Session H35: Population and Evolutionary Dynamics III

Standing variation in spatially growing populations

Patterns of genetic diversity not only reflect the evolutionary history of a species but they can also determine the evolutionary response to environmental change. For instance, the standing genetic diversity of a microbial population can be key to rescue in the face of an antibiotic attack. While genetic diversity is in general shaped by both demography and evolution, very little is understood when both factors matter, as e.g. for biofilms with pronounced spatial organization. Here, we quantitatively explore patterns of genetic diversity by using microbial colonies and well-mixed test tube populations as antipodal model systems with extreme and very little spatial structure, respectively. We find that Eden model simulations and KPZ theory can remarkably reproduce the genetic diversity in microbial colonies obtained via population sequencing. The excellent agreement allows to draw conclusions on the resilience of spatially-organized populations and to uncover new strategies to contain antibiotic resistance.   

Crowds as an Excitable Medium for Spiral Wave Dynamics

Spiral wave (SW) patterns are studied in many physical, biological, and chemical excitable systems. Of particular importance are SW of electrical activity that develop in the heart and give rise to arrhythmias such as tachycardia (single SW) and fibrillation (multiple SWs). We investigate if a crowd of people given simple rules for activation and deactivation, modeled on cardiac cells, can act as a living simulation for SW dynamics. For group sizes ranging from 50 to 650 people we demonstrate, experimentally, the existence of stable spiral waves and of spiral wave breakup leading to chaotic dynamics. Numerical simulation predicts the simple rules lead to well define wave fronts. People, however, respond with various degrees of anticipation and misinformation. This human behavior can lead to smoothed fronts or even lead to spiral wave breakup and chaos. We present a new cell model that includes variations in reaction to account for the observed behavior in crowds. This model may be useful in the study of coupling and decoupling of cardiac cells that lead to arrhythmic behavior.   

Adapting populations in space: clonal interference and genetic diversity

Most species inhabit ranges much larger than the scales over which individuals interact. How does this spatial structure interact with adaptive evolution? We consider a simple model of a spatially-extended, adapting population and show that, while clonal interference severely limits the adaptation of purely asexual populations, even rare recombination is enough to allow adaptation at rates approaching those of well-mixed populations. We also find that the genetic hitchhiking produced by the adaptive alleles sweeping through the population has strange effects on the patterns of genetic diversity. In large spatial ranges, even low rates of adaptation cause all individuals in the population to rapidly trace their ancestry back to individuals living in a small region in the center of the range. The probability of fixation of an allele is thus strongly dependent on the allele’s spatial location, with alleles from the center favored. Surprisingly, these effects are seen genome-wide (instead of being localized to the regions of the genome undergoing the sweeps). The spatial concentration of ancestry produces a power-law dependence of relatedness on distance, so that even individuals sampled far apart are likely to be fairly closely related, masking the underlying spatial structure.   

3-D Technology Approaches for Biological Ecologies

Constructing three dimensional (3-D) landscapes is an inevitable issue in deep study of biological ecologies, because in whatever scales in nature, all of the ecosystems are composed by complex 3-D environments and biological behaviors. Just imagine if a 3-D technology could help complex ecosystems be built easily and mimic in vivo microenvironment realistically with flexible environmental controls, it will be a fantastic and powerful thrust to assist researchers for explorations. For years, we have been utilizing and developing different technologies for constructing 3-D micro landscapes for biophysics studies in in vitro. Here, I will review our past efforts, including probing cancer cell invasiveness with 3-D silicon based Tepuis, constructing 3-D microenvironment for cell invasion and metastasis through polydimethylsiloxane (PDMS) soft lithography, as well as explorations of optimized stenting positions for coronary bifurcation disease with 3-D wax printing and the latest home designed 3-D bio-printer. Although 3-D technologies is currently considered not mature enough for arbitrary 3-D micro-ecological models with easy design and fabrication, I hope through my talk, the audiences will be able to sense its significance and predictable breakthroughs in the near future.   

