Acceleration of evolutionary spread by long-range dispersal

How fast are viruses spreading in the wild?

Genomic data collected from viral outbreaks can be exploited to reconstruct the dispersal history of viral lineages in a two-dimensional space using continuous phylogeographic inference. These spatially explicit reconstructions can subsequently be used to estimate dispersal metrics allowing to unveil the dispersal dynamics and evaluate the capacity to spread among hosts. Heterogeneous sampling intensity of genomic sequences can however impact the accuracy of dispersal insights gained through phylogeographic inference. In our study, we implement a simulation framework to evaluate the robustness of three dispersal metrics - a lineage dispersal velocity, a diffusion coefficient, and an isolation-by-distance signal metric - to the sampling effort. Our results reveal that both the diffusion coefficient and isolation-by-distance signal metrics appear to be robust to the number of samples considered for the phylogeographic reconstruction. We then use these two dispersal metrics to compare the dispersal pattern and capacity of various viruses spreading in animal populations. Our comparative analysis reveals a broad range of isolation-by-distance patterns and diffusion coefficients mostly reflecting the dispersal capacity of the main infected host species but also, in some cases, the likely signature of rapid and/or long-distance dispersal events driven by human-mediated movements through animal trade. Overall, our study provides key recommendations for the lineage dispersal metrics to consider in future studies and illustrates their application to compare the spread of viruses in various settings.

Asynchronous abundance fluctuations can drive giant genotype frequency fluctuations

Large stochastic population abundance fluctuations are ubiquitous across the tree of life1-7, impacting the predictability of population dynamics and influencing eco-evolutionary outcomes. It has generally been thought that these large abundance fluctuations do not strongly impact evolution (in contrast to genetic drift), as the relative frequencies of alleles in the population will be unaffected if the abundance of all alleles fluctuate in unison. However, we argue that large abundance fluctuations can lead to significant genotype frequency fluctuations if different genotypes within a population experience these fluctuations asynchronously. By serially diluting mixtures of two closely related E. coli strains, we show that such asynchrony can occur, leading to giant frequency fluctuations that far exceed expectations from models of genetic drift. We develop a flexible, effective model that explains the abundance fluctuations as arising from correlated offspring numbers between individuals, and the large frequency fluctuations result from even slight decoupling in offspring numbers between genotypes. This model accurately describes the observed abundance and frequency fluctuation scaling behaviors. Our findings suggest chaotic dynamics underpin these giant fluctuations, causing initially similar trajectories to diverge exponentially; subtle environmental changes can be magnified, leading to batch correlations in identical growth conditions. Furthermore, we present evidence that such decoupling noise is also present in mixed-genotype S. cerevisiae populations. We demonstrate that such decoupling noise can strongly influence evolutionary outcomes, in a manner distinct from genetic drift. Given the generic nature of asynchronous fluctuations, we anticipate they are widespread in biological populations, significantly affecting evolutionary and ecological dynamics.

A mechanistic statistical approach to infer invasion characteristics of human-dispersed species with complex life cycle

The rising introduction of invasive species through trade networks threatens biodiversity and ecosystem services. Yet, we have a limited understanding of how transportation networks determine patterns of range expansion. This is partly because current analytical models fail to integrate the invader's life-history dynamics with heterogeneity in human-mediated dispersal patterns. And partly because classical statistical methods often fail to provide reliable estimates of model parameters due to spatial biases in the presence-only records and lack of informative demographic data. To address these gaps, we first formulate an age-structured metapopulation model that uses a probability matrix to emulate human-mediated dispersal patterns. The model reveals that an invader spreads along the shortest network path, such that the inter-patch network distances decrease with increasing traffic volume and reproductive value of hitchhikers. Next, we propose a Bayesian statistical method to estimate model parameters using presence-only data and prior demographic knowledge. To show the utility of the statistical approach, we analyze zebra mussel (Dreissena polymorpha) expansion in North America through the commercial shipping network. Our analysis underscores the importance of correcting spatial biases and leveraging priors to answer questions, such as where and when the zebra mussels were introduced and what life-history characteristics make these mollusks successful invaders.

