# Hildegard Uecker

## Population genetics models of rapid adaptation to environmental change

Severe changes in the environment of a population can lead to maladaptation and ultimately extinction unless evolution is rapid, giving rise to genotypes that are well-adapted to the new conditions and rise in frequency. Such a scenario is termed "evolutionary rescue". Whether populations confronted with environmental change survive or go extinct is a key question in evolutionary biology. Which populations have the greatest chances to survive? How do genetic and environmental factors interact to slow down or to speed up adaptation? The extent of human-induced environmental change endangering biodiversity makes answering these questions a pressing need. An answer is equally important in medicine and in agriculture where we aim to eradicate the pathogens or pests and to inhibit the evolution of resistance. How do we need to modulate the environment to make the desired outcome - persistence or extinction - more likely?

Mathematical models can help to answer these questions. Through their clarity, they allow to identify important mechanisms and interactions. They are moreover

general and make a rapid exploration of a large range of scenarios possible. Besides laboratory experiments and field studies, mathematical modeling therefore greatly contributes to our understanding of rapid adaptation to environmental change. The aim of this project is to develop mathematical models for the eco-evolutionary dynamics of evolutionary rescue within the framework of theoretical population genetics. The precise project will be developed together with the student according to his/her interests. Potential directions could be (1) to explore how heterogeneity in the environment in combination with behavioral or genetic factors infuences the evolutionary dynamics (2) to explore the effect of seed banks in plant adaptation, leading to immigration from the past.

On the mathematical side, the project involves stochastic modeling in combination with deterministic approaches. Depending on the interests and profile of the student, the focus can be more on analytical work (where branching process theory will be an important tool) or on computer simulations.

Applicants should have a degree in mathematics, physics, biology, computer science or another related field. A prerequisite is a keen interest both in mathematical modeling and in biological systems. Good quantitative skills are essential. Experience in mathematical modeling and knowledge of a programming language (Matlab, Python, Java, R, C, C++,...) is an advantage.

Mathematical models for the evolution of antibiotic resistance

Antibiotic resistance has become one of the greatest dangers to health care worldwide. The evolution of antibiotic resistance is a prime example of natural selection in action. Sensitive bacteria are killed by the antibiotic while resistant bacteria thrive. The development of new antibiotic compounds is too slow to keep up with the current speed of bacterial adaptation. However, with a better understanding of the adaptive process, we might be able to influence the evolutionary path and to delay the emergence of resistant strains.

Mathematical models are an extremely valuable tool to identify factors that slow down bacterial adaptation to antibiotic treatment. While evolution experiments and clinical studies are ultimately indispensable, mathematical modeling offers several advantages. The clarity of models and the fact that they are fully controlled makes a detailed understanding of the processes, the relevant factors and their interactions possible. Moreover, models can be held general such that we can draw general conclusions. Furthermore, they allow to study evolution in time-lapse such that large parameter ranges and many replicates of the evolutionary process can be considered. Unlike clinical studies, mathematical models are not subject to ethical restrictions. Last, no animals get harmed.

The goal of the project is to develop and analyse mathematical models for the evolution of antibiotic resistance during treatment that incorporate interactions with the patient. This includes in particular the interactions of pathogenic bacteria with commensal bacteria and with the human immune system. Depending on the interests and profile of the student, the focus can be entirely on the evolutionary process within a single patient or can extend to the spread of the infection in the community.

On the mathematical side, the project involves stochastic modeling in combination with deterministic approaches. Depending on the interests and profile of the student, the focus can be more on analytical work (where branching process theory will be an important tool) or on computer simulations.

Applicants should have a degree in mathematics, physics, biology, computer science or another related field. A prerequisite is a keen interest both in mathematical modeling and in biological systems. Good quantitative skills are essential. Experience in mathematical modeling and knowledge of a programming language (Matlab, Python, Java, R, C, C++,...) is an advantage.

## Antibiotic resistance evolution: Evolution experiments & theoretical modeling (joint project with Hinrich Schulenburg)

The emergence and spread of drug resistant pathogens poses a major threat for human health. Evolution is at the core of the current antibiotic crisis. Yet, the enormous potential of bacterial pathogens to adapt is usually ignored in current health programs. The aim of this project is to gain a better understanding of the dynamics of antibiotic resistance evolution within and across patients and to develop and assess new concepts for evolution-informed antibiotic therapy. The project involves (1) experimental evolution and in parallel (2) the development of theoretical models that are tailored to the experiments. For the evolution experiments, we use the opportunistic human pathogen *Pseudomonas aeruginosa* as a model organism. Experimental evolution is combined with genomic and functional genetic analysis. The proportion of mathematical modeling and computer simulations can be adjusted to the interests and profile of the student.

The student will have a joint appointment in two groups with an experimental and a theoretical focus, respectively, and be co-supervised by two PIs (Hinrich Schulenburg - PI of experimental part; Hildegard Uecker - PI of theoretical part). The project therefore offers an excellent opportunity to acquire a broad skill set and gain experience in interdisciplinary work.