A hierarchical framework for segmenting movement paths

Comparative applications of animal movement path analyses are hampered by the lack of a comprehensive framework for linking structures and processes conceived at different spatio-temporal scales. Although many analyses begin by generating step-length (SL) and turning-angle (TA) distributions from relocation time-series data--some of which are linked to ecological, landscape, and environmental covariates--the frequency at which these data are collected may vary from sub-seconds to several hours, or longer. The kinds of questions that may be asked of these data, however, are very much scale-dependent. It thus behooves us to clarify how the scale at which SL and TA data are collected and relate to one another, as well as the kinds of ecological questions that can be asked. Difficulties arise because the information contained in SL and TA time series is not semantically aligned with the physiological, ecological, and sociological factors that influence the structure of movement paths. I address these difficulties by classifying movement types at salient temporal scales using two different kinds of vocabularies. The first is the language derived from behavioral and ecological concepts. The second is the language derived from mathematically formulated stochastic walks. The primary tools for analyzing these walks are fitting time-series and stochastic-process models to SL and TA statistics (means, variances, correlations, individual-state and local environmental covariates), while paying attention to movement patterns that emerge at various spatial scales. The purpose of this paper is to lay out a more coherent, hierarchical, scale-dependent, appropriate-complexity framework for conceptualizing path segments at different spatio-temporal scales and propose a method for extracting a simulation model, referred to as M3, from these data when at a relatively high frequencies (ideally minute-by-minute). Additionally, this framework is designed to bridge biological and mathematical movement ecology concepts; thereby stimulating the development of conceptually-rooted methods that facilitates the formulation of our M3 model for simulating theoretical and analyzing empirical data, which can then be used to test hypothesis regarding mechanisms driving animal movement and make predications of animal movement responses to management and global change.