Lukas Eigentler
Assistant Professor
Warwick Mathematics Institute
Office: MSB 5.12
Email: Lukas.Eigentler@warwick.ac.uk
Webpage: https://lukaseigentler.github.io
![Portrait of Lukas Eigentler](portrait.jpg)
Research interests:
- dryland vegetation patterns
- bacterial biofilms
- evolution of individual variability
- competition and coexistence
Selected publications:
- L. Eigentler, J.A. Sherratt: Long-range seed dispersal stabilises almost stationary patterns in a model for dryland vegetation. J. Math. Biol. 86:15 (2023), DOI: 10.1007/s00285-022-01852-x
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L. Eigentler, F.A. Davidson, N.R. Stanley-Wall: Mechanisms driving spatial distribution of residents in colony biofilms: an interdisciplinary perspective. Open Biol. 12:220194 (2022), DOI: 10.1098/rsob.220194
- L. Eigentler: Species coexistence in resource-limited patterned ecosystems is facilitated by the interplay of spatial self-organisation and intraspecific competition. Oikos, 130.4 (2021), 609--623. DOI: 10.1111/oik.07880.
Selected research:
![Alternating stripes of vegetated areas and bare soil](somalia.jpg)
Dryland vegetation patterns
Vegetation patterns are a ubiquitous feature of dryland ecosystems, occurring on all continents except Antarctica. Such mosaics of alternating patches of biomass and bare soil develop as a consequence of a self-organisation principle induced by a positive feedback between local vegetation growth and water redistribution towards areas of high biomass. Patterns occur in many different forms but on sloped terrain, patterns occur as regular stripes.
A detailed understanding of the dynamics of vegetation patterns is of considerable socio-economic importance as they hold valuable information on the health of ecosystems. In particular, changes to a pattern's properties may act as an early warning signal of desertification, a major threat to economies of countries in arid regions. Data acquisition for vegetation patterns is notoriously difficult due to the spatial and temporal scales associated with the ecosystem dynamics. In particular, their recreation in laboratory settings is infeasible. Thus, a powerful tool to overcome these challenges is the use of mathematical models. The theoretical study of dryland ecosystems, in particular continuum approaches utilising PDEs, has thrived over the last two decades.
In our research, we use reaction-advection-diffusion systems based on the Klausmeier model to describe vegetation patterns as periodic travelling waves. We determine conditions for pattern onset, pattern existence and pattern stability to investigate the impact of processes such as nonlocal seed dispersal or temporal rainfall variability on vegetation patterns. Moreover, we use the modelling framework to reveal mechanisms that enable species coexistence despite the competition for a sole limiting resource (water).
![A side-by-side of lab-grown and in-silico biofilms](biofilms.jpg)
Competition and cooperation in biofilms
Bacterial biofilms are dense aggregates of bacterial cells embedded in a self-produced extracellular matrix. Many different species (Bacillus subtilis, Escherichia coli, Pseudomonas aeruginosa, ...) form biofilms and thus biofilms occur in many different biological, industrial and medical environments. From a human perspective, biofilms can have both positive (e.g. use in waste water treatment, essential for correct functioning of the human gastrointestinal tract, ...) and negative (e.g. cause of chronic infections, biofouling, ...) impacts on the environment.
The significant impact of biofilms on the environment they grow in makes synthetically created biofilm-forming strains ideally suited for targeted modification of the environment. For example, the soil dwelling bacterium B. subtilis forms biofilms on plant roots and some B. subtilis strains are capable of promoting plant growth and offering protection from plant pathogens, thus rendering those strains as ideal candidates for being used as the basis for biofertilisers and/or biopesticides. Any successful biocontrol agent not only needs to be able to complete the intended task but is also required to be capable of establishing itself within an existing community.
In our research, we investigate competitive and cooperative dynamics within biofilms using an interdisciplinary approach that combines mathematical modelling with experimental assays. In particular, we focus on competition for space using an isogenic strain pair (strains that express different fluorescent proteins but are otherwise identical) and competition through antagonistic actions using B. subtilis strains as model systems. These reveal that the dominant mode of competition fundamentally depends on the cell density used for biofilm inoculation ("founder density"). Moreover, we investigate the role of extracellular proteases, which we show to be a public good, in the biofilm growth dynamics.