PEM are a set of eigenfunctions obtained from the structure of a phylogenetic graph, which can be a standard phylogenetic tree or a phylogenetic tree with added reticulations. These eigenfunctions depict a set of potential patterns of phenotype variation among species from the structure of the phylogenetic graph. A subset of eigenfunctions from a PEM is selected for the purpose of predicting the phenotypic values of traits for species that are represented in a tree, but for which trait data are otherwise lacking. This paper introduces a comprehensive view and the computational details of the PEM framework (with calculation examples), a simulation study to demonstrate the ability of PEM to predict trait values and four real data examples of the use of the framework. 3. Simulation results show that PEM are robust in representing phylogenetic signal and in estimating trait values. 4. The method also performed well when applied to the real-world data: prediction coefficients were high (0Á76-0Á88), and no notable model biases were found. 5. Phylogenetic modelling using PEM is shown to be a useful methodological asset to disciplines such as ecology, ecophysiology, ecotoxicology, pharmaceutical botany, among others, which can benefit from estimating trait values that are laborious and often expensive to obtain.

Metabolic heat production in archosaurs has played an important role in their evolutionary radiation during the Mesozoic, and their ancestral metabolic condition has long been a matter of debate in systematics and palaeontology. The study of fossil bone histology provides crucial information on bone growth rate, which has been used to indirectly investigate the evolution of thermometabolism in archosaurs. However, no quantitative estimation of metabolic rate has ever been performed on fossils using bone histological features. Moreover, to date, no inference model has included phylogenetic information in the form of predictive variables. Here we performed statistical predictive modeling using the new method of phylogenetic eigenvector maps on a set of bone histological features for a sample of extant and extinct vertebrates, to estimate metabolic rates of fossil archosauromorphs. This modeling procedure serves as a case study for eigenvector-based predictive modeling in a phylogenetic context, as well as an investigation of the poorly known evolutionary patterns of metabolic rate in archosaurs. Our results show that Mesozoic theropod dinosaurs exhibit metabolic rates very close to those found in modern birds, that archosaurs share a higher ancestral metabolic rate than that of extant ectotherms, and that this derived high metabolic rate was acquired at a much more inclusive level of the phylogenetic tree, among non-archosaurian archosauromorphs. These results also highlight the difficulties of assigning a given heat production strategy (i.e., endothermy, ectothermy) to an estimated metabolic rate value, and confirm findings of previous studies that the definition of the endotherm/ectotherm dichotomy may be ambiguous.

Tolerance to toxic substances is a characteristic of an organism that determines whether it is able to withstand the concentrations occurring in its environment. The measurement of tolerance is therefore of fundamental importance when assessing the impact of anthropogenic chemicals on ecosystems and ecological communities. Although an appreciable amount of information on species tolerance to chemicals has been collected through the last 50 years, substantial gaps remain in our knowledge of tolerance relative to the diversity of organisms inhabiting aquatic ecosystems and the great and increasing number of chemicals released in these ecosystems. Within that context, methods allowing one to reliably and accurately estimate a species' tolerance using other known characteristics would be valuable. In the present study we introduce an approach that uses phylogeny to estimate the tolerance of a species using that of a set of other species related to the focus species at different phylogenetic scales. We estimated phylogenies from molecular data (DNA sequences) or inferred them from taxonomy. Up to 83% of the among‐species variation in tolerance (log‐transformed median lethal concentration over 96 hours; LC50) was found to be phylogenetically structured and was therefore usable for making predictions. The ability of phylogenetic models to produce accurate estimates of species tolerances is apparently related to the availability of information within species groups and the variation in pesticide tolerance within these groups. Toxicity models integrating phylogeny therefore appear suitable to assist in risk assessment.

Direct estimation of species' tolerance to pesticides and other toxic organic substances is a combinatorial problem, because of the large number of species-substance pairs. We propose a statistical modelling approach to predict tolerances associated with untested species-substance pairs, by using models fitted to tested pairs. This approach is based on the phylogeny of species and physico-chemical descriptors of pesticides, with both kinds of information combined in a bilinear model. This bilinear modelling approach predicts tolerance in untested species-compound pairs based on the facts that closely related species often respond similarly to toxic compounds and that chemically similar compounds often have similar toxic effects. The three tolerance models (median lethal concentration after 96 h) used up to 25 aquatic animal species and up to nine pesticides (organochlorines, organophosphates and carbamates). Phylogeny was estimated using DNA sequences, while the pesticides were described by their mode of toxic action and their octanol-water partition coefficients. The models explained 77-84% of the among-species variation in tolerance (log 10 LC 50 ). In cross-validation, 84-87% of the predicted tolerances for individual species were within a factor of 10 of the observed values. The approach can also be used to model other species response to multivariate stress factors.

The spatial and temporal organization of ecological processes and features and the scales at which they occur are central topics to landscape ecology and metapopulation dynamics, and increasingly regarded as a cornerstone paradigm for understanding ecological processes. Hence, there is need for computational approaches which allow the identification of the proper spatial or temporal scales of ecological processes and the explicit integration of that information in models. For that purpose, we propose a new method (multiscale codependence analysis, MCA) to test the statistical significance of the correlations between two variables at particular spatial or temporal scales. Validation of the method (using Monte Carlo simulations) included the study of type I error rate, under five statistical significance thresholds, and of type II error rate and statistical power. The method was found to be valid, in terms of type I error rate, and to have sufficient statistical power to be useful in practice. MCA has assumptions that are met in a wide range of circumstances. When applied to model the river habitat of juvenile Atlantic salmon, MCA revealed that variables describing substrate composition of the river bed were the most influential predictors of parr abundance at 0.4-4.1 km scales whereas mean channel depth was more influential at 200-300 m scales. When properly assessed, the spatial structuring observed in nature may be used purposefully to refine our understanding of natural processes and enhance model representativeness.

We explored the mechanisms of density-dependent growth in Arctic char ( Salvelinus alpinus ) by comparing the energetics of growth, consumption, and activity obtained under three replicated density treatments in a large-scale enclosure (90 m2 surface area) experiment. The enclosures permitted the entry of zooplankton and allowed char to feed on the bottom and at the surface of the lake. We found a negative (power) relationship between growth and density. Char consumption rate decreased linearly with increasing density. Growth efficiency was affected by fish density in a similar manner as growth rate. Finally, activity increased with fish density and was particularly high at high densities. Our findings illustrate the complexity of the relationships among consumption, activity, growth rates, and fish density and bring further evidence to the possible involvement of behavioural mechanisms in density-dependent processes, notably by modulating activity costs with density.

Ecological risk assessment depends strongly on species sensitivity data. Typically, sensitivity data are based on laboratory toxicity bioassays, which for practical constraints cannot be exhaustively performed for all species and chemicals available. Bilinear models integrating phylogenetic information of species and physicochemical properties of compounds allow to predict species sensitivity to chemicals. Combining the molecular information (DNA sequences) of 31 invertebrate species with the physicochemical properties of six bivalent metals, we built bilinear models that explained 70-80% of the variability in species sensitivity to heavy metals. Phylogeny was the most important component of the bilinear models, as it explained the major part of the explained variance (> 40%). Predicted values from bilinear modeling were in agreement with experimental values (> 50%); therefore, this approach is a good starting point to build statistical models which can potentially predict heavy metal toxicity for untested invertebrate species based on empirical values for similar species. Despite their good performance, development of the presented bilinear models would benefit from improved phylogenetic and toxicological datasets. Our analysis is an example for linking evolutionary biology with applied ecotoxicology. Its future applications may encompass other stress factors or traits influencing the survival of aquatic organisms in polluted environments.

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