Maximum likelihood estimation for randomized shortest paths with trajectory data

Randomized shortest paths (RSPs) are tool developed in recent years for different graph and network analysis applications, such as modelling movement or flow in networks. In essence, the RSP framework considers the temperature-dependent Gibbs–Boltzmann distribution over paths in the network. At low temperatures, the distribution focuses solely on the shortest or least-cost paths, while with increasing temperature, the distribution spreads over random walks on the network. Many relevant quantities can be computed conveniently from this distribution, and these often generalize traditional network measures in a sensible way. However, when modelling real phenomena with RSPs, one needs a principled way of estimating the parameters from data. In this work, we develop methods for computing the maximum likelihood estimate of the model parameters, with focus on the temperature parameter, when modelling phenomena based on movement, flow or spreading processes. We test the validity of the derived methods with trajectories generated on artificial networks as well as with real data on the movement of wild reindeer in a geographic landscape, used for estimating the degree of randomness in the movement of the animals. These examples demonstrate the attractiveness of the RSP framework as a generic model to be used in diverse applications. randomized shortest paths; random walk; shortest path; parameter estimation; maximum likelihood; animal movement modellingpublishedVersio

Heuristics for the sustainable harvest of wildlife in stochastic social-ecological systems

Sustainable wildlife harvest is challenging due to the complexity of uncertain social-ecological systems, and diverse stakeholder perspectives of sustainability. In these systems, semi-complex stochastic simulation models can provide heuristics that bridge the gap between highly simplified theoretical models and highly context-specific case-studies. Such heuristics allow for more nuanced recommendations in low-knowledge contexts, and an improved understanding of model sensitivity and transferability to novel contexts. We develop semi-complex Management Strategy Evaluation (MSE) models capturing dynamics and variability in ecological processes, monitoring, decision-making, and harvest implementation, under a diverse range of contexts. Results reveal the fundamental challenges of achieving sustainability in wildlife harvest. Environmental contexts were important in determining optimal harvest parameters, but overall, evaluation contexts more strongly influenced perceived outcomes, optimal harvest parameters and optimal harvest strategies. Importantly, simple composite metrics popular in the theoretical literature (e.g. focusing on maximizing yield and population persistence only) often diverged from more holistic composite metrics that include a wider range of population and harvest objectives, and better reflect the trade-offs in real world applied contexts. While adaptive harvest strategies were most frequently preferred, particularly for more complex environmental contexts (e.g. high uncertainty or variability), our simulations map out cases where these heuristics may not hold. Despite not always being the optimal solution, overall adaptive harvest strategies resulted in the least value forgone, and are likely to give the best outcomes under future climatic variability and uncertainty. This demonstrates the potential value of heuristics for guiding applied management.publishedVersio

Maximum likelihood estimation for randomized shortest paths with trajectory data

Randomized shortest paths (RSPs) are tool developed in recent years for different graph and network analysis applications, such as modelling movement or flow in networks. In essence, the RSP framework considers the temperature-dependent Gibbs–Boltzmann distribution over paths in the network. At low temperatures, the distribution focuses solely on the shortest or least-cost paths, while with increasing temperature, the distribution spreads over random walks on the network. Many relevant quantities can be computed conveniently from this distribution, and these often generalize traditional network measures in a sensible way. However, when modelling real phenomena with RSPs, one needs a principled way of estimating the parameters from data. In this work, we develop methods for computing the maximum likelihood estimate of the model parameters, with focus on the temperature parameter, when modelling phenomena based on movement, flow or spreading processes. We test the validity of the derived methods with trajectories generated on artificial networks as well as with real data on the movement of wild reindeer in a geographic landscape, used for estimating the degree of randomness in the movement of the animals. These examples demonstrate the attractiveness of the RSP framework as a generic model to be used in diverse applications. randomized shortest paths; random walk; shortest path; parameter estimation; maximum likelihood; animal movement modellingpublishedVersio

Temperature-mediated habitat use and selection by a heat-sensitive northern ungulate.

