The geometry of the Pareto front in biological phenotype space
Article first published online: 17 APR 2013
© 2013 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd.
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Ecology and Evolution
Volume 3, Issue 6, pages 1471–1483, June 2013
How to Cite
Ecology and Evolution 2013; 3(6): 1471–1483
- Issue published online: 12 JUN 2013
- Article first published online: 17 APR 2013
- Manuscript Accepted: 14 FEB 2013
- Manuscript Revised: 10 FEB 2013
- Manuscript Received: 21 JAN 2013
- European Union's Seventh Framework Programme. Grant Numbers: FP7/2007-2013, 249919
- Human Frontiers Science Program
- Israel Science Foundation. Grant Number: ISF 675/09
- Ecological morphology;
- efficiency front;
- evolutionary theory;
- evolutionary trade-offs;
- location theory;
- multi-objective optimality
When organisms perform a single task, selection leads to phenotypes that maximize performance at that task. When organisms need to perform multiple tasks, a trade-off arises because no phenotype can optimize all tasks. Recent work addressed this question, and assumed that the performance at each task decays with distance in trait space from the best phenotype at that task. Under this assumption, the best-fitness solutions (termed the Pareto front) lie on simple low-dimensional shapes in trait space: line segments, triangles and other polygons. The vertices of these polygons are specialists at a single task. Here, we generalize this finding, by considering performance functions of general form, not necessarily functions that decay monotonically with distance from their peak. We find that, except for performance functions with highly eccentric contours, simple shapes in phenotype space are still found, but with mildly curving edges instead of straight ones. In a wide range of systems, complex data on multiple quantitative traits, which might be expected to fill a high-dimensional phenotype space, is predicted instead to collapse onto low-dimensional shapes; phenotypes near the vertices of these shapes are predicted to be specialists, and can thus suggest which tasks may be at play.