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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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An overview of Pareto theory for evolutionary tradeoffs. (A) The classical viewpoint of a fitness landscape: phenotypes are arranged along the slopes near the peak of a fitness hill maximum. (B) In contrast, the Pareto viewpoint suggests a tradeoff between tasks. For each task there is a performance function, which is maximal at a point known as the archetype for that task. The fitness function in each niche is a combination of the different performance functions (in general, fitness is an increasing function of performances, possibly a nonlinear function). (C) Optimality in a niche in which task 1 is most important, is achieved near archetype 1 (red maximum). Optimality in a niche in which all tasks are equally important, is achieved close to the middle of the Pareto front (green maximum). (D) The entire Pareto front- the set of maxima of all possible fitness functions that combine these performances- is contained within the convex hull of the archetypes. (E) Different numbers of tasks give various polygons or polyhedra, generally known as polytopes. Two tasks lead to a suite of variation along a line segment. Three tasks lead to a suite of variation on the triangle whose vertices are the three archetypes. Four archetypes form a tetrahedron. This is true while there are enough traits measured: in lower dimensional trait spaces one finds projections of these polytopes.
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Fig1: An overview of Pareto theory for evolutionary tradeoffs. (A) The classical viewpoint of a fitness landscape: phenotypes are arranged along the slopes near the peak of a fitness hill maximum. (B) In contrast, the Pareto viewpoint suggests a tradeoff between tasks. For each task there is a performance function, which is maximal at a point known as the archetype for that task. The fitness function in each niche is a combination of the different performance functions (in general, fitness is an increasing function of performances, possibly a nonlinear function). (C) Optimality in a niche in which task 1 is most important, is achieved near archetype 1 (red maximum). Optimality in a niche in which all tasks are equally important, is achieved close to the middle of the Pareto front (green maximum). (D) The entire Pareto front- the set of maxima of all possible fitness functions that combine these performances- is contained within the convex hull of the archetypes. (E) Different numbers of tasks give various polygons or polyhedra, generally known as polytopes. Two tasks lead to a suite of variation along a line segment. Three tasks lead to a suite of variation on the triangle whose vertices are the three archetypes. Four archetypes form a tetrahedron. This is true while there are enough traits measured: in lower dimensional trait spaces one finds projections of these polytopes.

Mentions: Organisms that need to perform multiple tasks face a fundamental tradeoff: no phenotype can be optimal at all tasks [1-8]. This tradeoff situation is reminiscent of tradeoffs in economics and engineering. These fields analyze tradeoffs using Pareto optimality theory [9-13]. Pareto optimality was recently used in biology to study tradeoffs in evolution [2,5-8,14]. In contrast to the classic fitness-landscape approaches in which organisms maximize a single fitness function [15], the Pareto approach deals with several performance functions, one for each task, that all contribute to fitness (FigureĀ 1A-B).Figure 1


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

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

An overview of Pareto theory for evolutionary tradeoffs. (A) The classical viewpoint of a fitness landscape: phenotypes are arranged along the slopes near the peak of a fitness hill maximum. (B) In contrast, the Pareto viewpoint suggests a tradeoff between tasks. For each task there is a performance function, which is maximal at a point known as the archetype for that task. The fitness function in each niche is a combination of the different performance functions (in general, fitness is an increasing function of performances, possibly a nonlinear function). (C) Optimality in a niche in which task 1 is most important, is achieved near archetype 1 (red maximum). Optimality in a niche in which all tasks are equally important, is achieved close to the middle of the Pareto front (green maximum). (D) The entire Pareto front- the set of maxima of all possible fitness functions that combine these performances- is contained within the convex hull of the archetypes. (E) Different numbers of tasks give various polygons or polyhedra, generally known as polytopes. Two tasks lead to a suite of variation along a line segment. Three tasks lead to a suite of variation on the triangle whose vertices are the three archetypes. Four archetypes form a tetrahedron. This is true while there are enough traits measured: in lower dimensional trait spaces one finds projections of these polytopes.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Fig1: An overview of Pareto theory for evolutionary tradeoffs. (A) The classical viewpoint of a fitness landscape: phenotypes are arranged along the slopes near the peak of a fitness hill maximum. (B) In contrast, the Pareto viewpoint suggests a tradeoff between tasks. For each task there is a performance function, which is maximal at a point known as the archetype for that task. The fitness function in each niche is a combination of the different performance functions (in general, fitness is an increasing function of performances, possibly a nonlinear function). (C) Optimality in a niche in which task 1 is most important, is achieved near archetype 1 (red maximum). Optimality in a niche in which all tasks are equally important, is achieved close to the middle of the Pareto front (green maximum). (D) The entire Pareto front- the set of maxima of all possible fitness functions that combine these performances- is contained within the convex hull of the archetypes. (E) Different numbers of tasks give various polygons or polyhedra, generally known as polytopes. Two tasks lead to a suite of variation along a line segment. Three tasks lead to a suite of variation on the triangle whose vertices are the three archetypes. Four archetypes form a tetrahedron. This is true while there are enough traits measured: in lower dimensional trait spaces one finds projections of these polytopes.
Mentions: Organisms that need to perform multiple tasks face a fundamental tradeoff: no phenotype can be optimal at all tasks [1-8]. This tradeoff situation is reminiscent of tradeoffs in economics and engineering. These fields analyze tradeoffs using Pareto optimality theory [9-13]. Pareto optimality was recently used in biology to study tradeoffs in evolution [2,5-8,14]. In contrast to the classic fitness-landscape approaches in which organisms maximize a single fitness function [15], the Pareto approach deals with several performance functions, one for each task, that all contribute to fitness (FigureĀ 1A-B).Figure 1

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