Figure 1

An overview of Pareto theory for evolutionary tradeoffs. (A) The classical viewpoint of a fitness landscape: phenotypes are arranged along the slopes near the peak of a fitness hill maximum. (B) In contrast, the Pareto viewpoint suggests a tradeoff between tasks. For each task there is a performance function, which is maximal at a point known as the archetype for that task. The fitness function in each niche is a combination of the different performance functions (in general, fitness is an increasing function of performances, possibly a nonlinear function). (C) Optimality in a niche in which task 1 is most important, is achieved near archetype 1 (red maximum). Optimality in a niche in which all tasks are equally important, is achieved close to the middle of the Pareto front (green maximum). (D) The entire Pareto front- the set of maxima of all possible fitness functions that combine these performances- is contained within the convex hull of the archetypes. (E) Different numbers of tasks give various polygons or polyhedra, generally known as polytopes. Two tasks lead to a suite of variation along a line segment. Three tasks lead to a suite of variation on the triangle whose vertices are the three archetypes. Four archetypes form a tetrahedron. This is true while there are enough traits measured: in lower dimensional trait spaces one finds projections of these polytopes.