Session C44: Focus Session: Population and Evolutionary Dynamics III

The physics of evolution and biodiversity: Old answers to new questions, and more...

In recent years there has been a contentious battle among prominent biologists about the validity of Kin versus Group Selection as models of evolutionary biology. I will show that the controversy is widely misunderstood and is rooted in the mean field basis of RA Fisher's statistical treatment of population biology, which is the origin of the ``gene centered view''--kin selection and inclusive fitness--but is also often used in analysis of group selection. As in statistical physics, symmetry breaking and pattern formation, and their spatial realizations, result in breakdown of the mean field approximation and the widely believed mathematical 'proofs' of the universality of the gene centered view. Our simulation and analysis (http://necsi.edu/research/evoeco/) of the role of this breakdown in spatial ecology, biodiversity, speciation and altruism, suggest there is an entire field of new opportunities to explore in the implications for evolutionary theory. The difference between biodiversity of wildtype populations and narrowly homogeneous laboratory types manifest the self-consistency of theoretical assumptions and laboratory experiments performed under conditions in which the mean field approximation applies. In contrast, the highly diverse natural populations manifest the role of boundaries between types (hybrid zones), speciation by spontaneous clustering, and spatio-temporal dynamics in predator prey systems. Altruism arises in evolving populations due to the spontaneous dynamic group formation and the heritability of environmental conditions created by parents and experienced by offspring (niche construction with symmetry breaking), so that altruists are better able to survive over the long term than selfish variants. Many versions of the mean field approximation that are traditionally used eliminate these spatio-temporal processes, leading to false analytic conclusions about their impossibility. The traditional view of altruism influenced views also of individuals in their relationship to society. In addition to the basic reframing of the origin of altruism, the role of space in evolution has important implications for understanding global dangers today, including pandemics driven by evolution of virulent pathogens that escape death through long-range transportation, and economic or environmental overexploitation when globalization enables exploiters to escape the consequences of their actions. References: 1) Y. Bar-Yam, Dynamics of Complex Systems (Perseus Press, 1997) Chapter 6 http://www.necsi.edu/publications/dcs/ 2) Y. Bar-Yam, Formalizing the gene-centered view of evolution, Advances in Complex Systems 2, 277 (1999). 3) E. Rauch, H. Sayama, Y. Bar-Yam, Relationship between measures of fitness and time scale in evolution, Phys Rev Lett 88, 228101 (2002). 4) J. K. Werfel, Y. Bar-Yam, The evolution of reproductive restraint through social communication, PNAS 101, 11019 (2004). 5) E. M. Rauch, Y. Bar-Yam, Long-range interactions and evolutionary stability in a predator-prey system, Physical Review E 73, 020903 (2006). 6) C. Goodnight, E. Rauch, H. Sayama, M. A. M. De Aguiar, M. Baranger,Y. Bar-Yam, Complexity 13, 5, 23 (2008) 7) M.A.M. de Aguiar, M. Baranger, E.M. Baptestini, L. Kaufman, Y. Bar-Yam, Global Patterns of Speciation and Diversity, Nature 460, 384 (2009). 8) B. C. Stacey, A. Gros, Y. Bar-Yam, Beyond the Mean Field in Host-Pathogen Spatial Ecology. arXiv:1110.3845, October 5, 2011 9) G. Wild, A. Gardner, S. A. West, Adaptation and the evolution of parasite virulence in a connected world. Nature 459:983 (18 June 2009). 10) M.J. Wade, D.S. Wilson, C. Goodnight, D. Taylor, Y. Bar-Yam, M.A.M. de Aguiar, B. Stacey, J. Werfel, G.A. Hoelzer, E.D. Brodie III, P. Fields, F. Breden, T.A. Linksvayer, J.A. Fletcher, P.J. Richerson, J.D. Bever, J.D. Van Dyken, P. Zee, Multilevel and kin selection in a connected world. Nature 463, E8 (2010). 11) M. A. Nowak, C. E. Tarnitam, E. O. Wilson, The evolution of eusociality, Nature 466, 1057 (26 August 2010) 12) P. Abbott, et al, Inclusive fitness theory and eusociality, Nature 471, E1 (24 March 2011)   

