Tradeoffs lead to polygonal suites of variation according to Pareto theory.

<p>(a) Mammalian metabolic rate goes as a clean allometric line with respect to mass, known as Kleiber’s law (data from anAge [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004524#pcbi.1004524.ref043" target="_blank">43</a>]). (b) Mammalian longevity does not fall cleanly on a line with respect to mass. Shown are regressions to a power law and a 1/4 power law. Shaded areas represent 95% confidence intervals. (c) The fitness landscape is given by the fitness of each phenotype in trait space. (d) When fitness is composed of several tasks, one can draw a performance landscape for each task. The phenotype that maximizes performance at a task is called the archetype. (e) Organisms in niches in which one task is more important than the others have a fitness maximum close to the corresponding archetype. Generalists have a fitness maximum near the middle of the Pareto front. (f) The suite of all fitness maxima in all conceivable niches in which fitness increases with task performance is called the Pareto front. It is a polygon (or a slightly curved polygon [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004524#pcbi.1004524.ref074" target="_blank">74</a>]) whose vertices are the archetype. In the case of three tasks, the Pareto front is a triangle. (g) Positive correlation between traits can occur even if there is a tradeoff between their corresponding tasks. Stearns’ life history theory considers performance space, with tradeoffs defined as negative correlations between performances. Pareto theory concerns trait space, not performance space. The performance functions, shown here as contours, can have maxima (archetypes) in any spatial relationship leading to either positive or negative correlation in trait space, even though in both cases the curves stem from tradeoffs.