Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session S48: Focus Session: Physics of Evolutionary and Population Dynamics I |
Hide Abstracts |
Sponsoring Units: DBIO Chair: Michel Pleimliung, Virginia Tech University Room: 217C |
Thursday, March 5, 2015 8:00AM - 8:12AM |
S48.00001: Diversity Driven Coexistence: Collective Stability in the Cyclic Competition of Three Species Kevin E. Bassler, Erwin Frey, R.K.P. Zia The basic physics of collective behavior are often difficult to quantify and understand, particularly when the system is driven out of equilibrium. Many complex systems are usefully described as complex networks, consisting of nodes and links. The nodes specify individual components of the system and the links describe their interactions. When both nodes and links change dynamically, or `co-evolve', as happens in many realistic systems, complex mathematical structures are encountered, posing challenges to our understanding. In this context, we introduce a minimal system of node and link degrees of freedom, co-evolving with stochastic rules. Specifically, we show that diversity of social temperament (intro- or extroversion) can produce collective stable coexistence when three species compete cyclically. It is well-known that when only extroverts exist in a stochastic rock-paper-scissors game, or in a conserved predator-prey, Lotka-Volterra system, extinction occurs at times of O(N), where N is the number of nodes. We find that when both introverts and extroverts exist, where introverts sever social interactions and extroverts create them, collective coexistence prevails in long-living, quasi-stationary states. [Preview Abstract] |
Thursday, March 5, 2015 8:12AM - 8:24AM |
S48.00002: Mixed Strategies in cyclic competition Ben Intoy, Michel Pleimling Physicists have been using evolutionary game theory to model and simulate cyclically competing species, with applications to lizard mating strategies and competing bacterial strains. However these models assume that each agent plays the same strategy, which is called a pure strategy in game theory, until they are beaten by a better strategy which they immediately adopt. We relax this constraint of an agent playing a single strategy by instead letting the agent pick its strategy randomly from a probability distribution, which is called a mixed strategy in game theory. This scheme is very similar to multiple occupancy models seen in the literature, the major difference being that interactions happen between sites rather than within them. Choosing strategies out of a distribution also has applications to economic/social systems such as the public goods game. We simulate a model of mixed strategy and cylic competition on a one-dimensional lattice with three and four strategies and find interesting spatial and stability properties depending on how discretized the choice of strategy is for the agents. [Preview Abstract] |
Thursday, March 5, 2015 8:24AM - 8:36AM |
S48.00003: Spatial games with cyclic interactions: the response of empty sites Bart Brown, Michel Pleimling Predator-prey models of the May-Leonard family employ empty sites in a spatial setting as an intermediate step in the reproduction process. This requirement makes the number and arrangement of empty sites important to the formation of space-time patterns. We study the density of empty sites in a stochastic predator-prey model in which the species compete in a cyclic way in two dimensions. In some cases systems of this type quickly form domains of neutral species after which all predation, and therefore, reproduction occur near the interface of competing domains. Using Monte Carlo simulations we investigate the relationship of this density of empty sites to the time-dependent domain length. We further explore the dynamics by introducing perturbations to the interaction rates of the system after which we measure the perturbed density, i.e. the response of empty sites, as the system relaxes. A dynamical scaling behavior is observed in the response of empty sites. [Preview Abstract] |
Thursday, March 5, 2015 8:36AM - 8:48AM |
S48.00004: Critical fluctuations near the pitchfork bifurcations of period-doubling maps Andrew Noble, Saba Karimeddiny, Alan Hastings, Jonathan Machta Period-doubling maps, such as the logistic map, have been a subject of intense study in both physics and biology.~ The period-doubling route to chaos proceeds through a sequence of supercritical pitchfork bifurcations.~ Here, motivated by applications to population ecology, we investigate the asymptotic behavior of period-doubling bifurcations subject to environmental or demographic noise.~ We demonstrate, analytically, that fluctuations in the vicinity of each noisy pitchfork bifurcation are described by finite-size mean-field theory.~ Our results establish an exact correspondence between the bifurcations of far-from-equilibrium systems and the mean-field critical phenomena of equilibrium systems. [Preview Abstract] |
Thursday, March 5, 2015 8:48AM - 9:00AM |
