Natural Way to See Multi-Level Selection

Banin D. Sukmono

Director and Head of Metaphysics and Science
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A review of Samir Okasha’s Evolution and the Levels of Selection (2006)

Units and levels of selection have never been easy to grasp, and this is primarily not merely because of the statistical formalism. As with other issues associated with higher- and lower-levels, the problem also lies in deciding at which levels the selection operates and whether the levels identified are a matter of convenience. Two possible disputations can be seen here: between the single-level and multi-level selection and between realism and conventionalism. While the former debates on how many levels, one, two, or three, selection can operate at a time, the latter argues whether the identification represents an objective causal process in the world.

Evolution and the Levels of Selection (2006) by Samir Okasha can be seen as an attempt to evaluate those two debates. This book provides the crux and solution of each issue without imposing much jargon and complicated formalism. The real essence of the book lies in his conceptual analysis that shows that, although adopting one-level selection only and conventionalism may be acceptable in some context, the conceptual value would not be as rich and wholesome as realist multi-level selection. If Okasha is correct, it will avoid a saying that only one entity matters, frequently gene, or none matters, as the natural way. It makes the book worth reading not only for evolutionary theorists but also philosophers of science in general since many scientific problems are usually entangled with the issues. I will try to represent part of his book and show how he found his argument. I will also briefly give my comments at the end. 

His first step can be traced from his position on the unit and level of selection. For him, the unit of selection should be any entity satisfying three Lewontin’s conditions: variation in character (z), the difference in fitness (w), and heritability (h). If individuals in a population have a difference in character that leads to a difference in the heritable number of offspring, the population is a subject evolution. This definition is abstract but can intuitively frame selection on many levels. Many biological entities, ranging from genes, chromosome, cell, multicellular to maybe species and clade, satisfy the conditions. Meanwhile, the level of selection is the hierarchical stage occupied by the unit. If a multi-level selection occurs, then the selection operates in more than one domain, e.g., genic and diploid.

Despite intuitive. Lewontin’s conditions’ abstract nature does not help much conceptually dissect the complexity of selection. Here Okasha chooses Price’s equation to reflect Lewontin’s conditions mathematically and decompose the process of natural selection in a more detailed way. The standard equation is as follows:

w̄Δz̄ =                    Cov (w, z)             +             E (wΔz)                        (1) 

Cov (w, z) measures the covariance between character and fitness, while E (wΔz) measures the transmission bias of character to the next generation. In terms of relative fitness, if the value of Cov (ω, z) is positive, the character is fitter than average, and negative, it means the inverse. For example, if being tall for giraffes is positively covariant with relative fitness, tall giraffes produce more offspring than the average giraffes. Zero value is when no association is found between character and fitness.

Meanwhile, E (wΔz) value is measured with its distance from 0. If the value of E (wΔz) = 0, the next generation inherits the parents’ characters perfectly. Therefore, if the parents are 2 meters high giraffes, assuming the E (wΔz) = 0, the next giraffes’ generation would have the same character. A non-zero value means there is a bias in the character.

The standard equation is enough to represent changes according to Lewontin’s condition. The equation also shows the importance of the relationship between character and fitness and heritability. However, it does not say anything about multi-level selection, whether another level affects the fitness. Here, Okasha adds additional assumptions, namely differentiating between particles and collectives and, following Damuth and Heisler, MLS1 and MLS2 (MLS= Multi-Level Selection).

Particles are members of a group, while collectives are a group itself containing particles. A buffalo in a buffalo herd is a particle, while the herd itself is a collective. MLS1 and MLS2 are selected in the level of collective, but while MLS1’s fitness is average particle’s fitness (how many particles produced by a collective), MLS’2 fitness is collective’s fitness (how many collectives produced by a collective).

An example of MLS1 is when the composition of altruists affects the average particle’s fitness in a population. Although selfish’s fitness particles are better between particles, the fitness is low in a group full of selfish particles. By contrast, in a group composed of many altruists, both selfish and altruists’ fitness is high. It is essential here that although the focus is on how many particles are produced, whether selfish or altruist, it is counted as a collective selection because a different group composition affects the number of particles produced. With the understanding in mind and assuming no transmission bias, the Price’s equation for MLS1 can be reformulated like this:

Selection between groups        Selection between individuals within a group

w̄Δz̄ =                    Cov (W, Z)                 +             E (Covk (w,z)        (2)

W and Z are the fitness and character of collectives, and Covk (w, z) are covariance in a group between particles. The Cov (W, Z) shows the relationship between a collective character and fitness (selection between groups), while Covk (w, z) shows the relationship of particle character with fitness in a collective (selection between individuals within a group).  Furthermore, since the focus of MLS1 is particles, W and Z are the average value of particles in collective. Now, to determine whether a selection occurs at the level particles is Cov (W, Z) < E (Covk (w, z), while the inverse is Cov (W, Z) > E (Covk (w, z).

