Does a rejection mean gene flow or horizontal transfer?

No. Incomplete lineage sorting, a paralog taken for the orthologue, alignment error and selection all make a gene fit another tree better. A rejection is a gene to read, not a cause.

Why are some genes discordant but not rejected?

A gene can prefer another tree by a margin its sites cannot distinguish from chance. The SH test asks whether the species tree is significantly worse, which needs more signal than preferring another tree does.

Is anything uploaded?

No. Every fit runs in the browser on the alignments in your project.

Analyze

Tree incongruence: genes whose own alignment rejects the species tree

Test every gene alignment against the species tree and find the genes whose own sites reject it. Each gene is fitted by maximum likelihood under GTR + Γ on the species tree and on each of its nearest-neighbour rearrangements, the Shimodaira–Hasegawa test asks whether the species tree is significantly worse than the best of them, and the false discovery rate is controlled across genes. Which alternative trees the discordant genes choose, and whether the two rearrangements of each branch are equally common as incomplete lineage sorting predicts, are reported beside.

Open Tree incongruence: genes whose own alignment rejects the species tree Open the Tree incongruence sample

122 human genes and their orthologues in chimpanzee, gorilla, orangutan and macaque, each tested against the species tree to find the genes that fit another tree better, and whether lineage sorting explains them

What it does

01A maximum-likelihood fit of every gene under GTR + Γ on the species tree and on each nearest-neighbour rearrangement of it
02The Shimodaira–Hasegawa test by RELL resampling, measured from the best tree as published or from the worst as phangorn computes it
03Benjamini–Hochberg or Benjamini–Yekutieli control of the false discovery rate across genes
04Which genes prefer another tree, rejected or not, and which alternative trees they choose
05An exact binomial test per branch of the two rearrangements' counts, which incomplete lineage sorting alone predicts are equal

What it runs on

Checked against phangorn's pml, optim.pml and SH.test on 122 great-ape genes. The panel runs on @ports/discover.

Everything runs client-side. Files are parsed in the browser and projects are saved on this machine, so an unpublished sequence is never uploaded.

Questions

Does a rejection mean gene flow or horizontal transfer?: No. Incomplete lineage sorting, a paralog taken for the orthologue, alignment error and selection all make a gene fit another tree better. A rejection is a gene to read, not a cause.
Why are some genes discordant but not rejected?: A gene can prefer another tree by a margin its sites cannot distinguish from chance. The SH test asks whether the species tree is significantly worse, which needs more signal than preferring another tree does.
Is anything uploaded?: No. Every fit runs in the browser on the alignments in your project.

Also searched as

gene tree species tree discordance · gene tree incongruence · Shimodaira-Hasegawa test · SH test of tree topologies · incomplete lineage sorting · which genes reject the species tree · topology test across genes · phylogenomic discordance