Population Dynamics of Viral Inactivation

We have investigated the population dynamics of viral inactivation \textit{in vitro }using time-resolved cryo electron microscopy combined with light and X-ray scattering techniques. Using bacteriophage $\lambda $ as a model system for pressurized double-stranded DNA viruses, we found that virions incubated with their cell receptor eject their genome in a stochastic triggering process. The triggering of DNA ejection occurs in a non synchronized manner after the receptor addition, resulting in an exponential decay of the number of genome-filled viruses with time. We have explored the characteristic time constant of this triggering process at different temperatures, salt conditions, and packaged genome lengths. Furthermore, using the temperature dependence we determined an activation energy for DNA ejections. The dependences of the time constant and activation energy on internal DNA pressure, affected by salt conditions and encapsidated genome length, suggest that the triggering process is directly dependent on the conformational state of the encapsidated DNA. The results of this work provide insight into how the \textit{in vivo} kinetics of the spread of viral infection are influenced by intra- and extra cellular environmental conditions.   

Coalescent Theory Analysis of Population Collapse and Recovery in a Neutral Evolution Model

As we move through the Anthropocene Epoch, human-driven climate change is predicted to accelerate extinction risk in the near future. Therefore, understanding basic underlying mechanisms of population loss and recovery could be paramount to saving key species in changing ecosystems. Here, we present an evolutionary model that investigates the dynamics of population collapse and recovery following a simulated mass extinction. Previously, we have shown that nonequilibrium, continuous phase transitions of the directed percolation universality class occur as a function of two different control parameters: the mutability, $\mu $, which dictates how phenotypically different an offspring can be from its parent, and the death probability, $\delta $, which probabilistically removes organisms within each generation. Here, we characterize the phylogenetic tree structures at two levels of biological organization---the organism and species level. Using methods from coalescent theory, we examine the phylogenetic tree structures at, and above, criticality, by considering common descent. The times to most recent common ancestor show phase transition behavior, as well as scale-free branching behavior at both levels of organization. We further examine these genealogical structures pre- and post-extinction.   

Confirming Time-reversal Symmetry of a Directed Percolation Phase Transition in a Model of Neutral Evolutionary Dynamics

Reaction-diffusion processes, such as branching-coalescing random walks, can be used to describe the underlying dynamics of nonequilibrium phase transitions. In an agent-based, neutral model of evolutionary dynamics, we have previously shown that our system undergoes a continuous, nonequilibrium phase transition, from extinction to survival, as various system parameters were tuned. This model was shown to belong to the directed percolation (DP) universality class, by measuring the critical exponents corresponding to correlation length $\xi_{\bot }$, correlation time $\xi_{\vert \vert }$, and particle density $\beta $. The fourth critical exponent that defines the DP universality class is $\beta $', which measures the survival probability of growth from a single seed organism. Since DP universality is theorized to have time-reversal symmetry, it is assumed that $\beta =\beta $'. In order to confirm the existence of time-reversal symmetry in our model, we evaluate the system growth from a single asexually reproducing organism. Importantly, the critical exponent $\beta $' could be useful for comparison to experimental studies of phase transitions in biological systems, since observing growth of microbial populations is significantly easier than observing death.   

Holes influence the mutation spectrum of human mitochondrial DNA.

Mutations drive evolution and disease, showing highly non-random patterns of variant frequency \textit{vs}. nucleotide position. We use computational DNA hole spectroscopy [M.Y. Suarez-Villagran {\&} J.H. Miller, Sci. Rep. 5, 13571 (2015)] to reveal sites of enhanced hole probability in selected regions of human mitochondrial DNA. A hole is a mobile site of positive charge created when an electron is removed, for example by radiation or contact with a mutagenic agent. The hole spectra are quantum mechanically computed using a two-stranded tight binding model of DNA. We observe significant correlation between spectra of hole probabilities and of genetic variation frequencies from the MITOMAP database. These results suggest that hole-enhanced mutation mechanisms exert a substantial, perhaps dominant, influence on mutation patterns in DNA. One example is where a trapped hole induces a hydrogen bond shift, known as tautomerization, which then triggers a base-pair mismatch during replication. Our results deepen overall understanding of sequence specific mutation rates, encompassing both hotspots and cold spots, which drive molecular evolution.   

A kinetic theory for age-structured stochastic birth-death processes

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Conversely, current theories that include size-dependent population dynamics (\textit{e.g.}, carrying capacity) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a BBGKY-like hierarchy. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.   

