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1. A hybrid stochastic-deterministic approach to explore multiple infection and evolution in HIV

   https://doi.org/10.1371/journal.pcbi.1009713  

   Kreger, Jesse ; Komarova, Natalia L. ; Wodarz, Dominik ( December 2021 , PLOS Computational Biology)

   Pascual, Mercedes (Ed.)

   To study viral evolutionary processes within patients, mathematical models have been instrumental. Yet, the need for stochastic simulations of minority mutant dynamics can pose computational challenges, especially in heterogeneous systems where very large and very small sub-populations coexist. Here, we describe a hybrid stochastic-deterministic algorithm to simulate mutant evolution in large viral populations, such as acute HIV-1 infection, and further include the multiple infection of cells. We demonstrate that the hybrid method can approximate the fully stochastic dynamics with sufficient accuracy at a fraction of the computational time, and quantify evolutionary end points that cannot be expressed by deterministic models, such as the mutant distribution or the probability of mutant existence at a given infected cell population size. We apply this method to study the role of multiple infection and intracellular interactions among different virus strains (such as complementation and interference) for mutant evolution. Multiple infection is predicted to increase the number of mutants at a given infected cell population size, due to a larger number of infection events. We further find that viral complementation can significantly enhance the spread of disadvantageous mutants, but only in select circumstances: it requires the occurrence of direct cell-to-cell transmission through virological synapses, asmore »well as a substantial fitness disadvantage of the mutant, most likely corresponding to defective virus particles. This, however, likely has strong biological consequences because defective viruses can carry genetic diversity that can be incorporated into functional virus genomes via recombination. Through this mechanism, synaptic transmission in HIV might promote virus evolvability.« less
2. Laws of Spatially Structured Population Dynamics on a Lattice

   https://doi.org/10.3390/physics4030052  

   Komarova, Natalia L. ; Rodriguez-Brenes, Ignacio A. ; Wodarz, Dominik ( September 2022 , Physics)

   We consider spatial population dynamics on a lattice, following a type of a contact (birth–death) stochastic process. We show that simple mathematical approximations for the density of cells can be obtained in a variety of scenarios. In the case of a homogeneous cell population, we derive the cellular density for a two-dimensional (2D) spatial lattice with an arbitrary number of neighbors, including the von Neumann, Moore, and hexagonal lattice. We then turn our attention to evolutionary dynamics, where mutant cells of different properties can be generated. For disadvantageous mutants, we derive an approximation for the equilibrium density representing the selection–mutation balance. For neutral and advantageous mutants, we show that simple scaling (power) laws for the numbers of mutants in expanding populations hold in 2D and 3D, under both flat (planar) and range population expansion. These models have relevance for studies in ecology and evolutionary biology, as well as biomedical applications including the dynamics of drug-resistant mutants in cancer and bacterial biofilms.
3. Effect of synaptic cell-to-cell transmission and recombination on the evolution of double mutants in HIV

   https://doi.org/10.1098/rsif.2019.0832  

   Kreger, Jesse ; Komarova, Natalia L ; Wodarz, Dominik ( March 2020 , Journal of the Royal Society interface)

   Recombination in HIV infection can impact virus evolution in vivo in complex ways, as has been shown both experimentally and mathematically. The effect of free virus versus synaptic, cell-to-cell transmission on the evolution of double mutants, however, has not been investigated. Here, we do so by using a stochastic agent-based model. Consistent with data, we assume spatial constraints for synaptic but not for free-virus transmission. Two important effects of the viral spread mode are observed: (i) for disadvantageous mutants, synaptic transmission protects against detrimental effects of recombination on double mutant persistence. Under free virus transmission, recombination increases double mutant levels for negative epistasis, but reduces them for positive epistasis. This reduction for positive epistasis is much diminished under predominantly synaptic transmission, and recombination can, in fact, lead to increased mutant levels. (ii) The mode of virus spread also directly influences the evolutionary fate of double mutants. For disadvantageous mutants, double mutant production is the predominant driving force, and hence synaptic transmission leads to highest double mutant levels due to increased transmission efficiency. For advantageous mutants, double mutant spread is the most important force, and hence free virus transmission leads to fastest invasion due to better mixing. For neutral mutants, bothmore »production and spread of double mutants are important, and hence an optimal mixture of free virus and synaptic transmission maximizes double mutant fractions. Therefore, both free virus and synaptic transmission can enhance or delay double mutant evolution. Implications for drug resistance in HIV are discussed.« less
4. Multiple infection of cells changes the dynamics of basic viral evolutionary processes

   https://doi.org/10.1002/evl3.95  

   Wodarz, Dominik ; Levy, David N. ; Komarova, Natalia L. ( February 2019 , Evolution Letters)

