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In grassland ecosystems, it is well known that increasing plant species diversity can improve ecosystem functions (i.e., ecosystem responses), for example, by increasing productivity and reducing weed invasion. Diversity-Interactions models use species proportions and their interactions as predictors in a regression framework to assess biodiversity and ecosystem function relationships. However, it can be difficult to model numerous interactions if there are many species, and interactions may be temporally variable or dependent on spatial planting patterns. We developed a new Diversity-Interactions mixed model for jointly assessing many species interactions and within-plot species planting pattern over multiple years. We model pairwise interactions using a small number of fixed parameters that incorporate spatial effects and supplement this by including all pairwise interaction variables as random effects, each constrained to have the same variance within each year. The random effects are indexed by pairs of species within plots rather than a plot-level factor as is typical in mixed models, and capture remaining variation due to pairwise species interactions parsimoniously. We apply our novel methodology to three years of weed invasion data from a 16-species grassland experiment that manipulated plant species diversity and spatial planting pattern and test its statistical properties in a simulation study.Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

The aim of this study was to compare the covariance structures by using Maximum Likelihood (ML), Restricted Maximum Likelihood (REML) and Minimum Variance Quadratic Unbiased Estimator (MIVQUE) in the estimation methods in repeated measures design with mixed model approach. In the study, live weight (birth, 30th, 60th, 90th, 120th day) values of 60 head Kilis goats from birth to 120 days old were used as research data. For the purpose of evaluate of the relationship among the data, Compound symmetry (CS), Variance components (VC), (First-order autoregressive (AR(1)), Unstructured (UN), Toeplitz (TOEP), Heterogenous compound symetry (CSH), Heterogenous first-order autoregressive (ARH(1)), Heterogenous toeplitz (TOEPH), First-Order Autoregressive Moving-Avarege (ARMA(1,1)), Toeplitz With Two Bands (TOEP(2)), First-order factor analytic (FA(1)), Equal Diagonal Factor Analytic (FA1(1)), Unstructured correlations (UNR), Banded Unstructured (UN(1)), Ante-Depence (ANTE(1)) covariance structures were used. The most appropriate covariance structure was selected according to 2Ln(L), AIC, AICC and BIC information criteria in modeling the relationship between data in all three estimation methods (ML, REML and MIVQUE0), UN and UNR covariance structures were determined as the most appropriate covariance structures, although they gave the same results. [ABSTRACT FROM AUTHOR]

A multivariate count model is developed by introducing a simple and practical formula. The formulation begins with a modification of the standard ordered response model to adopt the count outcomes nature. This modification is accomplished by introducing a non-linear asymmetric interdependence structure among the error terms using the copula-based model. To avoid simulation maximum-likelihood for evaluating the multi-outcome density, we utilize the composite marginal likelihood (CML) approach. The proposed copula-based model with the CML approach allows for asymmetric (tail) dependency without a need for a simulation mechanism. Non-parametric graphical techniques with the empirical copula as well as conventional goodness-of-fit statistics are utilized to guide copula selection. In addition, unobserved heterogeneity across observations is also addressed through a heterogeneous dispersion parameter in the proposed model. The heterogeneous dispersion parameter model is a suitable alternative to random parameter count models in that captures heterogeneity in variance, while allowing for closed form while the latter needs numerical integration or simulation. We apply these techniques to study the interdependence structure among four types of traffic crashes using three years (2005–2007) of cross-sectional crash data record for 274 multilane freeway segments in the State of Washington, USA. These four categories of crash types are the rear end; sideswipe; fixed objects and other crash types. The empirical results show a significant presence of unobserved heterogeneous dependency across these types of crashes. The results indicate the important role of unobserved heterogeneity in variance and covariance structure estimation. An important outcome of this result is that it can affect inference on the relative impact of roadway geometrics on crash occurrence. For example, we find that horizontal curve related parameters on freeway segments substantially increase the joint likelihood of rear-end, sideswipe, fixed objects and other crash types, when compared to the characteristics of vertical curves. [ABSTRACT FROM AUTHOR]

