Evolutionary tradeoffs and the geometry of biological shape space

Organisms, tissues and molecules often need to perform multiple tasks. But usually no phenotype can be optimal at all tasks at once. This leads to a fundamental tradeoff. We study this using the concept of Pareto optimality from engineering and economics. Tradeoffs lead to an unexpected simplicity in the range of optimal phenotypes- they fall on low dimensional shapes in trait space such as lines, triangles and tetrahedrons. At the vertices of these polygons are phenotypes that specialize at a single task. One does not need to know the tasks in advance; tasks  can be inferred from the data. We demonstrate this using animal and fossil morphology, bacterial and stem-cell gene expression and other biological systems.