## Theory and models in evolutionary biology (EVO)

#### Course coordinators

Sarah Samadi (sarah.samadi@mnhn.fr) et Anouk Barberousse (anouk.barberousse@paris-sorbonne.fr)

#### Goals

To propose a general framework for work in evolutionary biology, starting from a historical and epistemological approach and using examples from contemporary work to address the major issues of the 21st century. To understand how theories and models shape the constitution of data sets and, conversely, how data challenges established theories and models.

#### Location

**Lecture room of the geology building (MNHN, entry from 43 rue Buffon, building 048, allée de la Bièvre)**

#### Schedule

This module will take place **from the 4th until the 8th of September 2023**

#### Assessment

Production of a critical analysis of a recent article chosen by the student in connection with the debate, of a maximum length of 2000 lines. Short oral defence (15 minutes including questions) to justify the position defended in this critical analysis.

## Refresher courses (Biology, Computer Science and Mathematics)

These refresher courses are optional, but highly recommended so as to ensure that participants have the prerequisites necessary to follow the obligatory modules. During the second week there will be a **conference intended for all EvoGEM** participants (Sorbonne University Campus – see Bio0 for more information).

#### General schedule

There is some overlap between the refresher courses. Below is the global schedule of the two weeks dedicated to these courses:

## Refresher course in Biology (BIO0)

#### Course coordinators

Ingrid Lafontaine (ingrid.lafontaine@ibpc.fr) et Maud Tenaillon (maud.tenaillon@inrae.fr)

#### Goals

This biology refresher course is intended for students from Mathematics and Computer Science backgrounds. It aims to acquire and/or consolidate basic knowledge in cellular and molecular biology, developmental biology, genetics, and genomics. We also illustrate, through examples, how data derived from ‘omics’ technologies can address fundamental questions in evolutionary biology, as well as current challenges related to health and threats to biodiversity.

#### Location

This refresher course will be given at the **ENS**, 45 rue d’Ulm, Paris 5. **The exact room will be communicated by the course coordinator.**

#### Schedule

This refresher course will be given over two weeks, **from the 11th to the 22nd of Septembre 2023**. Morning classes start at 9 am, and afternoon class at 1:30 pm.

## Refresher course in Computer Science (INFO0)

#### Goals

This programming course is intended for students from any background. It aims to acquire basic knowledge in Unix commands, algorithmics and programming in Python and R. Sessions will comprise theoretical and practical sessions. Computers are available in the room but students are strongly encouraged to bring their own laptops.

#### Location

This refresher course will be given at the **Sorbonne Université, Campus Pierre et Marie Curie**, 4 place Jussieu Paris 5^{ème}. All classes will take place in **Room RC03, in the basement of the Atrium building**. Go down one floor after entering, and take the blue corridor marked “info bio” (next to the library).

For a map of the location, follow this link:

https://sciences.sorbonne-universite.fr/vie-de-campus-sciences/accueil-vie-pratique/plan-du-campus*.*

#### Schedule

This refresher course will be given over two weeks, **from the 11th to the 22nd of Septembre 2023**. Morning classes start at 9 am, and afternoon class at 1:30 pm.

## Refresher course in Mathematics (Maths0)

#### Course coordinators

Christine Dillmann (christine.dillmann@inrae.fr) et Pierre de Villemereuil (pierre.devillemereuil@ephe.psl.eu)

#### Goals

This teaching unit aims to consolidate/revise basic knowledge in mathematics and statistics. The objective is to recall the use of mathematical formalisms, especially matrix notation, review fundamental elements of probability and statistical inference, introduce Bayesian approaches, and revise basic concepts in the treatment of ordinary differential equations.

**Linear Algebra:** Notions of matrices and vectors, matrix calculations, usual matrix properties, inversion, diagonalization.

**Probability Basics:** Random variables and common probability distributions, expected value and variance, convergence in distribution, central limit theorem, and law of large numbers. Properties of random vectors and matrices, Markov chains.

**Statistics:** Inference, likelihood, linear models, multivariate analyses (PCA, DFA, …), introduction to Bayesian approaches.

**Ordinary Differential Equations:** Review of derivatives and integrals, concept of differential equations, solving a simple linear equation, system of differential equations, notion of dynamic equilibrium in systems.

