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Muscle volume must increase substantially during childhood growth to generate the power required to propel the growing body. One unresolved but fundamental question about childhood muscle growth is whether muscles grow at equal rates; that is, if muscles grow in synchrony with each other. In this study, we used magnetic resonance imaging (MRI) and advances in artificial intelligence methods (deep learning) for medical image segmentation to investigate whether human lower leg muscles grow in synchrony. Muscle volumes were measured in 10 lower leg muscles in 208 typically developing children (eight infants aged less than 3 months and 200 children aged 5 to 15 years). We tested the hypothesis that human lower leg muscles grow synchronously by investigating whether the volume of individual lower leg muscles, expressed as a proportion of total lower leg muscle volume, remains constant with age. There were substantial age-related changes in the relative volume of most muscles in both boys and girls (p < 0.001). This was most evident between birth and five years of age but was still evident after five years. The medial gastrocnemius and soleus muscles, the largest muscles in infancy, grew faster than other muscles in the first five years. The findings demonstrate that muscles in the human lower leg grow asynchronously. This finding may assist early detection of atypical growth and allow targeted muscle-specific interventions to improve the quality of life, particularly for children with neuromotor conditions such as cerebral palsy., (© 2023 The Authors. Journal of Anatomy published by John Wiley & Sons Ltd on behalf of Anatomical Society.)

New technologies for monitoring biodiversity such as environmental (e)DNA, passive acoustic monitoring, and optical sensors promise to generate automated spatiotemporal community observations at unprecedented scales and resolutions. Here, we introduce 'novel community data' as an umbrella term for these data. We review the emerging field around novel community data, focusing on new ecological questions that could be addressed; the analytical tools available or needed to make best use of these data; and the potential implications of these developments for policy and conservation. We conclude that novel community data offer many opportunities to advance our understanding of fundamental ecological processes, including community assembly, biotic interactions, micro- and macroevolution, and overall ecosystem functioning., Competing Interests: Declaration of interests D.W.Y. is a cofounder of NatureMetrics, which provides commercial eDNA services and is a minor shareholder in the NatureSpace Partnership. No further conflicts of interest to declare., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

In regression modelling, measurement error models are often needed to correct for uncertainty arising from measurements of covariates/predictor variables. The literature on measurement error (or errors-in-variables) modelling is plentiful, however, general algorithms and software for maximum likelihood estimation of models with measurement error are not as readily available, in a form that they can be used by applied researchers without relatively advanced statistical expertise. In this study, we develop a novel algorithm for measurement error modelling, which could in principle take any regression model fitted by maximum likelihood, or penalised likelihood, and extend it to account for uncertainty in covariates. This is achieved by exploiting an interesting property of the Monte Carlo Expectation-Maximization (MCEM) algorithm, namely that it can be expressed as an iteratively reweighted maximisation of complete data likelihoods (formed by imputing the missing values). Thus we can take any regression model for which we have an algorithm for (penalised) likelihood estimation when covariates are error-free, nest it within our proposed iteratively reweighted MCEM algorithm, and thus account for uncertainty in covariates. The approach is demonstrated on examples involving generalized linear models, point process models, generalized additive models and capture-recapture models. Because the proposed method uses maximum (penalised) likelihood, it inherits advantageous optimality and inferential properties, as illustrated by simulation. We also study the model robustness of some violations in predictor distributional assumptions. Software is provided as the refitME package on R, whose key function behaves like a refit() function, taking a fitted regression model object and re-fitting with a pre-specified amount of measurement error., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Stoklosa et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

The life span of leaves increases with their mass per unit area (LMA). It is unclear why. Here, we show that this empirical generalization (the foundation of the worldwide leaf economics spectrum) is a consequence of natural selection, maximizing average net carbon gain over the leaf life cycle. Analyzing two large leaf trait datasets, we show that evergreen and deciduous species with diverse construction costs (assumed proportional to LMA) are selected by light, temperature, and growing-season length in different, but predictable, ways. We quantitatively explain the observed divergent latitudinal trends in evergreen and deciduous LMA and show how local distributions of LMA arise by selection under different environmental conditions acting on the species pool. These results illustrate how optimality principles can underpin a new theory for plant geography and terrestrial carbon dynamics.

