Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session A44: Focus Session: Population and Evolutionary Dynamics I |
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Sponsoring Units: DBIO GSNP Chair: Michel Pleimling, Virginia Tech Room: Hilton Baltimore Holiday Ballroom 1 |
Monday, March 18, 2013 8:00AM - 8:36AM |
A44.00001: Evolutionary dynamics in finite populations Invited Speaker: Christoph Hauert Traditionally, evolutionary dynamics has been studied based on infinite populations and deterministic frameworks such as the replicator equation. Only more recently the focus has shifted to the stochastic dynamics arising in finite populations. Over the past years new concepts have been developed to describe such dynamics and has lead to interesting results that arise from the stochastic, microscopic updates, which drive the evolutionary process. Here we discuss a transparent link between the dynamics in finite and infinite populations. The focus on microscopic processes reveals interesting insights into (sometimes implicit) assumptions in terms of biological interactions that provide the basis for deterministic frameworks and the replicator equation in particular. More specifically, we demonstrate that stochastic differential equations can provide an efficient approach to model evolutionary dynamics in finite populations and we use the rock-scissors-paper game with mutations as an example. For sufficiently large populations the agreement with individual based simulations is excellent, with the interesting caveat that mutation events may not be too rare. In the absence of mutations, the excellent agreement extends to small population sizes. [Preview Abstract] |
Monday, March 18, 2013 8:36AM - 8:48AM |
A44.00002: Neutral species domination on different lattices for the symmetric stochastic cyclic competition of four species Ben Intoy, Sven Dorosz, Michel Pleimling Although the mean-field solution for four species in cyclic competition is generally in good agreement with stochastic results, it fails to describe the extinction and absorbing states that finite size systems inevitably fall into. We study the effects of dimension, lattice type, and swapping rate between particles on the time it takes for the system to go into a static absorbing state, which consists of a neutral species pair. Lattice types discussed are the well mixed environment, the one-dimensional chain, the Sierpinski triangle, and the two-dimensional square lattice. Data presented were acquired with simulations that have around the order of a thousand lattice sites or less, to capture finite size effects. The formation of domains composed of neutral species yields long lived states which promote coexistence. [Preview Abstract] |
Monday, March 18, 2013 8:48AM - 9:00AM |
A44.00003: Biodiversity and co-existence of competing species Ahmed Roman, Debanjan Dasgupta, Michel Pleimling Understanding why and how species co-exist is a necessary step to the program of manipulating multispecies environments in order to preserve the biodiversity of the environment of interest. To this end we consider a generalization of the cyclic competition of species model. We show that our model enjoys a $Z_n$ symmetry which is explained via a simple graph theoretic technique. This symmetry gives rise to pattern formation and cluster coarsening of the species. We show that biodiversity is achievable in the mean field limit provided that the species in the clusters have reaction rates which correspond to non-trivial equilibria. [Preview Abstract] |
Monday, March 18, 2013 9:00AM - 9:12AM |
A44.00004: Population oscillations in stochastic Lotka--Volterra models: field theory and perturbational analysis Uwe C. T\"auber Field theory tools are applied to analytically study fluctuation and correlation effects in spatially extended stochastic predator-prey systems. In the mean-field rate equation approximation, the classic Lotka--Volterra model is characterized by neutral cycles in phase space, describing undamped oscillations for both predator and prey populations. In contrast, Monte Carlo simulations for stochastic two-species predator-prey reaction systems on regular lattices display complex spatio-temporal structures associated with persistent erratic population oscillations. The Doi--Peliti path integral representation of the master equation for stochastic particle interaction models is utilized to arrive at a field theory action for spatial Lotka--Volterra models in the continuum limit. In the species coexistence phase, a perturbation expansion with respect to the nonlinear predation rate is employed to demonstrate that spatial degrees of freedom and stochastic noise induce instabilities toward structure formation, and to compute the fluctuation corrections for the oscillation frequency and diffusion coefficient. The drastic downward renormalization of the frequency and the enhanced diffusivity are in excellent qualitative agreement with Monte Carlo simulation data. [Preview Abstract] |
