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Variance-covariance Matrix (variance-covariance + matrix)
Selected AbstractsEPISTASIS AND THE TEMPORAL CHANGE IN THE ADDITIVE VARIANCE-COVARIANCE MATRIX INDUCED BY DRIFTEVOLUTION, Issue 8 2004Carlos López-Fanjul Abstract The effect of population bottlenecks on the components of the genetic covariance generated by two neutral independent epistatic loci has been studied theoretically (additive, covA; dominance, covD; additive-by-additive, covAA; additive-by-dominance, covAD; and dominance-by-dominance, covDD). The additive-by-additive model and a more general model covering all possible types of marginal gene action at the single-locus level (additive/dominance epistatic model) were considered. The covariance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium over replicates randomly derived from the base population, after t consecutive bottlenecks of equal size N (derived components). Formulae were obtained in terms of the allele frequencies and effects at each locus, the corresponding epistatic effects and the inbreeding coefficient Ft. These expressions show that the contribution of nonadditive loci to the derived additive covariance (covAt) does not linearly decrease with inbreeding, as in the pure additive case, and may initially increase or even change sign in specific situations. Numerical examples were also analyzed, restricted for simplicity to the case of all covariance components being positive. For additive-by-additive epistasis, the condition covAt > covA only holds for high frequencies of the allele decreasing the metric traits at each locus (negative allele) if epistasis is weak, or for intermediate allele frequencies if it is strong. For the additive/dominance epistatic model, however, covAt > covA applies for low frequencies of the negative alleles at one or both loci and mild epistasis, but this result can be progressively extended to intermediate frequencies as epistasis becomes stronger. Without epistasis the same qualitative results were found, indicating that marginal dominance induced by epistasis can be considered as the primary cause of an increase of the additive covariance after bottlenecks. For all models, the magnitude of the ratio covAt/covA was inversely related to N and t. [source] INTERPRETATION OF THE RESULTS OF COMMON PRINCIPAL COMPONENTS ANALYSESEVOLUTION, Issue 3 2002David Houle Abstract Common principal components (CPC) analysis is a new tool for the comparison of phenotypic and genetic variance-covariance matrices. CPC was developed as a method of data summarization, but frequently biologists would like to use the method to detect analogous patterns of trait correlation in multiple populations or species. To investigate the properties of CPC, we simulated data that reflect a set of causal factors. The CPC method performs as expected from a statistical point of view, but often gives results that are contrary to biological intuition. In general, CPC tends to underestimate the degree of structure that matrices share. Differences of trait variances and covariances due to a difference in a single causal factor in two otherwise identically structured datasets often cause CPC to declare the two datasets unrelated. Conversely, CPC could identify datasets as having the same structure when causal factors are different. Reordering of vectors before analysis can aid in the detection of patterns. We urge caution in the biological interpretation of CPC analysis results. [source] A SPATIAL CLIFF-ORD-TYPE MODEL WITH HETEROSKEDASTIC INNOVATIONS: SMALL AND LARGE SAMPLE RESULTS,JOURNAL OF REGIONAL SCIENCE, Issue 2 2010Irani Arraiz ABSTRACT In this paper, we specify a linear Cliff-and-Ord-type spatial model. The model allows for spatial lags in the dependent variable, the exogenous variables, and disturbances. The innovations in the disturbance process are assumed to be heteroskedastic with an unknown form. We formulate multistep GMM/IV-type estimation procedures for the parameters of the model. We also give the limiting distributions for our suggested estimators and consistent estimators for their asymptotic variance-covariance matrices. We conduct a Monte Carlo study to show that the derived large-sample distribution provides a good approximation to the actual small-sample distribution of our estimators. [source] MULTIVARIATE QUANTITATIVE GENETICS AND THE LEK PARADOX: GENETIC VARIANCE IN MALE SEXUALLY SELECTED TRAITS OF DROSOPHILA SERRATA UNDER FIELD CONDITIONSEVOLUTION, Issue 12 2004Emma Hine Abstract Single male sexually selected traits have been found to exhibit substantial genetic variance, even though natural and sexual selection are predicted to deplete genetic variance in these traits. We tested whether genetic variance in multiple male display traits of Drosophila serrata was maintained under field conditions. A breeding design involving 300 field-reared males and their laboratory-reared offspring