Unmeasured or latent variables are often the cause of correlations between multivariate measurements, which are studied in a variety of fields such as psychology, ecology, and medicine. For Gaussian measurements, there are classical tools such as factor analysis or principal component analysis with a well-established theory and fast algorithms. Generalized Linear Latent Variable models (GLLVMs) generalize such factor models to non-Gaussian responses. However, current algorithms for estimating model parameters in GLLVMs require intensive computation and do not scale to large datasets with thousands of observational units or responses. In this article, we propose a new approach for fitting GLLVMs to high-dimensional datasets, based on approximating the model using penalized quasi-likelihood and then using a Newton method and Fisher scoring to learn the model parameters. Computationally, our method is noticeably faster and more stable, enabling GLLVM fits to much larger matrices than previously possible. We apply our method on a dataset of 48,000 observational units with over 2,000 observed species in each unit and find that most of the variability can be explained with a handful of factors. We publish an easy-to-use implementation of our proposed fitting algorithm.

Multiple imputation and maximum likelihood estimation (via the expectation-maximization algorithm) are two well-known methods readily used for analyzing data with missing values. While these two methods are often considered as being distinct from one another, multiple imputation (when using improper imputation) is actually equivalent to a stochastic expectation-maximization approximation to the likelihood. In this article, we exploit this key result to show that familiar likelihood-based approaches to model selection, such as Akaike's information criterion (AIC) and the Bayesian information criterion (BIC), can be used to choose the imputation model that best fits the observed data. Poor choice of imputation model is known to bias inference, and while sensitivity analysis has often been used to explore the implications of different imputation models, we show that the data can be used to choose an appropriate imputation model via conventional model selection tools. We show that BIC can be consistent for selecting the correct imputation model in the presence of missing data. We verify these results empirically through simulation studies, and demonstrate their practicality on two classical missing data examples. An interesting result we saw in simulations was that not only can parameter estimates be biased by misspecifying the imputation model, but also by overfitting the imputation model. This emphasizes the importance of using model selection not just to choose the appropriate type of imputation model, but also to decide on the appropriate level of imputation model complexity., (© 2021 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.)

Urbanised estuaries, ports and harbours are often utilised for recreational purposes, notably recreational angling. Yet there has been little quantitative assessment of the footprint and intensity of these activities at scales suitable for spatial management. Urban and industrialised estuaries have previously been considered as having low conservation value, perhaps due to issues with contamination and disturbance. Studies in recent decades have demonstrated that many of these systems are still highly biodiverse and of high value to local residents. As a response, urbanised estuaries are now being considered by coastal spatial management initiatives, where assessments of recreational use in these areas can help avoid 'user-environmental' and 'user-user' conflict. The models of these activities need to be developed at a scale relevant to governments and regulatory authorities, but the few human-use models that do exist integrate fishing intensity to a regional or even continental scale; too large to capture the fine scale variation inherent in complex urban fisheries. Species Distribution Modeling (SDM) is a tool commonly used to assess drivers of species range, but can be applied to models of recreational fishing in complex environments, at a scale relevant to regulatory bodies. Using point-data from 573 visual surveys with recently developed Poisson point process models, we examine the recreational fishery in Australia's busiest estuarine port, Sydney Harbour. We demonstrate the utility of these models for understanding the distribution of boat and shore-based fishers, and the effects of a range of temporally static (geographical) and dynamic (weather) predictors on these distributions., (Copyright © 2020. Published by Elsevier Ltd.)

Generalized linear latent variable models (GLLVM) are popular tools for modeling multivariate, correlated responses. Such data are often encountered, for instance, in ecological studies, where presence-absences, counts, or biomass of interacting species are collected from a set of sites. Until very recently, the main challenge in fitting GLLVMs has been the lack of computationally efficient estimation methods. For likelihood based estimation, several closed form approximations for the marginal likelihood of GLLVMs have been proposed, but their efficient implementations have been lacking in the literature. To fill this gap, we show in this paper how to obtain computationally convenient estimation algorithms based on a combination of either the Laplace approximation method or variational approximation method, and automatic optimization techniques implemented in R software. An extensive set of simulation studies is used to assess the performances of different methods, from which it is shown that the variational approximation method used in conjunction with automatic optimization offers a powerful tool for estimation., Competing Interests: The authors have declared that no competing interests exist.

