Lorentz Center - Fluctuations in Population Biology, Epidemiology and Evolution from 11 Aug 2014 through 15 Aug 2014
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    Fluctuations in Population Biology, Epidemiology and Evolution
    from 11 Aug 2014 through 15 Aug 2014

 

Registered:

Talk/Poster

Title

Assaf

T

Title: The effects of extrinsic noise on cellular decision making

Author: Michael Assaf  

 

Abstract:

Analysis of complex gene regulation networks gives rise to a landscape of metastable phenotypic states for cells. Heterogeneity within a population arises due to infrequent noise-driven transitions of individual cells between nearby metastable states. While most previous work has focused on the role of intrinsic fluctuations in driving such transitions, in this work we investigate the role of extrinsic fluctuations. We develop an analytical framework to study the combined effect of intrinsic and extrinsic noise on the dynamics of simple network motifs that comprise more complex genetic networks. In particular, we quantify the effects of extrinsic noise on the steady state distribution of protein copy numbers. We then investigate simple genetic switches and their stability when applying extrinsic noise.

We show that extrinsic noise can significantly alter the lifetimes of the phenotypic states, and may fundamentally change the escape mechanism compared to intrinsic-noise-driven escape. All our analytical results are corroborated by extensive Monte-Carlo simulations, which are also used to study more complex higher-dimensional decision-making networks in biology.

Ben-Naim

T

Title: Extreme Statistics of Extreme Values

Author: Eli Ben-Naim

 

Abstract:

I will survey recent results on first-passage properties of extreme values. The talk will highlight two problems, one involving uncorrelated random variables and one involving correlated random variables. In both cases, first-passage probabilities decay algebraically with the total number of variables, a behavior that is governed by nontrivial exponents.  The first problem involves extreme positions of two Brownian particles, and the second problem involves incrementally improving records. A number of related problems will be mentioned as well as relevance for analysis of empirical data.

Biancalani

T

Title: Pattern formation in population systems

Authors: Tommaso Biancalani and Nigel Goldenfeld

 

Abstract:

Population systems exhibit ordered structures in space and time which are traditionally described by the formalisms of deterministic pattern formation, originating in fluid dynamics, reaction-diffusion problems and other areas of physical sciences. The parameter range for which these patterns exist in models can be very restricted; for example in Turing instabilities, the ratio of the diffusivities of the inhibitor and activator must be large.  In ecosystems in particular, it is not clear that this parameter regime applies, yet there is a general understanding that activator-inhibitor dynamics should be operative, for example in herbivore-plankton systems.  Over the last few years, we have proposed a solution to this paradox: pattern formation occurs for a much greater range of parameter values if the shot noise due to discreteness at low population size is taken into account. Inclusion of demographic stochasticity into spatially-extended systems is accomplished using master equation and field theoretic techniques, and the resulting patterns exhibit features that can be compared readily with experiment. I will review these advances, and in addition will mention briefly how similar techniques can be applied to model speciation in ecosystems.

Chaudhury

T

Title: Spontaneous Clearance of Viral Infections by Mesoscopic Fluctuations

Author: Srabanti Chaudhury

 

Abstract:

Deterministic models of viral infection are based on a large population of infected cells and virions, so they fail to capture some important stages of viral infection dynamics for which intrinsic stochastic effects play a dominant role. One of the remarkable phenomena observed in stochastic population dynamics is the spontaneous extinction of a disease via a rare fluctuation. In this talk I will discuss about the role of mesoscopic fluctuations in disease extinction in the context of viral infection kinetics. I will explore two minimal models of stochastic viral infection dynamics. I will highlight the utilized methodology of a semi-classical path integral technique that deals with the full counting statistics of the reaction events. I will show how a coarse graining method can reduce the complexity of viral infection dynamics by separating the fast and slow degrees of freedom and calculate the mean disease extinction time. The obtained theoretical results will be implanted to identify parameters that are most important for determining the extinction time for specific stages of HIV and HCV infection. My results show that the clearance time is exponentially sensitive to the viral decay rate. This suggests that if standard drug therapy fails to clear an infection then intensifying therapy by adding a drug that reduces the rate of cell infection may be useful in clearing small pockets of infection.

