  We argue that C. Darwin and more recently W. Hennig worked at times under the
simplifying assumption of an eternal biosphere. So motivated, we explicitly
consider the consequences which follow mathematically from this assumption, and
the infinite graphs it leads to. This assumption admits certain clusters of
organisms which have some ideal theoretical properties of species, shining some
light onto the species problem. We prove a dualization of a law of T.A. Knight
and C. Darwin, and sketch a decomposition result involving the internodons of
D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond
to B. Sturmfels' question, "Can biology lead to new theorems?"