Generalized linear latent variable models (GLLVMs) offer a general framework for flexibly analyzing data involving multiple responses. When fitting such models, two of the major challenges are selecting the order, that is, the number of factors, and an appropriate structure for the loading matrix, typically a sparse structure. Motivated by the application of GLLVMs to study marine species assemblages in the Southern Ocean, we propose the Ordered Factor LASSO or OFAL penalty for order selection and achieving sparsity in GLLVMs. The OFAL penalty is the first penalty developed specifically for order selection in latent variable models, and achieves this by using a hierarchically structured group LASSO type penalty to shrink entire columns of the loading matrix to zero, while ensuring that non-zero loadings are concentrated on the lower-order factors. Simultaneously, individual element sparsity is achieved through the use of an adaptive LASSO. In conjunction with using an information criterion which promotes aggressive shrinkage, simulation shows that the OFAL penalty performs strongly compared with standard methods and penalties for order selection, achieving sparsity, and prediction in GLLVMs. Applying the OFAL penalty to the Southern Ocean marine species dataset suggests the available environmental predictors explain roughly half of the total covariation between species, thus leading to a smaller number of latent variables and increased sparsity in the loading matrix compared to a model without any covariates., (© 2018, The International Biometric Society.)

While data transformation is a common strategy to satisfy linear modeling assumptions, a theoretical result is used to show that transformation cannot reasonably be expected to stabilize variances for small counts. Under broad assumptions, as counts get smaller, it is shown that the variance becomes proportional to the mean under monotonic transformations g(·) that satisfy g(0)=0, excepting a few pathological cases. A suggested rule-of-thumb is that if many predicted counts are less than one then data transformation cannot reasonably be expected to stabilize variances, even for a well-chosen transformation. This result has clear implications for the analysis of counts as often implemented in the applied sciences, but particularly for multivariate analysis in ecology. Multivariate discrete data are often collected in ecology, typically with a large proportion of zeros, and it is currently widespread to use methods of analysis that do not account for differences in variance across observations nor across responses. Simulations demonstrate that failure to account for the mean-variance relationship can have particularly severe consequences in this context, and also in the univariate context if the sampling design is unbalanced., (© 2017 The Authors. Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.)

Bootstrap methods are widely used in statistics, and bootstrapping of residuals can be especially useful in the regression context. However, difficulties are encountered extending residual resampling to regression settings where residuals are not identically distributed (thus not amenable to bootstrapping)-common examples including logistic or Poisson regression and generalizations to handle clustered or multivariate data, such as generalised estimating equations. We propose a bootstrap method based on probability integral transform (PIT-) residuals, which we call the PIT-trap, which assumes data come from some marginal distribution F of known parametric form. This method can be understood as a type of "model-free bootstrap", adapted to the problem of discrete and highly multivariate data. PIT-residuals have the key property that they are (asymptotically) pivotal. The PIT-trap thus inherits the key property, not afforded by any other residual resampling approach, that the marginal distribution of data can be preserved under PIT-trapping. This in turn enables the derivation of some standard bootstrap properties, including second-order correctness of pivotal PIT-trap test statistics. In multivariate data, bootstrapping rows of PIT-residuals affords the property that it preserves correlation in data without the need for it to be modelled, a key point of difference as compared to a parametric bootstrap. The proposed method is illustrated on an example involving multivariate abundance data in ecology, and demonstrated via simulation to have improved properties as compared to competing resampling methods.

