Memory is critical to understanding animal movement but has proven challenging to study. Advances in animal tracking technology, theoretical movement models and cognitive sciences have facilitated research in each of these fields, but also created a need for synthetic examination of the linkages between memory and animal movement. Here, we draw together research from several disciplines to understand the relationship between animal memory and movement processes. First, we frame the problem in terms of the characteristics, costs and benefits of memory as outlined in psychology and neuroscience. Next, we provide an overview of the theories and conceptual frameworks that have emerged from behavioural ecology and animal cognition. Third, we turn to movement ecology and summarise recent, rapid developments in the types and quantities of available movement data, and in the statistical measures applicable to such data. Fourth, we discuss the advantages and interrelationships of diverse modelling approaches that have been used to explore the memory–movement interface. Finally, we outline key research challenges for the memory and movement communities, focusing on data needs and mathematical and computational challenges. We conclude with a roadmap for future work in this area, outlining axes along which focused research should yield rapid progress.

Understanding animal movement is essential to elucidate how animals interact, survive, and thrive in a changing world. Recent technological advances in data collection and management have transformed our understanding of animal “movement ecology” (the integrated study of organismal movement), creating a big-data discipline that benefits from rapid, cost-effective generation of large amounts of data on movements of animals in the wild. These high-throughput wildlife tracking systems now allow more thorough investigation of variation among individuals and species across space and time, the nature of biological interactions, and behavioral responses to the environment. Movement ecology is rapidly expanding scientific frontiers through large interdisciplinary and collaborative frameworks, providing improved opportunities for conservation and insights into the movements of wild animals, and their causes and consequences.

Organismal movement is ubiquitous and facilitates important ecological mechanisms that drive community and metacommunity composition and hence biodiversity. In most existing ecological theories and models in biodiversity research, movement is represented simplistically, ignoring the behavioural basis of movement and consequently the variation in behaviour at species and individual levels. However, as human endeavours modify climate and land use, the behavioural processes of organisms in response to these changes, including movement, become critical to understanding the resulting biodiversity loss. Here, we draw together research from different subdisciplines in ecology to understand the impact of individual‐level movement processes on community‐level patterns in species composition and coexistence. We join the movement ecology framework with the key concepts from metacommunity theory, community assembly and modern coexistence theory using the idea of micro–macro links, where various aspects of emergent movement behaviour scale up to local and regional patterns in species mobility and mobile‐link‐generated patterns in abiotic and biotic environmental conditions. These in turn influence both individual movement and, at ecological timescales, mechanisms such as dispersal limitation, environmental filtering, and niche partitioning. We conclude by highlighting challenges to and promising future avenues for data generation, data analysis and complementary modelling approaches and provide a brief outlook on how a new behaviour‐based view on movement becomes important in understanding the responses of communities under ongoing environmental change.

Analyses of animal movement data have primarily focused on understanding patterns of space use and the behavioural processes driving them. Here, we analyzed animal movement data to infer components of individual fitness, specifically parturition and neonate survival. We predicted that parturition and neonate loss events could be identified by sudden and marked changes in female movement patterns. Using GPS radio‐telemetry data from female woodland caribou (Rangifer tarandus caribou), we developed and tested two novel movement‐based methods for inferring parturition and neonate survival. The first method estimated movement thresholds indicative of parturition and neonate loss from population‐level data then applied these thresholds in a moving‐window analysis on individual time‐series data. The second method used an individual‐based approach that discriminated among three a priori models representing the movement patterns of non‐parturient females, females with surviving offspring, and females losing offspring. The models assumed that step lengths (the distance between successive GPS locations) were exponentially distributed and that abrupt changes in the scale parameter of the exponential distribution were indicative of parturition and offspring loss. Both methods predicted parturition with near certainty (>97% accuracy) and produced appropriate predictions of parturition dates. Prediction of neonate survival was affected by data quality for both methods; however, when using high quality data (i.e., with few missing GPS locations), the individual‐based method performed better, predicting neonate survival status with an accuracy rate of 87%. Understanding ungulate population dynamics often requires estimates of parturition and neonate survival rates. With GPS radio‐collars increasingly being used in research and management of ungulates, our movement‐based methods represent a viable approach for estimating rates of both parameters.

This note reviews the Peano-Baker series and its use to solve the general linear system of ODEs. The account is elementary and self-contained, and is meant as a pedagogic introduction to this approach, which is well known but usually treated as a folklore result or as a purely formal tool. Here, a simple convergence result is given, and two examples illustrate that the series can be used explicitly as well.