title: Evolutionary tradeoffs, Pareto optimality and the morphology of ammonite shells.
abstract: BACKGROUND
  Organisms that need to perform multiple tasks face a fundamental tradeoff: no design can be optimal at all tasks at once. Recent theory based on Pareto optimality showed that such tradeoffs lead to a highly defined range of phenotypes, which lie in low-dimensional polyhedra in the space of traits. The vertices of these polyhedra are called archetypes- the phenotypes that are optimal at a single task. To rigorously test this theory requires measurements of thousands of species over hundreds of millions of years of evolution. Ammonoid fossil shells provide an excellent model system for this purpose. Ammonoids have a well-defined geometry that can be parameterized using three dimensionless features of their logarithmic-spiral-shaped shells. Their evolutionary history includes repeated mass extinctions.
  
  
  RESULTS
  We find that ammonoids fill out a pyramid in morphospace, suggesting five specific tasks - one for each vertex of the pyramid. After mass extinctions, surviving species evolve to refill essentially the same pyramid, suggesting that the tasks are unchanging. We infer putative tasks for each archetype, related to economy of shell material, rapid shell growth, hydrodynamics and compactness.
  
  
  CONCLUSIONS
  These results support Pareto optimality theory as an approach to study evolutionary tradeoffs, and demonstrate how this approach can be used to infer the putative tasks that may shape the natural selection of phenotypes.
authors.affiliation: Department of Molecular cell biology, Weizmann Institute of Science, Rehovot, 76100, Israel. tendlea@gmail.com.
authors.forename: Avichai
authors.initials: A
authors.lastname: Tendler
authors.affiliation: Department of Molecular cell biology, Weizmann Institute of Science, Rehovot, 76100, Israel. mayoavi@gmail.com.
authors.forename: Avraham
authors.initials: A
authors.lastname: Mayo
authors.affiliation: Department of Molecular cell biology, Weizmann Institute of Science, Rehovot, 76100, Israel. urialonw@gmail.com.
authors.forename: Uri
authors.initials: U
authors.lastname: Alon
mesh_terms: D060105:Animal Shells / Q000033:anatomy & histology*; D000818:Animals; D049830:Cephalopoda / Q000033:anatomy & histology* / Q000502:physiology*; D019295:Computational Biology; D019143:Evolution, Molecular; D053476:Extinction, Biological; D057446:Hydrodynamics; D012641:Selection, Genetic