Theoretical ecology without species

The sequencing-driven revolution in microbial ecology demonstrated that discrete ``species'' are an inadequate description of the vast majority of life on our planet. Developing a novel theoretical language that, unlike classical ecology, would not require postulating the existence of species, is a challenge of tremendous medical and environmental significance, and an exciting direction for theoretical physics. Here, it is proposed that community dynamics can be described in a naturally hierarchical way in terms of population fluctuation eigenmodes. The approach is applied to a simple model of division of labor in a multi-species community. In one regime, effective species with a core and accessory genome are shown to naturally appear as emergent concepts. However, the same model allows a transition into a regime where the species formalism becomes inadequate, but the eigenmode description remains well-defined. Treating a community as a black box that expresses enzymes in response to resources reveals mathematically exact parallels between a community and a single coherent organism with its own fitness function. This coherence is a generic consequence of division of labor, requires no cooperative interactions, and can be expected to be widespread in microbial ecosystems.   

A new model for biological effects of radiation and the driven force of molecular evolution.

We proposed a new mathematical model to estimate biological effects of radiation, which we call Whack-A-Mole (WAM) model. A special feature of WAM model is that it involves the dose rate of radiation as a key ingredient. We succeeded to reproduce the experimental data of various species concerning the radiation induced mutation frequencies. From the analysis of the mega-mouse experiments, we obtained the mutation rate per base-pair per year for mice which is consistent with the so-called molecular clock in evolution genetics, 10$^{\mathrm{-9}}$ mutation/base-pair/year. Another important quantity is the equivalent dose rate for the whole spontaneous mutation, $d_{\mathrm{eff}}$. The value of $d_{\mathrm{eff}}$ for mice is 1.1*10$^{\mathrm{-3}}$ Gy/hour which is much larger than the dose rate of natural radiation (10$^{\mathrm{-(6-7)}}$ Gy/hour) by several orders of magnitude. We also analyzed Drosophila data and obtained essentially the same numbers. This clearly indicates that the natural radiation is not the dominant driving force of the molecular evolution, but we should look for other factors, such as miscopy of DNA in duplication process. We believe this is the first quantitative proof of the small contribution of the natural radiation in the molecular evolution.   

Scaling of expected survival time in a stochastic harvesting model

We explore the dynamics of modified version of a standard fishery model (Gordon-Schafer-Munro [1]), with additive and multiplicative noise, under a quota-based harvest. A harvest quota induces an effective strong Allee effect (a positive unstable steady state population level, below which populations die out), with expected survival time following generalized Ornstein-Uhlenbeck dynamics [2]. In particular, for additive noise, the expected survival time is exponential in $s^{3}$/$\sigma^{\mathrm{2}}$, where $s$ is the difference between stable and unstable steady state populations and $\sigma $ the noise level. Thus survival time depends sensitively upon harvest quota (which determines steady state population), perhaps a warning to avoid future collapses such as that of the Atlantic cod fishery [3]. 1. Gordon HS. \textit{J Fisheries Board Canada} \textbf{10}, 442 (1953); Schaefer MB. \textit{ibid }\textbf{14}, 669 (1957); Clark, CW, Munro GR. \textit{J Environ Econ and Management} \textbf{2}, 92 (1975). 2. Beale PD. \textit{Phys Rev A} \textbf{40}, 3998 (1989). 3. c.f. www.millenniumassessment.org/   

Computational design of hepatitis C vaccines using maximum entropy models and population dynamics

Hepatitis C virus (HCV) afflicts 170 million people and kills 350,000 annually. Vaccination offers the most realistic and cost effective hope of controlling this epidemic. Despite 20 years of research, no vaccine is available. A major obstacle is the virus' extreme genetic variability and rapid mutational escape from immune pressure. Improvements in the vaccine design process are urgently needed. Coupling data mining with spin glass models and maximum entropy inference, we have developed a computational approach to translate sequence databases into empirical fitness landscapes. These landscapes explicitly connect viral genotype to phenotypic fitness and reveal vulnerable targets that can be exploited to rationally design immunogens. Viewing these landscapes as the mutational "playing field" over which the virus is constrained to evolve, we have integrated them with agent-based models of the viral mutational and host immune response dynamics, establishing a data-driven immune simulator of HCV infection. We have employed this simulator to perform in silico screening of HCV immunogens. By systematically identifying a small number of promising vaccine candidates, these models can accelerate the search for a vaccine by massively reducing the experimental search space.