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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

Archetypes in trait space and in Westermann space. (A) Ammonoids in Westermann space. The red ellipses are the pyramid archetypes projected on the Westermann space, with 5% error in the archetype positions. Three of the pyramid archetypes lies near the vertices of the triangle, another archetype is near the edge because both D and S are dominant. The region near archetype 2 is severely warped (large red ellipse) because D,S and W are all relatively small. (note that archetypes 1,3 and 4 are inside the corresponding ellipses) (B) The pyramid in the W-D-S trait space, the ellipsoids are 5% errorbars around each vertex. These small ellipsoids translates to the red ellipses of subfigure A when switching to Westermann morphospace.
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Fig7: Archetypes in trait space and in Westermann space. (A) Ammonoids in Westermann space. The red ellipses are the pyramid archetypes projected on the Westermann space, with 5% error in the archetype positions. Three of the pyramid archetypes lies near the vertices of the triangle, another archetype is near the edge because both D and S are dominant. The region near archetype 2 is severely warped (large red ellipse) because D,S and W are all relatively small. (note that archetypes 1,3 and 4 are inside the corresponding ellipses) (B) The pyramid in the W-D-S trait space, the ellipsoids are 5% errorbars around each vertex. These small ellipsoids translates to the red ellipses of subfigure A when switching to Westermann morphospace.

Mentions: Finally, we mapped the five archetypes of the pyramid to the Westremann morphospace. We find that that three archetypes, 1, 3 and 5, map near the three vertices of the Westermann triangle (serpenticone, oxycone and sphericone, respectively). The two other vertices of the pyramid map closer to the edges of the triangle. Some of the archetypes map slightly outside of the triangle since they are exptrapolated points which lie outside of the ammonite dataset. We also asked about the sensitivity of this transformation, by testing a small region around each archetype (a sphere of radius 5% of the total variation in each coordinate). We find that one of the archetypes, archetype 2, lies in a region of morphospace which is severely warped by the Westermann transformation, and maps to a wide region in the triangle. The other archetypes are less sensitive and map to relatively small regions of the triangle (FigureĀ 7).


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

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

Archetypes in trait space and in Westermann space. (A) Ammonoids in Westermann space. The red ellipses are the pyramid archetypes projected on the Westermann space, with 5% error in the archetype positions. Three of the pyramid archetypes lies near the vertices of the triangle, another archetype is near the edge because both D and S are dominant. The region near archetype 2 is severely warped (large red ellipse) because D,S and W are all relatively small. (note that archetypes 1,3 and 4 are inside the corresponding ellipses) (B) The pyramid in the W-D-S trait space, the ellipsoids are 5% errorbars around each vertex. These small ellipsoids translates to the red ellipses of subfigure A when switching to Westermann morphospace.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Fig7: Archetypes in trait space and in Westermann space. (A) Ammonoids in Westermann space. The red ellipses are the pyramid archetypes projected on the Westermann space, with 5% error in the archetype positions. Three of the pyramid archetypes lies near the vertices of the triangle, another archetype is near the edge because both D and S are dominant. The region near archetype 2 is severely warped (large red ellipse) because D,S and W are all relatively small. (note that archetypes 1,3 and 4 are inside the corresponding ellipses) (B) The pyramid in the W-D-S trait space, the ellipsoids are 5% errorbars around each vertex. These small ellipsoids translates to the red ellipses of subfigure A when switching to Westermann morphospace.
Mentions: Finally, we mapped the five archetypes of the pyramid to the Westremann morphospace. We find that that three archetypes, 1, 3 and 5, map near the three vertices of the Westermann triangle (serpenticone, oxycone and sphericone, respectively). The two other vertices of the pyramid map closer to the edges of the triangle. Some of the archetypes map slightly outside of the triangle since they are exptrapolated points which lie outside of the ammonite dataset. We also asked about the sensitivity of this transformation, by testing a small region around each archetype (a sphere of radius 5% of the total variation in each coordinate). We find that one of the archetypes, archetype 2, lies in a region of morphospace which is severely warped by the Westermann transformation, and maps to a wide region in the triangle. The other archetypes are less sensitive and map to relatively small regions of the triangle (FigureĀ 7).

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