Doering

T

Title: Stochastic injections in a polymerization process

Author: Charles R. Doering and Yen Ting Lin

 

Abstract:

Recent research has raised questions regarding system size dependence of the ratio of monomer and dimer concentrations in a simple chemical reaction network, attributing concentration ratio inversions to "small N" fluctuations.  We show that many features reported in simulations can be accounted for by the stochastic injection protocols used to sustain the system in a steady state: inputing monomers in "clumps" rather than independently individually and evolving concentrations via deterministic mean-field dynamics produces the same phenomena.  We report exact result for one version of the problem.

Dykman

T

Title: Rare events in systems with delay

Authors: Mark Dykman, Ira B. Schwartz, Thomas W. Carr, and Lora Billings

 

Abstract:

We consider the tails of the probability distribution, the rates of switching between coexisting stable states, and the extinction rates in stochastic systems with delay. Both large rare fluctuations due to the external noise and, in the case of population dynamics, due to the discrete change of the population in an elementary reaction are considered. Finding exponents of the rates of rare events is reduced to a variational problem. We show that, in contrast to systems without delay, the variational equations of motion are acausal, the variational trajectories depend both on the “past” and the “future”. They have interesting time-reversal symmetry for delayed systems in thermal equilibrium. The analytical results are in good agreement with numerical simulations.

Forgoston

T

Title: Stochastic Center Manifolds and Epidemics: Outbreak Prediction and Extinction

Authors: Eric Forgoston and Lora Billings

 

Abstract:

Modeling epidemics to predict the occurrence of disease outbreaks is of paramount importance since population case data is deficient when compared to model simulation.  However, the prediction of epidemic outbreaks is difficult due to the complex nature of the dynamics.  This complexity arises from random fluctuations in the population, the nonlinear mass action contact between individuals, and the high dimension of the models.  In this talk, a class of epidemic models which includes random fluctuations will be presented.  New tools of model reduction for random dynamical systems will be introduced and applied to the epidemic models to enhance the analysis of predictability of disease outbreaks.  Moreover, these tools allow for improved prediction of the overall probability of the number of cases, as well as improved prediction of the correct phase at which the outbreaks occur. Additionally, epidemic extinction as an application of center manifold reduction will be discussed.

Grun

T

Title: Validation of noise models for single-cell transcriptomics

Abstract: The impact of stochastic gene expression on phenotypic variation has been subject to intense research during the last years. The availability of diverse single-cell sequencing methods now permits the analysis of single-cell transcriptomes with high sensitivity. However, due to low amounts of input material single-cell sequencing still suffers from substantial levels of technical noise. Here we identify two major sources of technical variability, sampling noise and global cell-to-cell variation in sequencing efficiency. We propose a noise model to correct for these sources of technical noise and to infer biological gene expression variability from single cell mRNA sequencing data. This model is then validated by single molecule fluorescent in-situ hybridization. 

We then apply the noise model to single cell mRNA sequencing data obtained from mouse embryonic stem cells grown either in Serum/LIF condition or in 2i/LIF condition and show that gene expression variability is significantly increased when cells are grown in Serum/LIF condition.

Gore

T

Title: Cooperation, cheating, and collapse in microbial populations

Author: Jeff Gore

 

Abstract:

Natural populations can suffer catastrophic collapse in response to small changes in environmental conditions, and recovery after such a collapse can be exceedingly difficult. We have used laboratory microbial ecosystems to directly measure theoretically proposed early warning signals of impending population collapse. Yeast cooperatively break down the sugar sucrose, meaning that below a critical size the population cannot sustain itself. We have demonstrated experimentally that changes in the fluctuations of the population size can serve as an early warning signal that the population is close to collapse. The cooperative nature of yeast growth on sucrose suggests that the population may be susceptible to "cheater" cells, which do not contribute to the public good and instead merely take advantage of the cooperative cells. We confirm this possibility experimentally and find that such social parasitism decreases the resilience of the population.

Hutt

T

Title: Additive noise in nonlinearly coupled neural systems becomes multiplicative noise through the backdoor.

