This review highlights the latest developments associated with the use of the Normalized Difference Vegetation Index (NDVI) in ecology. Over the last decade, the NDVI has proven extremely useful in predicting herbivore and non-herbivore distribution, abundance and life history traits in space and time. Due to the continuous nature of NDVI since mid-1981, the relative importance of different temporal and spatial lags on population performance can be assessed, widening our understanding of population dynamics. Previously thought to be most useful in temperate environments, the utility of this satellite-derived index has been demonstrated even in sparsely vegetated areas. Climate models can be used to reconstruct historical patterns in vegetation dynamics in addition to anticipating the effects of future environmental change on biodiversity. NDVI has thus been established as a crucial tool for assessing past and future population and biodiversity consequences of change in climate, vegetation phenology and primary productivity.

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.

Abstract. Quantifying animals' home ranges is a key problem in ecology and has important conservation and wildlife management applications. Kernel density estimation (KDE) is a workhorse technique for range delineation problems that is both statistically efficient and nonparametric. KDE assumes that the data are independent and identically distributed (IID). However, animal tracking data, which are routinely used as inputs to KDEs, are inherently autocorrelated and violate this key assumption. As we demonstrate, using realistically autocorrelated data in conventional KDEs results in grossly underestimated home ranges. We further show that the performance of conventional KDEs actually degrades as data quality improves, because autocorrelation strength increases as movement paths become more finely resolved. To remedy these flaws with the traditional KDE method, we derive an autocorrelated KDE (AKDE) from first principles to use autocorrelated data, making it perfectly suited for movement data sets. We illustrate the vastly improved performance of AKDE using analytical arguments, relocation data from Mongolian gazelles, and simulations based upon the gazelle's observed movement process. By yielding better minimum area estimates for threatened wildlife populations, we believe that future widespread use of AKDE will have significant impact on ecology and conservation biology.