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Abstract PremiseReticulate evolution, often accompanied by polyploidy, is prevalent in plants, and particularly in the ferns. Resolving the resulting non‐bifurcating histories remains a major challenge for plant phylogenetics. Here, we present a phylogenomic investigation into the complex evolutionary history of the vining ferns,Lygodium(Lygodiaceae, Schizaeales). MethodsUsing a targeted enrichment approach with theGoFlag 408flagellate land plant probe set, we generated large nuclear and plastid sequence datasets for nearly all taxa in the genus and constructed the most comprehensive phylogeny of the family to date using concatenated maximum likelihood and coalescence approaches. We integrated this phylogeny with cytological and spore data to explore karyotype evolution and generate hypotheses about the origins of putative polyploids and hybrids. ResultsOur data and analyses support the origins of several putative allopolyploids (e.g.,L. cubense, L. heterodoxum) and hybrids (e.g.,L.×fayae) and also highlight the potential prevalence of autopolyploidy in this clade (e.g.,L. articulatum, L. flexuosum, andL. longifolium). ConclusionsOur robust phylogenetic framework provides valuable insights into dynamic reticulate evolution in this clade and demonstrates the utility of target‐capture data for resolving these complex relationships.
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Mixed Norm l 2 Decoupling for Paraboloids
Abstract We prove the sharp mixed norm $$(l^{2}, L^{q}_{t}L^{r}_{x})$$ decoupling estimate for the paraboloid in $d + 1$ dimensions.
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- PAR ID:
- 10470757
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- International Mathematics Research Notices
- Volume:
- 2023
- Issue:
- 20
- ISSN:
- 1073-7928
- Format(s):
- Medium: X Size: p. 17972-18000
- Size(s):
- p. 17972-18000
- Sponsoring Org:
- National Science Foundation
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