ArticleEcology and evolution2013
The geometry of the Pareto front in biological phenotype space.
Article in Ecology and evolution, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 35 papers.
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Who cites it
35 citing papers in PubMed.
- The exact mathematical form of the Pareto principle.Theory in biosciences = Theorie in den Biowissenschaften · 2026Article
- Exploring psychological tradeoffs: Developing and demonstrating an R Shiny app for Pareto optimization.Behavior research methods · 2026Review
- From Plato to Pareto: Defining the shape of infection's disease space.Science advances · 2026Article
- ArchetypeShift: An R Package Integrating KEGG-Informed Pathway Analysis and IPA-Derived Functional Predictions for Validation of Single-Cell Archetypes.Bioinformatics and biology insights · 2026Article
- Chronic pain is linked to a resting-state neural archetype that optimizes learning from punishments.bioRxiv : the preprint server for biology · 2025Article
- Permutation Tests to Identify Significant Constraint or Promotion Within Biological Scatterplots.Ecology and evolution · 2024Article
- Breaking constraints: The development and evolution of extreme fin morphology in the Bramidae.Evolution & development · 2022Article
- Pareto optimality, economy-effectiveness trade-offs and ion channel degeneracy: improving population modelling for single neurons.Open biology · 2022Review
- Proteomic traits vary across taxa in a coastal Antarctic phytoplankton bloom.The ISME journal · 2022Article
- The seasonal behaviour of COVID-19 and its galectin-like culprit of the viral spike.Methods in microbiology · 2022Article
- The geometry of clinical labs and wellness states from deeply phenotyped humans.Nature communications · 2021Article
- Trade-off drives Pareto optimality of within- and among-year emergence timing in response to increasing aridity.Evolutionary applications · 2021Article
- Transmetabolism: the non-conformist approach to biotechnology.Microbial biotechnology · 2021Article
- Extreme Morphology, Functional Trade-offs, and Evolutionary Dynamics in a Clade of Open-Ocean Fishes (Perciformes: Bramidae).Integrative organismal biology (Oxford, England) · 2021Article
- The Compressed Vocabulary of Microbial Life.Frontiers in microbiology · 2021Article
- Strategies to Assure Optimal Trade-Offs Among Competing Objectives for the Genetic Improvement of Soybean.Frontiers in genetics · 2021Article
- Hydrodynamic Simulations of the Performance Landscape for Suction-Feeding Fishes Reveal Multiple Peaks for Different Prey Types.Integrative and comparative biology · 2020Article
- Are our phylomorphospace plots so terribly tangled? An investigation of disorder in data simulated under adaptive and nonadaptive models.Current zoology · 2020Article
- Tumour heterogeneity and the evolutionary trade-offs of cancer.Nature reviews. Cancer · 2020Review
- Network trade-offs and homeostasis in Arabidopsis shoot architectures.PLoS computational biology · 2019Article
Corrections and comments
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Authors and funding
4 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
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.
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