Analysis of a Class of Low-Dimensional Models of Mutation and Predation

We consider a class of simple two-dimensional discrete models representative of a system incorporating both mutation and predation. A selection of analytic and numerical results are presented, classifying the dynamic behavior of the system by means of Lyapunov exponents over a biologically-reasonable region of parameter space, and illustrating the occurrence of hyperchaos and a Neimark–Sacker bifurcation producing regions of quasiperiodicity.</jats:p

Sequences of patch disturbance in a spatial eco-evolutionary model

An eco-evolutionary food web model assembles two heterogeneous meta-communities on a 6 X 6 spatial network, which are subjected to a series of patch disturbances that either kill or evict the local population. If patch destruction is permanent, displacement of affected populations is as severe as eliminating them. If re-colonisation of cleared patches is permitted, the meta-community can endure repeated displacement indefinitely but with limited biodiversity. Whether repeated elimination of local populations can be endured depends on the rules governing migration. In meta-communities composed of rare, low-range species, displacing the inhabitants of low-diversity individual patches can be more damaging to global biodiversity than eliminating them, demonstrating the destructive potential of small invasions and the need for careful efforts when relocating endangered populations

Allometry in an eco-evolutionary network model

An eco-evolutionary food web model is modified to incorporate a body-size trait, enabling a framework for non- uniform mortality and ecological efficiency between species. Evolved communities feature increased connectance, with according benefits to community robustness, and persistent top predators but reduced omnivory and food chain lengths. Body-size maintains a strong positive correlation to trophic level, but does not correlate to an individual species' contribution to network stability. A spatially-explicit extension of the model assembles large metacommunities with distinct distributions of body-size amongst local food webs

A model of invasion by bodysnatchers from the far reaches of space

A discrete model of invasion by subversive alien bodysnatchers is constructed and analysed numerically as a proposed undergraduate project. Several extensions of the model are demonstrated, including a spatial system of ten planets arranged on a one-dimensional lattice, and we discuss some of the practical considerations that arise when supervising such a project. Exercises for further student investigations of the model are suggested

The role of migration in a spatial extension of the Webworld eco-evolutionary model

We extend an eco-evolutionary food web model to a spatially-explicit metacommunity model which features migration of populations between multiple local sites on the same time-scale as feeding and reproduction. We study how factors including the implementation and rate of dispersal, properties of the local environments, and the spatial topology of the metacommunity interact to determine the local and global diversity and the degree of synchronisation between local food webs. We investigate the influence of migration on the stability of local networks to perturbation, and simulate a 5 x 5 spatial arrangement of cells, demonstrating that combining adaptive migration and heterogeneous habitats allows distinct food webs to coevolve from the beginning of the simulation. When coupling food webs by diffusion migration after an initial period of isolation, the Webworld model can construct metacommunities of distinct food webs if the local sites have spatially-homogeneous environmental parameters. If the sites have heterogeneous parameters, synchronisation between food webs increases greatly, but this can be o�set by a greater number of sites and less-connected spatial topologies

Optimal COVID-19 lockdown strategies in an age-structured SEIR model of Northern Ireland

An age-structured SEIR model simulates the propagation of COVID-19 in the population of Northern Ireland. It is used to identify optimal timings of short-term lockdowns that enable long-term pandemic exit strategies by clearing the threshold for herd immunity or achieving time for vaccine development with minimal excess deaths

Zombies: a simple discrete model of the apocalypse

A simple discrete-time two-dimensional dynamical system is constructed and analyzed numerically, with modelling motivations drawn from the zombie virus of popular horror fiction, and with suggestions for further exercises or extensions suitable for an introductory undergraduate course

Zombies: a simple discrete model of the apocalypse

A simple discrete-time two-dimensional dynamical system is constructed and analyzed numerically, with modelling motivations drawn from the zombie virus of popular horror fiction, and with suggestions for further exercises or extensions suitable for an introductory undergraduate course