Is there any kind of software/program can test bi-branch or multi-branch phylogensis of the speciation?
Speciations do never occur perfectly simultaneously: neither the respective isolating (e.g. geographical) barriers nor reproductive isolation mechanisms develop at exactly the same moment, so one of the branches is always somewhat earlier separated than other, i.e. branching is always dichotomous! However, to detect the difference we need markers: at least one character-state changed in one of the descendants while remaining "plesiomorphous" in the other[-s], so if the second (in time) branching occurred before any such "apomorphy" has developed in the first, i.e. if there is no detectable difference between all the respective taxa (or if both descendants developed different "apomorphies" - e.g. ancestor green, descendant A blue, descendant B golden) then we are not able to reconstruct the order of branchings and for practical purposes must accept them as simultaneous ("multi-branch" in your formulation) - but in such situation no software can provide reliable solution!.
Thanks Roman, for your fundamentally explanation for the speciation process. At this moment, I'm interested whether we can test the mode of multi-decedent speciation. For a example, we always know the speciation mode A generate B & C and B generate D & E based on phylogenetic tree, whether we can get an evidence from the phylogeny that A generate the B, C, D & E directly rather than the former mode?
This is just what I tried to explain - sorry if I did it not clearly enough! In principle it is always the former "mode" that does really occur, but we can only discriminate it from the latter if the sequence of branchings has been accompanied by sequence of changes of character-states (as reconstructed just by "mapping" character-transformations on phylogenetic tree). So e.g., if the ancestor (A) has the characters a0 and b0, those in B remain the same but in C, D and E a0 has been changed to a1, and in E also b0 transformed into b1, then we can infer that A generated B and C, and only then C generated D and E. On the other hand, if in B a0 changed to a1, in C to a2, in D to a3, and in E to a4 (while b0 remained unchanged), then we are not able (and no - however ingenious - software can help!) to say whether, say, B separated from A earlier, later, or at the same time as C, D, or E from one another, and therefore we must accept that all the respective speciations occurred in practice simultaneously, i.e. that A "generated the B, C, D & E directly".
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