Quaternary environmental changes substantially impacted the landscape and promoted rapid evolutionary changes in many species; however, analyses of adaptive phenotypic variation in plants have usually neglected the underlying historical context. Here, we associate phylogeography and phenotypic evolution by analysing the divergence of Calceolaria polyrhiza multivariate floral phenotype after a Pleistocene post-glacial expansion in Patagonia. Phenotypic matrix ( P) properties (size, shape, orientation and phenotypic integration) of six refugium and six recent populations from two different phylogroups were compared following different approaches. We found that P-matrix shape and orientation remained stable despite the strong phylogeographic footprint of post-glacial expansion. However, average proportional reductions in matrix size supported the expectation that drift had a significant effect on the floral phenotype in the northern phylogroup. When phylogeographic history was not included in the analyses, the results overestimated phenotypic differences, whereas under explicit phylogeographic control, drift appeared as the best explanation for matrix differences. In general, recent populations showed a larger phenotypic divergence among them, but a lower overall phenotypic variation than refugium populations. Random Skewers analyses indicated a lower potential response to selection in recently colonized populations than in refugium populations. We discuss that the combination of phylogeographic analyses with geographical distribution of functional phenotypic (genotypic) variation is critical not only to understand how historical effects influence adaptive evolution, but also to improve field comparisons in evolutionary ecology studies. [ABSTRACT FROM AUTHOR]

Environmental perturbations of many kinds influence growth and development. Little is known, however, about the influence of environmental factors on the patterns of phenotypic integration observed in complex morphological traits. We analyze the changes in phenotypic variance-covariance structure of the rat skull throughout the early postnatal ontogeny (from birth to weaning) and evaluate the effect of intrauterine growth retardation (IUGR) on this structure. Using 2D coordinates taken from lateral radiographs obtained every 4 days, from birth to 21 days old, we show that the pattern of covariance is temporally dynamic from birth to 21 days. The environmental perturbation provoked during pregnancy altered the skull growth, and reduced the mean size of the IUGR group. These environmental effects persisted throughout lactancy, when the mothers of both groups received a standard diet. More strikingly, the effect grew larger beyond this point. Altering environmental conditions did not affect all traits equally, as revealed by the low correlations between covariance matrices of treatments at the same age. Finally, we found that the IUGR treatment increased morphological integration as measured by the scaled variance of eigenvalues. This increase coincided and is likely related to an increase in morphological variance in this group. This result is expected if somatic growth is a major determinant of covariance structure of the skull. In summary, our findings suggest that environmental perturbations experienced in early ontogeny alter fundamental developmental processes and are an important factor in shaping the variance-covariance structure of complex phenotypic traits. [ABSTRACT FROM AUTHOR]

• Floral integration has been deemed an adaptation to increase the benefits of animal pollination, yet no attempts have been made to estimate its adaptive value under natural conditions. • Here, the variation in the magnitude and pattern of phenotypic floral integration and the variance–covariance structure of floral traits in four species of Rosaceae were examined. The intensity of natural selection acting on floral phenotypic integration was also estimated and the available evidence regarding the magnitude of floral integration reviewed. • The species studied had similar degrees of floral integration, although significant differences were observed in their variance–covariance structure. Selection acted on subsets of floral traits (i.e. selection on intrafloral integration) rather than on the integration of the whole flower. Average integration was 20% and similar to the estimated mean value of flowering plants. • The review indicated that flowering plants present lower integration than expected by chance. Numerical simulations suggest that this pattern may result from selection favouring intrafloral integration. Phenotypic integration at the flower level seems to have a low adaptive value among the species surveyed. Moreover, it is proposed that pollinator-mediated selection promotes the evolution of intrafloral integration. [ABSTRACT FROM AUTHOR]

This paper focuses on modeling unobserved effects in route-switching dynamics under advanced traveler information systems (ATIS). The analysis explicitly accounts for the presence of heterogeneity in behavior and a general stochastic pattern for the unobservables. The dynamic kernel logit (DKL) framework (also referred to as dynamic mixed logit) is proposed and applied to model route-switching dynamics (with 55 repeated decisions per user), based on data from interactive simulator experiments. In contrast to the multinomial probit framework, the DKL is well-suited for calibrating dynamic travel behavior models with a large number of panel periods. To increase computational efficiency, the proposed formulation exploits a components of variance scheme to represent the correlation of error-terms (both within-day and day-to-day).The empirical results indicate that unobserved effects account significantly for the observed variability in route-switching behavior. Among the observed effects, users’ route-switching behavior is influenced by the nature, timeliness, and extent of real-time information, as also its quality. In addition, route switching is influenced by the level-of-service attributes on the alternative routes and users’ prior traffic experience. Among the unobserved effects, the results present evidence of considerable heterogeneity in route switching. The significance of experience variables, and the correlation of unobservables over time and within-day, indicate the presence of dynamic learning and adjustment processes in user behavior under ATIS. Although observed and unobserved preference and response heterogeneity are all significant, the largest improvement in model fit is achieved by incorporating observed heterogeneity followed by unobserved preference and response heterogeneity respectively. These findings have significant applications in route assignment models under information, design and evaluation of ATIS products and services, and assessment of various policy measures aimed at travel demand management. [Copyright &y& Elsevier]