Proportional data, in which response variables are expressed as percentages or fractions of a whole, are analysed in many subfields of ecology and evolution. The scale‐independence of proportions makes them appropriate to analyse many biological phenomena, but statistical analyses are not straightforward, since proportions can only take values from zero to one and their variance is usually not constant across the range of the predictor. Transformations to overcome these problems are often applied, but can lead to biased estimates and difficulties in interpretation. In this paper, we provide an overview of the different types of proportional data and discuss the different analysis strategies available. In particular, we review and discuss the use of promising, but little used, techniques for analysing continuous (also called non‐count‐based or non‐binomial) proportions (e.g. percent cover, fraction time spent on an activity): beta and Dirichlet regression, and some of their most important extensions. A major distinction can be made between proportions arising from counts and those arising from continuous measurements. For proportions consisting of two categories, count‐based data are best analysed using well‐developed techniques such as logistic regression, while continuous proportions can be analysed with beta regression models. In the case of >2 categories, multinomial logistic regression or Dirichlet regression can be applied. Both beta and Dirichlet regression techniques model proportions at their original scale, which makes statistical inference more straightforward and produce less biased estimates relative to transformation‐based solutions. Extensions to beta regression, such as models for variable dispersion, zero‐one augmented data and mixed effects designs have been developed and are reviewed and applied to case studies. Finally, we briefly discuss some issues regarding model fitting, inference, and reporting that are particularly relevant to beta and Dirichlet regression. Beta regression and Dirichlet regression overcome some problems inherent in applying classic statistical approaches to proportional data. To facilitate the adoption of these techniques by practitioners in ecology and evolution, we present detailed, annotated demonstration scripts covering all variations of beta and Dirichlet regression discussed in the article, implemented in the freely available language for statistical computing, r.

Plant species diversity in Eurasian wetlands and grasslands depends not only on productivity but also on the relative availability of nutrients, particularly of nitrogen and phosphorus. Here we show that the impacts of nitrogen:phosphorus stoichiometry on plant species richness can be explained by selected plant life-history traits, notably by plant investments in growth versus reproduction. In 599 Eurasian sites with herbaceous vegetation we examined the relationship between the local nutrient conditions and community-mean life-history traits. We found that compared with plants in nitrogen-limited communities, plants in phosphorus-limited communities invest little in sexual reproduction (for example, less investment in seed, shorter flowering period, longer lifespan) and have conservative leaf economy traits (that is, a low specific leaf area and a high leaf dry-matter content). Endangered species were more frequent in phosphorus-limited ecosystems and they too invested little in sexual reproduction. The results provide new insight into how plant adaptations to nutrient conditions can drive the distribution of plant species in natural ecosystems and can account for the vulnerability of endangered species.

Dynamic Global Vegetation Models (DGVMs) are indispensable for our understanding of climate change impacts. The application of traits in DGVMs is increasingly refined. However, a comprehensive analysis of the direct impacts of trait variation on global vegetation distribution does not yet exist. Here, we present such analysis as proof of principle. We run regressions of trait observations for leaf mass per area, stem-specific density, and seed mass from a global database against multiple environmental drivers, making use of findings of global trait convergence. This analysis explained up to 52% of the global variation of traits. Global trait maps, generated by coupling the regression equations to gridded soil and climate maps, showed up to orders of magnitude variation in trait values. Subsequently, nine vegetation types were characterized by the trait combinations that they possess using Gaussian mixture density functions. The trait maps were input to these functions to determine global occurrence probabilities for each vegetation type. We prepared vegetation maps, assuming that the most probable (and thus, most suited) vegetation type at each location will be realized. This fully traits-based vegetation map predicted 42% of the observed vegetation distribution correctly. Our results indicate that a major proportion of the predictive ability of DGVMs with respect to vegetation distribution can be attained by three traits alone if traits like stem-specific density and seed mass are included. We envision that our traits-based approach, our observation-driven trait maps, and our vegetation maps may inspire a new generation of powerful traits-based DGVMs.T o understand and predict the impacts of climate change on system Earth, it is essential to predict global vegetation distribution and its attributes. Vegetation determines the fluxes of energy, water, and CO 2 to and from terrestrial ecosystems. Socalled Dynamic Global Vegetation Models (DGVMs) (reviewed in ref. 1) are indispensable tools to make predictions on such biosphere-climate interactions. Despite their importance, DGVMs are among the most uncertain components of earth system models when predicting climate change (2).DGVMs have been built around the concept of Plant Functional Types (PFTs) (3). Traditionally, various functional attributes (or traits) were assumed to be constant for a given PFT. This assumption has various drawbacks (reviewed in ref. 4). For instance, it implies assuming that trait values used to parameterize PFTs are valid under past environmental conditions and will be valid under future conditions. As such, this assumption neglects acclimation and adaptation (5), nonrandom species extinction (6), and major differences in dispersal rates among species and within PFTs (7). Moreover, this assumption strongly hampers quantifying feedback mechanisms between vegetation and its environment.For these reasons, the application of traits in DGVMs is increasingly refined. Trait responses to, for example, different soil fertility conditions are desc...