This is the postprint version of the article. The published version can be located on the publisher's webpageWhile the behavioural response of animals to unfavourable climatic conditions has received increased attention recently, most habitat selection studies nonetheless ignore effects of ambient temperature. Thermoregulatory behaviour in endotherms should be most notable in species susceptible to heat stress. We evaluated whether a heat-sensitive northern ungulate, the moose (Alces alces), showed thermoregulatory behaviour in response to ambient temperature in two populations in southern Norway. We quantified the seasonal habitat use of GPS-collared adult females, as well as fine-scale habitat selection patterns, in relation to time of day and critical temperature thresholds thought to induce heat stress. We also assessed whether temperature driven changes in spatial behaviour led to a trade-off between thermal cover and forage availability. Frequent exposure to temperatures above critical thresholds occurred in both summer and winter and in both study areas. Moose responded by seeking thermal shelter in mature coniferous forest and avoiding open habitat types, leading to a trade-off between forage and cover availability in summer but not winter. Differences in habitat choice in response to temperature were most pronounced at twilight. We found that fine-scale habitat selection analyses, using step selection functions, more effectively revealed thermoregulatory behaviour in both seasons and populations than habitat use. This is because habitat selection analyses are better able to identify limiting factors operating at different spatiotemporal scales than habitat use. Future studies on thermoregulatory animal behaviour should focus on the effect of abiotic factors, such as climate, on habitat-fitness relationships, which may be critical to understanding population responses to a changing climate

Accelerating advances in landscape connectivity modelling with the ConScape library

Increasingly precise spatial data (e.g. high-resolution imagery from remote sensing) allow for improved representations of the landscape network for assessing the combined effects of habitat loss and connectivity declines on biodiversity. However, evaluating large landscape networks presents a major computational challenge both in terms of working memory and computation time. We present the ConScape (i.e. “connected landscapes”) software library implemented in the high-performance open-source Julia language to compute metrics for connected habitat and movement flow on high-resolution landscapes. The combination of Julia's ‘just-in-time’ compiler, efficient algorithms and ‘landmarks’ to reduce the computational load allows ConScape to compute landscape ecological metrics—originally developed in metapopulation ecology (such as ‘metapopulation capacity’ and ‘probability of connectivity’)—for large landscapes. An additional major innovation in ConScape is the adoption of the randomized shortest paths framework to represent connectivity along the continuum from optimal to random movements, instead of only those extremes. We demonstrate ConScape's potential for using large datasets in sustainable land planning by modelling landscape connectivity based on remote-sensing data paired with GPS tracking of wild reindeer in Norway. To guide users, we discuss other applications, and provide a series of worked examples to showcase all ConScape's functionalities in Supplementary Material. Built by a team of ecologists, network scientists and software developers, ConScape is able to efficiently compute landscape metrics for high-resolution landscape representations to leverage the availability of large data for sustainable land use and biodiversity conservation. As a Julia implementation, ConScape combines computational efficiency with a transparent code base, which facilitates continued innovation through contributions from the rapidly growing community of landscape and connectivity modellers using Julia. circuitscape, conefor, ecological networks, least-cost path, metapopulation, random walk, randomized shortest pathspublishedVersio

‘You shall not pass!’: quantifying barrier permeability and proximity avoidance by animals

1. Impediments to animal movement are ubiquitous and vary widely in both scale and permeability. It is essential to understand how impediments alter ecological dynamics via their influence on animal behavioural strategies governing space use and, for anthropogenic features such as roads and fences, how to mitigate these effects to effectively manage species and landscapes.2. Here, we focused primarily on barriers to movement, which we define as features that cannot be circumnavigated but may be crossed. Responses to barriers will be influenced by the movement capabilities of the animal, its proximity to the barriers, and habitat preference. We developed a mechanistic modelling framework for simultaneously quantifying the permeability and proximity effects of barriers on habitat preference and movement.3. We used simulations based on our model to demonstrate how parameters on movement, habitat preference and barrier permeability can be estimated statistically. We then applied the model to a case study of road effects on wild mountain reindeer summer movements.4. This framework provided unbiased and precise parameter estimates across a range of strengths of preferences and barrier permeabilities. The quality of permeability estimates, however, was correlated with the number of times the barrier is crossed and the number of locations in proximity to barriers. In the case study we found that reindeer avoided areas near roads and that roads are semi-permeable barriers to movement. There was strong avoidance of roads extending up to c. 1 km for four of five animals, and having to cross roads reduced the probability of movement by 68·6% (range 3·5–99·5%).5. Human infrastructure has embedded within it the idea of networks: nodes connected by linear features such as roads, rail tracks, pipelines, fences and cables, many of which divide the landscape and limit animal movement. The unintended but potentially profound consequences of infrastructure on animals remain poorly understood. The rigorous framework for simultaneously quantifying movement, habitat preference and barrier permeability developed here begins to address this knowledge gap

A Migratory Northern Ungulate in the Pursuit of Spring: Jumping or Surfing the Green Wave?