allowed the estimation of the genetic variance-covariance matrix for six male cuticular hydrocarbons (CHCs) under field conditions. Despite individual CHCs displaying substantial genetic variance under field conditions, the vast majority of genetic variance in CHCs was not closely associated with the direction of sexual selection measured on field phenotypes. Relative concentrations of three CHCs correlated positively with body size in the field, but not under laboratory conditions, suggesting condition-dependent expression of CHCs under field conditions. Therefore condition dependence may not maintain genetic variance in preferred combinations of male CHCs under field conditions, suggesting that the large mutational target supplied by the evolution of condition dependence may not provide a solution to the lek paradox in this species. Sustained sexual selection may be adequate to deplete genetic variance in the direction of selection, perhaps as a consequence of the low rate of favorable mutations expected in multiple trait systems. [source] EVOLUTION AND STABILITY OF THE G-MATRIX ON A LANDSCAPE WITH A MOVING OPTIMUMEVOLUTION, Issue 8 2004Adam G. Jones Abstract In quantitative genetics, the genetic architecture of traits, described in terms of variances and covariances, plays a major role in determining the trajectory of evolutionary change. Hence, the genetic variance-covariance matrix (G-matrix) is a critical component of modern quantitative genetics theory. Considerable debate has surrounded the issue of G-matrix constancy because unstable G-matrices provide major difficulties for evolutionary inference. Empirical studies and analytical theory have not resolved the debate. Here we present the results of stochastic models of G-matrix evolution in a population responding to an adaptive landscape with an optimum that moves at a constant rate. This study builds on the previous results of stochastic simulations of G-matrix stability under stabilizing selection arising from a stationary optimum. The addition of a moving optimum leads to several important new insights. First, evolution along genetic lines of least resistance increases stability of the orientation of the G-matrix relative to stabilizing selection alone. Evolution across genetic lines of least resistance decreases G-matrix stability. Second, evolution in response to a continuously changing optimum can produce persistent maladaptation for a correlated trait, even if its optimum does not change. Third, the retrospective analysis of selection performs very well when the mean G-matrix (,) is known with certainty, indicating that covariance between G and the directional selection gradient (3 is usually small enough in magnitude that it introduces only a small bias in estimates of the net selection gradient. Our results also show, however, that the contemporary ,-matrix only serves as a rough guide to ,. The most promising approach for the estimation of G is probably through comparative phylogenetic analysis. Overall, our results show that directional selection actually can increase stability of the G-matrix and that retrospective analysis of selection is inherently feasible. One ?riajor remaining challenge is to gain a sufficient understanding of the G-matrix to allow the confident estimation of ,. [source] CONSTANCY OF THE G MATRIX IN ECOLOGICAL TIMEEVOLUTION, Issue 6 2004Mats BjÖrklund Abstract The constancy of the genetic variance-covariance matrix (G matrix) across environments and populations has been discussed and tested empirically over the years but no consensus has so far been reached. In this paper, I present a model in which morphological traits develop hierarchically, and individuals differ in their resource allocation and acquisition patterns. If the variance in resource acquisition is many times larger than the variance in resource allocation then strong genetic correlations are expected, and with almost isometric relations among traits. As the variation in resource acquisition decreases below a certain threshold, the correlations decrease overall and the relations among traits become a function of the allocation patterns, and in particular reflecting the basal division of allocation. A strong bottleneck can break a pattern of strong genetic correlation, but this effect diminishes rapidly with increasing bottleneck size. This model helps to understand why some populations change their genetic correlations in different environments, whereas others do not, since the key factor is the relation between the variances in resource acquisition and allocation. If a change in environment does not lead to a change in this ratio, no change can be expected, whereas if the ratio is changed substantially then major changes can be expected. This model can also help to understand the constancy of morphological patterns within larger taxa as a function of constancy in resource acquisition patterns over time and environments. When this