   The infection of cells by multiple copies of a given virus can impact viral evolution in a variety of ways, yet some of the most basic evolutionary dynamics remain underexplored. Using computational models, we investigate how infection multiplicity affects the fixation probability of mutants, the rate of mutant generation, and the timing of mutant invasion. An important insight from these models is that for neutral and disadvantageous phenotypes, rare mutants initially enjoy a fitness advantage in the presence of multiple infection of cells. This arises because multiple infection allows the rare mutant to enter more target cells and to spread faster, while it does not accelerate the spread of the resident wild-type virus. The rare mutant population can increase by entry into both uninfected and wild-type-infected cells, while the established wild-type population can initially only grow through entry into uninfected cells. Following this initial advantageous phase, the dynamics are governed by drift or negative selection, respectively, and a higher multiplicity reduces the chances that mutants fix in the population. Hence, while increased infection multiplicity promotes the presence of neutral and disadvantageous mutants in the short-term, it makes it less likely in the longer term. We show how these theoreticalmore »insights can be useful for the interpretation of experimental data on virus evolution at low and high multiplicities. The dynamics explored here provide a basis for the investigation of more complex viral evolutionary processes, including recombination, reassortment, as well as complementary/inhibitory interactions.

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5. Biogeographic Drivers of Evolutionary Radiations

   https://doi.org/10.3389/fevo.2021.644328  

   Tao, Ran ; Sack, Lawren ; Rosindell, James ( August 2021 , Frontiers in Ecology and Evolution)

   Some lineages radiate spectacularly when colonizing a region, but others do not. Large radiations are often attributed to species’ adaptation into niches, or to other drivers, such as biogeography including dispersal ability and spatial structure of the landscape. Here we aim to disentangle the factors determining radiation size, by modeling simplified scenarios without the complexity of explicit niches. We build a spatially structured neutral model free from niches and incorporating a form of protracted speciation that accounts for gene flow between populations. We find that a wide range of radiation sizes are possible in this model depending on the combination of geographic isolation and species’ dispersal ability. At extremely low rates of dispersal between patches, each patch maintains its own endemic species. Intermediate dispersal rates foster larger radiations as they allow occasional movement between patches whilst sufficiently restricting gene flow to support further speciation in allopatry. As dispersal rates increase further, a critical point is reached at which demographically identical lineages may vary greatly in radiation size due to rare and stochastic dispersal events. At the critical point in dispersal frequency, some lineages remain a single species for a comparatively long time, whilst others with identical characteristics produce the largestmore »radiations of all via a new mechanism for rapid radiation that we term a ‘radiation cascade’. Given a single species covering many patches connected with gene flow, a radiation cascade is triggered when stochastic dispersal is unusually low for a period, leading to an initial speciation event. This speciation means there are fewer individuals per species and thus further reduced gene flow between conspecifics. Reduced gene flow in turn makes it easier for further speciation to occur. During a radiation cascade, dispersal of individuals between patches continues at the same rate as before, but due to the increasing diversity it primarily introduces novel species that will later speciate, rather than adding to gene flow of existing species. Once a radiation cascade begins, it continues rapidly until it is arrested by a new equilibrium between speciation and extinction. We speculate that such radiation cascades may occur more generally and are not only present in neutral models. This process may help to explain rapid radiation, and the extreme radiation sizes of certain lineages with dispersing ancestors. Whilst niches no doubt play a role in community assembly, our findings lead us to question whether diversification and adaptation into niches is sometimes an effect of speciation and rapid radiation, rather than its cause.« less