Aim Despite their importance for predicting fluxes to and from terrestrial ecosystems, dynamic global vegetation models have insufficient realism because of their use of plant functional types (PFTs) with constant attributes. Based on recent advances in community ecology, we explore the merits of a traits-based vegetation model to deal with current shortcomings. Location Global.Methods A research review of current concepts and information, providing a new perspective, supported by quantitative analysis of a global traits database.Results Continuous and process-based trait-environment relations are central to a traits-based approach and allow us to directly calculate fluxes based on functional characteristics. By quantifying community assembly concepts, it is possible to predict trait values from environmental drivers, although these relations are still imperfect. Through the quantification of these relations, effects of adaptation and species replacement upon environmental changes are implicitly accounted for. Such functional links also allow direct calculation of fluxes, including those related to feedbacks through the nitrogen and water cycle. Finally, a traits-based model allows the prediction of new trait combinations and no-analogue ecosystem functions projected to arise in the near future, which is not feasible in current vegetation models. A separate calculation of ecosystem fluxes and PFT occurrences in traitsbased models allows for flexible vegetation classifications.Main conclusions Given the advantages described above, we argue that traitsbased modelling deserves consideration (although it will not be easy) if one is to aim for better climate projections.

Aim Most vascular plants on Earth form mycorrhizae, a symbiotic relationship between plants and fungi. Despite the broad recognition of the importance of mycorrhizae for global carbon and nutrient cycling, we do not know how soil and climate variables relate to the intensity of colonization of plant roots by mycorrhizal fungi. Here we quantify the global patterns of these relationships. Location Global.Methods Data on plant root colonization intensities by the two dominant types of mycorrhizal fungi world-wide, arbuscular (4887 plant species in 233 sites) and ectomycorrhizal fungi (125 plant species in 92 sites), were compiled from published studies. Data for climatic and soil factors were extracted from global datasets. For a given mycorrhizal type, we calculated at each site the mean root colonization intensity by mycorrhizal fungi across all potentially mycorrhizal plant species found at the site, and subjected these data to generalized additive model regression analysis with environmental factors as predictor variables. ResultsWe show for the first time that at the global scale the intensity of plant root colonization by arbuscular mycorrhizal fungi strongly relates to warm-season temperature, frost periods and soil carbon-to-nitrogen ratio, and is highest at sites featuring continental climates with mild summers and a high availability of soil nitrogen. In contrast, the intensity of ectomycorrhizal infection in plant roots is related to soil acidity, soil carbon-to-nitrogen ratio and seasonality of precipitation, and is highest at sites with acidic soils and relatively constant precipitation levels. Main conclusionsWe provide the first quantitative global maps of intensity of mycorrhizal colonization based on environmental drivers, and suggest that environmental changes will affect distinct types of mycorrhizae differently. Future analyses of the potential effects of environmental change on global carbon and nutrient cycling via mycorrhizal pathways will need to take into account the relationships discovered in this study.