Movement Ecology of Adult Western Corn Rootworm: Implications for Management

Movement of adult western corn rootworm, Diabrotica virgifera virgifera LeConte, is of fundamental importance to this species' population dynamics, ecology, evolution, and interactions with its environment, including cultivated cornfields. Realistic parameterization of dispersal components of models is needed to predict rates of range expansion, development, and spread of resistance to control measures and improve pest and resistance management strategies. However, a coherent understanding of western corn rootworm movement ecology has remained elusive because of conflicting evidence for both short- and long-distance lifetime dispersal, a type of dilemma observed in many species called Reid's paradox. Attempts to resolve this paradox using population genetic strategies to estimate rates of gene flow over space likewise imply greater dispersal distances than direct observations of short-range movement suggest, a dilemma called Slatkin's paradox. Based on the wide-array of available evidence, we present a conceptual model of adult western corn rootworm movement ecology under the premise it is a partially migratory species. We propose that rootworm populations consist of two behavioral phenotypes, resident and migrant. Both engage in local, appetitive flights, but only the migrant phenotype also makes non-appetitive migratory flights, resulting in observed patterns of bimodal dispersal distances and resolution of Reid's and Slatkin's paradoxes.

Motility mediates satellite formation in confined biofilms

Bacteria have spectacular survival capabilities and can spread in many, vastly different environments. For instance, when pathogenic bacteria infect a host, they expand by proliferation and squeezing through narrow pores and elastic matrices. However, the exact role of surface structures-important for biofilm formation and motility-and matrix density in colony expansion and morphogenesis is still largely unknown. Using confocal laser-scanning microscopy, we show how satellite colonies emerge around Escherichia coli colonies embedded in semi-dense hydrogel in controlled in vitro assays. Using knock-out mutants, we tested how extra-cellular structures, (e.g., exo-polysaccharides, flagella, and fimbria) control this morphology. Moreover, we identify the extra-cellular matrix' density, where this morphology is possible. When paralleled with mathematical modelling, our results suggest that satellite formation allows bacterial communities to spread faster. We anticipate that this strategy is important to speed up expansion in various environments, while retaining the close interactions and protection provided by the community.

Operator Growth in Open Quantum Systems

The spreading of quantum information in closed systems, often termed scrambling, is a hallmark of many-body quantum dynamics. In open systems, scrambling competes with noise, errors, and decoherence. Here, we provide a universal framework that describes the scrambling of quantum information in open systems: we predict that the effect of open-system dynamics is fundamentally controlled by operator size distributions and independent of the microscopic error mechanism. This framework allows us to demonstrate that open quantum systems exhibit universal classes of information dynamics that fundamentally differ from their unitary counterparts. Implications for the Loschmidt echo, nuclear magnetic resonance experiments, and the classical simulability of open quantum dynamics will be discussed.

From localized to well mixed: How commuter interactions shape disease spread

Interactions between commuting individuals can lead to large-scale spreading of rumors, ideas, or disease, even though the commuters have no net displacement. The emergent dynamics depend crucially on the commuting distribution of a population, that is how the probability to travel to a destination decays with distance from home. Applying this idea to epidemics, we will demonstrate the qualitatively different infection dynamics emerging from populations with different commuting distributions. If the commuting distribution is exponentially localized, then we recover a reaction-diffusion system and observe Fisher waves traveling at a speed proportional to the characteristic commuting distance. If the commuting distribution has a long tail, then no finite-velocity waves can form, but we show that, in some regimes, there is nontrivial spatial dependence that the well-mixed approximation neglects. We discuss how, in all cases, an initial dispersal-dominated regime can allow the disease to go undetected for a finite amount of time before exponential growth takes over. This "offset time" is a quantity of huge importance for epidemic surveillance and yet largely ignored in the literature.

Operator growth from global out-of-time-order correlators

In chaotic many-body systems, scrambling or the operator growth can be diagnosed by out-of-time-order correlators of local operators. We show that operator growth also has a sharp imprint in out-of-time-order correlators of global operators. In particular, the characteristic spacetime shape of growing local operators can be accessed using global measurements without any local control or readout. Building on an earlier conjectured phase diagram for operator growth in chaotic systems with power-law interactions, we show that existing nuclear spin data for out-of-time-order correlators of global operators are well fit by our theory. We also predict super-polynomial operator growth in dipolar systems in 3d and discuss the potential observation of this physics in future experiments with nuclear spins and ultra-cold polar molecules.

