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The local abiotic and environmental conditions of a grass‐based farming system may influence the agricultural benefits of mixtures in comparison to pure stands. We investigated the effects of species identities and interactions between grass, legume, and herb species on dry matter yield and sward digestibility and explored how contrasting environments may affect these relationships. We established experimental plots across 11 mixtures and 4 monocultures of perennial ryegrass (Lolium perenne L.), chicory (Cichorium intybus L.), white clover (Trifolium repens L.), and red clover (Trifolium pratense L.) established at two seeding densities in two sites Brody and Szelejewo (Poland) and managed them over a 3‐year period. The two sites were close geographically and had similar climates, but differed in soil types (Luvisols and Cambisols, respectively). We confirmed that the annual DM yields were generally higher on Cambisols soil as compared to Luvisols soil; both individual species effects and species interaction strengths differed across the two contrasting environments. The predicted annual DM yield for the 4‐species mixtures in general gave comparable or higher yields compared to monocultures across the 3 years, with the mixtures giving around 10%–30% higher yields than the weighted average of the monocultures of the constituent species. Analysing the transgressive overyielding it turned out that there was no significant difference between the 4‐species mixtures and best performing monoculture. The benefits of species diversity in our study was greater on less productive site because we found larger overyielding of the 4‐species sward on the Luvisols soil than on the Cambisols soil. Additionally, the effect of mixtures composed by 4‐species increased the yield stability compared to monocultures in the 3‐year period of our study, particularly on Cambisols soil. Sward digestibility applied to average values did not differ much between sites with mixtures performing similarly to monocultures. The reason for that could have been the dynamics of sward botanical composition during study years shifted towards increased perennial ryegrass and decreased proportions of chicory in the sward as well as the observed phenomenon that the species in mixed swards progressed to successive growth stages more slowly than in pure sowing. [ABSTRACT FROM AUTHOR]

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]

In this paper, we describe an in-class experiment that is easy to implement with large groups of students. The experiment takes approximately 15-20 minutes to run and involves each student completing one of four types of Sudoku puzzles and recording the time it takes to completion. The resulting data set can be used as a teaching tool at an introductory level right through to an advanced level of statistics. Basic methods for describing and displaying data as well as the intricacies that arise with real data may be discussed in an introductory course. The range of more sophisticated analyses that can be taught with the data set include chi-squared tests for independence, ANOVA, t- and F-tests, logistic regression and survival analysis. We describe and provide the tools to implement the experiment and illustrate several potential teaching topics using a collected data set.

Fluctuations in population abundances are often correlated through time across multiple locations, a phenomenon known as spatial synchrony. Spatial synchrony can exhibit complex spatial structures, termed 'geographies of synchrony', that can reveal mechanisms underlying population fluctuations. However, most studies have focused on spatial extents of 10s to 100s of kilometres, making it unclear how synchrony concepts and approaches should apply to dynamics at finer spatial scales.We used network analyses, multiple regression on similarity matrices, and wavelet coherence analyses to examine micro‐scale synchrony and geographies of synchrony, over distances up to 30 m, in a serpentine grassland plant community.We found that species' populations exhibited a geography of synchrony even over such short distances. Often, well‐synchronized populations were geographically separate, a spatial structure that was shaped mainly by gopher disturbance and dispersal limitation, and to a lesser extent by relationships with other plant species. Precipitation was a significant driver of site‐ and community‐wide temporal dynamics. Gopher disturbance appeared to drive synchrony on 2‐ to 6‐year timescales, and we detected coherent fluctuations among pairs of focal plant taxa.Synthesis. Micro‐geographies of synchrony are an intriguing phenomenon that may also help us better understand community dynamics. Additionally, the related geographies of synchrony and coherent temporal dynamics among some species pairs indicate that incorporating interspecific interactions can improve understanding of population spatial synchrony. [ABSTRACT FROM AUTHOR]