Technological advances have enabled a new class of multivariate models for ecology, with the potential now to specify a statistical model for abundances jointly across many taxa, to simultaneously explore interactions across taxa and the response of abundance to environmental variables. Joint models can be used for several purposes of interest to ecologists, including estimating patterns of residual correlation across taxa, ordination, multivariate inference about environmental effects and environment-by-trait interactions, accounting for missing predictors, and improving predictions in situations where one can leverage knowledge of some species to predict others. We demonstrate this by example and discuss recent computation tools and future directions., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

A functional traits-based theory of organismal communities is critical for understanding the principles underlying community assembly, and predicting responses to environmental change. This is particularly true for terrestrial arthropods, of which only 20% are described. Using epigaeic ant assemblages, we asked: (1) can we use morphological variation among species to predict trophic position or preferred microhabitat; (2) does the strength of morphological associations suggest recent trait divergence; (3) do environmental variables at site scale predict trait sets for whole assemblages? We pitfall-trapped ants from a revegetation chronosequence and measured their morphology, trophic position [using C:N stoichiometry and stable isotope ratios (δ)] and characteristics of microhabitat and macrohabitat. We found strong associations between high trophic position (low C:N and high δ(15)N) in body tissue and morphological traits: predators were larger, had more laterally positioned eyes, more physical protection and tended to be monomorphic. In addition, morphological traits were associated with certain microhabitat features, e.g. smaller heads were associated with the bare ground microhabitat. Trait-microhabitat relationships were more pronounced when phylogenetic adjustments were used, indicating a strong influence of recent trait divergences. At the assemblage level, our fourth corner analysis revealed associations between the prevalence of traits and macrohabitat, although these associations were not the same as those based on microhabitat associations. This study shows direct links between species-level traits and both diet and habitat preference. Trait-based prediction of ecological roles and community structure is thus achievable when integrating stoichiometry, morphology and phylogeny, but scale is an important consideration in such predictions.

We propose a new variable selection criterion designed for use with forward selection algorithms; the score information criterion (SIC). The proposed criterion is based on score statistics which incorporate correlated response data. The main advantage of the SIC is that it is much faster to compute than existing model selection criteria when the number of predictor variables added to a model is large, this is because SIC can be computed for all candidate models without actually fitting them. A second advantage is that it incorporates the correlation between variables into its quasi-likelihood, leading to more desirable properties than competing selection criteria. Consistency and prediction properties are shown for the SIC. We conduct simulation studies to evaluate the selection and prediction performances, and compare these, as well as computational times, with some well-known variable selection criteria. We apply the SIC on a real data set collected on arthropods by considering variable selection on a large number of interactions terms consisting of species traits and environmental covariates., (© 2013, The International Biometric Society.)

Presence-only data, where information is available concerning species presence but not species absence, are subject to bias due to observers being more likely to visit and record sightings at some locations than others (hereafter "observer bias"). In this paper, we describe and evaluate a model-based approach to accounting for observer bias directly--by modelling presence locations as a function of known observer bias variables (such as accessibility variables) in addition to environmental variables, then conditioning on a common level of bias to make predictions of species occurrence free of such observer bias. We implement this idea using point process models with a LASSO penalty, a new presence-only method related to maximum entropy modelling, that implicitly addresses the "pseudo-absence problem" of where to locate pseudo-absences (and how many). The proposed method of bias-correction is evaluated using systematically collected presence/absence data for 62 plant species endemic to the Blue Mountains near Sydney, Australia. It is shown that modelling and controlling for observer bias significantly improves the accuracy of predictions made using presence-only data, and usually improves predictions as compared to pseudo-absence or "inventory" methods of bias correction based on absences from non-target species. Future research will consider the potential for improving the proposed bias-correction approach by estimating the observer bias simultaneously across multiple species.

In allometry, the study of how size variables scale against each other, it is often of interest to fit lines to bivariate data and test hypotheses about slope and elevation about one or several lines. The nature of the problem suggests that bivariate techniques related to principal component analysis are more appropriate than linear regression. Inference methods have been developed for this problem and are in widespread use, however, we demonstrate that such methods are not robust to bivariate contamination, and propose alternative approaches which are. The new approaches use Huber's M-estimator via a plug-in approach, where robust test procedures have the same form as classical ones, but where we plug in robust estimators of parameters and standard errors in place of classical estimators. Simulations demonstrate that these new procedures are robust against bivariate contamination, and can make accurate inferences even from small samples., (Copyright © 2013 Elsevier Ltd. All rights reserved.)