Proliferating active matter

The fascinating patterns of collective motion created by autonomously driven particles have fuelled active-matter research for over two decades. So far, theoretical active-matter research has often focused on systems with a fixed number of particles. This constraint imposes strict limitations on what behaviours can and cannot emerge. However, a hallmark of life is the breaking of local cell number conservation by replication and death. Birth and death processes must be taken into account, for example, to predict the growth and evolution of a microbial biofilm, the expansion of a tumour, or the development from a fertilized egg into an embryo and beyond. In this Perspective, we argue that unique features emerge in these systems because proliferation represents a distinct form of activity: not only do the proliferating entities consume and dissipate energy, they also inject biomass and degrees of freedom capable of further self-proliferation, leading to myriad dynamic scenarios. Despite this complexity, a growing number of studies document common collective phenomena in various proliferating soft-matter systems. This generality leads us to propose proliferation as another direction of active-matter physics, worthy of a dedicated search for new dynamical universality classes. Conceptual challenges abound, from identifying control parameters and understanding large fluctuations and nonlinear feedback mechanisms to exploring the dynamics and limits of information flow in self-replicating systems. We believe that, by extending the rich conceptual framework developed for conventional active matter to proliferating active matter, researchers can have a profound impact on quantitative biology and reveal fascinating emergent physics along the way.

Isolation by distance in populations with power-law dispersal

Limited dispersal of individuals between generations results in isolation by distance, in which individuals further apart in space tend to be less related. Classic models of isolation by distance assume that dispersal distances are drawn from a thin-tailed distribution and predict that the proportion of the genome that is identical by descent between a pair of individuals should decrease exponentially with the spatial separation between them. However, in many natural populations, individuals occasionally disperse over very long distances. In this work, we use mathematical analysis and coalescent simulations to study the effect of long-range (power-law) dispersal on patterns of isolation by distance. We find that it leads to power-law decay of identity-by-descent at large distances with the same exponent as dispersal. We also find that broad power-law dispersal produces another, shallow power-law decay of identity-by-descent at short distances. These results suggest that the distribution of long-range dispersal events could be estimated from sequencing large population samples taken from a wide range of spatial scales.

Plausible explanation for the third COVID-19 wave in India and its implications

Recently some of us used a random-walk Monte Carlo simulation approach to study the spread of COVID-19. The calculations were reasonably successful in describing secondary and tertiary waves of infection, in countries such as the USA, India, South Africa and Serbia. However, they failed to predict the observed third wave for India. In this work we present a more complete set of simulations for India, that take into consideration two aspects that were not incorporated previously. These include the stochastic movement of an erstwhile protected fraction of the population, and the reinfection of some recovered individuals because of their exposure to a new variant of the SARS-CoV-2 virus. The extended simulations now show the third COVID-19 wave for India that was missing in the earlier calculations. They also suggest an additional fourth wave, which was indeed observed during approximately the same time period as the model prediction.

Standardised empirical dispersal kernels emphasise the pervasiveness of long-distance dispersal in European birds

Dispersal is a key life-history trait for most species and is essential to ensure connectivity and gene flow between populations and facilitate population viability in variable environments. Despite the increasing importance of range shifts due to global change, dispersal has proved difficult to quantify, limiting empirical understanding of this phenotypic trait and wider synthesis. Here, we introduce a statistical framework to estimate standardised dispersal kernels from biased data. Based on this, we compare empirical dispersal kernels for European breeding birds considering age (average dispersal; natal, before first breeding; and breeding dispersal, between subsequent breeding attempts) and sex (females and males) and test whether different dispersal properties are phylogenetically conserved. We standardised and analysed data from an extensive volunteer-based bird ring-recoveries database in Europe (EURING) by accounting for biases related to different censoring thresholds in reporting between countries and to migratory movements. Then, we fitted four widely used probability density functions in a Bayesian framework to compare and provide the best statistical descriptions of the different age and sex-specific dispersal kernels for each bird species. The dispersal movements of the 234 European bird species analysed were statistically best explained by heavy-tailed kernels, meaning that while most individuals disperse over short distances, long-distance dispersal is a prevalent phenomenon in almost all bird species. The phylogenetic signal in both median and long dispersal distances estimated from the best-fitted kernel was low (Pagel's λ < 0.25), while it reached high values (Pagel's λ >0.7) when comparing dispersal distance estimates for fat-tailed dispersal kernels. As expected in birds, natal dispersal was on average 5 km greater than breeding dispersal, but sex-biased dispersal was not detected. Our robust analytical framework allows sound use of widely available mark-recapture data in standardised dispersal estimates. We found strong evidence that long-distance dispersal is common among European breeding bird species and across life stages. The dispersal estimates offer a first guide to selecting appropriate dispersal kernels in range expansion studies and provide new avenues to improve our understanding of the mechanisms and rules underlying dispersal events.