The forage-maturation hypothesis (FMH) states that herbivores migrate along a phenological gradient of plant development in order to maximize energy intake. Despite strong support for the FMH, the actual relationship between plant phenology and ungulate movement has remained enigmatic. We linked plant phenology (MODIS–normalized difference vegetation index [NDVI] data) and space use of 167 migratory and 78 resident red deer (Cervus elaphus), using a space-time-time matrix of “springness,” defined as the instantaneous rate of green-up. Consistent with the FMH, migrants experienced substantially greater access to early plant phenology than did residents. Deer were also more likely to migrate in areas where migration led to greater gains in springness. Rather than “surfing the green wave” during migration, migratory red deer moved rapidly from the winter to the summer range, thereby “jumping the green wave.” However, migrants and, to a lesser degree, residents did track phenological green-up through parts of the growing season by making smaller-scale adjustments in habitat use. Despite pronounced differences in their life histories, we found only marginal differences between male and female red deer in this study. Those differences that we did detect pointed toward additional constraints on female space-use tactics, such as those posed by calving and caring for dependent offspring.We conclude that whereas in some systems migration itself is a way to surf the green wave, in others it may simply be a means to reconnect with phenological spring at the summer range. In the light of ubiquitous anthropogenic environmental change, understanding the relationship between the green wave and ungulate space use has important consequences for the management and conservation of migratory ungulates and the phenomenon of migration itself

Estimating the cumulative impact and zone of influence of anthropogenic features on biodiversity

1. The concept of cumulative impacts is widespread in policy documents, regulations and ecological studies, but quantification methods are still evolving. Infrastructure development usually takes place in landscapes with preexisting anthropogenic features. Typically, their impact is determined by computing the distance to the nearest feature only, thus ignoring the potential cumulative impacts of multiple features. We propose the cumulative ZOI approach to assess whether and to what extent anthropogenic features lead to cumulative impacts.2. The approach estimates both effect size and zone of influence (ZOI) of anthropogenic features and allows for estimation of cumulative effects of multiple features distributed in the landscape. First, we use simulations and an empirical study to understand under which circumstances cumulative impacts arise. Second, we demonstrate the approach by estimating the cumulative impacts of tourist infrastructure in Norway on the habitat of wild reindeer (Rangifer t. tarandus), a near-threatened species highly sensitive to anthropogenic disturbance.3. In the simulations, we showed that analyses based on the nearest feature and our cumulative approach are indistinguishable in two extreme cases: when features are few and scattered and their ZOI is small, and when features are clustered and their ZOI is large. The empirical analyses revealed cumulative impacts of private cabins and tourist resorts on reindeer, extending up to 10 and 20 km, with different decaying functions. Although the impact of an isolated private cabin was negligible, the cumulative impact of `cabin villages' could be much larger than that of a single large tourist resort. Focusing on the nearest feature only underestimates the impact of `cabin villages' on reindeer.4. The suggested approach allows us to quantify the magnitude and spatial extent of cumulative impacts of point, linear, and polygon features in a computationally efficient and flexible way and is implemented in the oneimpact R package. The formal framework offers the possibility to avoid widespread underestimations of anthropogenic impacts in ecological and impact assessment studies and can be applied to a wide range of spatial response variables, including habitat selection, population abundance, species richness and diversity, community dynamics and other ecological processes

Estimating and managing broad risk of chronic wasting disease spillover among cervid species

The management of infectious wildlife diseases often involves tackling pathogens that infect multiple host species. Chronic wasting disease (CWD) is a prion disease that can infect most cervid species. CWD was detected in reindeer (Rangifer tarandus) in Norway in 2016. Sympatric populations of red deer (Cervus elaphus) and moose (Alces alces) are at immediate risk. However, the estimation of spillover risk across species and implementation of multispecies management policies are rarely addressed for wildlife. Here, we estimated the broad risk of CWD spillover from reindeer to red deer and moose by quantifying the probability of co-occurrence based on both (1) population density and (2) habitat niche overlap from GPS data of all three species in Nordfjella, Norway. We describe the practical challenges faced when aiming to reduce the risk of spillover through a marked reduction in the population densities of moose and red deer using recreational hunters. This involves setting the population and harvest aims with uncertain information and how to achieve them. The niche overlap between reindeer and both moose and red deer was low overall but occurred seasonally. Migratory red deer had a moderate niche overlap with the CWD-infected reindeer population during the calving period, whereas moose had a moderate niche overlap during both calving and winter. Incorporating both habitat overlap and the population densities of the respective species into the quantification of co-occurrence allowed for more spatially targeted risk maps. An initial aim of a 50% reduction in abundance for the Nordfjella region was set, but only a moderate population decrease of less than 20% from 2016 to 2021 was achieved. Proactive management in the form of marked population reduction is invasive and unpopular when involving species of high societal value, and targeting efforts to zones with a high risk of spillover to limit adverse impacts and achieve wider societal acceptance is important. disease management, host range, moose, multihost pathogens, niche overlap, Norway, population estimation, red deer, reindeerpublishedVersio