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?”. (shrink)

Contemporary biology has inherited two key assumptions from the Modern Synthesis about the nature of population lineages: sexual reproduction is the exemplar for how individuals in population lineages inherit traits from their parents, and random mating is the exemplar for reproductive interaction. While these assumptions have been extremely fruitful for a number of fields, such as population genetics and phylogenetics, they are increasingly unviable for studying the full diversity and evolution of life. I introduce the “mixture” account of population lineages (...) that escapes these assumptions by dissolving the Modern Synthesis’s sharp line separating reproduction and development and characterizing reproductive integration in population lineages by the ephemerality of isolated subgroups rather than random mating. The mixture account provides a single criterion for reproductive integration that accommodates both sexual and asexual reproduction, unifying their treatment under Kevin de Queiroz’s generalized lineage concept of species. The account also provides a new basis for empirically assessing the effect of random mating as an idealization on the empirical adequacy of population genetic models. (shrink)

According to a recent suggestion, the names of gene taxa should be conceived of as referring to individuals with concrete genes as their parts, just as the names of biological species are often understood as denoting individuals with organisms as their parts. Although prima facie this suggestion might advance the debate on gene concepts in a similar way as the species-are-individuals thesis advanced the debate on species concepts, I argue that the principal arguments in support of the gene-individuality thesis are (...) much less compelling than the parallel arguments in the species case. In addition, I argue that the notion of biological function invoked in the gene-individuality thesis (selected effect) is not the one that biologists actually use when individuating genes. Contra the gene-individuality thesis, I argue that gene names refer to kinds, defined primarily (though not exclusively) by causal-role functions. (shrink)