ECOP Subgroup Contributed Talks

Eduardo Muñoz-Hernández

Complutense University of Madrid

"Minimal complexity of subharmonics in two classes of periodic Volterra predator-prey models"

This contribution analyzes the existence and minimal complexity of positive subharmonics of arbitrary order in the planar periodic Volterra predator-prey model. If the support of the birth rate of the prey intersects the support of the death rate of the predator, then the existence of positive subharmonics can be derived with a refinement of the Poincaré-Birkhoff theorem. However, in the “degenerate” case when these supports do not intersect, then, the last Poincaré theorem can fails. Still in these degenerate situations, some local and global bifurcations techniques combined with a refinement of the Poincaré-Birkhoff theorem provide us with the existence of positive subharmonics of arbitrary order.

Thomas Woolley

Cardiff University

"Locating bat roosts through the coupling of motion modelling and microphone data"

Bats play an important role in the UK ecosystem, but their populations are declining due to many reasons, including loss of habitat from human activity. As a result, ecological surveys are legally required when undertaking large-scale building work to locate breeding, or resting places (roosts). However, locating roosts is generally a difficult task, requiring many hours of manual searching. In collaboration with ecological experts we propose a novel approach for modelling bat motion dynamics and use it to predict roost locations using data from static acoustic detectors. Specifically, radio tracking studies of Greater Horseshoe bats demonstrate that bat movement can be split into two phases: dispersion and return. Dispersion is easily understood and can be modelled as simple random motion. The return phase is much more complex, as it requires intelligent directed motion and results in all agents returning home in a stereotypical manner. Critically, combining reaction-diffusion theory and domain shrinking we deterministically and stochastically model a ``leap-frogging'' motion, which fits favourably with the observed tracking data.

Christopher Kribs

University of Texas at Arlington

"Competition between obligate & facultative scavengers & infection: vulture-jackal-anthrax dynamics in Etosha National Park"

Different species of scavengers may compete for the same food in an ecosystem. This case study considers the competition between jackals, vultures and anthrax outbreaks in Etosha National Park in Namibia. While jackals are facultative scavengers, able to hunt for food if necessary, vultures are obligate scavengers wholly dependent on carcasses of animals like zebras for persistence. This competition is further affected by outbreaks of infections such as anthrax, which temporarily increase the number of carcasses but lower the zebra population, acting in some ways as a third competitor. We use a dynamical system to model the interplay between competition dynamics and infection dynamics, and how it is affected by the nature of the competition: indirect (exploitative) or direct (interference). A bifurcation analysis using reproduction numbers shows how vultures' survival may depend on their direct competitive edge in reaching carcasses faster than jackals, and how the infection and the scavengers complicate each other's persistence.

Lukas Eigentler

University of Dundee

"Spatial dynamics underpin competitive interactions within bacterial biofilms"

Bacterial biofilms are surface-adhering multicellular collectives embedded in a self-produced extracellular matrix. They can have both beneficial and detrimental effects on the surrounding environment. For example, the soil-dwelling bacterium Bacillus subtilis forms biofilms on the roots of plants, where some strains promote the growth of plants. However, to fully realise their potential as biocontrol agents, strains need to be capable of coexisting with (or outcompeting) other biofilm-forming strains in the rhizosphere. Many antagonistic interaction mechanisms require spatial colocation of competing strains. In this talk, we discuss the crucial role of spatial dynamics on competitive interactions within biofilms using an interdisciplinary approach. Mathematical modelling using a continuum approach predicts that the density of biofilm founder cells has a profound impact on competitive outcome and that randomly allocated cell locations in the biofilm inoculum significantly affect competitive dynamics. We define a predictor for competitive outcome that quantifies a strain's “access to free space” in the initial condition and show that a favourable initial cell placement can lead to domination of a weaker strain (in the sense of interactions of well-mixed populations) in the biofilm. Finally, we present validation of model hypotheses through biofilm assays using strains of B. subtilis.