Species distribution models (SDMs) are an important tool for studying the patterns of species across environmental and geographic space. For community data, a common approach involves fitting an SDM to each species separately, although the large number of models makes interpretation difficult and fails to exploit any similarities between individual species responses. A recently proposed alternative that can potentially overcome these difficulties is species archetype models (SAMs), a model-based approach that clusters species based on their environmental response. In this paper, we compare the predictive performance of SAMs against separate SDMs using a number of multi-species data sets. Results show that SAMs improve model accuracy and discriminatory capacity compared to separate SDMs. This is achieved by borrowing strength from common species having higher information content. Moreover, the improvement increases as the species become rarer.

We provide the first global test of the idea that introduced species have greater seed dispersal distances than do native species, using data for 51 introduced and 360 native species from the global literature. Counter to our expectations, there was no significant difference in mean or maximum dispersal distance between introduced and native species. Next, we asked whether differences in dispersal distance might have been obscured by differences in seed mass, plant height and dispersal syndrome, all traits that affect dispersal distance and which can differ between native and introduced species. When we included all three variables in the model, there was no clear difference in dispersal distance between introduced and native species. These results remained consistent when we performed analyses including a random effect for site. Analyses also showed that the lack of a significant difference in dispersal distance was not due to differences in biome, taxonomic composition, growth form, nitrogen fixation, our inclusion of non-invasive introduced species, or our exclusion of species with human-assisted dispersal. Thus, if introduced species do have higher spread rates, it seems likely that these are driven by differences in post-dispersal processes such as germination, seedling survival, and survival to reproduction.

Modeling the spatial distribution of a species is a fundamental problem in ecology. A number of modeling methods have been developed, an extremely popular one being MAXENT, a maximum entropy modeling approach. In this article, we show that MAXENT is equivalent to a Poisson regression model and hence is related to a Poisson point process model, differing only in the intercept term, which is scale-dependent in MAXENT. We illustrate a number of improvements to MAXENT that follow from these relations. In particular, a point process model approach facilitates methods for choosing the appropriate spatial resolution, assessing model adequacy, and choosing the LASSO penalty parameter, all currently unavailable to MAXENT. The equivalence result represents a significant step in the unification of the species distribution modeling literature., (Copyright © 2013, The International Biometric Society.)

• It has long been believed that plant species from the tropics have higher levels of traits associated with resistance to herbivores than do species from higher latitudes. A meta-analysis recently showed that the published literature does not support this theory. However, the idea has never been tested using data gathered with consistent methods from a wide range of latitudes. • We quantified the relationship between latitude and a broad range of chemical and physical traits across 301 species from 75 sites world-wide. • Six putative resistance traits, including tannins, the concentration of lipids (an indicator of oils, waxes and resins), and leaf toughness were greater in high-latitude species. Six traits, including cyanide production and the presence of spines, were unrelated to latitude. Only ash content (an indicator of inorganic substances such as calcium oxalates and phytoliths) and the properties of species with delayed greening were higher in the tropics. • Our results do not support the hypothesis that tropical plants have higher levels of resistance traits than do plants from higher latitudes. If anything, plants have higher resistance toward the poles. The greater resistance traits of high-latitude species might be explained by the greater cost of losing a given amount of leaf tissue in low-productivity environments., (© 2011 The Authors. New Phytologist © 2011 New Phytologist Trust.)