Stochastic Fluctuations Drive Non-genetic Evolution of Proliferation in Clonal Cancer Cell Populations

Evolutionary dynamics allows us to understand many changes happening in a broad variety of biological systems, ranging from individuals to complete ecosystems. It is also behind a number of remarkable organizational changes that happen during the natural history of cancers. These reflect tumour heterogeneity, which is present at all cellular levels, including the genome, proteome and phenome, shaping its development and interrelation with its environment. An intriguing observation in different cohorts of oncological patients is that tumours exhibit an increased proliferation as the disease progresses, while the timescales involved are apparently too short for the fixation of sufficient driver mutations to promote explosive growth. Here, we discuss how phenotypic plasticity, emerging from a single genotype, may play a key role and provide a ground for a continuous acceleration of the proliferation rate of clonal populations with time. We address this question by combining the analysis of real-time growth of non-small-cell lung carcinoma cells (N-H460) together with stochastic and deterministic mathematical models that capture proliferation trait heterogeneity in clonal populations to elucidate the contribution of phenotypic transitions on tumour growth dynamics.

Modeling the spatiotemporal spread of beneficial alleles using ancient genomes

Ancient genome sequencing technologies now provide the opportunity to study natural selection in unprecedented detail. Rather than making inferences from indirect footprints left by selection in present-day genomes, we can directly observe whether a given allele was present or absent in a particular region of the world at almost any period of human history within the last 10,000 years. Methods for studying selection using ancient genomes often rely on partitioning individuals into discrete time periods or regions of the world. However, a complete understanding of natural selection requires more nuanced statistical methods which can explicitly model allele frequency changes in a continuum across space and time. Here we introduce a method for inferring the spread of a beneficial allele across a landscape using two-dimensional partial differential equations. Unlike previous approaches, our framework can handle time-stamped ancient samples, as well as genotype likelihoods and pseudohaploid sequences from low-coverage genomes. We apply the method to a panel of published ancient West Eurasian genomes to produce dynamic maps showcasing the inferred spread of candidate beneficial alleles over time and space. We also provide estimates for the strength of selection and diffusion rate for each of these alleles. Finally, we highlight possible avenues of improvement for accurately tracing the spread of beneficial alleles in more complex scenarios.

Spatial structure alters the site frequency spectrum produced by hitchhiking

The reduction of genetic diversity due to genetic hitchhiking is widely used to find past selective sweeps from sequencing data, but very little is known about how spatial structure affects hitchhiking. We use mathematical modeling and simulations to find the unfolded site frequency spectrum left by hitchhiking in the genomic region of a sweep in a population occupying a 1D range. For such populations, sweeps spread as Fisher waves, rather than logistically. We find that this leaves a characteristic 3-part site frequency spectrum at loci very close to the swept locus. Very low frequencies are dominated by recent mutations that occurred after the sweep and are unaffected by hitchhiking. At moderately low frequencies, there is a transition zone primarily composed of alleles that briefly "surfed" on the wave of the sweep before falling out of the wavefront, leaving a spectrum close to that expected in well-mixed populations. However, for moderate-to-high frequencies, there is a distinctive scaling regime of the site frequency spectrum produced by alleles that drifted to fixation in the wavefront and then were carried throughout the population. For loci slightly farther away from the swept locus on the genome, recombination is much more effective at restoring diversity in 1D populations than it is in well-mixed ones. We find that these signatures of space can be strong even in apparently well-mixed populations with negligible spatial genetic differentiation, suggesting that spatial structure may frequently distort the signatures of hitchhiking in natural populations.

