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Stochastic diffusion is the noisy process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. These processes are increasingly important to better prepare for pandemics and as species ranges shift in response to climate change. Unfortunately, modelling is mostly done with expensive computational simulations or inaccurate deterministic tools that ignore the randomness of dispersal. We introduce ‘mean-FLAME’ models, tracking stochastic dispersion using approximate master equations to follow the probability distribution over all possible states of an area of interest, up to states active enough to be approximated using a mean-field model. In the limit where we track all states, this approach is locally exact, and in the other limit collapses to traditional deterministic models. In predator–prey systems, we show that tracking a handful of states around key absorbing states is sufficient to accurately model extinction. In disease models, we show that classic mean-field approaches underestimate the heterogeneity of epidemics. And in nonlinear dispersal models, we show that deterministic tools fail to capture the speed of spatial diffusion. These effects are all important for marginal areas that are close to unsuitable for diffusion, like the edge of a species range or epidemics in small populations. 

Understanding the role of humans as ‘ecosystem engineers’ requires a deep-time perspective rooted in evolutionary history and the fossil record. However, no con-ceptual framework exists for studying the rise of ecosystem engineering in deep time, requiring us to consider effects that fall outside the scope of traditional defini-tions. Here, we present a new framework applicable to both modern and ancient engineering-type effects. We propose a new term – ‘Earth system engineering’ – to describe biological processes that alter the structure and function of planetary spheres, and which combines core tenets of ecosystem engineering, niche construction, and legacy effects. We illustrate this framework using the fossil record, and show how it can be applied across the tree of life, and throughout Earth history. 

Abstract While human activities are known to elicit rapid turnover in species composition through time, the properties of the species that increase or decrease their spatial occupancy underlying this turnover are less clear. Here, we used an extensive dataset of 238 metacommunity time series of multiple taxa spread across the globe to evaluate whether species that are more widespread (large-ranged species) differed in how they changed their site occupancy over the 10–90 years the metacommunities were monitored relative to species that are more narrowly distributed (small-ranged species). We found that on average, large-ranged species tended to increase in occupancy through time, whereas small-ranged species tended to decrease. These relationships were stronger in marine than in terrestrial and freshwater realms. However, in terrestrial regions, the directional changes in occupancy were less extreme in protected areas. Our findings provide evidence for systematic decreases in occupancy of small-ranged species, and that habitat protection could mitigate these losses in the face of environmental change. 

Estimating biodiversity change across the planet in the context of widespread human modification is a critical challenge. Here, we review how biodiversity has changed in recent decades across scales and taxonomic groups, focusing on four diversity metrics: species richness, temporal turnover, spatial beta-diversity and abundance. At local scales, change across all metrics includes many examples of both increases and declines and tends to be centred around zero, but with higher prevalence of declining trends in beta-diversity (increasing similarity in composition across space or biotic homogenization) and abundance. The exception to this pattern is temporal turnover, with changes in species composition through time observed in most local assemblages. Less is known about change at regional scales, although several studies suggest that increases in richness are more prevalent than declines. Change at the global scale is the hardest to estimate accurately, but most studies suggest extinction rates are probably outpacing speciation rates, although both are elevated. Recognizing this variability is essential to accurately portray how biodiversity change is unfolding, and highlights how much remains unknown about the magnitude and direction of multiple biodiversity metrics at different scales. Reducing these blind spots is essential to allow appropriate management actions to be deployed. This article is part of the theme issue ‘Detecting and attributing the causes of biodiversity change: needs, gaps and solutions’. 