In allometry, bivariate techniques related to principal component analysis are often used in place of linear regression, and primary interest is in making inferences about the slope. We demonstrate that the current inferential methods are not robust to bivariate contamination, and consider four robust alternatives to the current methods -- a novel sandwich estimator approach, using robust covariance matrices derived via an influence function approach, Huber's M-estimator and the fast-and-robust bootstrap. Simulations demonstrate that Huber's M-estimators are highly efficient and robust against bivariate contamination, and when combined with the fast-and-robust bootstrap, we can make accurate inferences even from small samples., (Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Leaf mechanical properties strongly influence leaf lifespan, plant-herbivore interactions, litter decomposition and nutrient cycling, but global patterns in their interspecific variation and underlying mechanisms remain poorly understood. We synthesize data across the three major measurement methods, permitting the first global analyses of leaf mechanics and associated traits, for 2819 species from 90 sites worldwide. Key measures of leaf mechanical resistance varied c. 500-800-fold among species. Contrary to a long-standing hypothesis, tropical leaves were not mechanically more resistant than temperate leaves. Leaf mechanical resistance was modestly related to rainfall and local light environment. By partitioning leaf mechanical resistance into three different components we discovered that toughness per density contributed a surprisingly large fraction to variation in mechanical resistance, larger than the fractions contributed by lamina thickness and tissue density. Higher toughness per density was associated with long leaf lifespan especially in forest understory. Seldom appreciated in the past, toughness per density is a key factor in leaf mechanical resistance, which itself influences plant-animal interactions and ecosystem functions across the globe., (© 2011 Blackwell Publishing Ltd/CNRS.)

A modification of generalized estimating equations (GEEs) methodology is proposed for hypothesis testing of high-dimensional data, with particular interest in multivariate abundance data in ecology, an important application of interest in thousands of environmental science studies. Such data are typically counts characterized by high dimensionality (in the sense that cluster size exceeds number of clusters, n>K) and over-dispersion relative to the Poisson distribution. Usual GEE methods cannot be applied in this setting primarily because sandwich estimators become numerically unstable as n increases. We propose instead using a regularized sandwich estimator that assumes a common correlation matrix R, and shrinks the sample estimate of R toward the working correlation matrix to improve its numerical stability. It is shown via theory and simulation that this substantially improves the power of Wald statistics when cluster size is not small. We apply the proposed approach to study the effects of nutrient addition on nematode communities, and in doing so discuss important issues in implementation, such as using statistics that have good properties when parameter estimates approach the boundary (), and using resampling to enable valid inference that is robust to high dimensionality and to possible model misspecification., (© 2010, The International Biometric Society.)

The arcsine square root transformation has long been standard procedure when analyzing proportional data in ecology, with applications in data sets containing binomial and non-binomial response variables. Here, we argue that the arcsine transform should not be used in either circumstance. For binomial data, logistic regression has greater interpretability and higher power than analyses of transformed data. However, it is important to check the data for additional unexplained variation, i.e., overdispersion, and to account for it via the inclusion of random effects in the model if found. For non-binomial data, the arcsine transform is undesirable on the grounds of interpretability, and because it can produce nonsensical predictions. The logit transformation is proposed as an alternative approach to address these issues. Examples are presented in both cases to illustrate these advantages, comparing various methods of analyzing proportions including untransformed, arcsine- and logit-transformed linear models and logistic regression (with or without random effects). Simulations demonstrate that logistic regression usually provides a gain in power over other methods.

In allometry, researchers are commonly interested in estimating the slope of the major axis or standardized major axis (methods of bivariate line fitting related to principal components analysis). This study considers the robustness of two tests for a common slope amongst several axes. It is of particular interest to measure the robustness of these tests to slight violations of assumptions that may not be readily detected in sample datasets. Type I error is estimated in simulations of data generated with varying levels of nonnormality, heteroscedasticity and nonlinearity. The assumption failures introduced in simulations were difficult to detect in a moderately sized dataset, with an expert panel only able to correct detect assumption violations 34-45% of the time. While the common slope tests were robust to nonnormal and heteroscedastic errors from the line, Type I error was inflated if the two variables were related in a slightly nonlinear fashion. Similar results were also observed for the linear regression case. The common slope tests were more liberal when the simulated data had greater nonlinearity, and this effect was more evident when the underlying distribution had longer tails than the normal. This result raises concerns for common slopes testing, as slight nonlinearities such as those in simulations are often undetectable in moderately sized datasets. Consequently, practitioners should take care in checking for nonlinearity and interpreting the results of a test for common slope. This work has implications for the robustness of inference in linear models in general.