S48.00005: Population dynamics of microbial communities in the zebrafish gut Matthew Jemielita, Michael Taormina, Adam Burns, Jennifer Hampton, Annah Rolig, Travis Wiles, Karen Guillemin, Raghuveer Parthasarathy The vertebrate intestine is home to a diverse microbial community, which plays a crucial role in the development and health of its host. Little is known about the population dynamics and spatial structure of this ecosystem, including mechanisms of growth and interactions between species. We have constructed an experimental model system with which to explore these issues, using initially germ-free larval zebrafish inoculated with defined communities of fluorescently tagged bacteria. Using light sheet fluorescence microscopy combined with computational image analysis we observe and quantify the entire bacterial community of the intestine during the first 24 hours of colonization, during which time the bacterial population grows from tens to tens of thousands of bacteria. We identify both individual bacteria and clusters of bacteria, and quantify the growth rate and spatial distribution of these distinct subpopulations. We find that clusters of bacteria grow considerably faster than individuals and are located in specific regions of the intestine.~Imaging colonization by two species reveals spatial segregation and competition. These data and their analysis highlight the importance of spatial organization in the establishment of gut microbial communities, and can provide inputs to physical models of real-world ecological dynamics. [Preview Abstract] |
Thursday, March 5, 2015 9:00AM - 9:12AM |
S48.00006: Responses of many-species predator-prey systems to perturbations Shadi Esmaily, Michel Pleimling We study the responses of many-species predator-prey systems, both in the well-mixed case as well as on a two-dimensional lattice, to permanent and transient perturbations. In the case of a weak transient perturbation the system returns to the original steady state, whereas a permanent perturbation pushes the system into a new steady state. Using Monte Carlo simulations, we monitor the approach to stationarity after a perturbation through a variety of quantities, as for example time-dependent particle densities and correlation functions. Different types of perturbations are studied, ranging from a change in reaction rates to the injection of additional individuals into the system, the latter perturbation mimicking immigration. [Preview Abstract] |
Thursday, March 5, 2015 9:12AM - 9:24AM |
S48.00007: Anticipating Changing in Environments: Adaptation in Fluctuating Environments in A Heterogeneous Microbial Communites Merzu Belete, G\'{a}bor B\'{a}lazsi The environments in which micro-organisms grow often fluctuate. To survive in temporally changing environments, cells have evolved mechanisms to survive environmental changes. One survival mechanism is generating phenotypic differences among identical cells in a given environment, with cells randomly switching between phenotypes. Such cells form subpopulations that proliferate at different rates. Optimal population fitness was attributed before to matching cellular and environmental switching rates. However, the conditions for this optimum are not well understood. In particular, it is unknown how the growth rates of the phenotypes affect the optimum. We use mathematical models to address this question. We find that the existence of the predicted optimum depends on cell growth rates in each phenotype. The predicted optimum exists for wider parameter regimes if the environmental durations are long. In addition, we study how mutants arising among such phenotypically heterogeneous cells spread in the population. [Preview Abstract] |
Thursday, March 5, 2015 9:24AM - 9:36AM |
S48.00008: The Statistical Mechanics of Zombies Alexander A. Alemi, Matthew Bierbaum, Christopher R. Myers, James P. Sethna We present results and analysis from a large scale exact stochastic dynamical simulation of a zombie outbreak. Zombies have attracted some attention lately as a novel and interesting twist on classic disease models. While most of the initial investigations have focused on the continuous, fully mixed dynamics of a differential equation model, we have explored stochastic, discrete simulations on lattices. We explore some of the basic statistical mechanical properties of the zombie model, including its phase diagram and critical exponents. We report on several variant models, including both homogeneous and inhomogeneous lattices, as well as allowing diffusive motion of infected hosts. We build up to a full scale simulation of an outbreak in the United States, and discover that for `realistic' parameters, we are largely doomed. [Preview Abstract] |
Thursday, March 5, 2015 9:36AM - 9:48AM |
S48.00009: Mutation Accumulation and Fitness Collapse at Population Frontiers Maxim Lavrentovich, David Nelson Rapid, deleterious mutations occurring in, e.g., viral populations and cancerous tissue, may accumulate and lead to fitness loss. Previous studies show that sufficiently rapid accumulation in one-dimensional populations leads to a fitness collapse, governed by the directed percolation (DP) universality class. We compare this situation to the collapse in effectively two-dimensional populations, such as the frontiers of three-dimensional range expansions. A phase diagram is computed as a function of the mutation rate $\mu$ and strength $s$. Relative to one-dimensional populations, we find that the collapse occurs in a smaller region of phase space. The scaling combination governing the phase diagram shape is $\mu |\ln s|/s$ ($\mu/s^2$ for one-dimensional populations). We argue that the evolutionary dynamics is described by a set of coupled DP Langevin equations near the transition, and that the coupling terms lead to deviations from expected DP scaling. [Preview Abstract] |
