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A common effect size metric used to quantify the outcome of experiments for ecological meta-analysis is the response ratio (RR): the log proportional change in the means of a treatment and control group. Estimates of the variance of RR are also important for meta-analysis because they serve as weights when effect sizes are averaged and compared. The variance of an effect size is typically a function of sampling error; however, it can also be influenced by study design. Here, I derive new variances and covariances for RR for several often-encountered experimental designs: when the treatment and control means are correlated; when multiple treatments have a common control; when means are based on repeated measures; and when the study has a correlated factorial design, or is multivariate. These developments are useful for improving the quality of data extracted from studies for meta-analysis and help address some of the common challenges meta-analysts face when quantifying a diversity of experimental designs with the response ratio.

The G-matrix summarizes the inheritance of multiple, phenotypic traits. The stability and evolution of this matrix are important issues because they affect our ability to predict how the phenotypic traits evolve by selection and drift. Despite the centrality of these issues, comparative, experimental, and analytical approaches to understanding the stability and evolution of the G-matrix have met with limited success. Nevertheless, empirical studies often find that certain structural features of the matrix are remarkably constant, suggesting that persistent selection regimes or other factors promote stability. On the theoretical side, no one has been able to derive equations that would relate stability of the G-matrix to selection regimes, population size, migration, or to the details of genetic architecture. Recent simulation studies of evolving G-matrices offer solutions to some of these problems, as well as a deeper, synthetic understanding of both the G-matrix and adaptive radiations.

A flexible approach for geometric modelling of point clouds obtained from Terrestrial Laser Scanning (TLS) is by means of B-splines. These functions have gained some popularity in the engineering geodesy as they provide a suitable basis for a spatially continuous and parametric deformation analysis. In the predominant studies on geometric modelling of point clouds by B-splines, uncorrelated and equally weighted measurements are assumed. Trying to overcome this, the elementary errors theory is applied for establishing fully populated covariance matrices of TLS observations that consider correlations in the observed point clouds. In this article, a systematic approach for establishing realistic synthetic variance–covariance matrices (SVCMs) is presented and afterward used to model TLS point clouds by B-splines. Additionally, three criteria are selected to analyze the impact of different SVCMs on the functional and stochastic components of the estimation results. Plausible levels for variances and covariances are obtained using a test specimen of several dm—dimension. It is used to identify the most dominant elementary errors under laboratory conditions. Starting values for the variance level are obtained from a TLS calibration. The impact of SVCMs with different structures and different numeric values are comparatively investigated. Main findings of the paper are that for the analyzed object size and distances, the structure of the covariance matrix does not significantly affect the location of the estimated surface control points, but their precision in terms of the corresponding standard deviations. Regarding the latter, properly setting the main diagonal terms of the SVCM is of superordinate importance compared to setting the off-diagonal ones. The investigation of some individual errors revealed that the influence of their standard deviation on the precision of the estimated parameters is primarily dependent on the scanning distance. When the distance stays the same, one-sided influences on the precision of the estimated control points can be observed with an increase in the standard deviations.

The recent demographic transitions to lower mortality and fertility rates in most human societies have led to changes and even quick reversals in phenotypic selection pressures. This can only result in evolutionary change if the affected traits are heritable, but changes in environmental conditions may also lead to subsequent changes in the genetic variance and covariance (the G matrix) of traits. It currently remains unclear if there have been concomitant changes in the G matrix of life-history traits following the demographic transition. Using 300 years of genealogical data from Finland, we found that four key life-history traits were heritable both before and after the demographic transition. The estimated heritabilities allow a quantifiable genetic response to selection during both time periods, thus facilitating continued evolutionary change. Further, the G matrices remained largely stable but revealed a trend for an increased additive genetic variance and thus evolutionary potential of the population after the transition. Our results demonstrate the validity of predictions of evolutionary change in human populations even after the recent dramatic environmental change, and facilitate predictions of how our biology interacts with changing environments, with implications for global public health and demography.

Metamorphosis is common in animals, yet the genetic associations between life cycle stages are poorly understood. Given the radical changes that occur at metamorphosis, selection may differ before and after metamorphosis, and the extent that genetic associations between pre- and post-metamorphic traits constrain evolutionary change is a subject of considerable interest. In some instances, metamorphosis may allow the genetic decoupling of life cycle stages, whereas in others, metamorphosis could allow complementary responses to selection across the life cycle. Using a diallel breeding design, we measured viability at four ontogenetic stages (embryo, larval, juvenile and adult viability), in the ascidian Ciona intestinalis and examined the orientation of additive genetic variation with respect to the metamorphic boundary. We found support for one eigenvector of G (gobsmax), which contrasted larval viability against embryo viability and juvenile viability. Target matrix rotation confirmed that while gobsmax shows genetic associations can extend beyond metamorphosis, there is still considerable scope for decoupled phenotypic evolution. Therefore, although genetic associations across metamorphosis could limit that range of phenotypes that are attainable, traits on either side of the metamorphic boundary are capable of some independent evolutionary change in response to the divergent conditions encountered during each life cycle stage.

