106 citations · 398 across the 15 of their papers we have counts for
15 papers
Distinguishing between long-transient and asymptotic states in a biological aggregation model
Jonathan R. Potts, Kevin J. Painter
Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion…
Understanding step selection analysis through numerical integration
Théo Michelot, Natasha J. Klappstein, Jonathan R. Potts +1
Step selection functions (SSFs) are flexible models to jointly describe animals' movement and habitat preferences. Their popularity has grown rapidly and extensions have been devel…
Biological Modelling with Nonlocal Advection Diffusion Equations
Kevin J Painter, Thomas Hillen, Jonathan R Potts
The employment of nonlocal PDE models to describe biological aggregation and other phenomena has gained considerable traction in recent years. For cell populations, these methods g…
Weakly nonlinear analysis of a two-species non-local advection-diffusion system
Valeria Giunta, Thomas Hillen, Mark A. Lewis +1
Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection…
Detecting minimum energy states and multi-stability in nonlocal advection-diffusion models for interacting species
Valeria Giunta, Thomas Hillen, Mark A. Lewis +1
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent pa…
Local and Global Existence for Non-local Multi-Species Advection-Diffusion Models
Valeria Giunta, Thomas Hillen, Mark A. Lewis +1
Non-local 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 be…
Spatial memory and taxis-driven pattern formation in model ecosystems
Jonathan R. Potts, Mark A. Lewis
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, signif…
Integrated step selection analysis: bridging the gap between resource selection and animal movement
Tal Avgar, Jonathan R. Potts, Mark A. Lewis +1
A resource selection function is a model of the likelihood that an available spatial unit will be used by an animal, given its resource value. But how do we appropriately define av…
Territorial pattern formation in the absence of an attractive potential
Jonathan R Potts, Mark A Lewis
Territoriality is a phenomenon exhibited throughout nature. On the individual level, it is the processes by which organisms exclude others of the same species from certain parts of…
Predicting local and non-local effects of resources on animal space use using a mechanistic step selection model
Jonathan R. Potts, Guillaume Bastille-Rousseau, Dennis L. Murray +2
1. Predicting space use patterns of animals from their interactions with the environment is fundamental for understanding the effect of habitat changes on ecosystem functioning. Re…
A mathematical approach to territorial pattern formation
Jonathan R. Potts, Mark A. Lewis
Territorial behaviour is widespread in the animal kingdom, with creatures seeking to gain parts of space for their exclusive use. It arises through a complicated interplay of many…
Step selection techniques uncover the environmental predictors of space use patterns in flocks of Amazonian birds
Jonathan R. Potts, Karl Mokross, Philip C Stouffer +1
1. Anthropogenic actions cause rapid ecological changes, meaning that animals have to respond before they have time to adapt. Tools to quantify emergent spatial patterns from anima…
A generalized residual technique for analyzing complex movement models using earth mover's distance
Jonathan R. Potts, Marie Auger-Méthé, Karl Mokross +1
1. Complex systems of moving and interacting objects are ubiquitous in the natural and social sciences. Predicting their behavior often requires models that mimic these systems wit…
A unifying framework for quantifying the nature of animal interactions
Jonathan R. Potts, Karl Mokross, Mark A. Lewis
Collective phenomena, whereby agent-agent interactions determine spatial patterns, are ubiquitous in the animal kingdom. On the other hand, movement and space use are also greatly…
An anti-symmetric exclusion process for two particles on an infinite 1D lattice
Jonathan R Potts, Stephen Harris, Luca Giuggioli
A system of two biased, mutually exclusive random walkers on an infinite 1D lattice is studied whereby the intrinsic bias of one particle is equal and opposite to that of the other…