Author: Axel Hutt

 

Abstract:

Neural systems are complex systems and exhibit a hierarchy of scales. The talk shows that additive noise on a low hierarchical level maps to additive and multiplicative noise on a higher hierarchical level. Applications are shown for a hierarchy delayed stochastic neural mass models which allow to describe experimental macroscopic neural activity, such as electroencephalogram.  

Kessler

T

Title: Optimal Dispersal: Beyond the Hamilton-May Model

Author: David Kessler

 

Abstract:

We investigate various extensions/variations of the classic Hamilton-May model for the evolutionary stable dispersal rate.  In particular, we consider: 1) a model where dispersal occurs post- rather than pre- competition; 2) a model where the population on each cluster after competition is subject to Poissonian fluctuations 3) a model comprising both modifications. We discuss the resulting phenomenology, and show that in general the effect of the changes is multifold, so that no simple argument can predict whether the change increases or decreases the selected dispersal rate.  Nevertheless, the large-N regime does exhibit universal behavior, except at very small or very large dispersal penalty. We also discuss a model of density-dependent dispersion.

Khain

T

Title: Clustering of migrating brain tumor cells: typical behavior and rare events

Author: Evgeniy Khain, Department of Physics, Oakland University, Rochester, MI 48309, USA

 

Abstract:
Glioblastoma tumors are highly invasive. Cancer cells detach from the inner tumor core and actively migrate away [1]. Invasive cells have a very low proliferation (division) rate compared to those on the tumor surface. Unfortunately, these invasive cells may eventually switch back to the “proliferative” phenotype, after a cell has migrated a large distance from the original solid tumor; this gives rise to recurrent tumors. The mechanisms of the phenotypic switch are poorly understood. We proposed [2] that it can be related to the observed clustering of invasive cells. Once such clusters are formed in the invasive region, cells on the surfaces of the clusters can become proliferative again, like the cells on a surface of a primary tumor. To investigate the mechanisms of cell clustering on a substrate, we formulated [2] a discrete stochastic model for cell migration.  The model accounts for cells diffusion, proliferation and adhesion. We predicted that cells typically form clusters if the effective strength of cell-cell adhesion exceeds a certain threshold. Our prediction was confirmed in a series of experiments [2].

 

However, for many glioma cell lines, the effective strength of cell-cell adhesion is below the threshold value necessary for cluster formation. For sub-critical adhesion, the invasive cells do not typically form clusters; despite this, tumor recurrence does exist for these cell lines. We hypothesize that the invasive-to-proliferative phenotypic switch can be triggered by a rare event - spontaneous clustering of invasive tumor cells [3]. Once a sufficiently large cluster is formed due to a large fluctuation, cells on the surface of the cluster may become proliferative, triggering rapid tumor growth. We develop a formalism for the analysis of this rare event employing a phenomenological master equation and measuring the transition rates in numerical simulations [3].

 

1. A. M. Stein et al, Biophys. J., 92, 356 (2007);

2. E. Khain et al, EPL 88, 28006 (2009);

3. E. Khain, M. Khasin, L.M. Sander, in review (2014).

Kogan

T

Title:  Two-strain competition in quasi-neutral stochastic disease dynamics

Author: Oleg Kogan

 

Abstract:

We developed a new perturbation method for studying quasi-neutral competition, and applied it to the analysis of fixation of competing strains in two stochastic epidemic models.  The first model is a two-strain generalization of the stochastic Susceptible-Infected-Susceptible (SIS) model.

Here we extended previous results due to Parsons and Quince (2007), Parsons et al (2008) and Lin, Kim and Doering (2012). The second model, a two-strain generalization of the stochastic Susceptible-Infected (SI) model with population turnover, was not studied previously. In each of the two models, when the basic reproduction numbers of the two strains are identical, a system with an infinite population size approaches a point on the deterministic coexistence line (CL): a straight line of fixed points in the phase space of sub-population sizes.  Shot noise drives one of the strain populations to fixation, and the other to extinction, on a time scale proportional to the total population size.  Our perturbation method explicitly tracks the dynamics of the probability distribution of the sub-populations in the vicinity of the CL.  We argue that, whereas the slow strain has a competitive advantage for mathematically ``typical" initial conditions, it is the fast strain that is more likely to win in the important situation when a few infectives of both strains are introduced into a susceptible population.

