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
Appendix S1. The Pareto front is the locus of all points in which the gradients of the performance functions are positive-linearly dependent.
Appendix S2. The Pareto front associated with 2 tasks in a 2D-morphospace is a hyperbola.
Appendix S3. The Pareto front of 2 tasks in an n-dimensional morphospace has hyperbolic projections.
Appendix S4. Calculation of the deviation of the Pareto front from a straight line for 2 tasks in a 2D-morphospace.
Appendix S5. Each Pareto front of 2 tasks in a 2D morphospace is generated by a 1-dimensional family of norm pairs.
Appendix S6. Generally, for 3 tasks in a 2D morphospace, the norms can be uniquely determined by the shape of the Pareto front.
Appendix S7. The boundary of the 3-tasks Pareto front is composed of the three 2-tasks Pareto fronts.
Appendix S8. The resulting Pareto front when one of the performance function is maximized in a region.
Appendix S9. Bounds on the Pareto front for general performance functions show that normally it is located in a region close to the archetype.
Appendix S10. The Pareto front of r strongly concave performance functions is a connected set of Hausdorff dimension of at most r-1.
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