Fig 1.
Tradeoffs lead to polygonal suites of variation according to Pareto theory.
(a) Mammalian metabolic rate goes as a clean allometric line with respect to mass, known as Kleiber’s law (data from anAge [43]). (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 [74]) 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.
Table 1.
Summary of taxa used in this manuscript.
Table 2.
Mass and longevity of selected animals.
Fig 2.
The longevity-mass data set is well described by a triangle in log space.
(a) Placental mammals (blue), birds (red) and marsupials (green) are presented in a log-log plot, black lines represent the best fit triangle and the three ellipses on the vertices represent the position and error of the archetypes determined by bootstrapping (see Methods). (b) Bats, naked mole rat are close to the B archetype. (c) Marsupials cover much of the same triangle. (d) Primates are close to the B archetype, flightless birds are far from it.
Fig 3.
Each archetype is enriched with specific life-history traits.
Trait values are plotted versus distance from an archetype. Species were binned to equal sized bins according to distance from an archetype. Median trait value in the bin normalized by median trait value in the dataset is shown, error bars are from bootstrapping. Curves for features enriched significantly at an archetype are marked with an asterisk (listed also in Table 3). Bin size selection is explained in S3 Text.
Table 3.
Enrichment analysis of the archetypes.
Fig 4.
Mammalian species fall approximately in a tetrahedron when considering a higher dimensional space of life-history traits.
(a) Axes are linear combination (PCs) of: adult weight, birth weight, longevity, and female maturity. PC1 is primarily related to mass (adult weight and birth weight), PC2 to time (longevity and female maturity), and PC3 to the difference between the adult weight and birth weight. The archetypes B, S, and W are indicated, and the new fourth archetype is marked by X. Species closest to the fourth archetype are indicated. The best fit tetrahedron is indicated in grey dashed lines; vertices (archetypes) are marked in red. (b) The new archetype (X) falls near the middle of the mass-longevity triangle. (c-e) The projections of the data and tetrahedron on the three principal planes are shown for additional perspective.