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**Theoretical tools**:

- Fitness landscape models: Fisher’s model, multivariate phenotype fitness models
- stochastic multitype models for the population genetics and demography of populations undergoing selection mutation drift and migration
- quantiative genetics: mutation selection balance, Qst/Fst comparisons
- frequent mathematical tools: differential equations (ODE,PDE), stochastic differential equations and diffusion, probabilistic geometry (fitness landscape), generating functions, random matrix theory. Discrete/continuous time, individual/genotype based simulations.

**Applications (past and ongoing)**:

- Distribution of mutation fitness effects in context (epistasis, environment dependence etc.)
- Evolutionary and demographic dynamics of populations away from equilibrium: abrupt change, moving optimum in space or time. Mainly asexual models so far (clonal interference), with mutation, selection and genetic drift.
- Selective sweeps and distribution of allele frequencies over time: biallelic, multiallelic loci, dominance
- Try to produce testable predictions for experimental evolution: stochastic growth processes, mutation effects, adaptation trajectories, fluctuation tests, evolutionary rescue.
- Evolution of life history traits and trade – offs in simple ecological contexts (first), but with an explicit genetic basis for life history traits: virulence/transmission, birth/death etc.
- Impact of various factors on the speed and probability of successful adaptation to a new environment vs. extinction : epistasis, demographic stochasticity, environmental variation, mutation rate and effects distribution, strength of the environmental stress, initial maladaptation and standing variance, migration from a source etc.
- neutrality test on quantiative traits from common garden experiments (Qst/Fst comparisons)

**Experimental evolution**of bacteria (

*E. coli*and

*P. fluorescens*): semi-high throughput measurements (microplates).

- empirically studying stochastic birth and death processes,
- kill curves and antibiotic dose effects on bacterial birth and death rates
- rescue probability and dynamics
- distribution of antibiotic resistance and its cost.

**R codes for multivariate Qst / Fst comparisons**: here (.rar file).

This .rar archive has the R code for multivariate Qst / Fst analysis from Martin et al.(2008) and an example application on Galba truncatula data from Chapuis et al. (2008).

**Supervised PhD theses**

Yoann Anciaux (2017), with Ophélie Ronce: text here

Noémie Harmand (2017) with Thomas Lenormand text here

Florian Lavigne (ongoing) with Lionel Roques

**Main Publications**:

Martin G., S. P. Otto, T. Lenormand (2006). “Selection for recombination in structured populations”.Genetics 172 : 593–609. here.

Martin G. & T. Lenormand (2006). “A general multivariate extension of Fisher’s Geometric model and the distribution of mutation fitness effects across species.” *Evolution*, 60(5) : 893–907. here.

Martin G., S.F. Elena, T. Lenormand (2007). « Distributions of epistasis in microbes fit predictions from a fitness landscape model. » *Nature Genetics* 39, 555 – 560 . here.

Martin G., E. Chapuis & J. Goudet (2008). « Multivariate Qst - Fst comparisons : a neutrality test for the evolution of the G-matrix in structured populations. » *Genetics*, 180:2135 – 2149. here.

Chapuis E., Martin G. & Goudet J. (2008) « Effects of Selection and Drift on G Matrix Evolution in a Heterogeneous Environment: A Multivariate Q(st)-F-st Test With the Freshwater Snail *Galba truncatula* » . *Genetics* 180: 2151-2161.

Martin G., S. Gandon (2010) « Lethal mutagenesis and evolutionary epidemiology ». *Phil. Trans. Roy. Soc.* 365 : 1953 – 1963. here.

Martin G., R. Aguilee, J. Ramsayer, O. Kaltz, and O. Ronce. (2012). “The probability of evolutionary rescue: towards a comparison of theory and evolution experiments”. *Phil. Trans. R. Soc. Lond. B* 368. here.

Martin G. (2014).“Fisher’s Geometrical Model Emerges as a Property of Complex Integrated Phenotypic Networks”. *Genetics*. here.

Martin G. & Lambert A. (2015) “A Simple, Semi-Deterministic Approximation to the Distribution of Selective Sweeps in Large Populations”. *Theoretical Population Biology*. here.

Martin G. & Roques L. (2016) “The Non-stationary Dynamics of Fitness Distributions: Asexual Model with Epistasis and Standing Variation”. *Genetics. here.*

Gill M.E., Hamel, F., Martin, G. & Roques L. (2017) “Mathematical properties of a class of integro-differential models from population genetics.” *SIAM J. Appl. Math*. here

Harmand N., Gallet R., Jabbour-Zahab R., Martin G. & Lenormand T. (2017) “Fisher’s geometrical model and the mutational patterns of antibiotic resistance across dose gradients”. *Evolution*. *here*.

Roques L., Garnier J., Martin G. (2017) “Beneficial mutation selection dynamics in finite asexual populations: a free boundary approach”. *Scientific Reports*. here

Anciaux Y., Chevin L.M., Ronce O., Martin G. (2018) Evolutionary rescue over a fitness landscape”. *Genetics*. here.

Harmand N., Gallet R., Martin G. & Lenormand T. (2018) “Evolution of bacteria specialization along an antibiotic dose gradient”. *Evolution Letters*. in press.