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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. 

Tree species appear to prefer distinct climatic conditions, but the true nature of these preferences is obscured by species interactions and dispersal, which limit species’ ranges. We quantified realized and potential thermal niches of 188 North American tree species to conduct a continental-scale test of the architecture of niches. We found strong and consistent evidence that species occurring at thermal extremes occupy less than three-quarters of their potential niches, and species’ potential niches overlap at a mean annual temperature of ~12°C. These results clarify the breadth of thermal tolerances of temperate tree species and support the centrifugal organization of thermal niches. Accounting for the nonrealized components of ecological niches will advance theory and prediction in global change ecology. 

ABSTRACT The Importance of the Regional Species PoolThe regional species pool—the set of species capable of entering a local community—is a foundational concept for understanding ecological processes that occur between local and extensive (biogeographic) spatial scales. However, the lack of precise definitions for the regional species pool, coupled with limited research into the dynamics of regional biodiversity, has impeded the development of a comprehensive framework to explain the mechanisms shaping these pools. Processes Governing Regional Species PoolsAlthough ecological processes at local and extensive scales are relatively well understood, the mechanisms shaping regional biota remain less clear. Regional species pools are likely shaped by a unique set of processes that often overlap minimally with those operating at local or extensive scales. Despite their significance, our understanding of the specific mechanisms driving the dynamics of regional species pools remains incomplete. The Need for a Theory of Regional Species PoolsWe argue that it is essential to prioritise the study of the regional species pool for two reasons. First, the regional species pool bridges spatial and temporal scales from ecological dynamics in landscapes to the long‐term processes shaping the biotas of entire biogeographic provinces. As such, understanding the dynamics of species pools addresses fundamental questions about the origin, maintenance, and dynamics of biodiversity. Second, effective biodiversity conservation in the Anthropocene hinges on understanding the processes that operate at regional scales. 

It has been proposed that climate adaptation research can benefit from an evolutionary approach. But related empirical research is lacking. We advance the evolutionary study of climate adaptation with two case studies from contemporary United States agriculture. First, we define ‘cultural adaptation to climate change’ as a mechanistic process of population-level cultural change. We argue this definition enables rigorous comparisons, yields testable hypotheses from mathematical theory and distinguishes adaptive change, non-adaptive change and desirable policy outcomes. Next, we develop an operational approach to identify ‘cultural adaptation to climate change’ based on established empirical criteria. We apply this approach to data on crop choices and the use of cover crops between 2008 and 2021 from the United States. We find evidence that crop choices are adapting to local trends in two separate climate variables in some regions of the USA. But evidence suggests that cover cropping may be adapting more to the economic environment than climatic conditions. Further research is needed to characterize the process of cultural adaptation, particularly the routes and mechanisms of cultural transmission. Furthermore, climate adaptation policy could benefit from research on factors that differentiate regions exhibiting adaptive trends in crop choice from those that do not. This article is part of the theme issue ‘Climate change adaptation needs a science of culture’. 

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. 

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.