A Note Against the Use of “Belonging To” Properties in Multilevel Selection Theory


In this short paper, I argue against what I call the “belonging to” interpretation of group selection in scenarios in which a group’s fitness is defined as the per capita reproductive output of the individuals of the group. According to this interpretation, group selection acts on “belonging to” properties of individuals, i.e. on relational or contextual properties that all the individuals of a group share simply by belonging to that group; thus, if differences in the individuals’ “belonging to” properties cause differences in their fitness, group selection sensu the “belonging to” interpretation is said to be at work. I argue that the main problem with the “belonging to” interpretation is that it confuses evolutionary changes due to differences in environmental quality with evolutionary changes due to selection. In other words, I argue that, in the majority of cases, this interpretation actually takes the “selection” out of the “group selection” notion it aims to interpret: by adopting this perspective, one implicitly commits to explaining the evolutionary change under consideration not by a kind of selection (be it individual or group selection), but by differences in the environmental quality experienced by individual types.

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  1. 1.

    My opinion is that the terms MLS1 and MLS2 should not be used in order to designate these two kinds of group selection and should be reserved for a different usage. However, since these terms are largely used in the literature in this sense, I will also adopt this terminology in this paper.

  2. 2.

    I adopt here a causal view of selection that is becoming increasingly popular among evolutionary theorists in general (e.g. Sober 1984; Shanahan 1990; Waters 2005; Glymour 2006, 2011; Godfrey-Smith 2007; Otsuka 2016), as well as among authors specifically working on multilevel selection (e.g. Arnold and Fristrup 1982; Okasha 2006; Jeler 2017).

  3. 3.

    Throughout this paper, I assume that individuals faithfully transmit their type to their offspring.

  4. 4.

    The trait may be, for example, the degree of reproductive competition in certain ant species, where an overabundance of egg-laying workers leads to a lack of workers taking care of the brood (Hölldobler and Wilson 2009).

  5. 5.

    Whether this correlation is spurious or not will only become relevant later on.

  6. 6.

    There are, however, some phrases in this article that seem to gesture towards an endorsement of the “group-level interpretation.” For example, when they speak of group selection of the MLS2 kind, Heisler and Damuth (1988, 410) state: “In this case, we have identified a different kind of fitness than in the first (i.e. than in the MLS1 case), a group-level fitness that is not simply the mean of the fitnesses of the group’s members,” which suggests that the relevant fitness for MLS1 is the mean fitness of a group, as in the “group-level interpretation” presented above.

  7. 7.

    Without dwelling on its details here, let me recall that, in MLS1 scenarios, contextual analysis allows us to partition the population average change in an individual-level character z in the following manner: \(\Delta \bar{z} = \frac{{\beta_{z} Var(z_{ij} )}}{{\bar{w}}} + \frac{{\beta_{Y} Cov(z_{ij} ,Y_{j} )}}{{\bar{w}}},\) where \(z_{ij}\) is the character of the ith individual in the jth group, \(Y_{j}\) is the group character of the jth group, \(\bar{w}\) is the average individual fitness in the global population, \(\beta_{z}\) is the partial regression coefficient of individual fitness on individual character and \(\beta_{Y}\) is the partial regression coefficient of individual fitness on group character. In cases in which the relevant group character is defined as the average character of its individual members, the equation becomes \(\Delta \bar{z} = \frac{{\beta_{z} Var(z_{ij} )}}{{\bar{w}}} + \frac{{\beta_{Z} Cov(z_{ij} ,Z_{j} )}}{{\bar{w}}},\) where \(Z_{j}\) is the average individual character in the jth group. In the latter kind of cases, a different partition is provided by Price’s (1972) hierarchical equation, namely: \(\Delta \bar{z} = \frac{{E\left[ {Cov(z_{ij} ,w_{ij} )} \right]}}{{\bar{w}}} + \frac{{Cov(Z_{j} ,W_{j} )}}{{\bar{w}}},\) where \(w_{ij}\) is the fitness of the ith individual in the jth group and \(W_{j}\) is the average fitness of the individuals of the jth group. Heisler and Damuth (1987) argue for the superiority of the contextual analysis partition over that of Price’s equation.

