The geometry of the P areto front in biological phenotype space
Open accessAbstract
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 P areto 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.
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- Authors
- Sheftel, H., Shoval, O., Mayo, A., & Alon, U.
- Affiliations
- Weizmann Institute of Science (IL)
- Corresponding author
- Alon, Uri
- Venue
- Ecology and Evolution
- Publisher
- Wiley
- Published
- 2013-04-17
- Volume
- 3
- Issue
- 6
- Pages
- 1471-1483
- ISSN
- 2045-7758 (ISSN-L)
- PMC
- PMC3686184
- OpenAlex
- W2042859590
- Cited by
- 79
- References
- 28
- Citations by year
- 2026: 5 · 2025: 9 · 2024: 4 · 2023: 4 · 2022: 6 · 2021: 11 · 2020: 5 · 2019: 9 · 2018: 5 · 2017: 3 · 2016: 3 · 2015: 9 · 2014: 5 · 2013: 1
- FWCI
- 3.98
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Ecology and Evolution (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Funders
- European Commission (2007–2013, FP7 2007-2013, FP7/2007)
- Israel Science Foundation (FP7/2007-2013, isf-67509)
- FP7 Ideas: European Research Council (249919)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
- Life Sciences › Agricultural and Biological Sciences › Ecology, Evolution, Behavior and Systematics › Animal Behavior and Reproduction
- Physical Sciences › Mathematics › Geometry and Topology › Morphological variations and asymmetry
- Keywords
- Pareto front, phenotype space, trade-offs, multiple tasks, limit state function, trait space, specialists, quantitative traits
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