Given a finite set K of lethal genes, a starting genome x and a desired target genome y, is there a sequence of base insertions, deletions, and substitutions, which from x produces the desired genome y, and such that no intermediate genome contains a lethal gene. The main result of this paper is that, appropriately formulated, this problem is undecidable, even when the underlying alphabet has only 2 symbols (e.g. two of the bases A,C,G,T). We prove that asexual evolutionary systems form a universal computation engine, in the sense that for any reversible Turing machine M and input x, there is a finite set K of lethal genes, which can guide the computation, so that all intermediate genomes are prefixes of (encodings of) configurations in the computation of M. Since reversible Turing machines retain the history of their entire computation, and axe essentially encoded by evolutionary systems, this suggests a encoding mechanism by which phylogeny recapitulates ontogeny.