  8. 8.

    One of these reasons is certainly the fact that “contextual analysis” detects a group selection component in cases of “soft selection,” i.e. cases in which, overall, groups do not vary in fitness, yet the fitnesses of individuals are influenced by their group’s character. For some recent attempts to solve this thorny issue, see Goodnight (2013) and Bourrat (2016).

  9. 9.

    Indeed, I suspect that Damuth and Heisler’s (1988) failure to acknowledge this distinction has occasioned their above-detailed apparent endorsement of the “belonging to” interpretation.

  10. 10.

    For detailed treatments of this issue, see Sober (1984), Okasha (2006), Godfrey-Smith (2008) and Glymour (2017).

  11. 11.

    I use density as the group character of interest because, as Damuth and Heisler (1988) note, this is a property that cannot be measured at the level of individuals.

  12. 12.

    It is crucial to stress that the kind of argument I am making here against the “belonging to” interpretation in populations with limited dispersal does not apply to kin selection theory. Like the “belonging to” interpretation, kin selection approaches do distinguish between two components of individual fitness, namely direct fitness, on one side, and, on the other side, indirect fitness (in the inclusive fitness approach) or the fitness benefit brought to the focal individual by genetically similar individuals (in the neighbor-modulated fitness approach). However, and this is the crucial difference, unlike the “belonging to” interpretation, kin selection approaches do not claim that the two components of fitness correspond to two different selection processes (namely, individual selection on the relevant individual trait, on one side, and selection on “belonging to” properties, one the other). On the contrary, when one says that a particular trait/behavior spreads by kin selection, this means that the combined effects of the two components of fitness lead to an increase in frequency of that trait/behavior. To put it otherwise, even though one may separate the components of fitness of each individual at a given moment (e.g. into direct and indirect fitness, in the inclusive fitness approach), it is the sum of these components that is taken as the fitness notion corresponding to the process of (kin) selection for the focal trait/behavior of that individual. It is this extension of the notion of fitness that constitutes the distinguishing feature of kin selection theory (see Marshall 2015). Indeed, Hamilton (1964, 8) is explicit about this: “Just as in the sense of classical selection we may consider whether a given character expressed in an individual is adaptive in the sense of being in the interest of his personal fitness or not, so in the present sense of selection we may consider whether the character or trait of behaviour is or is not adaptive in the sense of being in the interest of his inclusive fitness.”

  13. 13.

    And, as pointed out above, nor does kin selection theory.


  1. Arnold AJ, Fristrup K (1982) The theory of evolution by natural selection: a hierarchical expansion. Paleobiology 8:113–129

    Article  Google Scholar 

  2. Bourrat P (2016) Generalizing contextual analysis. Acta Biotheor 64:197–217

    Article  Google Scholar 

  3. Brandon RN (1990) Adaptation and environment. Princeton University Press, Princeton

    Google Scholar 

  4. Damuth J, Heisler L (1988) Alternative formulations of multilevel selection. Biol Philos 3:407–430

    Article  Google Scholar 

  5. Glymour B (2006) Wayward modeling: population genetics and natural selection. Philos Sci 73:369–389

    Article  Google Scholar 

  6. Glymour B (2008) Correlated interaction and group selection. Br J Philos Sci 59:835–855

    Article  Google Scholar 

  7. Glymour B (2011) Modeling environments: interactive causation and adaptations to environmental conditions. Philos Sci 78:448–471