#### Prerequisites

Expected mathematical proficiency after completing an M1 in Biology and a liking for and interest in mathematical formalism.

#### Location

This refresher course will be given at **two different campuses:****Week 1**: the **Sorbonne Université, Campus Pierre et Marie Curie**, 4 place Jussieu Paris 5^{ème}.

For a map of the location, follow this link:

https://sciences.sorbonne-universite.fr/vie-de-campus-sciences/accueil-vie-pratique/plan-du-campus*The exact rooms are given in the schedule below. ***So as to understand where each room is situated, use the following example:** Room 14.24.203 is located in the corridor connecting tower 14 and tower 24, on the 2nd floor.**Week 2:** All courses will take place in **room Baleine 1** in the **Pavillon La Baleine building (Rue Cuvier – Jardin des plantes)** – the map for which can be accessed here:

https://www.mnhn.fr/system/files/atoms/files/plan_jardin_des_plantes_baleine1.pdf

**THURSDAY 21st of SEPTEMBER: Due to the closer of the Jardin des Plantes – Classes will be given on the Sorbonne Université, Campus Pierre et Marie Curie campus** room 15.16.201 at 13:30

#### Schedule

This refresher course will be given over two weeks, **from the 11th to the 22nd of Septembre 2023**. Morning classes start at 9:30 am, and afternoon class at 1:30 pm.

**Stochastic Models in Ecology and Evolution **(MAEE)

#### Course coordinators

Stéphane ROBIN (stephane.robin@sorbonne-universite.fr), Gabriel LANG (gabriel.lang@agroparistech.fr)

#### Goals

At the end of the module, the student will be able to:

- Define classical probabilistic dynamical models (random walks, birth-and-death processes, coalescent, Brownian motion);
- Deduce Markov chain characteristics (ergodicity, stationarity, periodicity) in discrete time and space from its transition law;
- Numerically implement a simulation code (exact or approximate) of a Markov process to study its properties empirically;

**Contents**

Introduction to classical probabilistic dynamic models in ecology and evolution, i.e. Markov processes:

- in discrete time and space (Markov chains);
- in continuous time and discrete space (Poisson processes, birth and death);
- in discrete time and continuous space (Gaussian random walk);
- in discrete time and continuous space (Brownian motion and stochastic differential equations);

#### Prerequisites

A student enrolling in the course should know:

- what a matrix is and the elementary operations that apply to it (multiplication, diagonalization, inversion);
- what a discrete and continuous random variable is, and the related concepts (law, density, distribution function, expectation, variance);

Knowledge of deterministic models of evolution, notably based on ordinary differential equations, is a plus.

For those who are interested in the course but for whom these notions are unknown or remote, don’t panic: you can acquire this knowledge by first taking the Math0 module.

#### Location

This module will be given at the **Sorbonne Université, Campus Pierre et Marie Curie**, 4 place Jussieu Paris 5^{ème}. *The exact rooms are given in the schedule below.***So as to understand where each room is situated, use the following example:** Room 14.24.203 is located in the corridor connecting tower 14 and tower 24, on the 2nd floor.**The tutoriels all take place in the** **Atrium building** (see rooms in the time table below)

**For a map of the location, follow this link:https://sciences.sorbonne-universite.fr/vie-de-campus-sciences/accueil-vie-pratique/plan-du-campus**

#### Schedule

This module will take place from **October 9th to 13th 2023.**

#### Assessment

Standard exam.

**Genomes Populations Species** (GPS)

#### Course coordinators

Guillaume Achaz (guillaume.achaz@mnhn.fr), Pierre Gérard (pierre.gerard@agroparistech.fr)

#### Goals

This course will address the fundamental processes that are at work in evolution through the lens of molecular evolution and population genetics. It will devote time to statistical inferences based on the patterns of polymorphisms in sequence data. The intended participants are students motivated by the understanding of evolutionary processes and not entirely reluctant to theoretical models.

#### Themes

Wright-Fisher model in prospective (drift) and retrospective (coalescence)

Mode of crossing (panmixing, consanguinity, self-fertilisation)

Mutations and molecular diversity (nucleotide diversity, frequency spectrum, neutrality tests)

Recombination and demography

Structuring, Isolation and Speciation (migration)

Natural selection (in haploids and diploids)

Selection-drive-mutation interaction (in finite populations)

Molecular Clock and Phylogeny

The complex notion of “Effective Size”

#### Prerequisites

Biology/genetics & mathematics fundamentals.

