### Program Spring 2020/21

**31.03.2021 | 16h00-17h00 | Piret Avila, UNIL**

*Hamilton’s rule meets the Hamiltonian and state-feedback effects: gradual evolution of phenotypically plastic traits using optimal control theory
*

Most traits expressed by organisms, such as gene expression profiles, developmental trajectories, behavioural sequences and reaction norms are function-valued traits (colloquially "phenotypically plastic traits"), since they vary across an individual's age and in response to various internal and/or external factors (state variables). Furthermore, most organisms live in populations subject to limited genetic mixing and are thus likely to interact with their relatives. We here formalise selection on genetically determined function-valued traits of individuals interacting in a group-structured population, by deriving the marginal version of Hamilton's rule for function-valued traits. This rule simultaneously gives a condition for the invasion of an initially rare mutant function-valued trait and its ultimate fixation in the population (invasion thus implies substitution). Hamilton's rule thus underlies the gradual evolution of function-valued traits and gives rise to necessary first-order conditions for their uninvadability (evolutionary stability). We develop a novel analysis using optimal control theory and differential game theory, to simultaneously characterise and compare the first-order conditions of (i) open-loop traits - functions of time (or age) only, and (ii) closed-loop (state-feedback) traits - functions of both time and state variables. We show that closed-loop traits can be represented as the simpler open-loop traits when individuals do not interact or when they interact with clonal relatives. Our analysis delineates the role of state-dependence and interdependence between individuals for trait evolution, which has implications to both life-history theory and social evolution.

**17.03.2021 | 16h00-17h00 | Xiang-Yi Li, UniNe**

*Applications of evolutionary game theory in understanding biological interactions
*

Evolutionary game theory is a very useful tool to solve problems where the outcome of adopting a given strategy depends on the strategies adopted by others. A simple example is a children’s rock-paper-scissors game, where there is there no obvious “best option” for an individual to choose. It has become an integral part of modern evolutionary theory, and has expanded in many directions and melded with other methods. In this talk, I will present a quick introduction to evolutionary game theory, and a few case studies based on my own research to show how we can use evolutionary game theory to better understand complex biological interactions, such as the “battle of the sexes” and the competition between different bacteria. We will cover diverse topics such as female preference for fancy males escalating into a “tragedy of the commons”, leading to reduced population growth rate (or even extinction); male offspring evolve to “altruistically” disperse early away from their natal habitat to leave more resources for their sisters; and why some males continue to provide intensive care to the offspring despite being cheated by their females; and how a slowly growing bacterium use a temperate phage as weapon against its fast growing competitor.

**03.03.2021 | 16h00-17h00 | Helena Todorov, UNIL**

*Structure learning to unravel mechanisms of the immune system
*

Our body constantly has to defend itself against harmful pathogens. Luckily, we have a powerful protective mechanism called the immune system. The immune system is at the center of extensive studies, facilitated by the appearance of new technologies that allow to measure unprecedented amounts of features in thousands to millions of cells. This leads to large-scale, high-dimensional data that typically contain many sources of variability. New automated tools are therefore needed to analyse this type of complex data, and to extract interesting patterns from it. We applied and designed various structure learning methods to gain insight into the complex nature of immune cell differentiation in response to a disease. We extracted cell trajectories, gene regulatory networks, and graphs of interacting molecules that helped us to generate new medical hypotheses. The types of machine learning tools that we applied represent a real asset in the analysis of complex data and help to shed light on the immune system’s response to diseases that are still difficult to characterise.

### Program Fall 2020/21

**02.12.2020 | 16h00-17h00 | Sven Bergmann, UNIL**

*GWAS meets networks: Assessment of network module identification across complex diseases*

Many bioinformatics methods have been proposed for reducing the complexity of large gene or protein networks into relevant subnetworks or modules. Yet, how such methods compare to each other in terms of their ability to identify disease-relevant modules in different types of network remains poorly understood. We launched the ‘Disease Module Identification DREAM Challenge’, an open competition to comprehensively assess module identification methods across diverse protein–protein interaction, signaling, gene co-expression, homology and cancer-gene networks. Predicted network modules were tested for association with complex traits and diseases using a unique collection of 180 genome-wide association studies. Our robust assessment of 75 module identification methods reveals top-performing algorithms, which recover complementary trait-associated modules. We find that most of these modules correspond to core disease-relevant pathways, which often comprise therapeutic targets. This community challenge establishes biologically interpretable benchmarks, tools and guidelines for molecular network analysis to study human disease biology.