Lin

T

Title: Fluctuation-Driven Shifts in Selection Regimes in Competitive Population Dynamics

Authors: Yen-Ting Lin, H. Kim, and C. R. Doering.

 

Abstract:

This talk reports the results of analytical and computational investigations of models of competitive population dynamics, specifically the competition between species in heterogeneous environments with different phenotypes of dispersal, fully accounting for demographic stochasticity. A novel asymptotic approximation is introduced and applied to derive remarkably simple analytical forms for key statistical quantities describing the populations' dynamical evolution. The analysis highlights the fundamental physical effect of the fluctuations and provides an intuitive interpretation of the complex dynamics. An interaction between stochasticity and nonlinearity is the foundation of noise-driven dynamical selection.

McKane

T

Title: Analysis of stochastic fluctuations in population ecology and genetics

Author: Alan McKane

 

Abstract:

Biological systems display a range of phenomena which are a consequence of stochastic fluctuations. In the previous meeting on this subject in Leiden in 2009, one of main topics that was discussed was the use of the linear noise approximation to understand stochastic cycles in population biology and epidemiology. In this talk I will describe some of the progress made since then to elucidate other stochastically-generated phenomena.

Topics will include the use of fast-mode elimination to reduce metapopulation models to effective models which are amenable to analysis, the role of demographic noise in the spontaneous formation of species and the effect of assuming discrete time in the modelling process. In all cases the starting point will be an individual based model, which will be used to derive a mesoscopic description of the system which will then form the basis of the analytical procedures discussed.

Meerson

T

Title: Large fluctuations of stochastic populations: extinction, colonization, invasion

Author: Baruch Meerson


Abstract:

There are many examples in population biology and ecology when a rare large fluctuation dramatically changes the course of events. One such example is extinction of a long-lived population caused by environmental and demographic noise. Another example is colonization, against all odds, of a territory by a small group of migrating individuals. The recent years have witnessed an increased interest in applications of WKB approximation, borrowed from physics, for the analysis of large fluctuations of stochastic populations. Here I will give a brief survey of these applications. I will start from a single well-mixed population, move on to two well-mixed populations, and then to populations in space.  I will conclude with large fluctuations of invasion fronts. In many of these problems the analysis boils down to finding an instanton-like trajectory in the phase space of an underlying Hamiltonian flow that emerges from the WKB theory. Of course, there are cases when the WKB theory does not work, and other methods should be developed. One example is quasi-neutral competition, the other involves positive fluctuations of invasion fronts propagating into an unstable state.

Mehlig

T

Title: Metapopulation dynamics

Author: Bernhard Mehlig

 

Abstract:

Abstract: The habitats of animal populations are often geographically divided into many small patches, either because of human interference or because natural habitats are patchy. Understanding the dynamics of such "metapopulations" is a problem of great theoretical and practical interest. We analyse stochastic metapopulation dynamics in terms of an

individual-based, stochastic model of a finite population, using the number of patches in the population as a large parameter. This approach does not require that the number of individuals per patch is large, neither is it necessary to assume a time-scale separation

between local population dynamics and migration. Our approach makes it possible to accurately describe the dynamics of metapopulations consisting of many small patches. We focus on metapopulations on the brink of extinction and estimate the time to extinction and describe the most likely path to extinction. We find that the logarithm of the time to extinction is proportional to the product of two vectors, a vector characterising the distribution of patch population sizes in the quasi-steady state, and a vector -- related to Fisher's reproduction vector -- that quantifies the sensitivity of the quasi-steady state distribution to demographic fluctuations. We compare our analytical results to stochastic simulations of the model, and discuss the range of validity of the analytical expressions. By identifying fast and slow degrees of freedom in the metapopulation dynamics, we show that the dynamics of large metapopulations close to extinction is approximately described by a deterministic equation

originally proposed by Levins (1969). We were able to compute the rates in Levins' equation in terms of the parameters of our stochastic, individual-based model. It turns out, however, that the interpretation of the dynamical variable depends strongly on the intrinsic growth rate and carrying capacity of the patches. Only when the growth rate and the carrying capacity are large does the slow variable correspond to the number of patches, as envisaged by Levins. Last but not least, we discuss how our findings relate to other, widely used metapopulation models.

