David J. Murrell

Time series are a critical component of ecological analysis, used to track changes in biotic and abiotic variables. Information can be extracted from the properties of time series for tasks such as classification (e.g., assigning species to individual bird calls); clustering (e.g., clustering similar responses in population dynamics to abrupt changes in the environment or management interventions); prediction (e.g., accuracy of model predictions to original time series data); and anomaly detection (e.g., detecting possible catastrophic events from population time series). These common tasks in ecological research all rely on the notion of (dis‐) similarity, which can be determined using distance measures. A plethora of distance measures have been described, predominantly in the computer and information sciences, but many have not been introduced to ecologists. Furthermore, little is known about how to select appropriate distance measures for time‐series‐related tasks. Therefore, many potential applications remain unexplored. Here, we describe 16 properties of distance measures that are likely to be of importance to a variety of ecological questions involving time series. We then test 42 distance measures for each property and use the results to develop an objective method to select appropriate distance measures for any task and ecological dataset. We demonstrate our selection method by applying it to a set of real‐world data on breeding bird populations in the UK and discuss other potential applications for distance measures, along with associated technical issues common in ecology. Our real‐world population trends exhibit a common challenge for time series comparisons: a high level of stochasticity. We demonstrate two different ways of overcoming this challenge, first by selecting distance measures with properties that make them well suited to comparing noisy time series and second by applying a smoothing algorithm before selecting appropriate distance measures. In both cases, the distance measures chosen through our selection method are not only fit‐for‐purpose but are consistent in their rankings of the population trends. The results of our study should lead to an improved understanding of, and greater scope for, the use of distance measures for comparing ecological time series and help us answer new ecological questions.

Aim The exceptional turnover in biota with elevation and number of species coexisting at any elevation makes tropical mountains hotspots of biodiversity. However, understanding the historical processes through which species arising in geographical isolation (i.e. allopatry) assemble along the same mountain slope (i.e. sympatry) remains a major challenge. Multiple models have been proposed including (1) the sorting of already elevationally divergent species, (2) the displacement of elevation upon secondary contact, potentially followed by convergence, or (3) elevational conservatism, in which ancestral elevational ranges are retained. However, the relative contribution of these processes to generating patterns of elevational overlap and turnover is unknown. Location Tropical mountains of Central‐ and South‐America. Time Period The last 12 myr. Major Taxa Studied Birds. Methods We collate a dataset of 165 avian sister pairs containing estimates of phylogenetic age, geographical and regional elevational range overlap. We develop a framework based on continuous‐time Markov models to infer the relative frequency of different historical pathways in explaining present‐day overlap and turnover of sympatric species along elevational gradients. Results We show that turnover of closely related bird species across elevation can predominantly be explained by displacement of elevation ranges upon contact (81%) rather than elevational divergence in allopatry (19%). In contrast, overlap along elevation gradients is primarily (88%) explained by conservatism of elevational ranges rather than displacement followed by elevational expansion (12%). Main Conclusions Bird communities across elevation gradients are assembled through a mix of processes, including the sorting, displacement and conservatism of species elevation ranges. The dominant role of conservatism in explaining co‐occurrence of species on mountain slopes rejects more complex scenarios requiring displacement followed by expansion. The ability of closely related species to coexist without elevational divergence provides a direct and faster pathway to sympatry and helps explain the exceptional species richness of tropical mountains.