[I invited Pierrick Bourrat to respond to my two posts about his new paper and to comments to those posts. He kindly agreed, and he provided the following guest post, which I have edited only for formatting.]

First of all, I would like to thank Matthew Herron for his interest in my work and his invitation to respond to his posts. Also, I would like to thank Rick Michod and Deborah Shelton for their comments.

I will respond to several issues pointed out both in the posts and the comments.

About the usefulness of the export of fitness view of ETI: I agree that it is a useful way of thinking about it, as long as it is used as a heuristic. This means that I am not inclined to think that building models with the assumption that the fitness of a cell would have been 0 had it been in an environment with not social partners will be able to explain in some deep sense ETIs (and even more so the origin of fitness at some level). In his comment to Matthew’s first post, Rick Michod claims that I somehow confuse realized fitness from a more counterfactual notion of fitness.  Well, to be honest, I do not see how one could simulate (I do not mean ‘explain’) the evolution of a process if the variables in the model do not correspond to realized properties of the system. If I want to model a particular phenomenon, I ought to use variables and parameters that represent the target system and clearly, at least for me, this counterfactual notion of fitness does not represent any properties the cells have because they always have social partners. It is common to use expected rather than realized fitness in models, but this assumption is justified when we can assume that population are large and the environment is overall not fluctuating too much. With the counterfactual notion of fitness, aside from being useful for explaining the ETIs, I fail to see how it could be successfully integrated in models (by successfully, I mean how it could represent meaningfully the target system).

So, to sum up, I am perfectly happy with the view that when an ETI is complete some particles invest everything in one fitness component of the collective while other particles invest in the other fitness component of the collective, but it should be clear that we are talking here about the components of the collective and that there is no transfer of fitness between levels whatsoever, or only in a metaphoric sense.

About particles not being able to evolve by natural selection anymore once an ETI is complete (in response to Deborah’s comment). I must confess that this kind of claim has always made me uncomfortable. Strictly speaking, when an ETI is complete and the same population is taken at both levels, cells are still able to evolve by natural selection. Of course not in any one collective where there is no variation anymore, but it is relevant to consider here other particles in other collectives and variation between particles of different collectives. Thus, comparing collectives to other collectives and cells to other cells but solely within each collective to claim that cells lost the ability to evolve by natural selection while the collectives gained this ability seems to me misleading or cheating. One should not compare apples and oranges. It reminds me the kind of arguments given to reductionists by anti-reductionist who claim that one cannot explain the fluidity of water because this property is not found in any one molecule of water. Of course this claim is true, but it is not an argument against reductionism (at least under some reasonable sense of reductionism). Reductionists only have to commit that they would be able to explain the fluidity of water by appealing solely to molecules of water. My claim about fitness of collectives is pretty similar. My claim is simply that, in principle, one would only need to appeal to particles fitness once the right or legitimate comparisons are made.

About formal reproduction being limited. I agree that the idea of formal reproduction, of which inclusive fitness is a kind, as it is used in my paper does not allow one to make the distinction between entities that are able to transmit acquired mutations and those that are not able to do so. (Note however that the idea of formal reproduction can include cases in which mutations are transmitted. Godfrey-Smith discuss some of these cases (e.g., retroviruses).) But if we are talking about natural selection I am not entirely sure how this is relevant. Sure, supplying variation is an important component of a population to be able to display complex adaptations, but evolution by natural selection in and of itself can run for some time with existing variation without the need for more variation to be supplied. It is also clear that if a cell does not materially reproduce while surrounding cells are able to do so, in the short term, cells unable to reproduce will have a lower fitness. There is certainly a challenge here to explain how this strategy could resist invasion from short-term cheaters, and my version of formal reproduction is of no help. I would not claim however that cells that do not reproduce have a fitness of zero, as this would assume they do not survive between two cell generations (if they survive, it is equivalent to them producing one offspring in a discrete generations model).

Finally, about the universality of the claim I made about any case of MLS2 being reducible, in principle, to cases where everything can be explained from the point of view of particles. I would like to stress that this claim should be universal only as long as the collectives are made of nothing more than the particles. Yet, when comparing different levels of selections this is not always what is done in practice. For instance organisms are often compared to alleles (e.g., in cases of meiotic drive) which, I believe, in some cases, can lead to some problems, for alleles should not be compared to organisms (at least they cannot be straightforwardly) because organisms are not groups of alleles. In fact, alleles and organisms do not belong to the same biological hierarchy. As the philosopher and biologist Sahotra Sarkar puts it, alleles belong to the biological hierarchy allele –> locus –> gene complex –> genotype, etc. and organisms belong to the biological hierarchy molecule –> organelle (including chromosome) –> cell –> tissue –> organism –> group, etc.  Comparing two entities at two different levels and two different hierarchies without realizing it can be another way to compare oranges and apples. I am not claiming that this can never be done, but some good reasons for doing it must be given. For instance, it can be assumed that in any organism the genetic background for each allele considered will, on average, be the same, so that it is fine to compare alleles at one level with organisms at another. But without this kind of assumption we will rapidly run into troubles. This problem, I suspect however, should generally not be of importance when cells and multicellular organisms are compared. This is because they belong to the same hierarchy. But even here one must be careful because what is considered as an organism often represents the cells plus some of the cellular environment (which is internal to the organism and is not the other cells). I suspect, although I cannot demonstrate it here, that this could potentially raise some problems when making claims about the emergence of a MLS2 process: the “emergence” would be spurious because the two levels compared would be made of different stuff.