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Abstract AimAre different fruit colours related to large‐scale patterns of dispersal, distribution and diversification? Here, we investigate this question for the first time, using phylogenetic approaches in the tribe Gaultherieae (Ericaceae). We test relationships between fruit colour and (a) biogeographic dispersal, (b) elevational and latitudinal species distributions and (c) rates of diversification. LocationGlobal. Time periodRecent to 30 million years ago. Major taxa studiedThe plant tribe Gaultherieae in the family Ericaceae (blueberries and relatives). MethodsWe estimated a new time‐calibrated phylogeny for Gaultherieae. Data on fruit colours and geographic distributions for each species were compiled from published sources and field observations. Using phylogenetic methods, we estimated major dispersal events across the tree and the most likely fruit colour associated with each dispersal event, and tested whether dispersal between major biogeographic regions was equally likely for different fruit colours, and whether dispersal distances were larger for certain colours. We then tested the relationships between fruit colours and geographic variables (latitude, elevation) and diversification rates. ResultsLarge‐scale dispersal events were significantly associated with red‐fruited lineages, even though red‐fruited species were relatively uncommon. Further, different fruit colours were associated with different elevations and latitudes (e.g. red at lower elevations, violet at lower latitudes, white at higher elevations). Violet colour was related to increased diversification rates, leading to more violet‐fruited species globally. Main conclusionsOverall, we show that different fruit colours can significantly impact the large‐scale dispersal, distribution and diversification of plant clades. Furthermore, the interplay between biogeography and fruit‐colour evolution seems to generate “taxon cycles” in fruit colour that may drive variation in fruit colour over macroevolutionary time‐scales.
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Master integrals for four-loop massless form factors
Abstract We present analytical results for all master integrals for massless three-point functions, with one off-shell leg, at four loops. Our solutions were obtained using differential equations and direct integration techniques. We review the methods and provide additional details.
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- Award ID(s):
- 2013859
- PAR ID:
- 10474337
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- The European Physical Journal C
- Volume:
- 83
- Issue:
- 11
- ISSN:
- 1434-6052
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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