The claim
Normalized stem length is the stem from a family’s prokaryotic sister to LECA divided by the family’s median branch inside eukaryotes, schematically (R_s·T_s)/(R_e·T_e). Since T_e is the same for every family, the ratio is proportional to the stem’s time only if R_s is proportional to R_e; Pittis and Gabaldón assume the rates are “correlated” (THEORY-1102, as read in NOTE-1240). Stem length is also distance to the closest sampled relative: in their own Lokiarchaeota analysis the 30 families reassigned to the new genome have the shortest archaeal stems, and archaea were sampled with 130 genomes against 3,318 bacterial ones. The separation of alphaproteobacterial from other bacterial families, on which the chimaeric host turns, has P = 0.044. On Tobiasson and colleagues’ data (THEORY-1101) the method’s ordering reverses below a stem length of 0.3 and co-acquired genes scatter over two orders of magnitude. So neither the late mitochondrion of Pittis and Gabaldón nor the waves of Bernabeu and colleagues (THEORY-1105) is established by stem length alone.
What comes nearest to defeating it
Pittis and Gabaldón’s positive control (THEORY-1102, NOTE-1240) finds plant families of cyanobacterial origin with shorter stems than alphaproteobacterial ones, as the later plastid predicts. That checks the method’s direction once, on one pair of donors whose order is known; it does not show that the order survives rate variation or uneven sampling, and on Tobiasson and colleagues’ data cyanobacterial stems show a weaker form of the same reversal (THEORY-1101). Their P = 0.044 comparison was repeated under stricter LECA definitions, other pipelines and support thresholds, on the same families and under the same assumption. Kay and colleagues’ relaxed clock (THEORY-1099, NOTE-1234) puts the mitochondrion after the archaeal host, the order stem lengths give, but puts 16 of 19 duplications in non-alphaproteobacterial bacterial families after the mitochondrion, at odds with the stem-length orderings of Pittis and Gabaldón and of Bernabeu and colleagues; it dates duplication, not acquisition. An independent clock that agrees on one ordering and not the other has not recovered the orderings. Bernabeu and colleagues cite functional classes with overlapping stem-length distributions (their Supplementary Fig. 13, unread here) against the worry that function sets stem length; that answers Tobiasson and colleagues’ suggested cause, not the rate assumption or sampling, and is not a test on genes of known acquisition time.
What it does not say
Not that the mitochondrion came early, or that the waves did not happen. Both orderings may hold on other evidence; Kay and colleagues (THEORY-1099) reach a late mitochondrion by a different clock. The claim is about what this method can show.