FIGURE 7.3 Fitness tradeoffs. Contribution to viability (v) on y axis and reproduction (b) on x axis. (A) A concave curve changes to a convex curve as group size increases. The piece-wise linear reproduction curve (solid line in B) with linear viability curve (dotted line in B) approximates a convex tradeoff curve (C) at the cell level. (D) Isoclines of group fitness are plotted with this convex tradeoff curve at the cell level. The reproductive effort e_N in B is the cost of reproduction, which increases with group size N, and in C v_max − v_max(1 − e_N) is the “bonus” of soma specialization. This bonus can be obtained only by groups. Alternatively, the bonus of specialization in soma may be viewed as the initial cost of somatic cells dedifferentiating into reproductive cells.

To illustrate how an increased cost of reproduction creates convex curvature, we construct a convex tradeoff curve between viability v and fecundity b in a piecewise linear fashion as shown in Fig. 7.3 B and C. The cost of reproduction e_N is defined as the effort needed to produce an offspring colony of size N. In volvocine algae (Fig. 7.1) this effort depends on the time, energy, and resources needed to grow and divide the embryo so as to produce a daughter colony with N cells. In Fig. 7.3D the convex tradeoff curve from Fig. 7.3C is plotted with isoclines of the additional fitness to the group contributed by a newly added cell. The construction of Fig. 7.3D illustrates qualitatively a prediction of our model (Michod, 2006; Michod et al., 2006), which is that the greater the cost of reproduction (e_N), the more likely the isocline touches the tradeoff curve at v_max (meaning the new cell will be soma-specialized; b = 0) as opposed to touching at an intermediate value 0 < b < b_max. Soma-specialized cells get a bonus to viability by virtue of their not paying the cost of reproduction