RESUMO
For more than 50 years the Mean Measure of Divergence (MMD) has been one of the most prominent tools used in anthropology for the study of non-metric traits. However, one of the problems, in anthropology including palaeoanthropology (more often there), is the lack of big enough samples or the existence of samples without sufficiently measured traits. Since 1969, with the advent of bootstrapping techniques, this issue has been tackled successfully in many different ways. Here, we present a parametric bootstrap technique based on the fact that the transformed θ, obtained from the Anscombe transformation to stabilize the variance, nearly follows a normal distribution with standard deviation $\sigma = 1 / \sqrt{N + 1/2}$σ=1/N+1/2, where N is the size of the measured trait. When the probabilistic distribution is known, parametric procedures offer more powerful results than non-parametric ones. We profit from knowing the probabilistic distribution of θ to develop a parametric bootstrapping method. We explain it carefully with mathematical support. We give examples, both with artificial data and with real ones. Our results show that this parametric bootstrap procedure is a powerful tool to study samples with scarcity of data.
RESUMO
We argue that an induced breaking of the genetic synonym symmetry due to the action of genetic operators such as mutation can enhance the adaptability of a species to changes in the environment. In the case of a virus, the claim is that the codon bias in the neutralization epitope improves the virus' ability to generate mutants that evade the induced immune response. We support our claim with a simple 'toy model' of a viral epitope evolving in competition with the immune system. The effective selective advantage of a higher mutability leads to a dominance of codons that favor non-synonymous mutations. As further evidence we present a simple model for a genetic regulatory network that leads to adaptive evolution in a population of giraffes by means of an induced symmetry breaking rather than through any direct selective advantage.