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Biodiversity and ecosystem function (BEF) studies aim to understand how ecosystems respond to a gradient of species diversity. Generalised Diversity‐Interactions (DI) models are suitable for analysing the BEF relationship. These models relate an ecosystem function response of a community to the identity of the species in the community, their evenness (proportions) and interactions. The number of species in the community (richness) is included implicitly in a DI model.It is common in BEF studies to model an ecosystem function as a function of richness; while this can uncover trends in the BEF relationship, by definition, species diversity is broader than richness alone, and important patterns in the BEF relationship may remain hidden. Here, we introduce the DImodels R package for implementing DI models. We show how richness is mathematically equivalent to a simplified DI model under certain conditions, and illustrate how using the DI multidimensional definition of species diversity can provide deeper insight to the BEF relationship compared to traditional approaches.Using DI models can lead to considerably improved model fit over other methods; it does this by incorporating variation due to the multiple facets of species diversity. Predicting from a DI model is not limited to the study design points, the model can interpolate or extrapolate to predict for any species composition and proportions (assuming there is sufficient coverage of this space in the study design).Expressing the BEF relationship as a function of richness alone can be useful to capture overall trends. However, collapsing the multiple dimensions of species diversity to a single dimension (such as richness) can result in valuable ecological information being lost. DI modelling provides a framework to test the multiple components of species diversity in the BEF relationship. It facilitates uncovering a deeper ecological understanding of the BEF relationship and can lead to enhanced inference. The open‐source DImodels R package provides a user‐friendly way to implement this modelling approach. [ABSTRACT FROM AUTHOR]

Models of natural processes necessarily sacrifice some realism for the sake of tractability. Detailed, parameter‐rich models often provide accurate estimates of system behaviour but can be data‐hungry and difficult to operationalize. Moreover, complexity increases the danger of 'over‐fitting', which leads to poor performance when models are applied to novel conditions. This challenge is typically described in terms of a trade‐off between bias and variance (i.e. low accuracy vs. low precision).In studies of ecological communities, this trade‐off often leads to an argument about the level of detail needed to describe interactions among species. Here, we used data from a grassland biodiversity experiment containing nine locally abundant plant species (the Jena 'dominance experiment') to parameterize models representing six increasingly complex hypotheses about interactions. For each model, we calculated goodness‐of‐fit across different subsets of the data based on sown species richness levels, and tested how performance changed depending on whether or not the same data were used to parameterize and test the model (i.e. within vs. out‐of‐sample), and whether the range of diversity treatments being predicted fell inside or outside of the range used for parameterization.As expected, goodness‐of‐fit improved as a function of model complexity for all within‐sample tests. In contrast, the best out‐of‐sample performance generally resulted from models of intermediate complexity (i.e. with only two interaction coefficients per species—an intraspecific effect and a single pooled interspecific effect), especially for predictions that fell outside the range of diversity treatments used for parameterization. In accordance with other studies, our results also demonstrate that commonly used selection methods based on AIC of models fitted to the full dataset correspond more closely to within‐sample than out‐of‐sample performance.Synthesis. Our results demonstrate that models which include only general intra and interspecific interaction coefficients can be sufficient for estimating species‐level abundances across a wide range of contexts and may provide better out‐of‐sample performance than do more complex models. These findings serve as a reminder that simpler models may often provide a better trade‐off between bias and variance in ecological systems, particularly when applying models beyond the conditions used to parameterize them. [ABSTRACT FROM AUTHOR]

Biodiversity and Ecosystem Function analyses aim to explain how individual species and their interactions affect ecosystem function. With this study, we asked in what ways do species interact, are these interactions affected by species planting pattern, and are initial (planted) proportions or previous year (realized) proportions a better reference point for characterizing grassland diversity effects?We addressed these questions with experimental communities compiled from a pool of 16 tallgrass prairie species. We planted all species in monocultures and mixtures that varied in their species richness, evenness, and spatial pattern. We recorded species‐specific biomass production over three growing seasons and fitted Diversity‐Interactions (DI) models to annual plot biomass yields.In the establishment season, all species interacted equally to form the diversity effect. In years 2 and 3, each species contributed a unique additive coefficient to its interaction with every other species to form the diversity effect. These interactions were affected by Helianthus maximiliani and the species planting pattern. Models based on species planted proportions better‐fit annual plot yield than models based on species previous contributions to plot biomass.Outcomes suggest that efforts to plant tallgrass prairies to maximize diversity effects should focus on the specific species present and in what arrangement they are planted. Furthermore, for particularly diverse grasslands, the effort of collecting annual species biomass data may not be necessary when quantifying diversity effects with DI models. [ABSTRACT FROM AUTHOR]

Understanding the biodiversity and ecosystem function relationship can be challenging in species-rich ecosystems. Traditionally, species richness has been relied on heavily to explain changes in ecosystem function across diversity gradients. Diversity-Interactions models can test how ecosystem function is affected by species identity, species interactions, and evenness, in addition to richness. However, in a species-rich system, there may be too many species interactions to allow estimation of each coefficient, and if all interaction coefficients are estimable, they may be devoid of any sensible biological meaning. Parsimonious descriptions using constraints among interaction coefficients have been developed but important variability may still remain unexplained. Here, we extend Diversity-Interactions models to describe the effects of diversity on ecosystem function using a combination of fixed coefficients and random effects. Our approach provides improved standard errors for testing fixed coefficients and incorporates lack-of-fit tests for diversity effects. We illustrate our methods using data from a grassland and a microbial experiment. Our framework considerably reduces the complexities associated with understanding how species interactions contribute to ecosystem function in species-rich ecosystems. [ABSTRACT FROM AUTHOR]

Most ecosystems provide multiple services, thus the impact of biodiversity losses on ecosystem functions may be considerably underestimated by studies that only address single functions. We propose a multivariate modelling framework for quantifying the relationship between biodiversity and multiple ecosystem functions (multifunctionality). Our framework consolidates the strengths of previous approaches to analysing ecosystem multifunctionality and contributes several advances. It simultaneously assesses the drivers of multifunctionality, such as species relative abundances, richness, evenness and other manipulated treatments. It also tests the relative importance of these drivers across functions, incorporates correlations among functions and identifies conditions where all functions perform well and where trade-offs occur among functions. We illustrate our framework using data from three ecosystem functions (sown biomass, weed suppression and nitrogen yield) in a four-species grassland experiment. We found high variability in performance across the functions in monocultures, but as community diversity increased, performance increased and variability across functions decreased. [ABSTRACT FROM AUTHOR]