Which sequences are biologically unavoidable?

None: the biologically unavoidable sequences are exactly the eventually periodic ones. For every non-eventually-periodic sequence over a finite alphabet there is an explicit avoiding population; for binary sequences it has two roots, two parents per non-root with complementary labels and at most two children per vertex, and the avoidance argument is a decreasing offset along any matching path. An indicator projection and a finite copy-lift extend this to every finite alphabet, including vertex-gendered witnesses. Combined with Alexander's positive theorem, reproduced with a boundary repair, this settles the last question of his section 6. The paper also characterises which members of the binary family are universal and draws finite-observation and computability corollaries; the ordinal and universal-object questions of the same section are not claimed.

None: the biologically unavoidable sequences are exactly the eventually periodic ones. For every non-eventually-periodic sequence over a finite alphabet there is an explicit avoiding population; for binary sequences it has two roots, two parents per non-root with complementary labels and at most two children per vertex, and the avoidance argument is a decreasing offset along any matching path. An indicator projection and a finite copy-lift extend this to every finite alphabet, including vertex-gendered witnesses. Combined with Alexander's positive theorem, reproduced with a boundary repair, this settles the last question of his section 6. The paper also characterises which members of the binary family are universal and draws finite-observation and computability corollaries; the ordinal and universal-object questions of the same section are not claimed.