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August 25-29, 2014 Workshop on Population Dynamics and Statistical Physics in Synergy
Prof. Friedrich Götze
(Bielefeld University) received a Royal Decoration from the mayor of Eindhoven
SUMMARY This workshop is part of the DFG Priority Program "Probabilistic Structures in Evolution" (DFG-SPP 1590). Themes of the workshop are genealogical processes; multiscale genetic models; adaptive dynamics; evolutionary branching; evolution for interaction networks. The programme will consist of 3-hour mini-courses and 1-hour talks. ORGANISERS
LIST OF INVITED SPEAKERS
MONDAY AUGUST 25
TUESDAY AUGUST 26
WEDNESDAY AUGUST 27
THURSDAY AUGUST 28
FRIDAY AUGUST 29
***************************************************************************************************************************************** Siva Athreya Dense Graph Limits under Respondent Driven Sampling We consider certain respondent-driven sampling
procedures on dense graphs. We show that if the sequence of the vertex-sets is
ergodic then the limiting graph can be expressed in terms of the original dense
graph via a transformation related to the invariant measure of the ergodic
sequence. For specific sampling procedures we describe the transformation
explicitly. Ellen Baake The Moran model with recombination: Type distributions on partitions, ancestry, and duality We consider the Moran model with recombination, which
describes the evolution of the genetic composition of a population under
recombination and resampling. There are $n$ loci (or sites), a finite number of
letters (or alleles) at every site, and we do not make any scaling assumptions.
In particular, we do not assume a diffusion limit. Due to the huge state space,
it is notoriously difficult to find the full distribution of types in a sample.
We therefore take an alternative route by concentrating on the joint
probabilities of types at tuples of loci. Taking the usual genealogical
approach, this is described via a process on the set of partitions of $\{1,\ldots,n\}$
(backward in time), which may be considered as a marginalised version of the
ancestral recombination graph, and sheds new light on the work of A. Bobrowski,
T. Wojdyla and M. Kimmel (2009). With the help of an inclusion-exclusion
principle we show that the type distribution corresponding to a given partition
may be represented in a systematic way, with the help of so-called recombinators.
The same is true of correlation functions (known as linkage disequilibria in
biology) of all orders. For presentation please contact Ellen Baake Martina Baar Stochastic individual-based models of adaptive dynamics We consider the limiting behavior of a model for the Darwinian evolution in an asexual population characterized by a natural birth rate, a logistic death rate due to age or competition and a probability of mutation at each birth event. In this stochastic individual-based model the population is described by a measure-valued Markov process, known as BPDL process. We focus on the limit of a large population with rare mutations and small mutation effects on a long time scale. More precisely, we study this three limits simultaneously on a timescale which separates birth and death events from mutation events and we will see that on this time scale coexistence of two traits cannot occur. In other words, the population stays essentially single modal centered around a trait, which evolves continuously. In fact, we are able to prove that for this combined limit the population process converges to an ODE, known as canonical equation of adaptive dynamics. This is a joint work with A. Bovier and N. Champagnat. Matthias Birkner Ancestral lineages in locally regulated populations Ancestral lineages of sampled individuals in the
stepping stone model form (delayed) coalescing random walks, and can thus be
viewed as a spatial coalescent process. The analogous object in spatial
population models which unlike the stepping stone model do allow random
fluctuations of local population sizes is a system of correlated coalescing
random walks in a space-time random environment. We discuss regeneration
approaches to study its long-time behaviour and implications for spatial type
distributions. A simple guiding example is the discrete time contact process,
with an ancestral lineage given by a directed walk on the backbone of an
oriented percolation cluster. Jochen Blath The seed-bank coalescent We identify a new natural coalescent structure, the
seed-bank coalescent , which describes the gene genealogy of populations under
the influence of a strong seedbank effect, that is, in which `dormant forms' of
individuals (such as seeds or spores) may jump a signicant number of generations
before joining the `active' population. Mathematically, our seed-bank coalescent
appears as scaling limit in a Wright-Fisher model with geometric seed-bank age
structure if the average time of seed dormancy scales with the order of the