Meanwhile, MLS2 is clearly collective selection since it does not care about the composition and number of particles produced. As long as a collective produces another collective, e.g., a human consisting of cells gives birth to another human, regardless of the composition or number of cells produced, MLS2 occurs. Therefore it needs a different equation in terms of fitness. Okasha puts it as Y. Also, because no fitness in the lower level is considered in MLS2 because the assumption is different, the standard equation would be as follows:

ȲΔZ̄ =                    Cov (Y, Z)                                                    (3)         

However, the proponent of single-level selection, whether gene only or organism only, can say that the collective levels, whether wholly or partly, is caused by the covariance of character and fitness at the particle level. Consequently, the selection identified by the equation is maybe just a by-product or, using Williams’s term (1966), fortuitous effects from the lower level. To illustrate, imagine three giraffe groups that vary in fitness. It s possible that the collective fitness difference is not due to group character, but just because the groups contain giraffes with different heights, and the fitness depends solely on height.

Therefore, the correlation between a cause and effect should be tested while fixing the other causes. If there are two possible causes, a, b, to determine how much a is efficacious, the cause b should be controlled. Here Okasha chooses to modify Price’s equation with contextual analysis since Price’s equation above cannot detect it perfectly.  What makes the latter special is twofold. First, it catches the intuition of the background effect. Secondly, it allows a calculation using a regression model. Let the by-product in different levels is represented with z and Z, then the model would look like this

w =  β̞1z + β̞2Z + e       (4)

In that equation, β̞1z calculates how much z affect w while Z is fixed, and β̞1Z calculates how much Z affect w while z is fixed; e is the residual. In the giraffes’ example above, if giraffes fitness depends only on their height, the β̞2Z would be zero, meaning the information about average height will not help predict the fitness or no background effect on the fitness. By contrast, if β̞2Z is non zero, there is a contribution from group selection. By-products particle –> collective happen if there is Cov (W, Z) but β̞2Z = 0, and the inverse is for by-products collective –> particle. With contextual analysis, Okasha demonstrates that there might be no error in deciding the level of selection.

Here, Okasha made two remarkable points. Firstly, he differentiates between lower-level selection and lower-level causal processes. While the former is significant for the concept of by-product, the latter is often not. This is because only the covariant between character and fitness at the particles is significant for higher-level selection. This argument is crucial since it makes multi-level selection by-products independent from mereological supervenience, notably MLS2. Unlike MLS1, MLS2 has a different concept of the character of fitness. Without making this difference, MLS2 will be deemed as an epiphenomenon of particle character. However, because the supervenience argument requires only a lower-level causal process that Z and Y are realized by z, not selection, or Cov (w, z), there are many cases where the Cov (Z, Y) is independent of z. Okasha then suggests that by-products should only be limited to the selection and not character. 

Secondly, Okasha shows that although contextual analysis is accurate in spotting by-product direction in many cases, it does not apply in diploid cases. An example is when diploid genotypes AA, AB, BB equals in fitness, but the A allele in AA is less fit than the A allele in AB. This is clearly genic distortion segregation since the diploid fitness remains the same, but the contextual analysis will detect selection at the diploid level. By contrast, standard multi-level Price’s equation will calculate it right. This is significant since two cases with an isomorphic form of particle and collective do not apply the same statistical formalism. Okasha’s then suggest that multi-level selection may not be able to be dealt with with a purely abstract approach.

Okasha’s analysis above is ample to vindicate multi-level selection. One level may be fully responsible for the selection, but it should be done after checking the selection at the collective level and its by-product, meaning that multi-level selection provides a wholesome default position. However, indirectly, it also shows that realism is a better choice in many cases than conventionalism. The conventionalist problem arises with the fact that different levels can explain changes in frequencies equivalently. For example, in MLS1, the global changes of the population can be tracked with multi-level selection or with single-gene only. Therefore, which level that is used as a perspective may not matter.

