Figure 2. Optimal control variables for uptake, α, and synthesis, γ.

Optimal values maximize fitness in Eq. (2) using the dynamics from Eq. (1). Each patch is purely clonal. The center panel shows the labeling for axes. All logarithms use base ten. The height of each surface, log(α∕γ), scaled between − 3 and 3, shows the relative magnitude of uptake versus synthesis. The flat regions show values outside of that range. For the costs of uptake and synthesis, a and g, it is convenient to present the two dimensions as the sum and the ratio of the parameters. The same dimensional split into sum and ratio also applies to the inflow and outflow parameters, v and m. Initial values for the state variables are N = 10⁻⁵, B = v∕m, and I = (αB + γ)∕p.