total population size N . This extends earlier results of Kaj, Krone and Lascaux
(2001) who show that the Anton Bovier Extremal Processes of Gaussian Processes Indexed by Trees Gaussian processes indexed by trees form an interesting class of correlated
random fields where the structure of extremal processes can be studied. One
popular example is Branching Brownian motion, which has Éric Brunet Existence of open evolutionary paths in a rugged landscape An evolving population under selection explores its fitness landscape by fixing favorable mutations. If one assumes that deleterious mutations cannot be fixed, it is however not obvious that the population can find an evolutionary path leading to the fittest possible state when the fitness landscape is rugged . I will present some rigourous results (and some conjecture, and some open questions) on the existence and the number of acceptable evolutionary paths in the "House of Cards" model. Nicolas Champagnat Adaptive dynamics and evolutionary branching in the limit of small mutations in a stochastic individual-based population model The mathematical study of adaptive dynamics, and more specifically of the phenomenon of evolutionary branching by which a population is driven by selective forces to sub-divide into two interacting subpopulations with different phenotypes, has been done in the last years using either an approach based on an assumption of rare mutations and large population on a stochastic individual-based model, or an approach based on a limit of small mutations on a PDE model. Both approaches suffer from irrealistic features: the first one requires a very long time scale to observe evolutionary branching; in the second one, exponentially small population densities can have a very strong impact on the future evolutionary dynamics. The goal of this talk is to present an intermediate approach that may solve these two drawbacks, consisting in applying a combination of limits of small mutations and large population on the stochastic individual-based model. Mark Dykman Scaling and fragility of the rates of rare events We discuss rare events that result from large classical and quantum fluctuations in systems away from thermal equilibrium. They include extinction in population dynamics and switching between coexisting stable states in dynamical systems. We review the results on the scaling of the rates with the distance to the bifurcation points, which turns out to be different for the extinction and switching problems even for the bifurcations of the similar type. We show that the rates of rare events can discontinuously change with the change of the parameters of the system, which we call the fragility effect. This change is accompanied by an abrupt change of the most probable path followed in the rare event. We discuss the criteria for the onset of fragility. The associated breakdown of the conventional analysis and the onset of a kink on the optimal path are considered. Lisa Hartung Variable speed branching Brownian motion In this talk I explain how the convergence of the
extremal process of variable speed BBM is obtained when the "speed function",
describing the time-inhomogeneous variance, lie strictly below their concave
hull. The resulting limiting objects turn out to be universal in the sense that
they only depend on the slope of the speed function at 0 and the final time t. Alex Kamenev Does noisy environment facilitate extinction, or stabilize the population? I will review population dynamics models, which incorporate an external environmental noise. The natural question is whether such a noise accelerates extinction, or works as a stabilizing factor. It appears that it can have both of these effects. I will present and explain models, where the noise facilitates extinction. Moreover, it may change the characteristic extinction time from being exponentially long in the population size into being only power-law long. On the other hand, I will present a family of models, where the strong noise is solely responsible for the population stability. (The effect bears a strong resemblance with the celebrated Coleman-Weinberg phenomenon of symmetry breaking by vacuum fluctuations in the high-energy physics.) In this latter scenario the population lifetime scales as a stretched exponential of the characteristic noise amplitude. Anton Klimovsky Is there more biodiversity in non-homogeneous environments than in homogeneous ones? Consider a spatially structured population of
individuals. The population is structured in a hierarchical manner into
colonies, macro-colonies (= collections of colonies), macro-macro-colonies (=
collections of macro-colonies), and so on. Within the colonies, the individuals
reproduce under a fixed amount of resources according to the Cannings model.
Next, the individuals move around from one colony to the other at given rates
which depend on the geographical distance between the colonies (= migration).