Metz

P

Title: Adaptive dynamics: some basic theory and an application

Nieddu

P

Title: The effect of pre-extinction dynamics on the mean time to extinction in stochastic populations

Sander

T

Title: Extinction of metapopulations: two cautionary tales

Author: Leonard Sander

 

Abstract:

We consider two problems involving the extinction of metapopulations. We consider a variable migration rate between patches of habitat. In both cases the behavior of the extinction rate is counter-intuitive.

In the first case we consider the criterion for the maximal survival time of species which live habitats of very different carrying capacity. For the typical behavior migration from a good to a poor habitat decreases the total population. But for extinction, a small migration rate is essential to maintain the population.

In the second case we show that for very fast migration rates a metapopulation does not necessarily look like a single system with averaged dynamics.

Schwartz

T

Title: Adaptive dynamics, control, and extinction in network populations

Authors: Ira B. Schwartz and Leah B. Shaw

 

Abstract:

Real networks consisting of social contacts do not possess static connections.That is, social connections may be time dependent due to a variety of individual behavioral decisions based on current network links between people. Examples of adaptive networks occur in epidemics, where information about infectious individuals may change the rewiring of healthy people, or in the recruitment of individuals to a cause or fad, where rewiring may optimize recruitment of susceptible individuals. In this talk, we will review some of the dynamical properties of adaptive networks, such as bifurcation structure and the size of fluctuations. We will also show how adaptive networks predict novel phenomena as well as yield insight into new controls. Applying a new transition rate approximation that incorporates link dynamics, we extend the theory of large deviations to stochastic network extinction to predict extinction times. In particular, we use the theory to find the most probable paths leading to extinction. We then apply the methodology to network models and discover how mean extinction times scale with network parameters in Erdos-Renyi networks. The results are shown to compare quite well with Monte Carlo simulations of the network in predicting both the most optimal paths to extinction and mean extinction times.

 

References:

MS Shkarayev, IB Schwartz, LB Shaw, Recruitment dynamics in adaptive social networks, Journal of Physics A: Mathematical and Theoretical 46 (24), 245003

LB Shaw, IB Schwartz, Enhanced vaccine control of epidemics in adaptive networks, Physical Review E 81 (4), 046120 (2010)

Ira B Schwartz, Leah B Shaw, Rewiring for adaptation Publication, Physics Volume 3 Issue 17 (2010) doi: 10.1103/Physics.3.17

Leah B Shaw, Ira B Schwartz Publication, Fluctuating epidemics on adaptive networks, Physical Review E 77 066101 (2008).

Shaw

P

Title:  Epidemic and information spread in an adaptive social network

Authors:  Leah Shaw, Yunhan Long, Thilo Gross

Szwaykowska

P

Title: Collective motion of heterogeneous swarms

Rein ten Wolde

T

Title: Simulating rare events in biochemical networks

Author: Pieter Rein Ten Wolde

 

Abstract:

Simulating rare events is a major computational challenge, because in conventional techniques most of the CPU time is wasted on the uneventful waiting time. In the past years, we have developed a new class of techniques, called Forward Flux Sampling (FFS), which makes it possible to simulate efficiently rare events in both equilibrium and non-equilibrium systems. More recently, we have extended these techniques so that they can also handle rare events in non-stationary systems. This Non-Stationary FFS technique can be used to study how sensitive systems are to transient fluctuations, or how efficiently they can be switched under the influence of an external signal. We apply NS-FFS to study the flipping of the phage lambda switch by an external signal. We show that there exists an optimal pulse that maximizes the switching efficiency.

