Session L14: Evolutionary and Ecological Dynamics II

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Much work has been devoted to inferring the fitness effects of mutations in evolving populations using models from population genetics. In parallel, many different models of disease spread have been developed in the field of epidemiology. But comparatively little work has been devoted to models of disease spread that are conducive to inferring the effects of mutations on disease transmission. Here we develop a model for disease spread in a localized population that accounts for both the possibility of a long tailed distribution for the number of people infected by a single individual, and that pathogen genetic variation may affect the probability of transmission, i.e., transmission fitness. Using this model, we develop a method of inferring the fitness for different mutations from time series data. We verify the model against simulations of disease spread that include super spreaders, as well as against standard susceptible-infected-recovered (SIR) models, and show that in both cases fitness is accurately recovered. Applied to SARS-CoV-2 data, we find a few groups of linked mutations that appear to strongly affect the viral transmission rate.   

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Whole genome studies have revealed an abundance of genes with no clear homologs. The origins of many of these genes is proposed to be in intergenic sequences that somehow gained expression and adaptive value – a process termed de novo gene birth. Here, we explore the mechanism of de novo gene birth in a first-principles stochastic evolution model taking into account the effects of mutations on both expression level and the adaptive value. In our model, gene birth appears as an abrupt dynamical phase transition from a mutation-dominated phase to a selection-dominated phase. Rather than a rare mutation incurred by a single lucky individual, we show that de novo gene birth is a whole population phenomenon. Through this study, we aim to infer the relationship between the mutational and epigenetic dynamics at intergenic regions, and the probability and timing of gene birth in natural populations.   

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Humans are systems with memory. In many cases, it is shown that this memory obeys power-law. Unstable systems with power-law memory may for a significant time exist as stable systems. Caputo fractional/fractional difference logistic map is a simple discrete system with power-/asymptotically power-law memory and quadratic nonlinearity. In the area of parameters where the fixed point is unstable the distribution of the times of system’s stable evolution under various types of random perturbations obeys the Gompertz-Makeham law, which is the observed distribution of the lifespans of living species, including humans. The underlying reasons for modeling the evolution of humans by fractional systems are the observed power law in human memory and the viscoelastic nature of organ tissues of living species. We also analyzed available data and found that the power law well fits the shortening of telomeres with time. Models with power-law memory may explain the observed decrease at very large ages of the rate of increase of the force of mortality and they imply limited lifespans.   

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Recent work has shown that many noisy coupled lattice maps inspired by ecological metapopulation models undergo a transition to synchrony in the Ising universality class [1]. Little emphasis, however, has been placed on a comparison of the dynamics of the zero temperature Ising model and coupled lattice maps without noise. In this talk, we will demonstrate that these two systems share two properties, both of which have been well studied in the zero temperature Ising model [2,3,4]: (1) both evolve with curvature driven dynamics and, (2) both freeze into final states with probabilities agreeing reasonably well with predictions from percolation theory. On the other hand, the coupled Ricker lattice map has stable final states, that are only metastable for the zero temperature Ising model. We will conclude with implications for synchronization in ecological metapopulations.


1. A. E. Noble, J. Machta, and A. Hastings, Nat Comm, 6:6664, (2015).
2. V. Spirin, P. Krapivsky, and S. Redner, Phys. Rev. E65, 016119 (2001).
3. J. Olejarz, P. L. Krapivsky, and S. Redner, Phys. Rev. Lett.109, 195702 (2012).
4. C. Godreche and M. Pleimling, Journal of Statistical Mechanics:Theory and Experiment, Volume 2018 (2018).   

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Cyclic and oscillatory behaviors are ubiquitous in ecological systems. These oscillations can be noise-induced or due to the intrinsic ecological interactions. Due to the stochastic nature of ecological systems, these types of oscillations appear to be very similar, and distinguishing between them, using ecological data, is a topic of active research. Classic discrete population models like Ricker and Logistic maps are well-known in their ability to model a wide variety of ecological systems. One of the characteristics of such maps is the famous period-doubling route to chaos. This feature provides us the opportunity to study the behavior of the system in different regimes, simply by choosing the appropriate parameter value. In the two-cycle regime and implemented on a lattice with nearest neighbor coupling, these models are shown to undergo a second order phase transition. We numerically investigated the dynamics of coupled, noisy oscillators, as we slowly change the parameter from the steady state to the two-cycle regime. Although for an individual map the steady-state is not easily distinguishable from the two-cycle regime in the presence of noise, the coupled, noisy system exhibits qualitatively different behavior in these two regimes.   

