Gabor-based region covariance matrices for face recognition

This paper presents a new method for human face recognition by utilizing Gabor-based region covariance matrices as face descriptors. Both pixel locations and Gabor coefficients are employed to form the covariance matrices. Experimental results demonstrate the advantages of this proposed method.

The stability of P in coral reef fishes

The constancy of phenotypic variation and covariation is an assumption that underlies most recent investigations of past selective regimes and attempts to predict future responses to selection. Few studies have tested this assumption of constancy despite good reasons to expect that the pattern of phenotypic variation and covariation may vary in space and time. We compared phenotypic variance-covariance matrices (P) estimated for Populations of six species of distantly related coral reef fishes sampled at two locations on Australia's Great Barrier Reef separated by more than 1000 km. The intraspecific similarity between these matrices was estimated using two methods: matrix correlation and common principal component analysis. Although there was no evidence of equality between pairs of P, both statistical approaches indicated a high degree of similarity in morphology between the two populations for each species. In general, the hierarchical decomposition of the variance-covariance structure of these populations indicated that all principal components of phenotypic variance-covariance were shared but that they differed in the degree of variation associated with each of these components. The consistency of this pattern is remarkable given the diversity of morphologies and life histories encompassed by these species. Although some phenotypic instability was indicated, these results were consistent with a generally conserved pattern of multivariate selection between populations.

Effects of Interspecific Gene Flow on the Phenotypic Variance-Covariance Matrix in Lake Victoria Cichlids

Quantitative genetics theory predicts adaptive evolution to be constrained along evolutionary lines of least resistance. In theory, hybridization and subsequent interspecific gene flow may however rapidly change the evolutionary constraints of a population and eventually change its evolutionary potential, but empirical evidence is still scarce. Using closely related species pairs of Lake Victoria cichlids sampled from four different islands with different levels of interspecific gene flow, we tested for potential effects of introgressive hybridization on phenotypic evolution in wild populations. We found that these effects differed among our study species. Constraints measured as the eccentricity of phenotypic variance-covariance matrices declined significantly with increasing gene flow in the less abundant species for matrices that have a diverged line of least resistance. In contrast we find no such decline for the more abundant species. Overall our results suggest that hybridization can change the underlying phenotypic variance-covariance matrix, potentially increasing the adaptive potential of such populations.

Covariance structure in the skull of Catarrhini: a case of pattern stasis and magnitude evolution

The study of the genetic variance/covariance matrix (G-matrix) is a recent and fruitful approach in evolutionary biology, providing a window of investigating for the evolution of complex characters. Although G-matrix studies were originally conducted for microevolutionary timescales, they could be extrapolated to macroevolution as long as the G-matrix remains relatively constant, or proportional, along the period of interest. A promising approach to investigating the constancy of G-matrices is to compare their phenotypic counterparts (P-matrices) in a large group of related species; if significant similarity is found among several taxa, it is very likely that the underlying G-matrices are also equivalent. Here we study the similarity of covariance and correlation structure in a broad sample of Old World monkeys and apes (Catarrhini). We made phylogenetically structured comparisons of correlation and covariance matrices derived from 39 skull traits, ranging from between species to the superfamily level. We also compared the overall magnitude of integration between skull traits (r(2)) for all Catarrhim genera. Our results show that P-matrices were not strictly constant among catarrhines, but the amount of divergence observed among taxa was generally low. There was significant and positive correlation between the amount of divergence in correlation and covariance patterns among the 30 genera and their phylogenetic distances derived from a recently proposed phylogenetic hypothesis. Our data demonstrate that the P-matrices remained relatively similar along the evolutionary history of catarrhines, and comparisons with the G-matrix available for a New World monkey genus (Saguinus) suggests that the same holds for all anthropoids. The magnitude of integration, in contrast, varied considerably among genera, indicating that evolution of the magnitude, rather than the pattern of inter-trait correlations, might have played an important role in the diversification of the catarrhine skull. (C) 2009 Elsevier Ltd. All rights reserved.

