@article{PottsSchlaegel2020,
  author    = {Potts, Jonathan R. and Schl{\"a}gel, Ulrike E.},
  title     = {Parametrizing diffusion-taxis equations from animal movement trajectories using step selection analysis},
  series = {Methods in ecology and evolution : an official journal of the British Ecological Society},
  volume    = {11},
  journal   = {Methods in ecology and evolution : an official journal of the British Ecological Society},
  number    = {9},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {2041-210X},
  doi       = {10.1111/2041-210X.13406},
  pages     = {1092 -- 1105},
  year      = {2020},
  abstract  = {Mathematical analysis of partial differential equations (PDEs) has led to many insights regarding the effect of organism movements on spatial population dynamics. However, their use has mainly been confined to the community of mathematical biologists, with less attention from statistical and empirical ecologists. We conjecture that this is principally due to the inherent difficulties in fitting PDEs to data. To help remedy this situation, in the context of movement ecology, we show how the popular technique of step selection analysis (SSA) can be used to parametrize a class of PDEs, calleddiffusion-taxismodels, from an animal's trajectory. We examine the accuracy of our technique on simulated data, then demonstrate the utility of diffusion-taxis models in two ways. First, for non-interacting animals, we derive the steady-state utilization distribution in a closed analytic form. Second, we give a recipe for deriving spatial pattern formation properties that emerge from interacting animals: specifically, do those interactions cause heterogeneous spatial distributions to emerge and if so, do these distributions oscillate at short times or emerge without oscillations? The second question is applied to data on concurrently tracked bank volesMyodes glareolus. Our results show that SSA can accurately parametrize diffusion-taxis equations from location data, providing the frequency of the data is not too low. We show that the steady-state distribution of our diffusion-taxis model, where it is derived, has an identical functional form to the utilization distribution given by resource selection analysis (RSA), thus formally linking (fine scale) SSA with (broad scale) RSA. For the bank vole data, we show how our SSA-PDE approach can give predictions regarding the spatial aggregation and segregation of different individuals, which are difficult to predict purely by examining results of SSA. Our methods provide a user-friendly way into the world of PDEs, via a well-used statistical technique, which should lead to tighter links between the findings of mathematical ecology and observations from empirical ecology. By providing a non-speculative link between observed movement behaviours and space use patterns on larger spatio-temporal scales, our findings will also aid integration of movement ecology into understanding spatial species distributions.},
  language  = {en}
}
@article{SchlaegelMerrillLewis2017,
  author    = {Schl{\"a}gel, Ulrike E. and Merrill, Evelyn H. and Lewis, Mark A.},
  title     = {Territory surveillance and prey management: Wolves keep track of space and time},
  series = {Ecology and evolution},
  volume    = {7},
  journal   = {Ecology and evolution},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {2045-7758},
  doi       = {10.1002/ece3.3176},
  pages     = {8388 -- 8405},
  year      = {2017},
  abstract  = {Identifying behavioral mechanisms that underlie observed movement patterns is difficult when animals employ sophisticated cognitive\&\#8208;based strategies. Such strategies may arise when timing of return visits is important, for instance to allow for resource renewal or territorial patrolling. We fitted spatially explicit random\&\#8208;walk models to GPS movement data of six wolves (Canis lupus; Linnaeus, 1758) from Alberta, Canada to investigate the importance of the following: (1) territorial surveillance likely related to renewal of scent marks along territorial edges, to reduce intraspecific risk among packs, and (2) delay in return to recently hunted areas, which may be related to anti\&\#8208;predator responses of prey under varying prey densities. The movement models incorporated the spatiotemporal variable "time since last visit," which acts as a wolf's memory index of its travel history and is integrated into the movement decision along with its position in relation to territory boundaries and information on local prey densities. We used a model selection framework to test hypotheses about the combined importance of these variables in wolf movement strategies. Time\&\#8208;dependent movement for territory surveillance was supported by all wolf movement tracks. Wolves generally avoided territory edges, but this avoidance was reduced as time since last visit increased. Time\&\#8208;dependent prey management was weak except in one wolf. This wolf selected locations with longer time since last visit and lower prey density, which led to a longer delay in revisiting high prey density sites. Our study shows that we can use spatially explicit random walks to identify behavioral strategies that merge environmental information and explicit spatiotemporal information on past movements (i.e., "when" and "where") to make movement decisions. The approach allows us to better understand cognition\&\#8208;based movement in relation to dynamic environments and resources.},
  language  = {en}
}