Clusters in an Epidemic Model with Long-Range Dispersal

In the presence of long-range dispersal, epidemics spread in spatially disconnected regions known as clusters. Here, we characterize exactly their statistical properties in a solvable model, in both the supercritical (outbreak) and critical regimes. We identify two diverging length scales, corresponding to the bulk and the outskirt of the epidemic. We reveal a nontrivial critical exponent that governs the cluster number and the distribution of their sizes and of the distances between them. We also discuss applications to depinning avalanches with long-range elasticity.

Population genetic models for the spatial spread of adaptive variants: A review in light of SARS-CoV-2 evolution

Theoretical population genetics has long studied the arrival and geographic spread of adaptive variants through the analysis of mathematical models of dispersal and natural selection. These models take on a renewed interest in the context of the COVID-19 pandemic, especially given the consequences that novel adaptive variants have had on the course of the pandemic as they have spread through global populations. Here, we review theoretical models for the spatial spread of adaptive variants and identify areas to be improved in future work, toward a better understanding of variants of concern in Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) evolution and other contemporary applications. As we describe, characteristics of pandemics such as COVID-19-such as the impact of long-distance travel patterns and the overdispersion of lineages due to superspreading events-suggest new directions for improving upon existing population genetic models.

Clustering and mapping the first COVID-19 outbreak in France

Background

With more than 160 000 confirmed COVID-19 cases and about 30 000 deceased people at the end of June 2020, France was one of the countries most affected by the coronavirus crisis worldwide. We aim to assess the efficiency of global lockdown policy in limiting spatial contamination through an in-depth reanalysis of spatial statistics in France during the first lockdown and immediate post-lockdown phases.

Methods

To reach that goal, we use an integrated approach at the crossroads of geography, spatial epidemiology, and public health science. To eliminate any ambiguity relevant to the scope of the study, attention focused at first on data quality assessment. The data used originate from official databases (Santé Publique France) and the analysis is performed at a departmental level. We then developed spatial autocorrelation analysis, thematic mapping, hot spot analysis, and multivariate clustering.

Results

We observe the extreme heterogeneity of local situations and demonstrate that clustering and intensity are decorrelated indicators. Thematic mapping allows us to identify five “ghost” clusters, whereas hot spot analysis detects two positive and two negative clusters. Our re-evaluation also highlights that spatial dissemination follows a twofold logic, zonal contiguity and linear development, thus determining a “metastatic” propagation pattern.

Conclusions

One of the most problematic issues about COVID-19 management by the authorities is the limited capacity to identify hot spots. Clustering of epidemic events is often biased because of inappropriate data quality assessment and algorithms eliminating statistical-spatial outliers. Enhanced detection techniques allow for a better identification of hot and cold spots, which may lead to more effective political decisions during epidemic outbreaks. 

Graphical Abstract

Spatial regulation of cell motility and its fitness effect in a surface-attached bacterial community

On a surface, microorganisms grow into a multi-cellular community. When a community becomes densely populated, cells migrate away to expand the community's territory. How microorganisms regulate surface motility to optimize expansion remains poorly understood. Here, we characterized surface motility of Proteus mirabilis. P. mirabilis is well known for its ability to expand its colony rapidly on a surface. Cursory visual inspection of an expanding colony suggests partial migration, i.e., one fraction of a population migrates while the other is sessile. Quantitative microscopic imaging shows that this migration pattern is determined by spatially inhomogeneous regulation of cell motility. Further analyses reveal that this spatial regulation is mediated by the Rcs system, which represses the expression of the motility regulator (FlhDC) in a nutrient-dependent manner. Alleviating this repression increases the colony expansion speed but results in a rapid drop in the number of viable cells, lowering population fitness. These findings collectively demonstrate how Rcs regulates cell motility dynamically to increase the fitness of an expanding bacterial population, illustrating a fundamental trade-off underlying bacterial colonization of a surface.

Slow expanders invade by forming dented fronts in microbial colonies

Living organisms never cease to evolve, so there is a significant interest in predicting and controlling evolution in all branches of life sciences. The most basic question is whether a trait should increase or decrease in a given environment. The answer seems to be trivial for traits such as the growth rate in a bioreactor or the expansion rate of a tumor. Yet, it has been suggested that such traits can decrease, rather than increase, during evolution. Here, we report a mutant that outcompeted the ancestor despite having a slower expansion velocity when in isolation. To explain this observation, we developed and validated a theory that describes spatial competition between organisms with different expansion rates and arbitrary competitive interactions.