    Article  Google Scholar 

  8. Glymour B (2017) Cross-unit causation and the identity of groups. Philos Sci 84:717–736

    Article  Google Scholar 

  9. Godfrey-Smith P (2007) Conditions for evolution by natural selection. J Philos 104:489–516

    Article  Google Scholar 

  10. Godfrey-Smith P (2008) Varieties of population structure and the levels of selection. Br J Philos Sci 59:25–50

    Article  Google Scholar 

  11. Godfrey-Smith P (2009) Darwinian populations and natural selection. Oxford University Press, Oxford

    Google Scholar 

  12. Goodnight CJ (2013) On multilevel selection and kin selection: contextual analysis meets direct fitness. Evolution 67:1539–1548

    Article  Google Scholar 

  13. Hamilton WD (1964) The genetical evolution of social behaviour, I. J Theor Biol 7:1–16

    Article  Google Scholar 

  14. Heisler IL, Damuth J (1987) A method for analyzing selection in hierarchically structured populations. Am Nat 130:582–602

    Article  Google Scholar 

  15. Hölldobler B, Wilson EO (2009) The superorganism: The beauty, elegance, and strangeness of insect societies. W. W. Norton, London

    Google Scholar 

  16. Jeler C (2017) Multi-level selection and the issue of environmental homogeneity. Biol Philos 32:651–681

    Article  Google Scholar 

  17. Lande R, Arnold SJ (1983) The measurement of selection on correlated characters. Evolution 37:1210–1226

    Article  Google Scholar 

  18. Marshall JAR (2015) Social evolution and inclusive fitness theory: an introduction. Princeton University Press, Princeton

    Google Scholar 

  19. Mayo DG, Gilinsky NL (1987) Models of group selection. Philos Sci 54:515–538

    Article  Google Scholar 

  20. Michod RE (1999) Darwinian dynamics: evolutionary transitions in fitness and individuality. Princeton University Press, Princeton

    Google Scholar 

  21. Okasha S (2006) Evolution and the levels of selection. Oxford University Press, Oxford

    Google Scholar 

  22. Okasha S (2016) The relation between kin and multilevel selection: an approach using causal graphs. Br J Philos Sci 67:435–470

    Article  Google Scholar 

  23. Otsuka J (2016) A critical review of the statisticalist debate. Biol Philos 31:459–482

    Article  Google Scholar 

  24. Price G (1972) Extension of covariance selection mathematics. Ann Hum Gen 35:485–490

    Article  Google Scholar 

  25. Shanahan T (1990) Evolution, phenotypic selection and the units of selection. Philos Sci 57:210–225

    Article  Google Scholar 

  26. Sober E (1984) The nature of selection: evolutionary theory in philosophical focus. MIT Press, Cambridge

    Google Scholar 

  27. Sober E, Wilson DS (1998) Unto others: the evolution and psychology of unselfish behavior. Harvard University Press, Cambridge

    Google Scholar 

  28. Waters CK (2005) Why genic and multilevel selection theories are here to stay. Philos Sci 72:311–333

    Article  Google Scholar 

  29. Wilson DS (1975) A theory of group selection. PNAS 72:143–146

    Article  Google Scholar 

  30. Wilson DS (1989) Levels of selection: an alternative to individualism in biology and the human sciences. Soc Netw 11:257–272

    Article  Google Scholar 

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I would like to thank two anonymous reviewers for their comments on a draft of this paper. This work was supported by a project funded by the Romanian Ministry of Research and Innovation within Program 1—Development of the national RD system, Subprogram 1.2—Institutional Performance—RDI excellence funding projects, Contract no.34PFE/19.10.2018.


This work was supported by a project funded by the Romanian Ministry of Research and Innovation within Program 1—Development of the national RD system, Subprogram 1.2—Institutional Performance—RDI excellence funding projects, Contract no. 34PFE/19.10.2018

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Jeler, C. A Note Against the Use of “Belonging To” Properties in Multilevel Selection Theory. Acta Biotheor (2020). https://doi.org/10.1007/s10441-020-09386-9

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  • Philosophy of biology
  • Multilevel selection
  • Group selection
  • “Belonging to” properties
  • Contextual analysis
  • Environmental quality