Thursday, March 5, 2015 9:48AM - 10:24AM |
S48.00010: Spiraling patterns in evolutionary models inspired by bacterial games with cyclic dominance Invited Speaker: Mauro Mobilia Understanding the mechanisms allowing the maintenance of biodiversity is a central issue in biology. Evolutionary game theory, where the success of one species depends on what the others are doing, provides a promising framework to investigate this complex problem. Experiments on microbial populations have shown that cyclic local interactions promote species coexistence. In this context, rock-paper-scissors games - in which rock crushes scissors, scissors cut paper, and paper wraps rock - are often used to model the dynamics of populations in cyclic competition. After a brief survey of some inspiring experiments, I will discuss the subtle interplay between individuals' mobility and their local interactions in two-dimensional rock-paper-scissors systems. This leads to the loss of biodiversity above a certain mobility threshold~[1], and to the formation of spiraling patterns below the critical mobility rate~[1-4]. I will then study a generic rock-paper-scissors metapopulation model formulated on a two-dimensional grid of patches. When these have a large carrying capacity, the model's dynamics is faithfully described in terms of the system's complex Ginzburg-Landau equation properly derived from a multiscale expansion. The properties of the ensuing complex Ginzburg-Landau equation are exploited to derive the system's phase diagram and to characterize the spatio-temporal properties of the spiraling patterns in each phase. This enables us to analyze the spiral waves stability, how these are influenced by linear and nonlinear diffusion, and to discuss phenomena such as far-field breakup [5-7].\\[4pt] [1] Nature {\bf 448}, 1046 (2007);\\[0pt] [2] Phys.~Rev.~Lett. {\bf 99}, 238105 (2007);\\[0pt] [3] J.~Theor.~Biol. {\bf 254}, 368 (2008);\\[0pt] [4] Eur.~Phys.~J.~B {\bf 82} 97 (2011);\\[0pt] [5] EPL {\bf 102}, 28012 (2013);\\[0pt] [6] Phys.~Rev. E {\bf 90}, 032702 (2014);\\[0pt] [7] J.~R.~Soc. Interface {\bf 11}, 20140735 (2014). [Preview Abstract] |
Thursday, March 5, 2015 10:24AM - 10:36AM |
S48.00011: Phase transition in predator-prey ecosystems and a connection to transitional turbulence Hong-Yan Shih, Nigel Goldenfeld We suggest how the transition from laminar fluid flow to turbulence can be connected to the extinction phase transition in spatially-extended predator-prey systems. By measuring the statistics of spontaneous relaminarization, spatiotemporal intermittency and expanding turbulent puffs in hydrodynamics equations and mapping them to the corresponding states in the predator-prey model, the extinction event and the formation and propagation of spatial patterns in ecology can be interpreted as the instabilities in fluid systems. We also summarize the general phenomena of such predator-prey dynamics in a wide class of transitional turbulence systems such as magnetohydrodynamics. [Preview Abstract] |
Thursday, March 5, 2015 10:36AM - 10:48AM |
S48.00012: Evolutionary games of condensates in coupled birth-death processes Markus F. Weber, Johannes Knebel, Torben Krueger, Erwin Frey Condensation phenomena occur in many systems, both in a classical and a quantum mechanical context. Typically, the entities that constitute a system collectively concentrate in one distinct state during condensation. For example, cooling of an equilibrated bosonic gas may lead to condensation into the quantum ground state. Notably, the mathematical theory of this Bose-Einstein condensation is not limited to quantum theory but was also successfully applied to condensation in random networks. In our work, we follow the opposite path. We apply the theory of evolutionary dynamics to describe condensation in a bosonic system that is driven and dissipative. It was shown that the system may condense into multiple quantum states, but into which states has remained elusive. We find that vanishing of relative entropy production determines these states. We illuminate the physical principles underlying the condensation and show that the condensates do not need to be static but may engage in ``evolutionary games'' with exchange of particles. On the mathematical level, the condensation is described by coupled birth-death processes. The generic structure of these processes implies that our results also apply to condensation in other systems, ranging from population biology to chemical kinetics. [Preview Abstract] |
Thursday, March 5, 2015 10:48AM - 11:00AM |
S48.00013: A Second Law for Markov Processes Blake Pollard In this talk we describe the notion of an open Markov process. An open Markov process is a generalization of an ordinary Markov process in which populations are allowed to flow in and out of the system at certain boundary states. We show that the rate of change of relative entropy in an open Markov process is less than or equal to the flow of relative entropy through its boundary states. This can be viewed as a generalization of the Second Law for open Markov processes. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2021 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
1 Research Road, Ridge, NY 11961-2701
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700