The evolutionary response to selection depends on the distribution of genetic variation in traits under selection within populations, as defined by the additive genetic variance-covariance matrix (G). The structure and evolutionary stability of G will thus influence the course of phenotypic evolution. However, there are few studies assessing the stability of G and its relationship with population divergence within foundation tree species. We compared the G-matrices of Mainland and Island population groups of the forest tree Eucalyptus globulus, and determined the extent to which population divergence aligned with within-population genetic (co)variation. Four key wood property traits exhibiting signals of divergent selection were studied—wood density, extractive content, and lignin content and composition. The comparison of G-matrices of the mainland and island populations indicated that the G-eigenstructure was relatively well preserved at an intra-specific level. Population divergence tended to occur along a major direction of genetic variation in G. The observed conservatism of G, the moderate evolutionary timescale, and close relationship between genetic architecture and population trajectories suggest that genetic constraints may have influenced the evolution and diversification of the E. globulus populations for the traits studied. However, alternative scenarios, including selection aligning genetic architecture and population divergence, are discussed.

Structural equation modeling (SEM) is a powerful statistical approach for the testing of networks of direct and indirect theoretical causal relationships in complex data sets with intercorrelated dependent and independent variables. SEM is commonly applied in ecology, but the spatial information commonly found in ecological data remains difficult to model in a SEM framework. Here we propose a simple method for spatially explicit SEM (SE-SEM) based on the analysis of variance/covariance matrices calculated across a range of lag distances. This method provides readily interpretable plots of the change in path coefficients across scale and can be implemented using any standard SEM software package. We demonstrate the application of this method using three studies examining the relationships between environmental factors, plant community structure, nitrogen fixation, and plant competition. By design, these data sets had a spatial component, but were previously analyzed using standard SEM models. Using these data sets, we demonstrate the application of SE-SEM to regularly spaced, irregularly spaced, and ad hoc spatial sampling designs and discuss the increased inferential capability of this approach compared with standard SEM. We provide an R package, sesem, to easily implement spatial structural equation modeling.

1. Functional variability (FV) of populations can be decomposed into three main features: the individual variability of multiple traits, the strength of correlations between those traits and the main direction of these correlations, the latter two being known as 'phenotypic integration'. Evolutionary biology has long recognized that FV in natural populations is key to determining potential evolutionary responses, but this topic has been little studied in functional ecology. 2. Here, we focus on the arctico-alpine perennial plant species Polygonum viviparum L.. We used a comprehensive sampling of seven functional traits in 29 wild populations covering the whole environmental niche of the species. The niche of the species was captured by a temperature gradient, which separated alpine stressful habitats from species-rich, competitive subalpine ones. We sought to assess the relative roles of abiotic stress and biotic interactions in shaping different aspects of functional variation within and among populations, that is, the multi-trait variability, the strength of correlations between traits and the main directions of functional trade-offs. 3. Populations with the highest extent of functional variability were found in the warm end of the gradient, whereas populations exhibiting the strongest degree of phenotypic integration were located in sites with intermediate temperatures. This could reveal both the importance of environmental filtering and population demography in structuring FV. Interestingly, we found that the main axes of multivariate functional variation were radically different within and across population. 4. Although the proximate causes of FV structure remain uncertain, our study presents a robust methodology for the quantitative study of functional variability in connection with species' niches. It also opens up new perspectives for the conceptual merging of intraspecific functional patterns with community ecology.

The adaptive landscape and the G-matrix are keys concepts for understanding how quantitative characters evolve during adaptive radiation. In particular, whether the adaptive landscape can drive convergence of phenotypic integration (i.e., the pattern of phenotypic variation and covariation summarized in the P-matrix) is not well studied. We estimated and compared P for 19 morphological traits in eight species of Caribbean Anolis lizards, finding that similarity in P among species was not correlated with phylogenetic distance. However, greater similarity in P among ecologically similar Anolis species (i.e., the trunk-ground ecomorph) suggests the role of convergent natural selection. Despite this convergence and relatively deep phylogenetic divergence, a large portion of eigenstructure of P is retained among our eight focal species. We also analyzed P as an approximation of G to test for correspondence with the pattern of phenotypic divergence in 21 Caribbean Anolis species. These patterns of covariation were coincident, suggesting that either genetic constraint has influenced the pattern of among-species divergence or, alternatively, that the adaptive landscape has influenced both G and the pattern of phenotypic divergence among species. We provide evidence for convergent evolution of phenotypic integration for one class of Anolis ecomorph, revealing yet another important dimension of evolutionary convergence in this group.

Measurements of the genetic variation and covariation underlying quantitative traits are crucial to our understanding of current evolutionary change and the mechanisms causing this evolution. This fact has spurred a large number of studies estimating heritabilities and genetic correlations in a variety of organisms. Most of these studies have been done in laboratory or greenhouse settings, but it is not well known how accurately these measurements estimate genetic variance and covariance expressed in the field. We conducted a quantitative genetic half‐sibling analysis on six floral traits in wild radish. Plants were grown from seed in the field and were exposed to natural environmental variation throughout their lives, including herbivory and intra‐ and interspecific competition. The estimates of heritabilities and the additive genetic variance‐covariance matrix (G) obtained from this analysis were then compared to previous greenhouse estimates of the same floral traits from the same natural population. Heritabilities were much lower in the field for all traits, and this was due to both large increases in environmental variance and decreases in additive genetic variance. Additive genetic covariance expressed was also much lower in the field. These differences resulted in highly significant differences in the G matrix between the greenhouse and field environments using two complementary testing methods. Although the G matrices shared some principal components in common, they were not simply proportional to each other. Therefore, the greenhouse results did not accurately depict how the floral traits would respond to natural selection in the field.