However, it is clear from the above explanation of within-group and between-group selection and by-products that whether selection occurs at the genic, organismic, or group level, or some of them, is not a matter of perspective. It can be identified by knowing the type of fitness (particles or collective), the group’s composition, and its relationship with fitness (within-group or between-group). Also, if there is no covariant of character and fitness at that level, there hardly will be a selection. Failing that, the picture gained is only the big picture (changes in frequency) without details on what is happening, making non-multi-level selection an impoverished account of reality, especially in explanation on which level is responsible. This is an invaluable proposal considering that many still think that any selection process is better represented as a change in gene’s frequencies (gene’s eye view) or that any level picked does not matter since mathematically they are equivalent (conventionalist).

Hopefully, the above explanation is enough to draw the mainline of Okasha’s exposition. Of course, the issues he discusses are not limited to the two problems above. In the book, Okasha clarifies many historical muds in the debate, ranging from additivity, reductionism, species and clade selection to transition, including problems that may not be the central issues, such as temporality. Okasha’s clear exposition is also striking, enable people who are not knowledgeable with evolutionary theories to engage with the issues easily (writer’s personal experience). In this term, it is not an exaggeration to say that if we only need a book to understand the general issues in the unit and level of selection and know the natural way to see the selection process, this Okasha’s work would be the answer. In 2009, this book won Lakatos Award, and it is clear why it deserves the recognition.

There may be some further comments that are worthy of considering regarding Okasha position. The first is concerning the status of the statistical tool used by Okasha and its implication. His conclusion of isomorphism that does not work relies on the limitation of Price’s equation and contextual analysis. However, as Sober (2011) mentioned, it does not deny that there may be a third way that can encompass it, such as Price’s equation with interactionist approach, making Okasha conclusion of isomorphism better be postponed. Okasha also uses the contextual analysis with regression model as if is an epitome to seize causation of selection, while in practice, the type of analysis is often seen as exploratory. Responding to this, Pigliucci (2009) suggests that Okasha should consider a more advanced and subtle formalism usually used in ecology, like structural equation modeling, should be considered. Although this reservation may not stand at the conceptual issues, the possibility of other more context-sensitive tools is strategic advice for merging the conceptual and practical.

The second comment is concerning his discussion on Price’s equation and causal decomposition in chapter 1. There, Okasha chooses an equation out of two that correctly decompose the equation causally. The equations do not need to be shown here since he does not use them in the book. What is important is that his reasoning is rather peculiar. For him, the correct causal decomposition is related to remoteness from reality. The less, the better. It makes him choose a decomposition that treats fitness and heritability as independence, not character and heritability. This may be better to spot common causal events, but it does not mean that the uncommon is insignificant. There is always a possibility of a marginal case in evolution that does not follow the paradigm pattern but is sometimes vital (Godfrey-Smith, 2009). Therefore, instead of choosing a correct one, the differences may just be seen as a correct causal decomposition for different cases, one of which is more prevalent than the other.

The last comment is about replicator and interactor distinction. Okasha does not use this distinction because of its incapability in spotting transition and its redundancy. Lewontin’s condition can talk about the beginning of life without assuming fidelity. Also, it posits fewer entities. However, Lewontin’s conditions seem not to catch whether a selection is due to interaction or not, while interaction is crucial in locating the cause. This point is shown by Mitchell:

In order to show that the evolution was due to natural selection, the additional condition that the interaction of the variant months and their environment was the cause of differential transmission of traits must also be satisfied … without specifying the relative adaptedness of the competing traits, the change … might well have been due to a mechanism other than natural selection. (Mitchell, 1987, p. 354)

The interaction is what the interactor tries to catch. Okasha does consider other causes, but his analysis focuses on cases where natural selection is already clear. If the case is different, he has prepared an equation that covers drift. However, here interactor has built the framework inherently. It is not clear whether Okasha is a realist with Lewontin’s condition. The choice may be just a matter of preference. However, as Okasha put forward, the replicator-interactor distinction is not preferable in many, but this distinction may be valuable and faster to spot the causes in some biological phenomena.


Godfrey-Smith, P. (2009). Darwinian Populations and Natural Selection. Oxford University Press.

Mitchell, S. D. (1987). Competing Units of Selection?: A Case of Symbiosis. Philosophy of Science, 545(3), 351–367.

Okasha, S. (2006). Evolution and the Levels of Selection. Oxford University Press.

Pigliucci, M. (2009). Samir Okasha: Evolution and the Levels of Selection. Biology & Philosophy, 24, 551–560.

Sober, E. (2011). Realism, Conventionalism, and Causal Decomposition in Units of Selection: Reflections on Samir Okasha’s Evolution and the Levels of Selection. Philosophy and Phenomenological Research, LXXXII(2), 221–231.

Williams, G. C. (1966). Adaptation and Natural Selection. Princeton University Press.