**19.11.2020 | 16h00-17h00 | Charles Mullon, UNIL**

*Eco-evolutionary dynamics under non-random interactions
*

Organisms continuously modify their living conditions, transforming their environment, microbiome, and sometimes culture. Where these modifications influence the fitness of conspecifics, a feedback emerges between the evolution of traits and the environment in which they are expressed. To investigate such feedback, it is typically assumed that individuals interact at random. In this case, one can study the invasion of a rare mutant trait in an environment set by a common resident ignoring mutant-mutant interactions. However, non-random interactions are common in nature. In this talk, I will report some results on the effect of non-random interactions on eco-evolutionary dynamics, focusing on two mechanisms that lead to such non-random interactions: spatial structure and biased behaviours between parents and their offspring. In both cases, selection depends on complex feedbacks between individuals of the same mutant lineage. By disentangling and quantifying these feedbacks, this research can help understand the nature of adaptation via non-genetic modifications, with implications for how organisms evolve to transform their environments.

**04.11.2020 | 16h00-17h00 | Christian Mazza, UNFR**

*Self-organization and pattern formation in auxin flow*

The plant hormone auxin plays a central role in growth and morphogenesis. In the shoot apical meristem, the auxin flow is polarized through its interplay with PIN proteins. Concentration based mathematical models of the auxin flow permit to explain some aspects of phyllotaxis, where auxin accumulation points act as auxin sinks and correspond to primordia. Simulations show that these models can reproduce geometrically regular patterns like spirals in sunflowers or Fibonacci numbers. We propose a mathematical study of a related non-linear o.d.e. using tools from Markov chain theory. We next consider a concurrent model which is based on the so-called canalization hypothesis, and show that it can explain the self-organization of plant vascular systems.

**22.10.2020 | 16h00-17h00 | Sara Mitri, UNIL**

*Combining theory and experiments in microbial ecology and evolution
*

Our lab strives to understand the ecology and evolution of small microbial communities and to control and design them to our benefit. This interest stems both from their practical importance - microbial communities affect our health and are heavily used in food production, environmental remediation and agriculture - and their advantages as model systems to ask fundamental questions about the interplay between ecology and evolution. To reach this understanding, we combine experiments with mathematical and computational models. In this talk, I will give an overview of this research, focusing on the strengths and challenges of an interdisciplinary approach.

**08.10.2020 | 16h00-17h00 | Michel Benaïm, UNINE**

*Stochastic persistence*

An important issue in mathematical ecology and population biology is to find out under which conditions a collection of interacting species can coexist over long periods of time. A similar question, in mathematical models of disease dynamics, is to understand whether or not a disease will be endemic (i.e persist in the population) or go extinct. The mathematical investigation of these types of questions began in the late 1970s, laying the foundation of what is now called the (deterministic) mathematical theory of persistence. The theory developed rapidly the past 35 years using the available tools from dynamical system theory. Beside biotic interactions, environmental fluctuations play a key role in population dynamics. In order to take into account these fluctuations and to understand how they may affect persistencedeterministic models need to be replaced by stochastic ones and the theory needs to be revisited. This talk will survey recent results in this direction laying the groundwork for a mathematical theory of stochastic persistence. Part of this work stems from a close collaboration between Neuchatel’s research group in probability and UC Davis department of Evolution and Ecology.

### Kick-off of the Network of Theoretical Biology in Western Switzerland

November 26 2019 |15h-19h | Biophore | UNIL

###### Speakers:

**Rachel Jeitziner**, SIB*Two-Tier Mapper: a topological tool for the analysis of biological data*

**Tadeas Priklopil**, UNIL*Modelling evolution in structured populations*

###### Organizing team of kick-off event

Piret Avila, UNIL

Stefania Ebli, EPFL

Daniela Egas, EPFL

Isaline Guex, UNIFR

Zena Hadjivasiliou, UNIGE

Joseph Lemaître, EPFL

Xiang-Yi Li, UNINE

Christian Mazza, UNIFR

Jose Negrete, EPFL

Xavier Richard, UNIFR

Pauline Ruegg-Reymond, EPFL

Björn Vessman, UNIL