Most organisms grow in space, whether they are viruses spreading within a host tissue or invasive species colonizing a new continent. Evolution typically selects for higher expansion rates during spatial growth, but it has been suggested that slower expanders can take over under certain conditions. Here, we report an experimental observation of such population dynamics. We demonstrate that mutants that grow slower in isolation nevertheless win in competition, not only when the two types are intermixed, but also when they are spatially segregated into sectors. The latter was thought to be impossible because previous studies focused exclusively on the global competitions mediated by expansion velocities, but overlooked the local competitions at sector boundaries. Local competition, however, can enhance the velocity of either type at the sector boundary and thus alter expansion dynamics. We developed a theory that accounts for both local and global competitions and describes all possible sector shapes. In particular, the theory predicted that a slower on its own, but more competitive, mutant forms a dented V-shaped sector as it takes over the expansion front. Such sectors were indeed observed experimentally, and their shapes matched quantitatively with the theory. In simulations, we further explored several mechanisms that could provide slow expanders with a local competitive advantage and showed that they are all well-described by our theory. Taken together, our results shed light on previously unexplored outcomes of spatial competition and establish a universal framework to understand evolutionary and ecological dynamics in expanding populations.

Single-cell tracking reveals super-spreading brain cancer cells with high persistence

Cell migration is a fundamental characteristic of vital processes such as tissue morphogenesis, wound healing and immune cell homing to lymph nodes and inflamed or infected sites. Therefore, various brain defect diseases, chronic inflammatory diseases as well as tumor formation and metastasis are associated with aberrant or absent cell migration. We embedded multicellular brain cancer spheroids in Matrigel™ and utilized single-particle tracking to extract the paths of cells migrating away from the spheroids. We found that - in contrast to local invasion - single cell migration is independent of Matrigel™ concentration and is characterized by high directionality and persistence. Furthermore, we identified a subpopulation of super-spreading cells with >200-fold longer persistence times than the majority of cells. These results highlight yet another aspect of cell heterogeneity in tumors.

A new logistic growth model applied to COVID-19 fatality data

BACKGROUND

Recent work showed that the temporal growth of the novel coronavirus disease (COVID-19) follows a sub-exponential power-law scaling whenever effective control interventions are in place. Taking this into consideration, we present a new phenomenological logistic model that is well-suited for such power-law epidemic growth.

METHODS

We empirically develop the logistic growth model using simple scaling arguments, known boundary conditions and a comparison with available data from four countries, Belgium, China, Denmark and Germany, where (arguably) effective containment measures were put in place during the first wave of the pandemic. A non-linear least-squares minimization algorithm is used to map the parameter space and make optimal predictions.

RESULTS

Unlike other logistic growth models, our presented model is shown to consistently make accurate predictions of peak heights, peak locations and cumulative saturation values for incomplete epidemic growth curves. We further show that the power-law growth model also works reasonably well when containment and lock down strategies are not as stringent as they were during the first wave of infections in 2020. On the basis of this agreement, the model was used to forecast COVID-19 fatalities for the third wave in South Africa, which was in progress during the time of this work.

CONCLUSION

We anticipate that our presented model will be useful for a similar forecasting of COVID-19 induced infections/deaths in other regions as well as other cases of infectious disease outbreaks, particularly when power-law scaling is observed.

A random-walk-based epidemiological model

Random walkers on a two-dimensional square lattice are used to explore the spatio-temporal growth of an epidemic. We have found that a simple random-walk system generates non-trivial dynamics compared with traditional well-mixed models. Phase diagrams characterizing the long-term behaviors of the epidemics are calculated numerically. The functional dependence of the basic reproductive number [Formula: see text] on the model's defining parameters reveals the role of spatial fluctuations and leads to a novel expression for [Formula: see text]. Special attention is given to simulations of inter-regional transmission of the contagion. The scaling of the epidemic with respect to space and time scales is studied in detail in the critical region, which is shown to be compatible with the directed-percolation universality class.

