I look at this from the tree's point of view. A Wu-1 infected individual will infect others at a given rate. Wu-1 will continue to increase prevalence until R changes. Wu-1's R only changes as Wu-1 produces immune resistance, and as behavior (masking, etc), and environment change. Introducing Alpha (or any variant) does not change Wu-1's R immediately. Nor do variants that infect very small proportions of the population "compete" directly. When humans meet, whichever variant is present has a chance to infect. Another variant is very rarely present for any "competition."
So I see the Alpha replacement of Wu-1 as a combination of Alpha's higher R, and the population's NPI efforts. NPI's decreased Wu-1's R below 1, and it went away. Alpha's somewhat higher R was enough to remain above 1 in the face of NPIs, so it remained ("replaced Wu-1").
Same for all the subsequent variants, though immunity from vaccination and infection also comes into play. E.g. in Nov/Dec delta's R appeared to be slightly above 1. Due to holidays, behavior changes were outweighing the slow immunity increase. Omicron comes along with a higher R (2 maybe), and rapidly rises. Delta pokes along for awhile, but both of them and vax together are raising immunity by maybe 0.2-0.4% per day. (That's a bigger percentage of the susceptible population, especially so for delta.) At the same time people become more cautious (omigosh omicron) also making R fall for both.
Anyway, I'm surprised if delta is gone already. I don't think its R could be below 0.5 and is probably higher. At New Years, I'd guess its R was still close to 1. There's just a lot more omicron, so percentage-wise there's a lot less delta.