Abstract There is considerable interest in understanding patterns of β‐diversity that measure the amount of change in species composition through space or time. Most hypotheses for β‐diversity evoke nonrandom processes that generate spatial and temporal within‐species aggregation; however, β‐diversity can also be driven by random sampling processes. Here, we describe a framework based on rarefaction curves that quantifies the nonrandom contribution of species compositional differences across samples to β‐diversity. We isolate the effect of within‐species spatial or temporal aggregation on beta‐diversity using a coverage standardized metric of β‐diversity (β_C). We demonstrate the utility of our framework using simulations and an empirical case study examining variation in avian species composition through space and time in engineered versus natural riparian areas. The primary strengths of our approach are that it provides an intuitive visual null model for expected patterns of biodiversity under random sampling that allows integrating analyses across α‐, γ‐, and β‐scales. Importantly, the method can accommodate comparisons between communities with different species pool sizes, and it can be used to examine species turnover both within and between meta‐communities. 

Abstract Biodiversity metrics often integrate data on the presence and abundance of multiple species. Yet our understanding of covariation between changes to the numbers of individuals, the evenness of species relative abundances, and the total number of species remains limited. Using individual‐based rarefaction curves, we show how expected positive relationships among changes in abundance, evenness and richness arise, and how they can break down. We then examined interdependencies between changes in abundance, evenness and richness in more than 1100 assemblages sampled either through time or across space. As predicted, richness changes were greatest when abundance and evenness changed in the same direction, and countervailing changes in abundance and evenness acted to constrain the magnitude of changes in species richness. Site‐to‐site differences in abundance, evenness, and richness were often decoupled, and pairwise relationships between these components across assemblages were weak. In contrast, changes in species richness and relative abundance were strongly correlated for assemblages varying through time. Temporal changes in local biodiversity showed greater inertia and stronger relationships between the component changes when compared to site‐to‐site variation. Overall, local variation in assemblage diversity was rarely due to repeated passive samples from an approximately static species abundance distribution. Instead, changing species relative abundances often dominated local variation in diversity. Moreover, how changing relative abundances combined with changes to total abundance frequently determined the magnitude of richness changes. Embracing the interdependencies between changing abundance, evenness and richness can provide new information to better understand biodiversity change in the Anthropocene. 

Social change in any society entails changes in both behaviours and institutions. We model a group-structured society in which the transmission of individual behaviour occurs in parallel with the selection of group-level institutions. We consider a cooperative behaviour that generates collective benefits for groups but does not spread between individuals on its own. Groups exhibit institutions that increase the diffusion of the behaviour within the group, but also incur a group cost. Groups adopt institutions in proportion to their fitness. Finally, the behaviour may also spread globally. We find that behaviour and institutions can be mutually reinforcing. But the model also generates behavioural source-sink dynamics when behaviour generated in institutionalized groups spreads to non-institutionalized groups and boosts their fitness. Consequently, the global diffusion of group-beneficial behaviour creates a pattern of institutional free-riding that limits the evolution of group-beneficial institutions. Our model suggests that, in a group-structured society, large-scale beneficial social change can be best achieved when the relevant behaviour and institutions remain correlated. 

Crop switching, in which farmers grow a crop that is novel to a given field, can help agricultural systems adapt to changing environmental, cultural, and market forces. Yet while regional crop production trends receive significant attention, relatively little is known about the local-scale crop switching that underlies these macrotrends. We characterized local crop-switching patterns across the United States using the US Department of Agriculture (USDA) Cropland Data Layer, an annual time series of high resolution (30 m pixel size) remote-sensed cropland data from 2008 to 2022. We found that at multiple spatial scales, crop switching was most common in sparsely cultivated landscapes and in landscapes with high crop diversity, whereas it was low in homogeneous, highly agricultural areas such as the Midwestern corn belt, suggesting a number of potential social and economic mechanisms influencing farmers’ crop choices. Crop-switching rates were high overall, occurring on more than 6% of all US cropland in the average year. Applying a framework that classified crop switches based on their temporal novelty (crop introduction versus discontinuation), spatial novelty (locally divergent versus convergent switching), and categorical novelty (transformative versus incremental switching), we found distinct spatial patterns for these three novelty dimensions, indicating a dynamic and multifaceted set of cropping changes across US farms. Collectively, these results suggest that innovation through crop switching is playing out very differently in various parts of the country, with potentially significant implications for the resilience of agricultural systems to changes in climate and other systemic trends.