Figure 1.

When fitness is a convex function of density (e.g., the a values in the accelerating part of the curve), oscillations in density can increase mean fitness as a consequence of Jensen’s inequality (reviewed in Ruel and Ayres 1999). A strain that alternates between densities a₁ and a₂ has higher mean fitness (red point) than a strain that maintains a constant density a_mean (black point). If fitness is a concave or decelerating function of density (d values), oscillations in numbers decrease mean fitness compared to a strain that maintains a constant density (red versus black point). Cumulative fitness is altered in an identical manner.