Question regarding when it's a homoplasy in a phylogenetic tree

Question

If you have 2 organisms that both come directly from the same common ancestor on a phylogenetic tree, and that common ancestor does not have trait "x", is it possible for both of its direct descendants to develop that trait "x" independently, and would that be an example of a homoplasy?

Answer 1

Phylogenetic tree vs first generation offspring

Please note that on a phylogenetic tree, the time scale is big enough so that the generation time is completely undistinguishable. Hence, questions of first generation offspring won't rise. Also, in practice when reconstructing a phylogenetic tree, our level of accuracy does not allow us to distinguish exactly at what generation did specific mutation occur.

Rephrasing your question

The term homoplasy is typically used in the context of phylogenetics. Also, most of the time the term homoplasy refer to phenotypic trait and not to genetic sequence but I will not go into these specific complications here. The term is also mainly used in intro textbook and not so much in the peer-reviewed literature. In all cases, one can define the concept of homoplasy as a shared trait that is caused by a mutation that is not identical by descent. In other words, if in two lineages/individuals that share the same trait, the trait is caused by the same mutation(s) (same, not only by its state but by descent), then the shared trait does not represent a homoplasy.

With this, I can rephrase your question as

If two siblings share a (heritable) trait that the direct parent does not have, are the traits identical by descent?

If two siblings share a (heritable) trait that the direct parent does not have, are the traits identical by descent?

Well.. it depends as to whether the mutations happened happened twice independently in the two different gametes or if the mutation happened once in the (germ line) lineage that gave rise to these gametes in the parent body.

The second is much more likely. Because, it is very unlikely for the same mutation to happen twice independently in two different gametes for the same individual and much more likely that the mutation happened once in a cell that gave rise to the two gametes, it is very much more likely that the shared trait among the two offsprings is caused by a mutation that is identical by descent. Hence, not a homoplasy.