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We explore the role of stochasticity and noise in the statistical outcomes of commonly studied population dynamics models within a space-independent (mean-field) perspective. Specifically, we consider a distributed population with logistic growth at each location, subject to ``seascape'' noise, wherein the population's fitness randomly varies with location and time. Despite its simplicity, the model actually incorporates variants of directed percolation, and directed polymers in random media, within a mean-field perspective. Probability distributions of the population can be computed self-consistently; and the extinction transition is shown to exhibit novel critical behavior with exponents dependent on the ratio of the strengths of migration and noise amplitudes. The results are compared and contrasted with the more conventional choice of demographic noise due to stochastic changes in reproduction.   

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Bacteria live in environments that are continuously fluctuating and changing. Those fluctuations are usually not purely random but to some extent predictable. Exploiting this predictability can lead to an increased fitness. On longer timescales bacteria can "learn" the structure of these fluctuations through evolution. However, on shorter timescales, inferring the statistics of the environment and acting upon this information would need to be accomplished by physiological mechanisms. Here, we use a model of metabolism to show that a simple generalization of a ubiquitous regulatory motif (end-product inhibition) is sufficient both for learning complex continuous-valued features of the environment and for translating this information into predictive behavior; moreover, it accomplishes these tasks near-optimally. We discuss plausible genetic circuits that could instantiate this learning, and argue that the key ingredients required for such predictive behavior are readily accessible to bacteria.   

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In recent years, there have been mounting evidence that evolutionary and ecological processes can occur over concurrent timescales and can affect each other. To better understand how this eco-evolutionary feedback shapes the diversity of an ecosystem, we develop a phenotypic reaction-diffusion model of a community where consumers compete for resources and mutate. Within this model, we explore the factors that determine the evolutionary fate of the ecosystem. Depending on the competition kernel, competitive strength, and mutation rate, the community can exhibit competitive exclusion which manifests as a static periodic pattern in phenotype space, or Red Queen dynamics which appears as a traveling wave of persisting species participating in a coevolutionary arms race. Beyond these Turing patterns, we also investigate the role of demographic noise in driving phenotypic diversification and discuss new behaviors that may arise due to fluctuations.   

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Different viruses such as influenza viruses, HIV, or coronaviruses exhibit characteristic traits, i.e. typical fitness landscapes and typical rates of movement within those landscapes via mutation and recombination. Those traits determine how well a virus can adapt to new environments. Epidemics and pandemics usually result from an animal virus adapting to human hosts, which allows the viral disease to spread in a susceptible human population. We investigate the pandemic risk for different viral types, using an analytical model. A viral type in our model is characterized by a typical distribution of fitness. Randomly created viral variants from that distribution enter the human population and their fitness, which influences the infection rate, determines the probability of spreading successfully. With the help of our model, we hope to gain mechanistic insights into the fundamental traits of viruses that interact with the human population and how those influence the likelihood that a new viral strain will develop into a pandemic.   

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Antagonistic interactions are widespread in the microbial world and affect microbial ecological and evolutionary dynamics. Microbial communities in the natural environment and within animal hosts often display spatial structure that affects biological interactions, but much of what we know about microbial antagonism comes from laboratory experiments performed with well-mixed communities. We manipulated two strains of the budding yeast Saccharomyces cerevisiae, expressing different "killer yeast" toxins, to independently control the rate at which they released their toxins. We developed mathematical models that predict the experimental population dynamics of antagonistic competition in both well-mixed and spatially structured populations. In both situations, we experimentally verified theory’s prediction that stronger antagonists can invade weaker ones only if the initial invading population exceeds a critical nucleation threshold. Finally, we found that toxin-resistant cells and weaker killers arose in spatially structured competitions between toxin-producing strains, suggesting that adaptive evolution can affect the outcome of microbial antagonism.   

