ECOP-10 Contributed Talks

Einar Bjarki Gunnarsson

Science Institute, University of Iceland

"The site frequency spectrum of an exponentially growing population: Theory and evolutionary history inference"

The site frequency spectrum (SFS) is a popular summary statistic of genomic data. In population genetics, the SFS has provided a simple means of inferring the rate of adaptation of a population and for distinguishing between neutral evolution and evolution under selection. The rapidly growing amount of cancer genomic data has attracted interest in the SFS of an exponentially growing population. In this talk, we discuss recent results on the expected value of the SFS of a population that grows according to a stochastic branching process, as well as (first-order) almost sure convergence results for the SFS in the large-time and large-population limits. Our results show that while the SFS depends linearly on the mutation rate, the branching process parameters of birth and death control the fundamental shape of the SFS at the low-frequency end. For the special case of a birth-death process (binary branching process), our results give rise to statistically consistent estimators for the mutation rate and extinction probability of the population, which stands in contrast to previous work which has indicated the need for additional data to decouple these two parameters. Overall, our work shows how single timepoint data on the SFS of an exponentially growing population can be used to infer important evolutionary parameters.

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Axa-Maria Laaperi

Newcastle University

"Quantifying the fires of the future: Modelling and inference of wildfire spread dynamics."

Wildfires disrupt ecosystems, with climate change exacerbating vulnerability in regions poorly adapted to such disturbances. These events are driven by complex, multi-scale interactions where small perturbations in environmental factors can trigger large-scale shifts, complicating prediction efforts. We propose a coupled convection-reaction-diffusion system as a framework for modelling wildfire spread dynamics. This system integrates spatial and temporal variability to identify thresholds for spread and quantify the impact of abrupt environmental changes on burnt areas and rates of propagation. Incorporating environmental, meteorological, and historical fire record data from the Global Wildfire Information System, the Department for Environment, Food and Rural Affairs (UK), and drone footage of heather burning. Bayesian inference and Monte Carlo methods are employed for parameter estimation and uncertainty quantification, ensuring robust model validation against unseen data. Recent wildfire events around the globe highlight the need for actionable insights into environmental vulnerability, property loss, and infrastructure risk. By enabling near-real-time simulations, this model aims to provide a computational tool for emergency response, long-term management strategies, and assessments of climate change-induced outlier weather patterns influencing fire behaviour. This work highlights the potential of mathematical modelling to advance understanding and management of critical ecological disturbances.

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Fabiana Russo

University of Naples Federico II

"Modeling biofilm growth and microbially induced corrosion in wastewater concrete pipes: a double free boundary problem"

Microbially induced corrosion (MIC) is a significant global issue impacting infrastructure, economies, and environment. In wastewater systems, MIC is primarily associated with biofilm formation on concrete sewer pipes, leading to severe degradation due to microbial metabolic activity. The proliferation of sewer biofilms occurs in both submerged and unsubmerged conditions, leading to distinct microbial communities. Commonly, these biofilms host microorganisms such as fermentation bacteria, hydrogen-producing acetogens, denitrifying bacteria, sulfate-reducing bacteria, sulfur-oxidizing bacteria, and methanogens. In particular, sulfur-oxidizing bacteria play a crucial role in corrosion, as they oxidize hydrogen sulfide from wastewater effluents, generating sulfuric acid that accelerates concrete deterioration. A one-dimensional model with double free boundaries has been developed to investigate the proliferation of biofilms and the related corrosion process in wastewater concrete pipes. The domain is composed of two free boundary regions: a biofilm that grows towards the interior cavity of the pipe, sitting on a gypsum layer formed by corrosion, which penetrates the concrete pipe. Diffusion-reaction equations govern the transport and the metabolic production or consumption of dissolved substances, such as hydrogen sulfide, oxygen, and sulfuric acid within the biofilm layer. The biofilm free boundary tracks the growth of the microbial community, regulated by microbial metabolic activity and detachment phenomena. The corrosion process is incorporated into the model through a Stefan-type condition, which drives the advancement of the gypsum free boundary into the concrete pipe, governed by microbial production of sulfuric acid. Numerical simulations have been carried out to investigate the model behavior, encompassing the development and progression of the biofilm as well as the corrosion advancement, with the aim of elucidating the key factors governing both phenomena.

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