pattern breaks, for example on islands, larger changes can be expected. [source] MODFLOW 2000 Head Uncertainty, a First-Order Second Moment MethodGROUND WATER, Issue 3 2003Harry S. Glasgow A computationally efficient method to estimate the variance and covariance in piezometric head results computed through MODFLOW 2000 using a first-order second moment (FOSM) approach is presented. This methodology employs a first-order Taylor series expansion to combine model sensitivity with uncertainty in geologic data. MOD-FLOW 2000 is used to calculate both the ground water head and the sensitivity of head to changes in input data. From a limited number of samples, geologic data are extrapolated and their associated uncertainties are computed through a conditional probability calculation. Combining the spatially related sensitivity and input uncertainty produces the variance-covariance matrix, the diagonal of which is used to yield the standard deviation in MODFLOW 2000 head. The variance in piezometric head can be used for calibrating the model, estimating confidence intervals, directing exploration, and evaluating the reliability of a design. A case study illustrates the approach, where aquifer transmis-sivity is the spatially related uncertain geologic input data. The FOSM methodology is shown to be applicable for calculating output uncertainty for (1) spatially related input and output data, and (2) multiple input parameters (trans-missivity and recharge). [source] Exploratory second-order analyses for components and factorsJAPANESE PSYCHOLOGICAL RESEARCH, Issue 1 2002Haruhiko Ogasawara Abstract: Exploratory methods using second-order components and second-order common factors were proposed. The second-order components were obtained from the resolution of the correlation matrix of obliquely rotated first-order principal components. The standard errors of the estimates of the second-order component loadings were derived from an augmented information matrix with restrictions for the loadings and associated parameters. The second-order factor analysis proposed was similar to the classical method in that the factor correlations among the first-order factors were further resolved by the exploratory method of factor analysis. However, in this paper the second-order factor loadings were estimated by the generalized least squares using the asymptotic variance-covariance matrix for the first-order factor correlations. The asymptotic standard errors for the estimates of the second-order factor loadings were also derived. A numerical example was presented with simulated results. [source] Do counter-cyclical payments in the 2002 US Farm Act create incentives to produce?,AGRICULTURAL ECONOMICS, Issue 2-3 2004Jesús Antón Abstract Analytical results in the literature suggest that counter-cyclical payments create risk-related incentives to produce even if they are ,decoupled' under certainty [Hennessy, D. A., 1998. The production effects of agricultural income support polices under uncertainty. Am. J. Agric. Econ. 80, 46,57]. This paper develops a framework to assess the risk-related incentives to produce created by commodity programmes like the loan deficiency payments (LDPs) and the counter-cyclical payments (CCPs) in the 2002 US Farm Act. Because CCPs are paid based on fixed production quantities they have a weaker risk-reducing impact than LDPs. The latter have a direct impact through the variance of the producer price distributions, while the impact of CCPs is due only to the covariance between the CCP and the producer price distributions. The methodology developed by [Chavas, J.-P., Holt, M. T., 1990. Acreage decisions under risk: the case of corn and soybeans. Am. J. Agric. Econ. 72 (3), 529,538] is applied to calculate the appropriate variance-covariance matrix of the truncated producer price distributions under the 2002 Farm Act. Risk premia are computed showing that the risk-related incentives created by CCPs are significant and do not disappear for levels of production above the base production on which CCPs are paid. [source] Mixed-effects models in psychophysiologyPSYCHOPHYSIOLOGY, Issue 1 2000Emilia Bagiella The current methodological policy in Psychophysiology stipulates that repeated-measures designs be analyzed using either multivariate analysis of variance (ANOVA) or repeated-measures ANOVA with the Greenhouse,Geisser or Huynh,Feldt correction. Both techniques lead to appropriate type I error probabilities under general assumptions about the variance-covariance matrix of the data. This report introduces mixed-effects models as an alternative procedure for the analysis of repeated-measures data in Psychophysiology. Mixed-effects models have many advantages over the traditional methods: They handle missing data more effectively and are more efficient, parsimonious, and flexible. We described mixed-effects modeling and illustrated its applicability with a simple example. [source] | ||||||||||