#### Location

The whole module will take place at the** Ecole Normale Supérieure (46, rue d’Ulm Paris 05)** in **room 321**. Wednesday mornings are reserved for the MMAGE module, which will deal with two mathematical results related to the module (Ewens’ sampling formula and Diffusion) taught by Amaury Lambert.

#### Schedule

This module spans two weeks, but will be interrupted by one week of vacation. **Week 1 will be October 2-6 and week 2 October 16-20, 2023.**

#### Assessment

Home report on a particular concept in evolutionary genetics (1-2 months delay for writing after the end of the teaching unit)

## Quantitative genetics (QG)

#### Course coordinators

Henrique Teotonio (teotonio@bio.ens.psl.eu), Diala Abu Awad (diala.abu-awad@universite-paris-saclay.fr) and Pierre de Villemereuil (pierre.devillemereuil@ephe.psl.eu)

#### Goals

The course will build on the biological, mathematical and genetic foundations of quantitative genetics (the study of the genetics of complex traits, coded by a large number of genes) to lead to a thorough and advanced study of the field. Students will learn the basics of quantitative genetic models and the partitioning of phenotypic variance (notably the notion of heritability), as well as the statistical study of these variance components on the one hand (animal models), and of selection and response to selection on the other hand (Price-Robertson identity). The course will cover a number of more advanced topics, such as genomic selection, genome-wide association, multivariate evolution (G-matrix, M-matrix, adaptive landscape). Finally, the course will present the modern uses of quantitative genetic tools to interpret experimental evolutionary results and the empirical study of adaptation in natural populations, especially with respect to global changes. A large part of the second week will be devoted to mathematical and computer modelling of the evolution of quantitative traits with the help of tutored projects.

#### Themes

- Quantitative genetics, heritability, relatedness,
- Components of genetic and phenotypic variance, animal model, selection gradients and intensity, response to selection,
- G matrix, M matrix,
- Genomic selection, genome-wide association, experimental selection, natural population.

#### Prerequisites

To be able to follow this course, there must be a basic understanding of population genetics. Familiarity with R, Python, and general ease with computer programs is highly recommended.

#### Location

The courses will take place on the campus of the University Paris-Saclay at the Institut Diversité, Ecologie, Evolution du Vivant:

IDEEV, 12 Route 128, Gif-sur-Yvette

B. McClintock room (Groundfloor)

How to get here:

RER B to Massy-Palaiseau then Bus 91.06 – bus stop Jolio-Curie

RER B to Le Guichet then Bus 09 – bus stop Jolio-Curie

#### Schedule

This module lasts two weeks and will take place from the **13th to the 24th of November 2023**

#### Assessment

The students will be divided into groups of two to do the “Simulating phenotypic evolution” project which will then be presented with supporting slides to the faculty and other students, for 15-20 min at the end of the semester. This presentation will account for 40% of the final grade. 40% of the final grade will be based on written answers to questions that will be given to the students in the last day of the course. Students are expected to send their answers to H. Teotónio (teotonio@bio.ens.psl.edu) before the end of the semester (date to be decided). The remaining 20% of the final grade will be based on discussions during the Journal Clubs.

## Advanced Mathematical Modeling for Evolutionary Genetics (MAGE)

#### Course Coordinator

Amaury Lambert (amaury.lambert@ens.fr)

#### Themes

**Lecturers:** Amaury Lambert (AL), Stéphane Robin (SR), Tristan Mary-Huard (TMH)

Lecture 1 (AL): Cannings model, coalescent, infinite-site model, infinite-allele model, Ewens sampling formula, Chinese restaurant process.

Lecture 2 (AL): Brownian motion, diffusion theory, stochastic differential equations, infinitesimal generator, hitting probabilities, Feller diffusion, Wright-Fisher diffusion.

Lecture 3 (SR): Multivariate methods: dimension reduction (PCA), clustering (hierarchical, k-means, mixture models).

Lecture 4 (AL): Coupling gene genealogies: ancestral recombination graph, sequential Markov coalescent.

Lecture 5 (SR): State space models: hidden Markov models (HMM), STRUCTURE, sequence evolution models.

