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March 2931, 2017
MultiScale Features
of Selection
SPONSORED BY:
SUMMARY
ORGANIZER
INVITED SPEAKERS
WEDNESDAY March 29
THURSDAY March 30
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 finetuned, times of fixation and extinctions are of the
same order. 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 subpopulations. 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 socalled "individualbased 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. Spatial FlemingViot 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 measurevalued 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 meanfield setting. 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
mutlilocus case with additive selection and provide probabilistic
proofs for results previously obtained via multilinear algebra. 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 individualbased level this
population can be modelled as a measurevalued 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. Hannah Mayer Applications of stochastics in pharmaceutical industry Martin Moehle On the block counting process and the fixation line of the BolthausenSznitman coalescent The block counting process and the fixation line of the BolthausenSznitman coalescent are analyzed. It is shown that these processes, properly scaled, converge in the Skorohod topology to the MittagLeffler process and to Neveu's continuousstate branching process respectively as the initial state tends to infinity. Strong relations to Siegmund duality, Mehler semigroups and selfdecomposability are pointed out. Furthermore, spectral decompositions for the generators and transition probabilities of the block counting process and the fixation line of the BolthausenSznitman 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
PRACTICAL INFORMATION ● VenueEurandom, 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).
● RegistrationRegistration is free, but compulsory for speakers and participants. Registration is now open. Please go to: REGISTRATION
● AccommodationFor 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.
● TravelFor 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&12The meetingroom 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 SecretariatUpon 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 daytoday running of the conference: registration, issuing certificates and receipts, etc.
● CancellationShould you need to cancel your participation, please contact Patty Koorn, the Workshop Officer.
● ContactMrs. Patty Koorn, Workshop Officer, Eurandom/TU Eindhoven, koorn"at"eurandom.tue.nl
Last updated
060317,

