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Evolutionary tradeoffs, Pareto optimality and the morphology of ammonite shells.

Tendler A, Mayo A, Alon U - BMC Syst Biol (2015)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Molecular cell biology, Weizmann Institute of Science, Rehovot, 76100, Israel. tendlea@gmail.com.

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.

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Related in: MedlinePlus

The three dimensional Pareto front of the ammonoid dataset. (A) The RMS error for PCHA optimal polygons and polyhedra is computed for different numbers of possible vertices: line, triangle, tetrahedron, 5-vertex polyhedron, etc. Error decreases with increasing the number of archetypes up to 5. Increasing the number beyond 5 doesn't improve the fit by much (for more evidence for the pyramidal shape of the data, see Additional file 1). (B-D) The best fit 5-archetype polygon resembles a square pyramid. Blue points denote FF to DM ammonoids, red are DM to PT and green are post PT ammonoids. Archetypes are numbered, their morphology is shown, and the suggested tasks are listed in panel A.
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Fig5: The three dimensional Pareto front of the ammonoid dataset. (A) The RMS error for PCHA optimal polygons and polyhedra is computed for different numbers of possible vertices: line, triangle, tetrahedron, 5-vertex polyhedron, etc. Error decreases with increasing the number of archetypes up to 5. Increasing the number beyond 5 doesn't improve the fit by much (for more evidence for the pyramidal shape of the data, see Additional file 1). (B-D) The best fit 5-archetype polygon resembles a square pyramid. Blue points denote FF to DM ammonoids, red are DM to PT and green are post PT ammonoids. Archetypes are numbered, their morphology is shown, and the suggested tasks are listed in panel A.

Mentions: Up to now, we considered ammonoid morphology projected on the W-D plane. We now turn to the analysis of the data in the three-dimensional morphospace, given by W,D and S—whorl expansion, radii ratio and the shape of the shell opening. Low values of the parameter S correspond to oblate elliptical openings, giving rise to compressed shells (Figure 5B, front). An S value of 1 corresponds to a circular shell opening; high values corresponding to depressed shell morphologies (Figure 5B, rear).Figure 6


Evolutionary tradeoffs, Pareto optimality and the morphology of ammonite shells.

Tendler A, Mayo A, Alon U - BMC Syst Biol (2015)

The three dimensional Pareto front of the ammonoid dataset. (A) The RMS error for PCHA optimal polygons and polyhedra is computed for different numbers of possible vertices: line, triangle, tetrahedron, 5-vertex polyhedron, etc. Error decreases with increasing the number of archetypes up to 5. Increasing the number beyond 5 doesn't improve the fit by much (for more evidence for the pyramidal shape of the data, see Additional file 1). (B-D) The best fit 5-archetype polygon resembles a square pyramid. Blue points denote FF to DM ammonoids, red are DM to PT and green are post PT ammonoids. Archetypes are numbered, their morphology is shown, and the suggested tasks are listed in panel A.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4404009&req=5

Fig5: The three dimensional Pareto front of the ammonoid dataset. (A) The RMS error for PCHA optimal polygons and polyhedra is computed for different numbers of possible vertices: line, triangle, tetrahedron, 5-vertex polyhedron, etc. Error decreases with increasing the number of archetypes up to 5. Increasing the number beyond 5 doesn't improve the fit by much (for more evidence for the pyramidal shape of the data, see Additional file 1). (B-D) The best fit 5-archetype polygon resembles a square pyramid. Blue points denote FF to DM ammonoids, red are DM to PT and green are post PT ammonoids. Archetypes are numbered, their morphology is shown, and the suggested tasks are listed in panel A.
Mentions: Up to now, we considered ammonoid morphology projected on the W-D plane. We now turn to the analysis of the data in the three-dimensional morphospace, given by W,D and S—whorl expansion, radii ratio and the shape of the shell opening. Low values of the parameter S correspond to oblate elliptical openings, giving rise to compressed shells (Figure 5B, front). An S value of 1 corresponds to a circular shell opening; high values corresponding to depressed shell morphologies (Figure 5B, rear).Figure 6

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Molecular cell biology, Weizmann Institute of Science, Rehovot, 76100, Israel. tendlea@gmail.com.

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.

Show MeSH
Related in: MedlinePlus