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Information processing is increasingly recognized as a fundamental component of life in variable environments, including the evolved use of environmental cues, biomolecular networks, and social learning. Despite this, ecology lacks a quantitative framework for understanding how population, community, and ecosystem dynamics depend on information processing. Here, we review the rationale and evidence for 'fitness value of information' (FVOI), and synthesize theoretical work in ecology, information theory, and probability behind this general mathematical framework. The FVOI quantifies how species' per capita population growth rates can depend on the use of information in their environment. FVOI is a breakthrough approach to linking information processing and ecological and evolutionary outcomes in a changing environment, addressing longstanding questions about how information mediates the effects of environmental change and species interactions. [ABSTRACT FROM AUTHOR]

Forecasting the impacts of climate change on biological diversity requires better ways to incorporate competitive interactions into predictions of species' range dynamics and persistence. This problem has been studied extensively in a different context by theoreticians evaluating the coexistence of species in spatially heterogeneous environments. Here, we show how spatial coexistence theory can be adapted to provide a mathematical framework for understanding species persistence in competitive communities under climate change. We first show how the spatial low‐density growth rate provides the relevant metric of species persistence along a climate gradient. We then analyse a model of multiple migrating competitors to show how mechanisms contributing to low‐density growth rates quantify the effect of different competitive processes on persistence, and how these processes change in strength with species' asynchronous migration under climate change. Finally, we outline the empirical utility of the framework, showing how the theory can scale up from local measurements of species performance and competitive interactions to range‐scale metrics of persistence. Treating species' range dynamics as a geographical‐scale coexistence problem presents its own set of challenges, but building from a well‐established body of theory may greatly improve the predictability of species persistence in competitive communities under climate change. [ABSTRACT FROM AUTHOR]