Figure 4.

(A) In biological application of portfolio selection, each individual is mapped on the yield–risk space. A culture of cells may contain multiple different subtypes with mutations and epigenetic modifications. Assume a culture of cells (or organisms) composed of subtypes A, B, C, and D. At the initial stage, A and B may be dominant and C and D may be negligible (Culture 1). However, subtype C better fits the environment and grows faster than A and B (Culture 2). Subtype D starts to grow faster than the others and changes the subtype composition of the culture (Culture 3). At this stage, the composition of the culture may be sufficiently optimized for the given culture condition. Suppose the culture condition is changed now to have greater perturbations. Subtype D may not be able to tolerate it and will decrease the rate of proliferation and may even reduce in number, and subtype C may grow faster than the other subtypes (Culture 4). Alternatively, subtype D may continue to grow faster than other subtypes if the environment becomes even more stable. (B) A population of cells may evolve toward the efficient frontier. Under the risk-aversion indifference curve, the population arrives at the blue circle on the efficient frontier. The risk-aversion curve represents cases in which higher-level perturbations are imposed on the culture compared with a risk-neutral case. Under the stable condition in which selection pressures other than growth speed are not significant, the risk-neutral indifference curve is likely to be applied. The population follows Trajectory A and maximizes its growth rate at the cost of robustness. Imposing a higher level of perturbation may result in transition of the state through Trajectory B. (C) Cost-free resistance may be a result of taking Trajectory E or F to a new efficient frontier. There may be cases in which the population moves back to suboptimal regions (Trajectories G). Chemotherapy for cancer may shift the point inside the efficient frontier with different end points because of heterogeneous subpopulations. However, tumor cells may again evolve to gain proliferation potential despite the presence of anticancer drugs (Trajectories H). Tumor cells that undergo this transition may be too optimized for this specific therapeutic intervention, which implies possible efficacy when therapeutic regimens are switched. This may explain the collateral sensitivity of drug resistance tumor cells (Skipper et al, 1972).