic reactions.
To illustrate my point, I assume that the weight each sculler has to carry is the same in each situation, which in reality is not the case. A boat for a single person is not four times lighter than a boat for four people. It is heavier than that.
One might want to attribute a phenotype of 0 to all particles taken independently, but the phenotype would be undefined since there would be no contrast phenotype (that is a phenotype with a value different from 0) to compare this phenotype to when particles are taken independently.
Note, however, that the procedure used to assess whether failure in non-aggregativity qua size scaling occurs will involve linearity, decomposition and recomposition, and intersubstitution.
Note, however, that the use of fitness transfer and associated terms seem to have meant different things in the different venues Michod has published.
It is still possible that in spite of a causal relationship from z to \(\omega \), it is a non-linear one in such a way that \(\beta _{wz}\) is nil. I will assume here that that is not the case. For a more careful analysis of the relationship between the Price equation and Lewontin’s three conditions see Okasha (2006, Chap. 1).
Note, however, that this last problem is taken care of by our assumption that the collective character is a statistical aggregate of the particle character of its constituent particles.
The point here is similar to the idea that the gene’s eye view does not describe a causal relationship between genes and phenotype, but merely accounts for it statistically. This idea is known as the ‘book keeping objection’ to the gene’s eye view (see Okasha 2006, p. 158ff, for a review of the literature on the book keeping objection). I should add that the distinction between statistical and functional aggregativity resonates with the distinction between statistical and physiological epistasis (also known as gene-gene interaction) sometimes made by quantitative geneticists (Goodnight 1988; Wade 2016; Wolf et al. 2000). Physiological epistasis corresponds to the notion of functional non-aggregativity: in spite of a high level of functional epistasis for a character, that is to say that the character would not be expressed in the absence of, or by the knocking out of, one of the alleles contributing to the organisms’ character, the effect might be considered as statistically additive in a population.
They might be correlated in specific cases, but not in the general case.
More accurrately it represents the particle contribution of the collective-level response to the particle contribtution of collective-level selection, which is a bit cumbersome and hence the reason why I use ‘particle response to particle-level selection’. Mutatis mutandis the same can be said for the other three response to selection terms.
Note however that when there is no variation in the aggregative component of particles between the collectives but there is some within each collective or when the correlation between collective fitness and the aggregative component is nil but there are differences in fitness between particles of a collective, the term \(\mathrm{Cov}(\varOmega _k, A_k)\) will be nil. This might be interpreted as a lack particle-level selection which seems wrong since there could exist differences in fitness between the particles with different aggregative components of a collective. Mutatis mutandis, the same will be true with the non-aggregative component of the collective-level character. That said, a situation in which all the collectives have the same aggregative (or non-aggregative) component, although possible, is rather artificial. In general, if there is variation within collectives, we can expect that this will translate into variation between collectives. Nevertheless, perhaps ways to address this potential worry—although this would require a careful assessment—would be either to apply the aggregative/non-aggregative distinction in the single-level version of the Price equation at the level of the particle rather than the collective level, or to apply it to the hierarchical version of the Price equation as opposed to the single-level version at the collective level. In this latter case, one would essentially have to insert Eq. (20) recursively in the transmission bias term of Eq. (20). In both cases, one could assess whether each component of particle-character is correlated with particle fitness (either globally or within each collective depending on the option chosen). Having flagged up this potential worry and provided possible directions to address it, I leave a full analysis for future work.
This, of course, relies on the assumption that the population is infinitely large. In a population with a finite size, the number and frequency of interactions of particles will always be limited.
The trait must be the same at both levels, and consequently for the different types of particles, even if they belong to different species. This poses some practical problems which, in many cases, can be overcome by standardizing the particle-level trait.
Although under some particular ecological conditions sharp separations between collectives might arise for free.
Such traits are typically called ‘emergent’, a term I find too vague. These traits are simply not easily definable at the particle level, rather than emergent.
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Acknowledgements
I am thankful to the Theory and Method in Biosciences group at the University of Sydney and two anonymous reviewers who provided useful feedback on previous versions of this manuscript. I am more particularly thankful to Stefan Gawronski who proofread the final manuscript. I also thank Katrin Hammerschmidt and Ellen Clarke for discussions on the topic. This research was supported by a Macquarie University Research Fellowship and a Large Grant from the John Templeton Foundation (Grant ID 60811).
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Bourrat, P. Transitions in evolution: a formal analysis. Synthese 198, 3699–3731 (2021). https://doi.org/10.1007/s11229-019-02307-5
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DOI: https://doi.org/10.1007/s11229-019-02307-5