rlogo

European Institute for Statistics, Probability, Stochastic Operations Research
and their Applications

About | Research | Events | People | Reports | Alumni | ContactHome


 

March 29-31, 2017

 

Multi-Scale Features of Selection
in
Population Genetics

 

    

SUMMARY REGISTRATION SPEAKERS

PROGRAMME

ABSTRACTS

SPONSORED BY:

 

 

SUMMARY


 


 

ORGANIZER

Frank den Hollander Leiden University

 

INVITED SPEAKERS

Anton Bovier Universität Bonn
Nicolas Champagnat Université de Lorraine
Fernando Cordero Universität Bielefeld
Don Dawson Carlton University
Andreas Greven Universität Erlangen-Nürnberg
Sebastian Hummel Universität Bielefeld
Anna Kraut Universität Bonn
Hannah Mayer Bayer
Martin Moehle Universität Tubingen
Jason Schweinsberg University of California

 

PROGRAMME

WEDNESDAY March 29

09.00 - 09.30 Registration    
09.30 - 10.30 Mini course Andreas Greven and Don Dawson Spatial Fleming-Viot processes with mutation and selection :From rare mutants to emergence
and fixation
10.30 - 11.00 Break    
11.00 - 12.30 Mini course Andreas Greven and Don Dawson Spatial Fleming-Viot processes with mutation and selection :From rare mutants to emergence
and fixation
12.30 - 14.00 Lunch    
14.00 - 15.30   Jason Schweinsberg The genealogy of populations undergoing selection
15.30 - 16.00 Break    
16.00 - 17.30   Nicolas Champagnat Probabilistic and deterministic approaches to adaptive dynamics
18.30 - Conference dinner    

 

THURSDAY March 30

09.30 - 10.30 Mini course Andreas Greven and Don Dawson Spatial Fleming-Viot processes with mutation and selection :From rare mutants to emergence
and fixation
10.30 - 11.00 Break    
11.00 - 12.30 Mini course Andreas Greven and Don Dawson Spatial Fleming-Viot processes with mutation and selection :From rare mutants to emergence
and fixation
12.30 - 14.00 Lunch    
14.00 - 15.00   Sebastian Hummel Mutation, selection, and ancestry in the deterministic limit of the Moran model
15.00 - 16.00   Martin Moehle On the block counting process and the fixation line of the Bolthausen-Sznitman coalescent
16.00 - 16.30 Break    
16.30 - 17.30   Fernando Cordero On the stationary distribution of the block counting process of some exchangeable populations with selection and mutation

 


FRIDAY March 31 (only morning programme)

09.00 - 10.00   Anton Bovier Adaptive dynamics, diploid models, and the escape from selection
10.00 - 11.00   Anna Kraut Evolution on the hypercube: From Adaptive Dynamics to Adaptive Walks
11.00 - 11.30 Break    
11.30 - 12.30   Hannah Mayer Applications of stochastics in pharmaceutical industry
12.30 - Closing and Lunch    


***************************************************************************************************************************************

ABSTRACTS


Anton Bovier

Adaptive dynamics, diploid models, and the escape from selection

Standard stochastic models of adaptive dynamics are based on haploid reproduction schemes. They are sometimes criticised for the difficulty to create genetic diversity. This can be traced to the fact that unless parameters are fine-tuned, times of fixation and extinctions are of the same order.
We show that in diploid models, it fitter alleles are dominant, extinction times are dramatically increased. We show that, under reasonable assumptions,
this can lead to the recovery of an initial unfit allele after the appearance of a second mutant allele, leading to the coexistence of two phenotypes without fin-tuning hypothesis.
(joint work with Rebecca Neukirch and Loren Coquille)


Nicolas Champagnat

Probabilistic and deterministic approaches to adaptive dynamics

The biological theory of adaptive dynamics studies the influence of ecological interactions on long term Darwinian evolution in living populations. Two mains tools were developed to predict long term evolution in a given ecological framework: the canonical equation of adaptive dynamics, which gives the evolution of the dominant (pheno)type in the population, and a criterion for evolutionary branching, which is a phenomenon of diversification in the population without geographical or reproductive separation of sub-populations. The mathematical justification of these tools have been the subject of many works since 2005, and the goal of my talk is to present an overview of the main concepts, ideas and tools used in this topic, as well as several open questions. One can distinguish two main approaches: the first one is deterministic and is based on scalings of small mutations applied to partial differential equations modeling the dynamics of the population; the second one starts from a stochastic model representing each birth, death and mutation events in the population (a so-called "individual-based model") and applies scalings of large population, rare mutations and small mutations to recover the canonical equation and the criterion for evolutionary branching. Both approaches give qualitatively similar results, but each of them has some limitations and many differences remain, which have important biological implications.


