Biological modeling with nonlocal advection–diffusion equations

KJ Painter, T Hillen, JR Potts - Mathematical Models and Methods in …, 2024‏ - World Scientific
The employment of nonlocal PDE models to describe biological aggregation and other
phenomena has gained considerable traction in recent years. For cell populations, these …

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

H Wang, Y Salmaniw - Journal of Mathematical Biology, 2023‏ - Springer
The inclusion of cognitive processes, such as perception, learning and memory, are
inevitable in mechanistic animal movement modelling. Cognition is the unique feature that …

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

JR Potts, L Börger - Journal of Animal Ecology, 2023‏ - Wiley Online Library
Uncovering the mechanisms behind animal space use patterns is of vital importance for
predictive ecology, thus conservation and management of ecosystems. Movement is a core …

Spatial movement with distributed memory

Q Shi, J Shi, H Wang - Journal of Mathematical Biology, 2021‏ - Springer
Diffusion has been widely applied to model animal movement that follows Brownian motion.
However, animals typically move in non-Brownian ways due to their perceptual judgment …

Bifurcations in a diffusive resource-consumer model with distributed memory

H Shen, Y Song, H Wang - Journal of Differential Equations, 2023‏ - Elsevier
Spatial memory is significant in modeling animal movement. For a diffusive consumer-
resource model, a memory-based diffusion of consumer can result in richer and more …

Local and global existence for nonlocal multispecies advection-diffusion models

V Giunta, T Hillen, M Lewis, JR Potts - SIAM Journal on Applied Dynamical …, 2022‏ - SIAM
Nonlocal advection is a key process in a range of biological systems, from cells within
individuals to the movement of whole organisms. Consequently, in recent years, there has …

Estimating interactions between individuals from concurrent animal movements

UE Schlägel, J Signer, A Herde, S Eden… - Methods in Ecology …, 2019‏ - Wiley Online Library
Animal movements arise from complex interactions of individuals with their environment,
including both conspecific and heterospecific individuals. Animals may be attracted to each …

Spatial memory and taxis-driven pattern formation in model ecosystems

JR Potts, MA Lewis - Bulletin of mathematical biology, 2019‏ - Springer
Mathematical models of spatial population dynamics typically focus on the interplay between
dispersal events and birth/death processes. However, for many animal communities …

Identifying signals of memory from observations of animal movements

D Kim, PR Thompson, DW Wolfson, JA Merkle… - Movement Ecology, 2024‏ - Springer
Incorporating memory (ie, some notion of familiarity or experience with the landscape) into
models of animal movement is a rising challenge in the field of movement ecology. The …

Turing instabilities are not enough to ensure pattern formation

AL Krause, EA Gaffney, TJ Jewell, V Klika… - Bulletin of Mathematical …, 2024‏ - Springer
Symmetry-breaking instabilities play an important role in understanding the mechanisms
underlying the diversity of patterns observed in nature, such as in Turing's reaction–diffusion …