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Controlling an evolving population is an important task in modern molecular genetics, including in directed evolution to improve the activity of molecules, in breeding experiments, and in devising public health strategies to suppress pathogens. An optimal intervention should be designed by considering its impact over an entire evolutionary trajectory that follows. As a result, a seemingly suboptimal intervention at a given time can be globally optimal as it can open opportunities for desirable actions. Here, we propose a feedback control formalism to devise globally optimal artificial selection protocol to direct evolution of molecular phenotypes. We show that artificial selection should counter evolutionary tradeoffs among multi-variate phenotypes to avoid undesirable outcomes in one phenotype by imposing selection on another. Control by artificial selection is challenged by our ability to predict evolution. We develop an information theoretical framework and show that molecular time-scales for evolution under natural selection can inform how to monitor a population to acquire sufficient predictive information for an effective intervention. Our formalism opens a new avenue for devising optimal artificial selection for directed evolution of molecular functions.   

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One of the best-known transitions in vertebrate evolution is from a short-bodied, limbed form to a limbless, snake-like form. Such transitions occur concurrently with a transition in locomotion patterns from almost standing-wave body bending to traveling-wave body undulation. How does such a transition in locomotion pattern occur in the context of the body form continuum? Here we studied the locomotion patterns of three species of Brachymeles skinks (B. kadwa with effective hind leg lengths (HLL)=0.17 relative to snout-vent length (SVL), B. taylori with HLL= 0.15 SVL , and B. mungtingkamay with the HLL=0.09 SVL) and compared them with stereotypical lizards, Uma scoparia (HLL=0.33 SVL) and Callisaurus draconoides (HLL=0.44 SVL), and an almost legless lizard, Lerista praepedita. We use new neural net tracking and theoretical geometric modeling tools to analyze animals’ locomotion on a fine granular[PB1] surface. All animals used body-leg coordination that geometric theory predicted to maximize forward propulsion. Surprisingly, the use of a traveling wave occurred after even a modest reduction in limb length, suggesting a sharp transition in locomotor mode along a gradual body form continuum.   

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Spatial heterogeneity can dramatically impact evolution in bacterial communities, raising the question of whether spatial profiles of drug concentration can be tuned to slow the emergence of antibiotic resistance. In this work, we combine lab evolution experiments in spatially connected, computer-controlled chemostats with mathematical models to investigate resistance evolution in E. faecalis, an opportunistic bacterial pathogen. We find that both the rate of adaptation to doxycycline, a protein-synthesis inhibiting antibiotic, and the associated cost of resistance in the associated mutants depends strongly on drug concentration in spatially uniform populations. Interestingly, when spatially separated subpopulations are exposed to different concentrations of drug, adaptation can be dramatically slowed by tuning the rate of migration between habitats, leading to selection for phenotypically distinct resistant mutants. Our results highlight the rich evolutionary dynamics of adaptation in spatially connected habitats and indicate that resistance evolution can be slowed by balancing evolutionary trade-offs of migration and heterogeneity.   

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Evolution allows living systems to produce novel properties that improve fitness when encountering new environments. At the same time organisms face the challenge of maintaining traits that might be dispensable under current circumstances but contribute to fitness when the environment changes. Such evolutionary decay of unused traits has important implications for the ability of organisms to cope with environmental changes. To investigate how organisms can deal with this, we performed experimental evolution with a strain of S. cerevisiae that has a cell polarity defect as well as a reduced capability to adjust to growth on different carbon sources. In two separate evolution experiments, we subjected this strain to an environment where diauxic growth on different carbon sources was relevant to fitness and one where it was not. We found that in both environments, repair of the cell polarity defect was accompanied by a better ability to perform diauxic growth. This suggests that cells could circumvent the loss of an unused trait through its pleiotropic coupling to the molecular network that regulates cell polarity. By analyzing mutations that drive adaptation in both environments, we give a first insight into what the molecular details of such pleiotropic couplings might look like.