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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. 

Pests and pathogens are a primary threat to honey bee(Apis mellifera)colonies worldwide. Selective breeding for honey bees resistant to these stressors represents a promising approach for mitigating their impacts on honey bee health. UBeeO is a novel hygiene-eliciting selection tool that has been used to identify honey bee colonies that are resistant to the parasitic miteVarroa destructor, and that are more likely to survive winter without beekeeper intervention. Here, we used three separate case studies to evaluate the effectiveness of the UBeeO assay in identifying colonies resist to disease. In three distinct geographic regions, we measured UBeeO scores along with the prevalence and load of key fungal and viral honey bee pathogens. We show that UBeeO can be used to identify colonies resistant to several other diseases, including the two fungal pathogens chalkbrood (Ascosphaera apis) andVairimorphaspp. (previouslyNosema), and multiple viruses, all critically important to honey bee health and survival. Furthermore, we identify potential UBeeO resistance thresholds for each pathogen, demonstrating an inverse relationship between pathogen virulence and the minimum UBeeO score associated with resistance to that pathogen. These findings suggest that UBeeO-guided selection strategies have the potential to significantly improve honey bee breeding programs by facilitating identification of resilient and pathogen-resistant colonies. The broad geographic range of our study sites underscores the robustness and applicability of UBeeO across varying environmental contexts. Since honey bees provide essential pollination services in both natural and agricultural ecosystems, this work has major implications for environmental health, crop productivity, and food security on a global scale.