Universality in a Neutral Evolution Model

Agent-based models are ideal for investigating the complex problems of biodiversity and speciation because they allow for complex interactions between individuals and between individuals and the environment. Presented here is a ``null'' model that investigates three mating types -- assortative, bacterial, and random -- in phenotype space, as a function of the percentage of random death $\delta $. Previous work has shown phase transition behavior in an assortative mating model with variable fitness landscapes as the maximum mutation size ($\mu )$ was varied (Dees and Bahar, 2010). Similarly, this behavior was recently presented in the work of Scott et al. (submitted), on a completely neutral landscape, for bacterial-like fission as well as for assortative mating. Here, in order to achieve an appropriate ``null'' hypothesis, the random death process was changed so each individual, in each generation, has the same probability of death. Results show a continuous nonequilibrium phase transition for the order parameters of the population size and the number of clusters (analogue of species) as $\delta$ is varied for three different mutation sizes of the system. The system shows increasing robustness as $\mu $ increases. Universality classes and percolation properties of this system are also explored.   

Characterizing Phase Transitions in a Model of Neutral Evolutionary Dynamics

An evolutionary model was recently introduced for sympatric, phenotypic evolution over a variable fitness landscape with assortative mating (Dees {\&} Bahar 2010). Organisms in the model are described by coordinates in a two-dimensional phenotype space, born at random coordinates with limited variation from their parents as determined by a mutation parameter, mutability. The model has been extended to include both neutral evolution and asexual reproduction in Scott et al (submitted). It has been demonstrated that a second order, non-equilibrium phase transition occurs for the temporal dynamics as the mutability is varied, for both the original model and for neutral conditions. This transition likely belongs to the directed percolation universality class. In contrast, the spatial dynamics of the model shows characteristics of an ordinary percolation phase transition. Here, we characterize the phase transitions exhibited by this model by determining critical exponents for the relaxation times, characteristic lengths, and cluster (species) mass distributions.   

Theory for the Emergence of Modularity in Complex Systems

Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here develop a theory for the dynamics of modularity in these systems. We find a principle of least action for the evolved modularity at long times. In addition, we find a fluctuation dissipation relation for the rate of change of modularity at short times. We discuss a number of biological and social systems that can be understood with this framework. The modularity of the protein-protein interaction network increases when yeast are exposed to heat shock, and the modularity of the protein-protein networks in both yeast and E. coli appears to have increased over evolutionary time. Food webs in low-energy, stressful environments are more modular than those in plentiful environments, arid ecologies are more modular during droughts, and foraging of sea otters is more modular when food is limiting. The modularity of social networks changes over time: stock brokers instant messaging networks are more modular under stressful market conditions, criminal networks are more modular under increased police pressure, and world trade network modularity has decreased   

The Evolution of Biological Complexity in Digital Organisms

When Darwin first proposed his theory of evolution by natural selection, he realized that it had a problem explaining the origins of traits of ``extreme perfection and complication'' such as the vertebrate eye. Critics of Darwin's theory have latched onto this perceived flaw as a proof that Darwinian evolution is impossible. In anticipation of this issue, Darwin described the perfect data needed to understand this process, but lamented that such data are ``scarcely ever possible'' to obtain. In this talk, I will discuss research where we use populations of digital organisms (self-replicating and evolving computer programs) to elucidate the genetic and evolutionary processes by which new, highly-complex traits arise, drawing inspiration directly from Darwin's wistful thinking and hypotheses. During the process of evolution in these fully-transparent computational environments we can measure the incorporation of new information into the genome, a process akin to a natural Maxwell's Demon, and identify the original source of any such information. We show that, as Darwin predicted, much of the information used to encode a complex trait was already in the genome as part of simpler evolved traits, and that many routes must be possible for a new complex trait to have a high probability of successfully evolving. In even more extreme examples of the evolution of complexity, we are now using these same principles to examine the evolutionary dynamics the drive major transitions in evolution; that is transitions to higher-levels of organization, which are some of the most complex evolutionary events to occur in nature. Finally, I will explore some of the implications of this research to other aspects of evolutionary biology and as well as ways that these evolutionary principles can be applied toward solving computational and engineering problems.   

Intervention-Based Stochastic Disease Eradication

Disease control is of paramount importance in public health with infectious disease extinction as the ultimate goal. Intervention controls, such as vaccination of susceptible individuals and/or treatment of infectives, are typically based on a deterministic schedule, such as periodically vaccinating susceptible children based on school calendars. In reality, however, such policies are administered as a random process, while still possessing a mean period. Here, we consider the effect of randomly distributed intervention as disease control on large finite populations. We show explicitly how intervention control, based on mean period and treatment fraction, modulates the average extinction times as a function of population size and the speed of infection. In particular, our results show an exponential improvement in extinction times even though the controls are implemented using a random Poisson distribution. Finally, we discover those parameter regimes where random treatment yields an exponential improvement in extinction times over the application of strictly periodic intervention. The implication of our results is discussed in light of the availability of limited resources for control.   

