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Apical meristematic zones of the roots and shoot tips clustered together and weakly clustered with leaves, shoots and stem tissues.
The core genotypes weakly clustered into two subgroups, but multiple branches connect the two subgroups (I, IV X and II, III, XIII, XIV, DAOM181602 respectively; Fig. 1).
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The second dinoflagellate CAD paralog weakly clusters with the diatom F. cylindrus single CAD homolog (59% support) and the second haptophyte paralog groups strongly with green algae (100%).
For both CCR and CAD, red algae are polyphyletic, with some paralogs weakly clustering with homologs from bacteria or heterotrophic eukaryotes.
This completes the proof of Step 4. In Step 5 and Step 6 of this theorem, we consider weakly clusters of { x k }.
From Step 5 and Step 6 it follows that for every weakly cluster point x ¯ of the sequence { x k }, x ¯ ∈ ⋂ i = 1 N F ( S i ) ∩ Sol ( EP ( f ) ).
Let C be a nonempty closed convex subset of a real Hilbert space H and x 0 ∈ H. Let { x k } be a bounded sequence such that every weakly cluster point x ¯ of { x k } belongs to C and ∥ x k − x 0 ∥ ≤ ∥ x 0 − Pr C ( x 0 ) ∥, ∀ k ≥ 0. Then { x k } converges strongly to Pr C ( x 0 ) as k → ∞.
Although the proposed evolutionary hypothesis predicts that all Urochordate DLX genes should be members of one or the other of the two main clades of vertebrate DLX genes (DLX genes 1/4/6 and DLX 2/3/5), only DLXc weakly clusters with the DLX 1/4/6 clade, while DLXa and DLXb genes do not cluster with members of one of the two main clades.
Dictyostelium ForC and ForG cluster together with the Cappuccino/Formin group (75% bootstraps), whereas ForI very weakly clusters with the FHOD subfamily (53% bootstraps).
Other diatom CCR paralogs weakly cluster with green algae (50% support), while the single CCR homolog found in the diatom Phaeodactylum tricornutum strongly groups with bacteria (91%) and was likely acquired from a member of this domain by LGT.
Diatoms and the haptophyte weakly cluster together (51%), the cryptophyte clusters strongly (100%) with another secondarily photosynthetic organism (Ectocarpus silicosis, a brown algae) and with green algae, while the dinoflagellate is found inside the same well-supported (97%) mixed green and red algal clade.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com