The Mass-Longevity Triangle: Pareto Optimality and the Geometry of Life-History Trait Space

Abstract

When organisms need to perform multiple tasks they face a fundamental tradeoff: no phenotype can be optimal at all tasks. This situation was recently analyzed using Pareto optimality, showing that tradeoffs between tasks lead to phenotypes distributed on low dimensional polygons in trait space. The vertices of these polygons are archetypes—phenotypes optimal at a single task. This theory was applied to examples from animal morphology and gene expression. Here we ask whether Pareto optimality theory can apply to life history traits, which include longevity, fecundity and mass. To comprehensively explore the geometry of life history trait space, we analyze a dataset of life history traits of 2105 endothermic species. We find that, to a first approximation, life history traits fall on a triangle in log-mass log-longevity space. The vertices of the triangle suggest three archetypal strategies, exemplified by bats, shrews and whales, with specialists near the vertices and generalists in the middle of the triangle. To a second approximation, the data lies in a tetrahedron, whose extra vertex above the mass-longevity triangle suggests a fourth strategy related to carnivory. Each animal species can thus be placed in a coordinate system according to its distance from the archetypes, which may be useful for genome-scale comparative studies of mammalian aging and other biological aspects. We further demonstrate that Pareto optimality can explain a range of previous studies which found animal and plant phenotypes which lie in triangles in trait space. This study demonstrates the applicability of multi-objective optimization principles to understand life history traits and to infer archetypal strategies that suggest why some mammalian species live much longer than others of similar mass.

Optimal Regulatory Circuit Topologies for Fold-Change Detection

“…The present use of Pareto optimality can in principle suggest which tasks may have been important for the selection of the circuits (speed, amplitude, and noise resistance in the present case). We note that Pareto optimality can also be used in a different way when the tasks are unknown à priori: the tasks at play can be discovered from the vertices of polygonal or polyhedral structures in data (Shoval et al, 2012;Korem et al, 2015;Szekely et al, 2015;Tendler et al, 2015)-an approach known as Pareto task inference .…”

The architecture of functional lateralisation and its relationship to callosal connectivity in the human brain

“…In evolutionary biology 29 , the theory posits that in complex systems (e.g. animal morphology 29, 46 , animal behaviour 47 , cancer 48 , ammonite shells 49 , bacterial and single gene expression 50,51 , biological circuits 46 , structure of polymorphisms 52 , Escherichia coli proteome 53 ) evolution forces trade-offs among traits: strength in one trait of high evolutionary significance, e.g. solving well one set of problems is associated with relative weakness on other problems.…”

Archetypes in human behavior and their brain correlates: An evolutionary trade-off approach

“…The Pareto Optimality approach has been successfully applied to datasets from animal behavior (Gallagher et al, 2013), animal morphology (Shoval et al, 2012; Szekely et al, 2015), cancer (Hart et al, 2015), bacterial gene expression (Thøgersen et al, 2013) and biological circuits (Szekely et al, 2015).…”

“…For instance, the study by Szekely et al (2015) demonstrated that animal species when analyzed in terms of size and longevity fall on a triangular distribution, with the vertices representing the three archetypes: large animals with high longevity (e.g. whales being the archetype), small animals with high longevity (e.g.…”