Phenotypic divergence along lines of genetic variance

Natural populations inhabiting the same environment often independently evolve the same phenotype. Is this replicated evolution a result of genetic constraints imposed by patterns of genetic covariation? We looked for associations between directions of morphological divergence and the orientation of the genetic variance-covariance matrix (G) by using an experimental system of morphological evolution in two allopatric nonsister species of rainbow fish. Replicate populations of both Melanotaenia eachamensis and Melanotaenia duboulayi have independently adapted to lake versus stream hydrodynamic environments. The major axis of divergence (z) among all eight study populations was closely associated with the direction of greatest genetic variance (g(max)), suggesting directional genetic constraint on evolution. However, the direction of hydrodynamic adaptation was strongly associated with vectors of G describing relatively small proportions of the total genetic variance, and was only weakly associated with g(max). In contrast, divergence between replicate populations within each habitat was approximately proportional to the level of genetic variance, a result consistent with theoretical predictions for neutral phenotypic divergence. Divergence between the two species was also primarily along major eigenvectors of G. Our results therefore suggest that hydrodynamic adaptation in rainbow fish was not directionally constrained by the dominant eigenvector of G. Without partitioning divergence as a consequence of the adaptation of interest (here, hydrodynamic adaptation) from divergence due to other processes, empirical studies are likely to overestimate the potential for the major eigenvectors of G to directionally constrain adaptive evolution.

Studying phenotypic evolution using multivariate quantitative genetics

Quantitative genetics provides a powerful framework for studying phenotypic evolution and the evolution of adaptive genetic variation. Central to the approach is G, the matrix of additive genetic variances and covariances. G summarizes the genetic basis of the traits and can be used to predict the phenotypic response to multivariate selection or to drift. Recent analytical and computational advances have improved both the power and the accessibility of the necessary multivariate statistics. It is now possible to study the relationships between G and other evolutionary parameters, such as those describing the mutational input, the shape and orientation of the adaptive landscape, and the phenotypic divergence among populations. At the same time, we are moving towards a greater understanding of how the genetic variation summarized by G evolves. Computer simulations of the evolution of G, innovations in matrix comparison methods, and rapid development of powerful molecular genetic tools have all opened the way for dissecting the interaction between allelic variation and evolutionary process. Here I discuss some current uses of G, problems with the application of these approaches, and identify avenues for future research.

Genetic covariance between indices of body condition and immunocompetence in a passerine bird

Background: Condition-dependence is a ubiquitous feature of animal life histories and has important implications for both natural and sexual selection. Mate choice, for instance, is typically based on condition-dependent signals. Theory predicts that one reason why condition-dependent signals may be special is that they allow females to scan for genes that confer high parasite resistance. Such explanations require a genetic link between immunocompetence and body condition, but existing evidence is limited to phenotypic associations. It remains unknown, therefore, whether females selecting males with good body condition simply obtain a healthy mate, or if they acquire genes for their offspring that confer high immunocompetence. Results: Here we use a cross-foster experimental design to partition the phenotypic covariance in indices of body condition and immunocompetence into genetic, maternal and environmental effects in a passerine bird, the zebra finch Taeniopygia guttata. We show that there is significant positive additive genetic covariance between an index of body condition and an index of cell-mediated immune response. In this case, genetic variance in the index of immune response explained 56% of the additive genetic variance in the index of body condition. Conclusion: Our results suggest that, in the context of sexual selection, females that assess males on the basis of condition-dependent signals may gain genes that confer high immunocompetence for their offspring. More generally, a genetic correlation between indices of body condition and imuunocompetence supports the hypothesis that parasite resistance may be an important target of natural selection. Additional work is now required to test whether genetic covariance exists among other aspects of both condition and immunocompetence.

Genetic constraints on the evolution of mate recognition under natural selection

Field populations of Drosophila serrata display reproductive character displacement in cuticular hydrocarbons (CHCs) when sympatric with Drosophila birchii. We have previously shown that the naturally occurring pattern of reproductive character displacement can be experimentally replicated by exposing field allopatric populations of D. serrata to experimental sympatry with D. birchii. Here, we tested whether the repeated evolution of reproductive character displacement in natural and experimental populations was a consequence of genetic constraints on the evolution of CHCs. The genetic variance-covariance (G) matrices for CHCs were determined for populations of D. serrata that had evolved in either the presence or absence of D. birchii under field and experimental conditions. Natural selection on mate recognition under both field and experimental sympatric conditions increased the genetic variance in CHCs consistent with a response to selection based on rare alleles. A close association between G eigenstructure and the eigenstructure of the phenotypic divergence (D) matrix in natural and experimental populations suggested that G matrix eigenstructure may have determined the direction in which reproductive character displacement evolved during the reinforcement of mate recognition.

