Markov invariants, plethysms, and phylogenetics

We explore model-based techniques of phylogenetic tree inference exercising Markov invariants. Markov invariants are group invariant polynomials and are distinct from what is known in the literature as phylogenetic invariants, although we establish a commonality in some special cases. We show that the simplest Markov invariant forms the foundation of the Log–Det distance measure. We take as our primary tool group representation theory, and show that it provides a general framework for analyzing Markov processes on trees. From this algebraic perspective, the inherent symmetries of these processes become apparent, and focusing on plethysms, we are able to define Markov invariants and give existence proofs. We give an explicit technique for constructing the invariants, valid for any number of character states and taxa. For phylogenetic trees with three and four leaves, we demonstrate that the corresponding Markov invariants can be fruitfully exploited in applied phylogenetic studies.     

Are Homo sapiens nonsupranuchal fossa and neanderthal suprainiac fossa convergent traits?

The autapomorphic status of the Neanderthal suprainiac fossa was recently confirmed. This was a result of a detailed analysis of the internal bone composition in the area of the suprainiac depression on Neanderthal and Homo sapiens specimens. However, while anatomical differences between Neanderthal suprainiac fossa and the depression in the inion region of the occipital bone of fossil and recent Homo sapiens have been discussed in detail, the etiology of these structures has not been resolved. In this article, the hypothesis that the Homo sapiens non-supranuchal fossa and the Neanderthal suprainiac fossa both formed to maintain the optimal shape of the occipital plane (to minimize strain on the posterior cranial vault) is tested. First, the variation in the expression of the fossa above inion in the crania of recent Homo sapiens from European, African, and Australian samples was examined, and the degree of structural similarity between these depressions and the Neanderthal suprainiac fossa was assessed. Next, the relationship between the shape of the occipital squama in the midsagittal plane and two particular features (the degree of the occipital torus development and the occurrence of a depression in the inion region that is not the supranuchal fossa) were analyzed. Based on the results, it is suggested that the Homo sapiens non-supranuchal fossa and Neanderthal suprainiac fossa are convergent traits.     

Through the Jungle of Biological Diversity

Biological diversity would apparently seem the most intuitive and easily studied of all the ecological concepts. However, in practice biodiversity has suffered from great number of definitions that vary with the specific needs of the different researchers, thus making it extremely confusing as an ecological concept. In this paper, I shortly review the concept of biodiversity showing that there exists a substantial ambiguity among ecologists as far as biodiversity conceptualization and evaluation is concerned. I conclude that, due to this major disagreement on its very nature, biodiversity may be defined simply as a set of multivariate summary statistics for quantifying different characteristics of community structure.     

The contribution of the glenoid labrum to glenohumeral stability under physiological joint loading using finite element analysis

The labrum contributes to passive glenohumeral joint stability. Cadaveric studies have demonstrated that this has position and load dependency, which has not been quantified under physiological loads. This study aims to validate subject-specific finite element (FE) models against in vitro measurements of joint stability and to utilise the FE models to predict joint stability under physiological loads. The predicted stability values were within ± one standard deviation of experimental data and the FE models showed a reduction in stability of 10–15% with high, physiological, loads. The developed regression equations provide the first representation of passive glenohumeral stability and will aid surgical decision-making.