Furthermore, the whole macro-colonies can suffer from occasional non-local
catastrophic events (e.g., droughts, forest fires). The population dynamics
respects the hierarchical structure of the geographical space. Larger-scale
events are less frequent that the smaller-scale ones. This results in a
hierarchy of space-time scales on which the system evolves. How does the
biodiversity in such a hierarchical Cannings process evolve? I will report on
our findings in the case, where both the Cannings reproduction and the
reshuffling-resampling mechanisms are spatially inhomogeneous. This is modelled
via a random environment. It turns out that the inhomogeneities increase
biodiversity (comparing to the homogeneous environment). Joachim Krug Fitness landscapes and adaptive evolution The adaptive dynamics of an evolving population is constrained by epistatic interactions encoded in the underlying fitness landscape. In recent years empirical data sets have become available that offer glimpses into the structure of real fitness landscapes and motivate theoretical work on classic probabilistic models such as NK-landscapes and the rough Mount Fuji model. In this talk I report on recent efforts aimed at quantifying the accessibility of these landscapes under asexual adaptation. Results concerning structural properties, such as the number of local maxima and the existence of fitness-monotonic pathways, as well as on the dynamics of adaptive walks will be presented, with particular emphasis on the subtle role of genetic architecture in the NK-model. If time permits, the role of recombination in speeding up or slowing down adaptation on rugged fitness landscapes will also be briefly addressed. Jorge Kurchan (mini course) Algorithmic aspects of adaptive dynamics Population dynamics offers a practical method to compute large deviations. Even without implementing an actual program, thinking in terms of a population allows one to understand several features of large deviation functions, in particular the particular features they take in the presence of metastability. Conversely, one may think of a large population of individuals undergoing natural selection as a natural algorithm that computed the large deviations of fitness. Marcel Ortgiese The Interface of the Symbiotic Branching Model The symbiotic branching model describes two interacting spatial populations
whose evolution is given by system of correlated SPDEs. Starting from two
spatially separated populations, one can consider the growth of the interface
where particles of both types are present. We show that for negative
correlations the system converges under a diffusive rescaling. We will discuss
first properties of the limiting system and their implications for the
interface. Etienne Pardoux A path-valued Markov process indexed by the ancestral mass We consider a Feller diffusion with a nonlinear drift which models the
interaction within the population. We study the resulting path-valued Markov
process, which is indexed by the ancestral population at time t=0. We write an
SDE driven by a Poisson random measure for that process, and explicit its
infinitesimal generator. Frank Redig Energy and wealth redistribution models We consider stochastic models where a configuration x_i, i\in V is updated
via binary exchanges along edges ij, of the form x’_i = u(x_i+x_j), x’_j=
(1-u)(x_i+x_j) (energy redistribution model) or x’_i =l x_i + (1-l) u(x_i+x_j),
x’_j= l x_j + (1-u)(x_i+x_j) (wealth distribution model). Christoph Richard (mini course) Combinatorial aspects of tree-like structures Exactly solvable models from statistical physics serve as a crude but
tractable approximation to real-world phenomena. In particular, solvable
subclasses of self-avoiding walks on a lattice have been used to understand the
behaviour of polymers. From a technical perspective, this involves enumerative
combinatorics and Jan Swart Balancing selection and rebellious voter models In biological populations, individuals that are genetically different from
their neighbours often have a selective advantage, since being different reduces
competition with neighbours and vulnerability to pests and Anita Winter Tree-valued spatial Lambda-Fleming-Viot diffusions: The finite system scheme We study the evolution of genealogies for interacting
spatially structured Λ-Fleming-Viot diffusions. 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).
● RegistrationRegistraton is closed.
● AccommodationFor invited participants, we will take care of accommodation. Other attendees will have to make their own arrangements. We have a preferred hotel, which can be booked at special rates. Please email Patty Koorn for instructions on how to make use of this special offer. For other hotels around the university, please see: Hotels (please note: prices listed are "best available"). 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 or see Eurandom web page location. 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 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 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 day-to-day running of the conference: registration, issueing certificates and receipts, etc.
● CancellationShould you need to cancel your participation, please contact Patty Koorn, the Workshop Officer. There is no registration fee, but should you need to cancel your participation after January 2, 2014, we will be obliged to charge a no-show fee of 30 euro.
● ContactMrs. Patty Koorn, Workshop Officer, Eurandom/TU Eindhoven, koorn@eurandom.tue.nl SPONSORSThe organisers acknowledge the financial support/sponsorship of:
Last updated
24-09-14,
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