Covariance Matrix Estimation and Mean-Variance Optimization in application to International Diversification

Tutkimus keskittyy kansainväliseen hajauttamiseen suomalaisen sijoittajan näkökulmasta. Tutkimuksen toinen tavoite on selvittää tehostavatko uudet kovarianssimatriisiestimaattorit minimivarianssiportfolion optimointiprosessia. Tavallisen otoskovarianssimatriisin lisäksi optimoinnissa käytetään kahta kutistusestimaattoria ja joustavaa monimuuttuja-GARCH(1,1)-mallia. Tutkimusaineisto koostuu Dow Jonesin toimialaindekseistä ja OMX-H:n portfolioindeksistä. Kansainvälinen hajautusstrategia on toteutettu käyttäen toimialalähestymistapaa ja portfoliota optimoidaan käyttäen kahtatoista komponenttia. Tutkimusaieisto kattaa vuodet 1996-2005 eli 120 kuukausittaista havaintoa. Muodostettujen portfolioiden suorituskykyä mitataan Sharpen indeksillä. Tutkimustulosten mukaan kansainvälisesti hajautettujen investointien ja kotimaisen portfolion riskikorjattujen tuottojen välillä ei ole tilastollisesti merkitsevää eroa. Myöskään uusien kovarianssimatriisiestimaattoreiden käytöstä ei synnytilastollisesti merkitsevää lisäarvoa verrattuna otoskovarianssimatrisiin perustuvaan portfolion optimointiin.

Spatially varying selection shapes life history clines among populations of Drosophila melanogaster from sub-Saharan Africa.

Clines in life history traits, presumably driven by spatially varying selection, are widespread. Major latitudinal clines have been observed, for example, in Drosophila melanogaster, an ancestrally tropical insect from Africa that has colonized temperate habitats on multiple continents. Yet, how geographic factors other than latitude, such as altitude or longitude, affect life history in this species remains poorly understood. Moreover, most previous work has been performed on derived European, American and Australian populations, but whether life history also varies predictably with geography in the ancestral Afro-tropical range has not been investigated systematically. Here, we have examined life history variation among populations of D. melanogaster from sub-Saharan Africa. Viability and reproductive diapause did not vary with geography, but body size increased with altitude, latitude and longitude. Early fecundity covaried positively with altitude and latitude, whereas lifespan showed the opposite trend. Examination of genetic variance-covariance matrices revealed geographic differentiation also in trade-off structure, and QST -FST analysis showed that life history differentiation among populations is likely shaped by selection. Together, our results suggest that geographic and/or climatic factors drive adaptive phenotypic differentiation among ancestral African populations and confirm the widely held notion that latitude and altitude represent parallel gradients.

The Evolution of Modularity in the Mammalian Skull I: Morphological Integration Patterns and Magnitudes

Morphological integration refers to the modular structuring of inter-trait relationships in an organism, which could bias the direction and rate of morphological change, either constraining or facilitating evolution along certain dimensions of the morphospace. Therefore, the description of patterns and magnitudes of morphological integration and the analysis of their evolutionary consequences are central to understand the evolution of complex traits. Here we analyze morphological integration in the skull of several mammalian orders, addressing the following questions: are there common patterns of inter-trait relationships? Are these patterns compatible with hypotheses based on shared development and function? Do morphological integration patterns and magnitudes vary in the same way across groups? We digitized more than 3,500 specimens spanning 15 mammalian orders, estimated the correspondent pooled within-group correlation and variance/covariance matrices for 35 skull traits and compared those matrices among the orders. We also compared observed patterns of integration to theoretical expectations based on common development and function. Our results point to a largely shared pattern of inter-trait correlations, implying that mammalian skull diversity has been produced upon a common covariance structure that remained similar for at least 65 million years. Comparisons with a rodent genetic variance/covariance matrix suggest that this broad similarity extends also to the genetic factors underlying phenotypic variation. In contrast to the relative constancy of inter-trait correlation/covariance patterns, magnitudes varied markedly across groups. Several morphological modules hypothesized from shared development and function were detected in the mammalian taxa studied. Our data provide evidence that mammalian skull evolution can be viewed as a history of inter-module parcellation, with the modules themselves being more clearly marked in those lineages with lower overall magnitude of integration. The implication of these findings is that the main evolutionary trend in the mammalian skull was one of decreasing the constraints to evolution by promoting a more modular architecture.

