Cladistic analysis of continuous modularized traits provides phylogenetic signals in Homo evolution

Evolutionary novelties in the skeleton are usually expressed as changes in the timing of growth of features intrinsically integrated at different hierarchical levels of development(1). As a consequence, most of the shape- traits observed across species do vary quantitatively rather than qualitatively(2), in a multivariate space(3) and in a modularized way(4,5). Because most phylogenetic analyses normally use discrete, hypothetically independent characters(6), previous attempts have disregarded the phylogenetic signals potentially enclosed in the shape of morphological structures. When analysing low taxonomic levels, where most variation is quantitative in nature, solving basic requirements like the choice of characters and the capacity of using continuous, integrated traits is of crucial importance in recovering wider phylogenetic information. This is particularly relevant when analysing extinct lineages, where available data are limited to fossilized structures. Here we show that when continuous, multivariant and modularized characters are treated as such, cladistic analysis successfully solves relationships among main Homo taxa. Our attempt is based on a combination of cladistics, evolutionary- development- derived selection of characters, and geometric morphometrics methods. In contrast with previous cladistic analyses of hominid phylogeny, our method accounts for the quantitative nature of the traits, and respects their morphological integration patterns. Because complex phenotypes are observable across different taxonomic groups and are potentially informative about phylogenetic relationships, future analyses should point strongly to the incorporation of these types of trait.

On E-functions of semisimple Lie groups

We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group G as their expansions into series of special functions that are invariant under the action of the even subgroup of the Weyl group of G. We distinguish two cases of even Weyl groups-one is the direct product of even Weyl groups of simple components of G and the second is the full even Weyl group of G. The problem is rather simple in two dimensions. It is much richer in dimensions greater than two-we describe in detail E-transforms of semisimple Lie groups of rank 3.