Fernando Cordero

On the stationary distribution of the block counting process of some exchangeable populations with selection and mutation

In exchangeable population models with mutation and selection the stationary distribution of the block counting process is characterised by a recursion formula.
In this talk we analyse this recursion for the Moran model and the Lambda-Wright-Fisher model with selection and mutation. We show that the
corresponding probability generating function satisfies an integro-differential equation; we discuss its solution for the Moran model, the Kingman model, the star-shaped model, the beta(3,1) model and the Bolthausen-Sznitman model. Expressions for the stationary distribution of the block counting process and the common ancestor type distribution are derived.
(jointwork with Martin Möhle)


Andreas Greven and Don Dawson

Spatial Fleming-Viot processes with mutation and selection :From rare mutants to emergence

In this short course we describe a rigorous framework in which to analyse some phenomena in the evolutionary theory of populations. In particular this framework incorporates the combined effects of migration, selection and mutation in a spatial stochastic population model and describes the evolution towards successively fitter and fitter types through a type of punctuated equilibria. The discussion is based on some new methods including multiple scale analysis, nonlinear Markov processes and their entrance laws, atomic measure-valued evolutions and new forms of duality. These methods are used to prove ergodic theorems and develop the renormalization analysis needed to analyse the phenomena of stasis, punctuated equilibrium and biodiversity in populations undergoing rare mutation, mutation, resampling, migration and selection. This is based on a mathematical formulation of the bridge between separating time and space scales in a hierarchical mean-field setting.
Literature:
Spatial Fleming-Viot models with selection and mutation
Donald A. Dawson/Andreas Greven
DOI 10.10007/978-3-319-02153-9


Sebastian Hummel

Mutation, selection, and ancestry in the deterministic limit of the Moran model

We consider a haploid Moran model with selection, mutation, and two allelic types. The large population limit, in which neither parameters nor time are rescaled, is called the deterministic limit of the Moran model. In this limit, the proportion of types over time is the solution of an ordinary differential equation. Despite the deterministic nature of this process, the ancestry of single individuals in the population is still stochastic. We describe it via a killed ancestral selection graph and connect it with the deterministic process via duality; this leads to a stochastic representation of the deterministic solution. In particular, the stationary state obtains a nice probabilistic interpretation. We generalise the construction to the mutli-locus case with additive selection and provide probabilistic proofs for results previously obtained via multilinear algebra.
(joint work with Ellen Baake and Fernando Cordero)


Anna Kraut

Evolution on the hypercube: From Adaptive Dynamics to Adaptive Walks

We consider an asexually reproducing population on a finite trait space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event. It has been shown that on the individual-based level this population can be modelled as a measure-valued Markov process and in the limit of large population size, the rescaled stochastic process converges to the solution of a system of deterministic differential equations.
We now investigate the asymptotic behaviour as the probability of mutation tends to zero. The evolution of the population consists of two main parts. In between invasions the growth of mutant traits in the presence of a sample of resident traits at equilibrium density can be approximated by a sum of exponentials corresponding to the growth rates of the different traits. Once a number of mutants has reached a fixed threshold, the invasion itself can then be approximated by the mutation-free Lotka-Volterra system consisting only of the supercritical traits. As a result, we can derive convergence to an adaptive walk that jumps between different equilibria of coexisting resident traits.
In the end we consider a modification of the deterministic system that only allows for mutation once a certain population size is reached and comment on a few preliminary results and the challenges that arise in this setting.


Hannah Mayer

Applications of stochastics in pharmaceutical industry

Mathematical models appear at various stages of drug development and their level of complexity varies. Accounting for different sources of randomness and understanding the variability and uncertainty involved in model predictions is highly relevant. One important aspect is the inclusion of prior knowledge with the help of Bayesian inference. We will discuss different aspects via examples.