Monday, March 18, 2013 9:12AM - 9:24AM |
A44.00005: Patterns and Oscillations in Reaction-Diffusion Systems with Intrinsic Fluctuations Michael Giver, Daniel Goldstein, Bulbul Chakraborty Intrinsic or demographic noise has been shown to play an important role in the dynamics of a variety of systems including predator-prey populations, biochemical reactions within cells, and oscillatory chemical reaction systems, and is known to give rise to oscillations and pattern formation well outside the parameter range predicted by standard mean-field analysis. Initially motivated by an experimental model of cells and tissues where the cells are represented by chemical reagents isolated in emulsion droplets, we study the stochastic Brusselator, a simple activator-inhibitor chemical reaction model. Our work extends the results of recent studies on the zero and one dimensional systems with the ultimate goals of understanding the role of noise in spatially structured systems and engineering novel patterns and attractors induced by fluctuations. In the zero dimensional system, we observe a noise induced switching between small and large amplitude oscillations when a separation of time scales is present, while the spatially extended system displays a similar switching between a stationary Turing pattern and uniform oscillations. [Preview Abstract] |
Monday, March 18, 2013 9:24AM - 9:36AM |
A44.00006: Flow-driven instabilities during aggregation and pattern formation of Dictyostelium Discoideum: Experiments and modeling Azam Gholami, Oliver Steinbock, Vladimir Zykov, Eberhard Bodenschatz We report the first experimental verification of the Differential Flow Induced Chemical Instability (DIFICI) in a signaling chemotactic biological population, where a differential flow induces traveling waves in the signaling pattern. The traveling wave speed was observed to be proportional to the flow velocity while the wave period was 7 min, which is comparable to that of starved Dictyostelium cells. Analysis and numerical simulations of the Goldbeter model show that the resulting DIFICI wave patterns appear in the oscillatory regime. In the experiments, we observe that the DIFICI wave pattern disappears after 4-5 h of starvation. We extrapolated the Goldbeter model to the experimental situation. This suggests that the dynamics switches from the oscillatory to the excitable regime as the DIFICI waves disappear in the experiment. [Preview Abstract] |
Monday, March 18, 2013 9:36AM - 9:48AM |
A44.00007: Statistical Thermodynamics of Populations Themis Matsoukas Suppose a population of $M$ individuals forms $N$ groups such that group $i$ contains $n_i$ individuals. Form all possible partitions of $M$ into $N$ and select distributions from this ensemble with selection bias $W[\{n_i\}]$, where $W$ is a functional of distribution $\{n_i\}$. We develop the thermodynamics of this ensemble and its most probable distribution for arbitrary bias $W$. We obtain the temperature of the ensemble and its relationship to the microcanonical and canonical partition functions; and (ii) show that, depending on the bias functional $W$, the population may exhibit the equivalent of a phase transition, manifested as the coexistence of two distinct subpopulations in equilibrium with each other. We apply this theory to binary clustering with special interest in conditions that result in the emergence of a single dominant group that overtakes all smaller coexisting groups when the number of groups $N$ is decreased. We show the emergence of the dominant group represents a formal phase transition that is governed by the maximization of the free energy of the ensemble. We provide closed analytical solutions for the special case that the merging probability between two groups is proportional to the product of the number of members in each group. [Preview Abstract] |
Monday, March 18, 2013 9:48AM - 10:24AM |
A44.00008: Predictability of evolution in complex fitness landscapes Invited Speaker: Joachim Krug Evolutionary adaptations arise from an intricate interplay of deterministic selective forces and random reproductive or mutational events, and the relative roles of these two types of influences is the subject of a long-standing controversy. In general, the predictability of adaptive trajectories is governed by the genetic constraints imposed by the structure of the underlying fitness landscape as well as by the supply rate and effect size of beneficial mutations. On the level of single mutational steps, evolutionary predictability depends primarily on the distribution of fitness effects, with heavy-tailed distributions giving rise to highly predictable behavior [1]. The genetic constraints imposed by the fitness landscape can be quantified through the statistical properties of accessible mutational pathways along which fitness increases monotonically. I will report on recent progress in the understanding of evolutionary accessibility in model landscapes and compare the predictions of the models to empirical data [2,3]. Finally, I will describe extensive Wright-Fisher-type simulations of asexual adaptation on an empirical fitness landscape [4]. By quantifying predictability through the entropies of the distributions of evolutionary trajectories and endpoints we show that, contrary to common wisdom, the predictability of evolution depends non-monotonically on population size. \\[4pt] [1] M.F. Schenk, I.G. Szendro, J. Krug and J.A.G.M. de Visser, PLoS Genetics 8, e1002783 (2012).