The Evolution of Modularity in the Mammalian Skull II: Evolutionary Consequences

Changes in patterns and magnitudes of integration may influence the ability of a species to respond to selection. Consequently, modularity has often been linked to the concept of evolvability, but their relationship has rarely been tested empirically. One possible explanation is the lack of analytical tools to compare patterns and magnitudes of integration among diverse groups that explicitly relate these aspects to the quantitative genetics framework. We apply such framework here using the multivariate response to selection equation to simulate the evolutionary behavior of several mammalian orders in terms of their flexibility, evolvability and constraints in the skull. We interpreted these simulation results in light of the integration patterns and magnitudes of the same mammalian groups, described in a companion paper. We found that larger magnitudes of integration were associated with a blur of the modules in the skull and to larger portions of the total variation explained by size variation, which in turn can exert a strong evolutionary constraint, thus decreasing the evolutionary flexibility. Conversely, lower overall magnitudes of integration were associated with distinct modules in the skull, to smaller fraction of the total variation associated with size and, consequently, to weaker constraints and more evolutionary flexibility. Flexibility and constraints are, therefore, two sides of the same coin and we found them to be quite variable among mammals. Neither the overall magnitude of morphological integration, the modularity itself, nor its consequences in terms of constraints and flexibility, were associated with absolute size of the organisms, but were strongly associated with the proportion of the total variation in skull morphology captured by size. Therefore, the history of the mammalian skull is marked by a trade-off between modularity and evolvability. Our data provide evidence that, despite the stasis in integration patterns, the plasticity in the magnitude of integration in the skull had important consequences in terms of evolutionary flexibility of the mammalian lineages.

Comparison of factor-analytic and reduced rank models for test-day milk yield in Gyr dairy cattle (Bos indicus)

We analyzed 46,161 monthly test-day records of milk production from 7453 first lactations of crossbred dairy Gyr (Bos indicus) x Holstein cows. The following seven models were compared: standard multivariate model (M10), three reduced rank models fitting the first 2, 3, or 4 genetic principal components, and three models considering a 2-, 3-, or 4-factor structure for the genetic covariance matrix. Full rank residual covariance matrices were considered for all models. The model fitting the first two principal components (PC2) was the best according to the model selection criteria. Similar phenotypic, genetic, and residual variances were obtained with models M10 and PC2. The heritability estimates ranged from 0.14 to 0.21 and from 0.13 to 0.21 for models M10 and PC2, respectively. The genetic correlations obtained with model PC2 were slightly higher than those estimated with model M10. PC2 markedly reduced the number of parameters estimated and the time spent to reach convergence. We concluded that two principal components are sufficient to model the structure of genetic covariances between test-day milk yields. © FUNPEC-RP.

MODULARITY, NOISE, AND NATURAL SELECTION

Most biological systems are formed by component parts that are to some degree interrelated. Groups of parts that are more associated among themselves and are relatively autonomous from others are called modules. One of the consequences of modularity is that biological systems usually present an unequal distribution of the genetic variation among traits. Estimating the covariance matrix that describes these systems is a difficult problem due to a number of factors such as poor sample sizes and measurement errors. We show that this problem will be exacerbated whenever matrix inversion is required, as in directional selection reconstruction analysis. We explore the consequences of varying degrees of modularity and signal-to-noise ratio on selection reconstruction. We then present and test the efficiency of available methods for controlling noise in matrix estimates. In our simulations, controlling matrices for noise vastly improves the reconstruction of selection gradients. We also perform an analysis of selection gradients reconstruction over a New World Monkeys skull database to illustrate the impact of noise on such analyses. Noise-controlled estimates render far more plausible interpretations that are in full agreement with previous results.