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: TommasoBiancalani 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: EvgeniyKhain, 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 onthe 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 determinethe outcome in evolutionary game dynamics?