Effect of disease-induced mortality on structural network properties

We study epidemic processes on complex networks, where infected nodes are either removed permanently or they can potentially recover. The process influences the localization of the infection by creating buffered zones, which in turn isolate large parts of the network. We show that there is an interesting interplay between the percentage and location of the removed population with the network structural integrity, even before reaching the critical point of total network disruption. The model can be used to determine the impact of disease-induced mortality to extinction of organisms, where destruction of the social structure can lead to loss of the species ability to recover.   

Contagion dynamics in time-varying metapopulation networks

The metapopulation framework is adopted in a wide array of disciplines to describe systems of well separated yet connected subpopulations. The subgroups/patches are often represented as nodes in a network whose links represent the migration routes among them. The connections are usually considered as static, an approximation that is appropriate for the description of many systems, such as cities connected by human mobility, but it is obviously inadequate in those real systems where links evolve in time on a faster timescale. In the case of farmed animals, for example, the connections between each farm/node vary in time according to the different stages of production. Here we address this case by investigating simple contagion processes on temporal metapopulation networks. We focus on the SIR process, and we determine the mobility threshold for the onset of an epidemic spreading in the framework of activity-driven network models. Remarkably, we find profound differences from the case of static networks, determined by the crucial role played by the dynamical parameters defining the average number of instantaneously migrating individuals. Our results confirm the importance of addressing the time-varying properties of complex networks pointed out by the recent literature.   

Controlling Contagion Processes in Time Varying Networks

The vast majority of strategies aimed at controlling contagion and spreading processes on networks consider the connectivity pattern of the system as quenched. In this paper, we consider the class of activity driven networks to analytically evaluate how different control strategies perform in time-varying networks. We consider the limit in which the evolution of the structure of the network and the spreading process are simultaneous yet independent. We analyze three control strategies based on node's activity patterns to decide the removal/immunization of nodes. We find that targeted strategies aimed at the removal of active nodes outperform by orders of magnitude the widely used random strategies. In time-varying networks however any finite time observation of the network dynamics provides only incomplete information on the nodes' activity and does not allow the precise ranking of the most active nodes as needed to implement targeted strategies. Here we develop a control strategy that focuses on targeting the egocentric time-aggregated network of a small control group of nodes.The presented strategy allows the control of spreading processes by removing a fraction of nodes much smaller than the random strategy while at the same time limiting the observation time on the system.   

Global and local threshold in a metapopulational SEIR model with quarantine

Diseases which have the possibility of transmission before the onset of symptoms pose a challenging threat to healthcare since it is hard to track spreaders and implement quarantine measures. More precisely, one main concerns regarding pandemic spreading of diseases is the prediction--and eventually control--of local outbreaks that will trigger a global invasion of a particular disease. We present a metapopulation disease spreading model with transmission from both symptomatic and asymptomatic agents and analyze the role of quarantine measures and mobility processes between subpopulations. We show that, depending on the disease parameters, it is possible to separate in the parameter space the local and global thresholds and study the system behavior as a function of the fraction of asymptomatic transmissions. This means that it is possible to have a range of parameters values where although we do not achieve local control of the outbreak it is possible to control the global spread of the disease. We validate the analytic picture in data-driven model that integrates commuting, air traffic flow and detailed information about population size and structure worldwide.   

Epidemic dynamics on a risk-based evolving social network

Social network models have been used to study how behavior affects the dynamics of an infection in a population. Motivated by HIV, we consider how a trade-off between benefits and risks of sexual connections determine network structure and disease prevalence. We define a stochastic network model with formation and breaking of links as changes in sexual contacts. Each node has an intrinsic benefit its neighbors derive from connecting to it. Nodes' infection status is not apparent to others, but nodes with more connections (higher degree) are assumed more likely to be infected. The probability to form and break links is determined by a payoff computed from the benefit and degree-dependent risk. The disease is represented by a SI (susceptible-infected) model. We study network and epidemic evolution via Monte Carlo simulation and analytically predict the behavior with a heterogeneous mean field approach. The dependence of network connectivity and infection threshold on parameters is determined, and steady state degree distribution and epidemic levels are obtained. We also study a situation where system-wide infection levels alter perception of risk and cause nodes to adjust their behavior. This is a case of an adaptive network, where node status feeds back to change network geometry.