Martin  Moehle

On the block counting process and the fixation line of the Bolthausen-Sznitman coalescent

The block counting process and the fixation line of the Bolthausen-Sznitman coalescent are analyzed. It is shown that these processes, properly scaled, converge in the Skorohod topology to the Mittag-Leffler process and to Neveu's continuous-state branching process respectively as the initial state tends to infinity. Strong relations to Siegmund duality, Mehler semigroups and self-decomposability are pointed out. Furthermore, spectral decompositions for the generators and transition probabilities of the block counting process and the fixation line of the Bolthausen-Sznitman coalescent are provided leading to explicit expressions for functionals such as hitting probabilities and absorption times. Extensions to exchangeable coalescents are discussed.


Jason Schweinsberg

The genealogy of populations undergoing selection

We consider two models of populations undergoing selection. First, we consider one-dimensional branching Brownian motion in which particles are absorbed when they hit zero. Here the positions of the particles represent the fitness levels of individuals in the population, and the absorption models the deaths of individuals with low fitness. Second, we consider a population with fixed size N in which each individual acquires beneficial mutations at a constant rate, each individual dies at rate one, and when a death occurs, an individual is chosen with probability proportional to the individual’s fitness to give birth. These two models behave quite differently if one considers the speed at which the fitness of the population increases, or the distribution of the fitnesses of individuals in the population at a given time. However, for both population models, we show that the genealogy of the population can be described by a process called the Bolthausen-Sznitman coalescent, confirming nonrigorous predictions of Brunet, Derrida, Mueller, and Munier (2007), Desai, Walczak, and Fisher (2013), and Neher and Hallatschek (2013).





 

 

 


 

PRACTICAL INFORMATION

      Venue

Eurandom, Mathematics and Computer Science Dept, TU Eindhoven,

Den Dolech 2, 5612 AZ  EINDHOVEN,  The Netherlands

Eurandom is located on the campus of Eindhoven University of Technology, in the Metaforum building (4th floor) (about the building). The university is located at 10 minutes walking distance from Eindhoven main railway station (take the exit north side and walk towards the tall building on the right with the sign TU/e).
Accessibility TU/e campus and map.

 

 

      Registration

Registration is free, but compulsory for speakers and participants. Registration is now open. Please go to: REGISTRATION

 

 

      Accommodation

For invited speakers and organizers we will take care of accommodation. Other attendees will have to make their own arrangements.

For hotels around the university, please see: Hotels (please note: prices listed are "best available").  Reimbursement available up to 80 euro per night.

More hotel options can be found on the webpages of the Tourist Information Eindhoven, Postbus 7, 5600 AA Eindhoven.

 

      Travel

For those arriving by plane, there is a convenient direct train connection between Amsterdam Schiphol airport and Eindhoven. This trip will take about one and a half hour. For more detailed information, please consult the NS travel information pages.

Many low cost carriers also fly to Eindhoven Airport. There is a bus connection to the Eindhoven central railway station from the airport. (Bus route number 401) For details on departure times consult http://www.9292ov.nl

The University  can be reached easily by car from the highways leading to Eindhoven (for details, see our route descriptions or consult our map with highway connections.

 

      Conference facilities : Conference room, Metaforum Building  MF11&12

The meeting-room is equipped with a data projector, an overhead projector, a projection screen and a blackboard. Please note that speakers and participants making an oral presentation are kindly requested to bring their own laptop or their presentation on a memory stick.

 

      Conference Secretariat

Upon arrival, participants should register with the workshop officer, and collect their name badges. The workshop officer will be present for the duration of the conference, taking care of the administrative aspects and the day-to-day running of the conference: registration, issuing certificates and receipts, etc.

 

      Cancellation

Should you need to cancel your participation, please contact Patty Koorn, the Workshop Officer.

 

     ●      Contact

Mrs. Patty Koorn, Workshop Officer, Eurandom/TU Eindhoven, koorn"at"eurandom.tue.nl

 

 


         

        

Last updated 06-03-17,
by PK

 P.O. Box 513, 5600 MB Eindhoven, The Netherlands
tel. +31 40 2478100  
  e-mail: info@eurandom.tue.nl