It was predicted that relationships of leaf mass per area (LMA) with juvenile shade tolerance will depend on leaf habit, and on whether species are compared at a common age as young seedlings, or at a common size as saplings. A meta-analysis of 47 comparative studies (372 species) was used to test predictions, and the effect of light environment on this relationship. The LMA of evergreens was positively correlated with shade tolerance, irrespective of ontogeny or light environment. The LMA of young seedlings (

Knowledge about the diversity, locomotor adaptations, and evolution of the marsupial forelimb is limited, resulting in an underrepresentation of marsupials in comparative anatomical literature on mammalian forelimb anatomy. This study investigated hand proportions in the diverse marsupial order Diprotodontia. Fifty-two measurements of 95 specimens representing 47 species, as well as 6 non-diprotodontian specimens, were explored using principal components analysis (PCA). Bootstrapping was used to assess the reliability of the loadings. Phylogenetically independent contrasts and phylogenetic ANOVA were used to test for correlation with size and functional adaptation of forelimbs for locomotor habit, scored as arboreal vs. terrestrial. Analysis of first principal component (PC1) scores revealed significant differences between arboreal and terrestrial species, and was related to relative slenderness of their phalangeal elements. Both locomotor groups displayed allometry along PC1 scores, but with different intercepts such that PC1 discriminated between the two locomotor habits almost completely. PC2 separated some higher-level clades and burrowing species. Analysis of locomotor predictors commonly applied by palaeontologists indicates that ratios between proximal and intermediate phalanges were unsuitable as predictors of arboreality/terrestriality, but the phalangeal index was more effective. From PCA results, a phalangeal slenderness ratio was developed which proved to be a useful discriminator, suggesting that a single unallocated phalanx can be used for an impression of locomotor mode in fossils. Most Diprotodontia are laterally paraxonic or ectaxonic, with the exception of digging species whose hands are medially paraxonic. Our results complement those of studies on placental mammals, suggesting that the demands of arboreality, terrestriality, or frequent digging on intrinsic hand proportions are met with similar anatomical adaptations in marsupials., (Copyright 2006 Wiley-Liss, Inc.)

Fitting a line to a bivariate dataset can be a deceptively complex problem, and there has been much debate on this issue in the literature. In this review, we describe for the practitioner the essential features of line-fitting methods for estimating the relationship between two variables: what methods are commonly used, which method should be used when, and how to make inferences from these lines to answer common research questions. A particularly important point for line-fitting in allometry is that usually, two sources of error are present (which we call measurement and equation error), and these have quite different implications for choice of line-fitting method. As a consequence, the approach in this review and the methods presented have subtle but important differences from previous reviews in the biology literature. Linear regression, major axis and standardised major axis are alternative methods that can be appropriate when there is no measurement error. When there is measurement error, this often needs to be estimated and used to adjust the variance terms in formulae for line-fitting. We also review line-fitting methods for phylogenetic analyses. Methods of inference are described for the line-fitting techniques discussed in this paper. The types of inference considered here are testing if the slope or elevation equals a given value, constructing confidence intervals for the slope or elevation, comparing several slopes or elevations, and testing for shift along the axis amongst several groups. In some cases several methods have been proposed in the literature. These are discussed and compared. In other cases there is little or no previous guidance available in the literature. Simulations were conducted to check whether the methods of inference proposed have the intended coverage probability or Type I error. We identified the methods of inference that perform well and recommend the techniques that should be adopted in future work.

Global-scale quantification of relationships between plant traits gives insight into the evolution of the world's vegetation, and is crucial for parameterizing vegetation-climate models. A database was compiled, comprising data for hundreds to thousands of species for the core 'leaf economics' traits leaf lifespan, leaf mass per area, photosynthetic capacity, dark respiration, and leaf nitrogen and phosphorus concentrations, as well as leaf potassium, photosynthetic N-use efficiency (PNUE), and leaf N : P ratio. While mean trait values differed between plant functional types, the range found within groups was often larger than differences among them. Future vegetation-climate models could incorporate this knowledge. The core leaf traits were intercorrelated, both globally and within plant functional types, forming a 'leaf economics spectrum'. While these relationships are very general, they are not universal, as significant heterogeneity exists between relationships fitted to individual sites. Much, but not all, heterogeneity can be explained by variation in sample size alone. PNUE can also be considered as part of this trait spectrum, whereas leaf K and N : P ratios are only loosely related.