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Residual Variation (residual + variation)
Selected AbstractsNumber of endemic and native plant species in the Galápagos Archipelago in relation to geographical parametersECOGRAPHY, Issue 1 2002Eske Willerslev By simple and multiple regression analyses we investigate updated species numbers of endemic and native vascular plants and seed plants in the Galápagos Archipelago in relation to geographical parameters. We find that the best models to describe species numbers are regression models with log-transformed species numbers as dependent and log-transformed modified area (i.e. area not covered with barren lava) as an independent variable. This holds both for total species number, for native species number, for endemic species number and for total number of seed plants as well as number of endemic seed plants. For the ratio between endemic and native species, modified area is also the major significant variable, but with a negative regression slope. Multiple regression models show that some isolation measures are significant contributors and may explain some of the residual variation, but their contribution to total explained variation is in general small. The results show that the species area relationships are different for native and endemic species. This is discussed in relation to classical island biogeographical models, and the concepts of radiative speciation. [source] Estimating within-field variation using a nonparametric density algorithmENVIRONMETRICS, Issue 5 2006A. Castrignanň Abstract The application of site-specific techniques and technologies in precision farming requires subdividing a field into a generally small number of contiguous homogeneous zones. The proposed algorithm of clustering is based on nonparametric density estimate, where a cluster is defined as a region surrounding a local maximum of the probability density function. Soil samples were collected in a 2-ha field of the experimental farm of the Agricultural Research Institute, located in Foggia (Southern Italy) and some of the most production-affecting soil properties were interpolated by using the geostatistical techniques of kriging and cokriging. The application of the clustering approach to the (co)kriged surface variables produced the subdivision of the field into five distinct classes. The proposed algorithm proves quite promising in identifying spatially contiguous zones, which are more homogeneous in soil properties than the whole-field. Its great advantage consists in giving an additional description of the residual variation within the class and such a piece of information is very useful in precision farming as a basis for the variable-rate application of agronomic inputs. Copyright © 2005 John Wiley & Sons, Ltd. [source] Geographic Variation in Male Sexual Signals in Strawberry Poison Frogs (Dendrobates pumilio)ETHOLOGY, Issue 9 2007Heike Pröhl In this paper, we compare the advertisement calls of 207 neotropical strawberry poison frogs (Dendrobates pumilio) collected in 21 localities along a transect from northern Costa Rica to western Panama. Populations varied most in call duration and call rate, while pulse rate and duty cycle were less variable. Multivariate analyses showed that call variation followed a cline with higher call rates, shorter calls, lower duty cycles and higher pulse rates in the southeast. Body size decreased towards the southeast and explained most variation in dominant frequency, as well as some residual variation in call rate. We conclude that a combination of geography and morphology is largely responsible for call variation within this species. Two inferred bio-acoustic groups were roughly in accordance with two genetic groups, geographically separated in central Costa Rica. However, genetic distances among populations did not co-vary with call dissimilarity after correction for geographic distances. Thus, differences in calls between genetic groups are probably mainly a result of clinal variation. These findings agree with the general observation that bio-acoustic variation is often not (highly) associated with genetic divergence. Moreover, colour polymorphism observed among Panamanian populations was not reflected in a higher variability in call parameters relative to the monomorphic Costa Rican populations. [source] PHYLOGENETIC COMPARATIVE ANALYSIS OF LIFE-HISTORY VARIATION AMONG POPULATIONS OF THE LIZARD SCELOPORUS UNDULATUS:AN EXAMPLE AND PROGNOSISEVOLUTION, Issue 3 2004Peter H. Niewiarowski Abstract Over the past 15 years, phylogenetic comparative methods (PCMs) have become standard in the study of life-history evolution. To date, most studies have focused on variation among species or higher taxonomic levels, generally revealing the presence of significant phylogenetic effects as well as residual variation potentially attributable to adaptive evolution. Recently, population-level phylogenetic hypotheses have become available for many species, making it possible to apply PCMs directly to the level at which experiments are typically used to test adaptive hypotheses. In this study, we present the results of PCMs applied to life-history variation among populations of the widespread and well-studied lizard Sceloporus undulatus. Using S. undulatus (which may represent four closely related species) as an example, we explore the benefits of using PCMs at the population level, as well as consider the importance of several thorny methodological problems including but not limited to nonindependence of populations, lack of sufficient variation in traits, and the typically small sample sizes dictated by the difficulty of collecting detailed demographic data. We show that phylogenetic effects on life-history variation among populations of S. undulatus appear to be unimportant, and that several classic trade-offs expected by theory and revealed by many interspecific comparisons are absent. Our results suggest that PCMs applied to variation in life-history traits below the species level may be of limited value, but more studies like ours are needed to draw a general conclusion. Finally, we discuss several outstanding problems that face studies seeking to apply PCMs below the species level. [source] Hierarchical patterns of invertebrate assemblage structure in stony upland streams change with time and flow permanenceFRESHWATER BIOLOGY, Issue 6 2005B. J. ROBSON Summary 1. Studies in several parts of the world have examined variation in univariate descriptors of macroinvertebrate assemblage structure in perennially flowing stony streams across hierarchies of spatial scale using nested analyses of variance. However, few have investigated whether this spatial variation changes with time or whether these results are representative of habitats other than riffles or of other stream types, such as intermittently flowing streams. 2. We describe patterns in taxon richness and abundance from two sets of samples from stony streams in the Otway Range and the Grampians Range, Victoria, Australia, collected using hierarchical designs. Sampling of riffles was repeated in the Otways, to determine whether spatial patterns were consistent among times. In the Grampians, spatial patterns were compared between intermittent and perennially flowing streams (stream type) by sampling pools. 3. In the Otways streams, most variation in the dependent variables occurred between sample units. Patterns of variation among the other scales (streams, segments, riffles, groups of stones) were not consistent between sampling times, suggesting that they may have little ecological significance. 