How to scale up from animal movement decisions to spatiotemporal patterns: An approach via step selection

Bridging the gap between movement data and connectivity analysis using the Time-Explicit Habitat Selection (TEHS) model

BACKGROUND

Understanding how to connect habitat remnants to facilitate the movement of species is a critical task in an increasingly fragmented world impacted by human activities. The identification of dispersal routes and corridors through connectivity analysis requires measures of landscape resistance but there has been no consensus on how to calculate resistance from habitat characteristics, potentially leading to very different connectivity outcomes.

METHODS

We propose a new model, called the Time-Explicit Habitat Selection (TEHS) model, that can be directly used for connectivity analysis. The TEHS model decomposes the movement process in a principled approach into a time and a selection component, providing complementary information regarding space use by separately assessing the drivers of time to traverse the landscape and the drivers of habitat selection. These models are illustrated using GPS-tracking data from giant anteaters (Myrmecophaga tridactyla) in the Pantanal wetlands of Brazil.

RESULTS

The time model revealed that the fastest movements tended to occur between 8 p.m. and 5 a.m., suggesting a crepuscular/nocturnal behavior. Giant anteaters moved faster over wetlands while moving much slower over forests and savannas, in comparison to grasslands. We also found that wetlands were consistently avoided whereas forest and savannas tended to be selected. Importantly, this model revealed that selection for forest increased with temperature, suggesting that forests may act as important thermal shelters when temperatures are high. Finally, using the spatial absorbing Markov chain framework, we show that the TEHS model results can be used to simulate movement and connectivity within a fragmented landscape, revealing that giant anteaters will often not use the shortest-distance path to the destination patch due to avoidance of certain habitats.

CONCLUSIONS

The proposed approach can be used to characterize how landscape features are perceived by individuals through the decomposition of movement patterns into a time and a habitat selection component. Additionally, this framework can help bridge the gap between movement-based models and connectivity analysis, enabling the generation of time-explicit connectivity results.

Looking forwards and backwards: dynamics and genealogies of locally regulated populations

We introduce a broad class of mechanistic spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial position and local population density, defined at a location to be the convolution of the point measure with a suitable non-negative integrable kernel centred on that location. We pass to three different scaling limits: an interacting superprocess, a nonlocal partial differential equation (PDE), and a classical PDE. The classical PDE is obtained both by a two-step convergence argument, in which we first scale time and population size and pass to the nonlocal PDE, and then scale the kernel that determines local population density; and in the important special case in which the limit is a reaction-diffusion equation, directly by simultaneously scaling the kernel width, timescale and population size in our individual based model. A novelty of our model is that we explicitly model a juvenile phase. The number of juveniles produced by an individual depends on local population density at the location of the parent; these juvenile offspring are thrown off in a (possibly heterogeneous, anisotropic) Gaussian distribution around the location of the parent; they then reach (instant) maturity with a probability that can depend on the local population density at the location at which they land. Although we only record mature individuals, a trace of this two-step description remains in our population models, resulting in novel limits in which the spatial dynamics are governed by a nonlinear diffusion. Using a lookdown representation, we are able to retain information about genealogies relating individuals in our population and, in the case of deterministic limiting models, we use this to deduce the backwards in time motion of the ancestral lineage of an individual sampled from the population. We observe that knowing the history of the population density is not enough to determine the motion of ancestral lineages in our model. We also investigate (and contrast) the behaviour of lineages for three different deterministic models of a population expanding its range as a travelling wave: the Fisher-KPP equation, the Allen-Cahn equation, and a porous medium equation with logistic growth.

Insights on the best release strategy from post-release movements and mortality patterns in an avian scavenger

Conservation translocations involving vultures rely either on soft- or hard-release strategies. To investigate whether these strategies affect home range stability and survival, we compared the spatial behavior and mortality of 38 Griffon vultures (Gyps fulvus) released in Sardinia. Griffons were released after no acclimatization or after 3 (short) or 15 (long acclimatization) months in an aviary. In the two years that followed their release, griffons without acclimatization did not stabilize their home range size, while those subjected to long acclimatization stabilized it in the second year. Short-acclimatized griffons always had a large home range, soon after their release. The number of individuals that reached sexual maturity was higher (71.4%) in long-acclimatized griffons than in short-acclimatized ones (40%) or in griffons that were hard released (28.6%). Soft release with a long acclimatization period seems to be the most successful method to ensure stable home ranges and the survival of griffon vultures.

Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping

The inclusion of cognitive processes, such as perception, learning and memory, are inevitable in mechanistic animal movement modelling. Cognition is the unique feature that distinguishes animal movement from mere particle movement in chemistry or physics. Hence, it is essential to incorporate such knowledge-based processes into animal movement models. Here, we summarize popular deterministic mathematical models derived from first principles that begin to incorporate such influences on movement behaviour mechanisms. Most generally, these models take the form of nonlocal reaction-diffusion-advection equations, where the nonlocality may appear in the spatial domain, the temporal domain, or both. Mathematical rules of thumb are provided to judge the model rationality, to aid in model development or interpretation, and to streamline an understanding of the range of difficulty in possible model conceptions. To emphasize the importance of biological conclusions drawn from these models, we briefly present available mathematical techniques and introduce some existing "measures of success" to compare and contrast the possible predictions and outcomes. Throughout the review, we propose a large number of open problems relevant to this relatively new area, ranging from precise technical mathematical challenges, to more broad conceptual challenges at the cross-section between mathematics and ecology. This review paper is expected to act as a synthesis of existing efforts while also pushing the boundaries of current modelling perspectives to better understand the influence of cognitive movement mechanisms on movement behaviours and space use outcomes.