\\[0pt] [2] J. Franke, A. Kl\"ozer, J.A.G.M. de Visser and J. Krug, PLoS Computational Biology 7, e1002134 (2011).\\[0pt] [3] J. Franke and J. Krug, Journal of Statistical Physics 148, 705 (2012).\\[0pt] [4] I.G. Szendro, J. Franke, J.A.G.M. de Visser and J. Krug (under review). [Preview Abstract] |
Monday, March 18, 2013 10:24AM - 10:36AM |
A44.00009: A Condition for Cooperation in a Game on Complex Networks Tomohiko Konno We study a condition of favoring cooperation in a Prisoner's Dilemma game on complex networks. There are two kinds of players: cooperators and defectors. Cooperators pay a benefit $b$ to their neighbors at a cost $c$, whereas defectors only receive a benefit. The game is a death-birth process with weak selection. Although it has been widely thought that $b/c>\langle k \rangle$ is a condition of favoring cooperation [2], we find that $b/c>\langle k_\textrm{nn} \rangle$ is the condition. We also show that among three representative networks, namely, regular, random, and scale-free, a regular network favors cooperation the most, whereas a scale-free network favors cooperation the least. In an ideal scale-free network, cooperation is never realized. Whether or not the scale-free network and network heterogeneity favor cooperation depends on the details of the game, although it is occasionally believed that these favor cooperation irrespective of the game structure.\\[4pt] [1] T.K, A condition for cooperation in a game on complex networks, Journal of Theoretical Biology 269, Issue 1, Pages 224-233, (2011)\\[0pt] [2] H. Ohtsuki, C. Hauert, E. Lieberman, M. A. Nowak, A simple rule for the evolution of cooperation on graphs and social networks, Nature 441 (7092) (2006) [Preview Abstract] |
Monday, March 18, 2013 10:36AM - 10:48AM |
A44.00010: Evolution of regulatory complexes: a many-body system Armita Nouemohammad, Michael Laessig In eukaryotes, many genes have complex regulatory input, which is encoded by multiple transcription factor binding sites linked to a common function. Interactions between transcription factors and site complexes on DNA control the production of protein in cells. Here, we present a quantitative evolutionary analysis of binding site complexes in yeast. We show that these complexes have a joint binding phenotype, which is under substantial stabilizing selection and is well conserved within Saccharomyces paradoxus populations and between three species of Saccharomyces. At the same time, individual low-affinity sites evolve near-neutrally and show considerable affinity variation even within one population. Thus, functionality of and selection on regulatory complexes emerge from the entire cloud of sites, but cannot be pinned down to individual sites. Our method is based on a biophysical model, which determines site occupancies and establishes a joint affinity phenotype for binding site complexes. We infer a fitness landscape depending on this phenotype using yeast whole-genome polymorphism data and a new method of quantitative trait analysis. Our fitness landscape predicts the amount of binding phenotype conservation, as well as ubiquitous compensatory changes between sites in the cloud. Our results open a new avenue to understand the regulatory ``grammar'' of eukaryotic genomes based on quantitative evolution models. [Preview Abstract] |
Monday, March 18, 2013 10:48AM - 11:00AM |
A44.00011: Inference of fitness from genealogical trees Marija Vucelja, Adel Dayarian, Boris Shraiman Natural populations are fitness diverse and can have numerous genes under selection. The genealogical trees, that one obtains by sampling, often bear hallmarks of selection, such multiple mergers, asymmetric tree branches and long terminal branches (the trees are squished towards the root). These are qualitative differences compared to trees in the absence of selection. We propose a theoretical model that links the morphology of a tree with the fitness of the leaves. We obtain multipoint correlation functions of the fitness along the tree. In this way we are able extract some quantitative information about the strength of selection from data-reconstructed trees. The extensions of this approach can potentially be useful for inferring relative fitness of sequenced genomes of tumors and for predicting viral outbreaks. [Preview Abstract] |
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