So far in this course we have dealt entirely with the evolution of characters that are controlled by simple Mendelian inheritance at a single locus. There are notes on the course website about gametic disequilibrium and how allele frequencies change at two loci simultaneously, but we didn’t discuss them. In every example we’ve considered we’ve imagined that we could understand something about evolution by examining the evolution of a single gene. That’s the domain of classical population genetics. For the next few weeks we’re going to be exploring a field that’s actually older than classical population genetics, although the approach we’ll be taking to it involves the use of population genetic machinery. If you know a little about the history of evolutionary biology, you may know that after the rediscovery of Mendel’s work in 1900 there was a heated debate between the “biometricians” (e.g., Galton and Pearson) and the “Mendelians” (e.g., de Vries, Correns, Bateson, and Morgan). Biometricians asserted that the really important variation in evolution didn’t follow Mendelian rules. Height, weight, skin color, and similar traits seemed to

Human biochemical genetics

Neandertals, the closest evolutionary relatives of present-day humans, lived in large parts of Europe and western Asia before disappearing 30,000 years ago. We present a draft sequence of the Neandertal genome composed of more than 4 billion nucleotides from three individuals. Comparisons of the Neandertal genome to the genomes of five present-day humans from different parts of the world identify a number of genomic regions that may have been affected by positive selection in ancestral modern humans, including genes involved in metabolism and in cognitive and skeletal development. We show that Neandertals shared more genetic variants with present-day humans in Eurasia than with present-day humans in sub-Saharan Africa, suggesting that gene flow from Neandertals into the ancestors of non-Africans occurred before the divergence of Eurasian groups from each other.

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A Draft Sequence of the Neandertal Genome

Genetics and analysis of quantitative traits

Most common human traits and diseases have a polygenic pattern of inheritance: DNA sequence variants at many genetic loci influence the phenotype. Genome-wide association (GWA) studies have identified more than 600 variants associated with human traits, but these typically explain small fractions of phenotypic variation, raising questions about the use of further studies. Here, using 183,727 individuals, we show that hundreds of genetic variants, in at least 180 loci, influence adult height, a highly heritable and classic polygenic trait. The large number of loci reveals patterns with important implications for genetic studies of common human diseases and traits. First, the 180 loci are not random, but instead are enriched for genes that are connected in biological pathways (P = 0.016) and that underlie skeletal growth defects (P < 0.001). Second, the likely causal gene is often located near the most strongly associated variant: in 13 of 21 loci containing a known skeletal growth gene, that gene was closest to the associated variant. Third, at least 19 loci have multiple independently associated variants, suggesting that allelic heterogeneity is a frequent feature of polygenic traits, that comprehensive explorations of already-discovered loci should discover additional variants and that an appreciable fraction of associated loci may have been identified. Fourth, associated variants are enriched for likely functional effects on genes, being over-represented among variants that alter amino-acid structure of proteins and expression levels of nearby genes. Our data explain approximately 10% of the phenotypic variation in height, and we estimate that unidentified common variants of similar effect sizes would increase this figure to approximately 16% of phenotypic variation (approximately 20% of heritable variation). Although additional approaches are needed to dissect the genetic architecture of polygenic human traits fully, our findings indicate that GWA studies can identify large numbers of loci that implicate biologically relevant genes and pathways.

Hundreds of variants clustered in genomic loci and biological pathways affect human height

Thank you very much for reading statistical parametric mapping the analysis of functional brain images. As you may know, people have search numerous times for their chosen novels like this statistical parametric mapping the analysis of functional brain images, but end up in malicious downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they cope with some infectious bugs inside their desktop computer.

Statistical Parametric Mapping The Analysis Of Functional Brain Images

Geometric morphometrics is the statistical analysis of form based on Cartesian landmark coordinates. After separating shape from overall size, position, and orientation of the landmark configurations, the resulting Procrustes shape coordinates can be used for statistical analysis. Kendall shape space, the mathematical space induced by the shape coordinates, is a metric space that can be approximated locally by a Euclidean tangent space. Thus, notions of distance (similarity) between shapes or of the length and direction of developmental and evolutionary trajectories can be meaningfully assessed in this space. Results of statistical techniques that preserve these convenient properties—such as principal component analysis, multivariate regression, or partial least squares analysis—can be visualized as actual shapes or shape deformations. The Procrustes distance between a shape and its relabeled reflection is a measure of bilateral asymmetry. Shape space can be extended to form space by augmenting the shape coordinates with the natural logarithm of Centroid Size, a measure of size in geometric morphometrics that is uncorrelated with shape for small isotropic landmark variation. The thin-plate spline interpolation function is the standard tool to compute deformation grids and 3D visualizations. It is also central to the estimation of missing landmarks and to the semilandmark algorithm, which permits to include outlines and surfaces in geometric morphometric analysis. The powerful visualization tools of geometric morphometrics and the typically large amount of shape variables give rise to a specific exploratory style of analysis, allowing the identification and quantification of previously unknown shape features.

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Advances in Geometric Morphometrics

Semilandmarks in Three Dimensions

Quantitative shape analysis using geometric morphometrics is based on the statistical analysis of landmark coordinates. Many structures, however, cannot be quantified using traditional landmarks. Semilandmarks make it possible to quantify two or three-dimensional homologous curves and sur- faces, and analyse them together with traditional landmarks. Here we first introduce the concept of sliding semilandmarks and discuss applications and limitations of this method. In a second part we show how the sliding semilandmark algorithm can be used to estimate missing data in incomplete specimens. Download the complete "Yellow Book" on "Virtual Morphology and Evolutionary Morphometrics in the new millenium".

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Semilandmarks: a method for quantifying curves and surfaces

Comparison of cranial ontogenetic trajectories among great apes and humans

Linear discriminant analysis (LDA) is a multivariate classification technique frequently applied to morphometric data in various biomedical disciplines. Canonical variate analysis (CVA), the generalization of LDA for multiple groups, is often used in the exploratory style of an ordination technique (a low-dimensional representation of the data). In the rare case when all groups have the same covariance matrix, maximum likelihood classification can be based on these linear functions. Both LDA and CVA require full-rank covariance matrices, which is usually not the case in modern morphometrics. When the number of variables is close to the number of individuals, groups appear separated in a CVA plot even if they are samples from the same population. Hence, reliable classification and assessment of group separation require many more organisms than variables. A simple alternative to CVA is the projection of the data onto the principal components of the group averages (between-group PCA). In contrast to CVA, these axes are orthogonal and can be computed even when the data are not of full rank, such as for Procrustes shape coordinates arising in samples of any size, and when covariance matrices are heterogeneous. In evolutionary quantitative genetics, the selection gradient is identical to the coefficient vector of a linear discriminant function between the populations before vs. after selection. When the measured variables are Procrustes shape coordinates, discriminant functions and selection gradients are vectors in shape space and can be visualized as shape deformations. Except for applications in quantitative genetics and in classification, however, discriminant functions typically offer no interpretation as biological factors.

Philipp Mitteroecker

Papers

Advances in Geometric Morphometrics

Semilandmarks in Three Dimensions

Semilandmarks: a method for quantifying curves and surfaces

Comparison of cranial ontogenetic trajectories among great apes and humans

Linear Discrimination, Ordination, and the Visualization of Selection Gradients in Modern Morphometrics