Consider again the model life cycle depicted in Figure 8.2. This model presumes that the transition has proceeded far enough so that the multicelled organisms can possess fitnesses in the MLS2 sense, that is, a process of reproduction at the organismic level takes place. An organism's fitness is its number of offspring propagules; this number may be influenced by various factors. One important factor, Michod argues, is the frequency of cooperating (C) cells in the adult. The higher this frequency, the greater the functionality of the adult organism, so the more propagules it will produce. Therefore, Michod and Roze (1999) suggest the following expression for the fitness of the ith organism:
where q- is the frequency of C cells in the adult, and ft is a parameter measuring the degree to which cooperation among cells benefits the organism.
Is expression (8.1) satisfactory? Clearly, this depends on whether frequency of C cells in the adult is the only factor that affects an organism's propagule production. Michod and Roze argue that another factor may be adult size, that is, total number of cells in the adult. Since there is no separate germ-line, the greater the number of cells in the adult, the more offspring propagules it can send out. Also important is the size of the propagules themselves—the smaller they are, the more of them can be produced. Therefore, Michod and Roze consider an alternative expression for organismic fitness:
where k; is the total number of cells in the adult, and N is propagule size. So expression (8.2) captures the idea that organismic fitness depends upon both adult functionality and adult size. Importantly, expression (8.2) does not imply that selection will automatically favour lower values of N, because as Michod and Roze note, adult size k; may itself depend linearly on N, in which case N will cancel when ki is expanded (1999 p. 10). Clearly, ki will depend positively on N, that is, larger propagules will turn into larger adults, but the dependence may or may not be linear. If the dependence is linear, this means there is no intrinsic advantage to producing lots of small propagules rather than a few large ones, because the large ones will grow to be a larger size, hence be fitter themselves.8
Note that expressions (8.1) and (8.2) are not competing definitions of organismic fitness. On the contrary, both define organismic fitness identically, as number of offspring propagules. Rather, they make competing claims about what organismic fitness, so defined, depends on. Expression (8.1) says that organismic fitness depends on adult functionality alone; (8.2) says that it also depends on adult size. So they represent alternative modelling assumptions, not alternative definitions.
Michod and Roze argue that the choice between (8.1) and (8.2) raises 'interesting issues' concerning the extent to which the emerging multi-celled creatures possess'individuality' (p. 56). For fully fledged organisms such as ourselves, the number of cells we contain as adults does not directly affect our fitness—there is no particular advantage to being fatter. However, Michod and Roze argue that for creatures 'on the threshold of multicellular life', fitness will probably depend on adult size, so is better captured by expression (8.2). However, this means that the creatures lack true 'individuality', because there is 'a direct contribution of cell fitness to organism fitness' (p. 10). This is because adult size is itself dependent on cell fitness—an organism whose constituent cells are very fit, that is, divide very fast, will achieve a larger adult size. So if organismic fitness is given by expression (8.2) rather than (8.1), then differences in organ-ismic fitness may stem directly from differences in cellular fitness. In Michod and Roze's terms, this means that organismic fitness has not been 'decoupled from the fitness of the component cells', which in turn reflects the fact that the organism has not evolved true individuality (p. 57).
This is important for three reasons. First, it helps elucidate the concept of 'fitness decoupling'. For fitness at the two levels to be decoupled, it is not sufficient that organismic fitness be defined in the MLS2 rather than the MLS1 way. What is needed, in addition, is that differences
8 Linear dependence of ki on N has another interesting consequence. It means that an organism's fitness in the MLS2 sense—given by expression (8.2)—will be directly proportional to its fitness in the MLS1 sense, i.e. to the total number of offspring cells, rather than propagules, that it produces; see Chapter 2, Section 2.2.3 for further discussion of this point.
in organismic fitness should not arise solely through differences in cell fitness. Michod and Roze (1999) give a nice example of how this condition can fail to be satisfied. Suppose that there are no interactions between cells, that is, no cooperation or defection, but that different cell types have different intrinsic rates of replication. Suppose C cells divide faster than D cells. Therefore, an organism starting life as a CCC propagule will achieve a larger adult size than one starting life as a DDD propagule, so will have more offspring. (In terms of expression (2), the first organism has a higher value of k;/N than the second.) This means that differences in organismic fitness are side effects of differences in cell division rates, and have nothing to do with organismic functionality; so fitness decoupling has not been achieved. Indeed in a sense these 'organisms' are not worthy of the name. Only once adult functionality, rather than adult size, becomes the main determinant of fitness does the emerging cell-group constitute a proper organism.
Secondly, Michod and Roze's discussion brings out an interesting link between fitness decoupling and the concept of a cross-level byproduct, developed previously. (The example of C and D cells with different intrinsic rates of replication is reminiscent of Sober's (1984) example of short and tall organisms in a group-structured population, which we used to introduce cross-level by-products.) Situations in which organismic and cell fitness have not been decoupled, and where organisms thus lack true individuality, are precisely those in which there is a cross-level by-product running in the cell^ organism direction. For as we saw in Chapter 3, particles collective by-products, in an MLS2 framework, occur when the fitness of a collective is directly determined by the average fitness of the particles it contains.9 And this is precisely the case in the example above. Given that C cells divide faster than D cells, the average cell fitness of an organism that starts as a CCC propagule is greater than the average cell fitness of one that starts as a DDD propagule; and it is this that explains why the former has higher organismic fitness. So the character-fitness covariance at the organism level will disappear when we control for average cell fitness.
Thirdly, this example has implications for Michod's use of the Price equation to model the evolution of multicellularity. As we know, where cross-level by-products are in play, the Price equation will detect selection at the higher level even when, intuitively, all the causality is at the
9 Recall that this is a sufficient condition for an MLS2 particles collective by-product, not a necessary condition.
lower level. This is precisely the case in the example above—all the selection is at the cellular level, so the character-fitness covariance at the organism level is spurious, or non-causal. Despite this, Michod makes extensive use of the Price equation in relation to this model, as a way of representing the effects of organismic and cellular selection on the overall change in frequency of the C allele/cell-type (Michod 1999; Michod and Roze 1999). Interestingly, however, in some of their papers Michod and Roze employ a different partitioning technique, which avoids the problem with the Price equation (Michod and Roze 2000; Roze and Michod 2001). This latter technique yields a temporal partition of the total change, into a component that happens during development, and a component that happens later, during reproduction (Figure 8.3). Michod and Roze then attribute these two components to selection at the cellular and organismic levels, respectively. This implies that if organismic fitness depends only on adult size, rather than adult functionality, all the selection is at the cellular level, for reproduction will not change the proportion of C cells in the population. Intuitively this is the correct result, but it is not compatible with taking organismic selection to be defined by the character-fitness covariance at the organism level, a la Price.
My purpose in pointing this out is not to criticize Michod and Roze, whose concept of fitness decoupling is surely invaluable for understanding evolutionary transitions. Rather, it is to emphasize the striking fact that the theoretical shortcomings of the Price approach, first pointed out by Sober (1984), Nunney (1985a), and Heisler and Damuth (1987) in relation to group selection, should reappear in relation to the evolution of multicellularity. It is particularly striking that the problem cases for the Price approach, where cross-level by-products are in play, represent transitional stages en route to the evolution of new hierarchical levels. The original critiques of the Price approach made no mention of this point, since they operated with a synchronic rather than a diachronic formulation of the levels-of-selection question.
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