4. In the Grampians streams, variation in macroinvertebrate taxon richness and abundance differed significantly between replicate streams within each stream type but not between stream types or pools. The largest source of variation in taxon richness was stream type. Little variation occurred among sample units. 5. The pattern of most variation occurring among sample units is robust both to differences in the method of sampling and different dependent variables among studies and increasingly appears to be a property of riffles in stony, perennial upland streams. High variation among sample units (residual variation) limits the explanatory power of linear models and therefore, where samples are from a single sampling time, small but significant components of variation are unlikely to represent features of assemblage structure that will be stable over time. [source] Maximum likelihood fitting using ordinary least squares algorithms,JOURNAL OF CHEMOMETRICS, Issue 8-10 2002Rasmus Bro Abstract In this paper a general algorithm is provided for maximum likelihood fitting of deterministic models subject to Gaussian-distributed residual variation (including any type of non-singular covariance). By deterministic models is meant models in which no distributional assumptions are valid (or applied) on the parameters. The algorithm may also more generally be used for weighted least squares (WLS) fitting in situations where either distributional assumptions are not available or other than statistical assumptions guide the choice of loss function. The algorithm to solve the associated problem is called MILES (Maximum likelihood via Iterative Least squares EStimation). It is shown that the sought parameters can be estimated using simple least squares (LS) algorithms in an iterative fashion. The algorithm is based on iterative majorization and extends earlier work for WLS fitting of models with heteroscedastic uncorrelated residual variation. The algorithm is shown to include several current algorithms as special cases. For example, maximum likelihood principal component analysis models with and without offsets can be easily fitted with MILES. The MILES algorithm is simple and can be implemented as an outer loop in any least squares algorithm, e.g. for analysis of variance, regression, response surface modeling, etc. Several examples are provided on the use of MILES. Copyright © 2002 John Wiley & Sons, Ltd. [source] Selection, structure and the heritability of behaviourJOURNAL OF EVOLUTIONARY BIOLOGY, Issue 2 2002D. G. Stirling Characters which are closely linked to fitness often have low heritabilities (VA/VP). Low heritabilities could be because of low additive genetic variation (VA), that had been depleted by directional selection. Alternatively, low heritabilities may be caused by large residual variation (VR=VP , VA) compounded at a disproportionately higher rate than VA across integrated characters. Both hypotheses assume that each component of quantitative variation has an independent effect on heritability. However, VA and VR may also covary, in which case differences in heritability cannot be fully explained by the independent effects of elimination-selection or compounded residual variation. We compared the central tendency of published behavioural heritabilities (mean=0.31, median=0.23) with morphological and life history data collected by Mousseau & Roff (1987). Average behavioural heritability was not significantly different from average life history heritability, but both were smaller than average morphological heritability. We cross-classified behavioural traits to test whether variation in heritability was related to selection (dominance, domestic/wild) or variance compounding (integration level). There was a significant three-way interaction between indices of selection and variance compounding, related to the absence of either effect at the highest integration level. At lower integration levels, high dominance variance indicated effects of selection. It was also indicated by the low CVA of domestic species. At the same time CVR increased disproportionately faster than CVA across integration levels, demonstrating variance compounding. However, neither CVR nor CVA had a predominant effect on heritability. The partial regression coefficients of CVR and CVA on heritability were similar and a path analysis indicated that their (positive) correlation was also necessary to explain variation in heritability. These results suggest that relationships between additive genetic and residual components of quantitative genetic variation can constrain their independent direct effects on behavioural heritability. [source] Non-Parametric Ecological Regression and Spatial VariationBIOMETRICAL JOURNAL, Issue 6 2003Isabel Natário Abstract Ecological studies aim to analyse the variation of disease risk in relation to exposure variables that are measured at an area unit level. In practice it is rarely possible to use the exposure variables themselves, either because the corresponding data are not available or because the causes of the disease are not fully understood. It is therefore quite common to use crude proxies of the real exposure to the disease in question. These proxies are rarely able to explain the disease variation and hence additional area level random effects are introduced to account for the residual variation. In this paper we investigate the possibility to model the effect of ecological covariates non-parametrically, with and without additional random effects for the residual spatial variation. We illustrate the issues arising through analyses of simulated and real data on larynx cancer mortality in Germany, during the years of 1986 to 1990, where we use the corresponding lung cancer rates as a proxy for smoking consumption. [source] Covariate Adjustment and Ranking Methods to Identify Regions with High and Low Mortality RatesBIOMETRICS, Issue 2 2010Huilin Li Summary Identifying regions with the highest and lowest mortality rates and producing the corresponding color-coded maps help epidemiologists identify promising areas for analytic etiological studies. Based on a two-stage Poisson,Gamma model with covariates, we use information on known risk factors, such as smoking prevalence, to adjust mortality rates and reveal residual variation in relative risks that may reflect previously masked etiological associations. In addition to covariate adjustment, we study rankings based on standardized mortality ratios (SMRs), empirical Bayes (EB) estimates, and a posterior percentile ranking (PPR) method and indicate circumstances that warrant the more complex procedures in order to obtain a high probability of correctly classifying the regions with the upper,100,%,and lower,100,%,of relative risks for,,= 0.05, 0.1, and 0.2. We also give analytic approximations to the probabilities of correctly classifying regions in the upper,100,%,of relative risks for these three ranking methods. Using data on mortality from heart disease, we found that adjustment for smoking prevalence has an important impact on which regions are classified as high and low risk. With such a common disease, all three ranking methods performed comparably. However, for diseases with smaller event counts, such as cancers, and wide variation in event counts among regions, EB and PPR methods outperform ranking based on SMRs. 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