Vucelja

T

Title: Emergence and interference of clones in populations, glassy aspects of evolution

Author: Marija Vucelja  

 

Abstract:

Recombination reshuffles genetic material, while selection acts to amplifies the fittest genotypes. Rapidly recombining populations typically consist of many diverse genotypes. In facultatively recombining organisms selection can amplify fit genotypes into large clones. The occurrence of this "clonal condensation" depends on the ratio of recombination and selection rates and on  the heritability of fitness. Clonal condensation is an important phenomenon, present in many populations, that has not been captured by traditional population genetics measures (such as linkage disequilibrium). I hope to convince you that our work provides a qualitative explanation of clonal condensation. In my talk I will point out the similarity between the clonal condensation and the freezing transition in the Random Energy Model of spin glasses. Guided by this analogy I will derive one of the key quantities of interest: the probability that two individuals are genetically identical. This quantity is the analog of the spin-glass order parameter and it is also closely related to rate of coalescence in population genetics: two individuals that are part of the same clone have a recent common ancestor. I will conclude with a summary of our present understanding of the clonal condensation phenomena and describe ongoing works on clonal interference.

Weissmann 

P

Title: Stochastic desertification

Wu

P

Title: When do microscopic assumptions determine the outcome in evolutionary game dynamics?

 

Abstract:

The modelling of evolutionary game dynamics in finite populations requires microscopic processes that determine how strategies spread. The exact details of these processes are often chosen without much further consideration. Deferent types of microscopic models, including in particular fitness-based selection rules and imitation-based dynamics, are often used as if they were interchangeable. We challenge this view and investigate how robust these choices on the micro-level really are. Focusing on a key macroscopic observable, the probability for a single mutant to take over a population of wild-type individuals, we show that there is a unique pair of a fitness-based process and an imitation process leading to identical outcomes for arbitrary games and for all intensities of selection. This highlights the perils of making arbitrary choices at the micro-level without regard of the consequences at the macro-level.

 

Registered:

Talk/Poster

Title

1

Assaf

T

The effects of extrinsic noise on cellular decision making

2

Baake

T

The Moran model with recombination: Type distributions on partitions,   ancestry, and duality

3

Ben-Naim

T

Extreme Statistics of Extreme Values

4

Biancalani

T

Pattern formation in population systems

5

Billings

6

Bruggeman

7

Chaudhury

T

Spontaneous Clearance of Viral Infections by Mesoscopic Fluctuations

8

Doering

T

Stochastic injections in a polymerization process

9

Dykman

T

Rare events in systems with delay

10

Forgoston

T

Stochastic Center Manifolds and Epidemics: Outbreak Prediction and Extinction

11

Gore

T

Cooperation, cheating, and collapse in microbial populations

12

Huang  

13

Hutt

T

Additive noise in nonlinearly coupled neural systems becomes multiplicative noise through the backdoor

14

Kessler

T

Optimal Dispersal: Beyond the Hamilton-May Model

15

Khain

16

Khasin

17

Kogan

T

Two-strain competition in quasi-neutral stochastic disease dynamics

18

Krumins

19

Lin

T

Fluctuation-Driven Shifts in Selection Regimes in Competitive Population Dynamics

20

McKane

T

Analysis of stochastic fluctuations in population ecology and genetics

21

Meerson

T

Large fluctuations of stochastic populations: extinction, colonization, invasion

22

Mehlig

T

TBA

23

Metz

P

Adaptive dynamics: some basic theory and an application

24

Nieddu

P

The effect of pre-extinction dynamics on the mean time to extinction in stochastic populations

25

Rogers

26

Ross

27

Sander

T

Extinction of metapopulations: two cautionary tales

28

Schwartz

T

Adaptive dynamics, control, and extinction in network populations

29

Shaw

P

Epidemic and information spread in an adaptive social network

30

Shnerb

31

Szwaykowska

P

Collective motion of heterogeneous swarms

32

Rein ten Wolde

T

Simulating rare events in biochemical networks

33

van Oudenaarden

T

Single-cell transcript counting in stem cells: from imaging to sequencing one molecule at a time.

34

Vucelja

T

Emergence and interference of clones in populations, glassy aspects of evolution

35

Weissmann 

P

Stochastic desertification

36

Wu

P

When do microscopic assumptions determine  the outcome in evolutionary game dynamics?

 

 



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