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Abstract BackgroundSince the mid-20th century, it has been argued by some that the transition from diploidy to polyploidy is an ‘evolutionary dead end’ in plants. Although this point has been debated ever since, multiple definitions of ‘dead end’ have been used in the polyploidy literature, without sufficient differentiation between alternative uses. ScopeHere, we focus on the two most common conceptions of the dead-end hypothesis currently discussed: the ‘lowering diversification’ hypothesis and the ‘rarely successful’ hypothesis. We discuss the evidence for both hypotheses, and we use a recently developed method of inferring tip diversification rates to demonstrate tests for the effect of ploidy on diversification in Solanaceae. ConclusionsWe find that diversification rates in the family are not strongly correlated with ploidy or with the closely related trait of breeding system. We also outline recent work in the field that moves beyond the relatively simple question of whether polyploidy increases, decreases or does not significantly affect diversification rates in plants.
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Two-scale methods for the normalized infinity Laplacian: rates of convergence
Abstract We propose a monotone and consistent numerical scheme for the approximation of the Dirichlet problem for the normalized infinity Laplacian, which could be related to the family of the so-called two-scale methods. We show that this method is convergent and prove rates of convergence. These rates depend not only on the regularity of the solution, but also on whether or not the right-hand side vanishes. Some extensions to this approach, like obstacle problems and symmetric Finsler norms, are also considered.
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- Award ID(s):
- 2111228
- PAR ID:
- 10546400
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- IMA Journal of Numerical Analysis
- Volume:
- 44
- Issue:
- 5
- ISSN:
- 0272-4979
- Format(s):
- Medium: X Size: p. 2603-2666
- Size(s):
- p. 2603-2666
- Sponsoring Org:
- National Science Foundation
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