Lecture 6 (TMH): Mixed models : Random effects, ReML inference, hypothesis testing for variance components and random effect prediction (BLUP).

Lecture 7 (TMH): GWAS : Oligogenic and polygenic models, random effect model accounting for relatedness, multiple testing.

Lecture 8 (AL): coalescent of birth-death processes, Luria-Delbrück distribution, $1/k^2$ SFS.

Lecture 9 (AL): Trait evolution on a tree, phylogenetic covariance matrix.

#### Prerequisites

Maths 0 and MAEE (Stochastic Models in Ecology and in Evolution)

#### Schedule and Location

Lectures are spread over the semester. Six lectures out of 9 are scheduled in the middle of a fortnight dedicated to one of the following modules: GPS (Genomes, Populations, Species), GQ (Quantitative genetics), CPA (Comparative Phylogenetic Approaches). When this is the case, the content of the lecture is in tight relation with the surrounding module and the classroom is the one used for this module. **Please refer to the schedule of the corresponding UE of each week to find the exact room.**

**Weeks 40 and 42 during GPS:**Wed 4 Oct and Wed 18 Oct, both 9-12am –**ENS****Week 44:**Thu 2 nov 9-12am –**ENS****Week 45 (2 lectures):**Wed 8 Nov 2-5pm, Thu 9 Nov 9-12am –**ENS****Weeks 46 and 47 during GQ:**Mon 13 Nov and Tue 21 Nov, both 2-5pm –**UPSaclay****Weeks 48 and 49 during CPA:**Wed 6 Dec and Wed 13 Dec, both 9-12am –**UPCité**

#### Assessment

Read one of the following book excerpts, select a passage that you like and present it in 10-15 minutes (chalk-talk, no slides), typically one (or more) math result and its proof:

- Chapter 2, Chapter 3 or Chapter 5 in Gillespie’s book

https://public.wsu.edu/~gomulki/mathgen/materials/gillespie_book.pdf - The first 20-25 pages of Chapter 1, or 2, or 6 or 7 in Durrett’s book

https://services.math.duke.edu/~rtd/Gbook/PM4DNA_0317.pdf - Section 1 or Section 3 in my lecture notes

https://projecteuclid.org/journals/brazilian-journal-of-probability-and-statistics/volume-31/issue-3/Probabilistic-models-for-the-subtrees-of-life/10.1214/16-BJPS320.full

## Comparative Phylogenetic Analysis (ACP)

**Work in progress**

#### Course Coordinators

Guillaume Achaz (guillaume.achaz@mnhn.fr), Nicolas Puillandre (nicolas.puillandre@mnhn.fr)

#### Location

This module will take place on the Université Paris-Cité Campus. All classes will be given in room **RH10A Buffon**.

#### Schedule

This module lasts two weeks and will take place from the **4th to the 15th of December 2023**

## Tutored projects (PRO)

#### Course coordinators

Sarah Samadi (sarah.samadi@mnhn.fr), Olivier Tenaillon (olivier.tenaillon@inserm.fr), Stéfano Mona (stefano.mona@mnhn.fr)

#### Goals

The aim of this cross-disciplinary module is to introduce students to working with data and models by means of a tutored project.

#### Prerequisites

BIO0/Maths0/info0 module and EVO module.

#### Location

The whole module will take place at the Ecole Normale Supérieure (46, rue d’Ulm Paris 05). The room will be communicated closer to the dates.

#### Schedule

This module will be spread out throughout the semester. The key dates/weeks to keep in mind are the following:

**Monday 25th September.**Evolution Day in Paris. Opportunity to discuss with researchers offering internships in the Ile-de-France region.**Tuesday 26 September**9am-12pm : presentation of project topics and identifying working teams of two people.**30**: Presentation of projects by teams. Lectures: from data production to data handling.^{th}of October to 4^{th}of November**6**: Work on the project. Each team will present a progress report to the whole group at the end of the week.^{th}of November to 10^{th}of November**27**: Project progress evaluation with the module coordinators (time-slot will be arranged with the students).^{th}of November to 1st of December**21**: Progress report on poster.^{st}December 9am-12pm

#### Assessment

Oral presentation of a scientific poster based on the project the team worked on. The presentation will take place **during the assessment week in January 2024**.