Understanding population structure in an evolutionary context: population-specific FST and pairwise FST

Populations are shaped by their history. It is crucial to interpret population structure in an evolutionary context. Pairwise F_ST measures population structure, whereas population-specific F_ST measures deviation from the ancestral population. To understand the current population structure and a population’s history of range expansion, we propose a representation method that overlays population-specific F_ST estimates on a sampling location map, and on an unrooted neighbor-joining tree and a multi-dimensional scaling plot inferred from a pairwise F_ST distance matrix. We examined the usefulness of our procedure using simulations that mimicked population colonization from an ancestral population and by analyzing published human, Atlantic cod, and wild poplar data. Our results demonstrated that population-specific F_ST values identify the source population and trace the evolutionary history of its derived populations. Conversely, pairwise F_ST values represent the current population structure. By integrating the results of both estimators, we obtained a new picture of the population structure that incorporates evolutionary history. The generalized least squares estimate of genome-wide population-specific F_ST indicated that the wild poplar population expanded its distribution to the north, where daylight hours are long in summer, to coastal areas with abundant rainfall, and to the south where summers are dry. Genomic data highlight the power of the bias-corrected moment estimators of F_ST, whether global, pairwise, or population-specific, that provide unbiased estimates of F_ST. All F_ST moment estimators described in this paper have reasonable processing times and are useful in population genomics studies.

A random walk Monte Carlo simulation study of COVID-19-like infection spread

Recent analysis of early COVID-19 data from China showed that the number of confirmed cases followed a subexponential power-law increase, with a growth exponent of around 2.2 (Maier and Brockmann, 2020). The power-law behavior was attributed to a combination of effective containment and mitigation measures employed as well as behavioral changes by the population. In this work, we report a random walk Monte Carlo simulation study of proximity-based infection spread. Control interventions such as lockdown measures and mobility restrictions are incorporated in the simulations through a single parameter, the size of each step in the random walk process. The step size l is taken to be a multiple of 〈 r 〉 , which is the average separation between individuals. Three temporal growth regimes (quadratic, intermediate power-law and exponential) are shown to emerge naturally from our simulations. For l = 〈 r 〉 , we get intermediate power-law growth exponents that are in general agreement with available data from China. On the other hand, we obtain a quadratic growth for smaller step sizes l ≲ 〈 r 〉 ∕ 2 , while for large l the growth is found to be exponential. We further performed a comparative case study of early fatality data (under varying levels of lockdown conditions) from three other countries, India, Brazil and South Africa. We show that reasonable agreement with these data can be obtained by incorporating small-world-like connections in our simulations.

Superlinear growth reveals the Allee effect in tumors

Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies emphasize the role of competition among tumor cells, they fail to explain recently observed superlinear growth dynamics across human tumors. Here we study tumor growth dynamics by developing a model that incorporates evolutionary dynamics inside tumors with tumor-microenvironment interactions. Our results reveal that tumor cells' ability to manipulate the environment and induce angiogenesis drives superlinear growth-a process compatible with the Allee effect. In light of this understanding, our model suggests that, for high-risk tumors that have a higher growth rate, suppressing angiogenesis can be the appropriate therapeutic intervention.

Universal scaling laws rule explosive growth in human cancers

Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a measure of the size of the system. Here we describe the discovery of universal superlinear metabolic scaling laws in human cancers. This dependence underpins increasing tumour aggressiveness, due to evolutionary dynamics, which leads to an explosive growth as the disease progresses. We validated this dynamic using longitudinal volumetric data of different histologies from large cohorts of cancer patients. To explain our observations we put forward increasingly-complex biologically-inspired mathematical models that captured the key processes governing tumor growth. Our models predicted that the emergence of superlinear allometric scaling laws is an inherently three-dimensional phenomenon. Moreover, the scaling laws thereby identified allowed us to define a set of metabolic metrics with prognostic value, thus providing added clinical utility to the base findings.

Scale invariance in the spatial-dynamics of biological invasions

Despite the enormous negative consequences of biological invasions, we have a limited understanding of how spatial demography during invasions creates population patterns observed at different spatial scales. Early stages of invasions, arrival and establishment, are considered distinct from the later stage of spread, but the processes of population growth and dispersal underlie all invasion phases. Here, we argue that the spread of invading species, to a first approximation, exhibits scale invariant spatial-dynamic patterns that transcend multiple spatial scales. Dispersal from a source population creates smaller satellite colonies, which in turn act as sources for secondary invasions; the scale invariant pattern of coalescing colonies can be seen at multiple scales. This self-similar pattern is referred to as “stratified diffusion” at landscape scales and the “bridgehead effect” at the global scale. The extent to which invasions exhibit such scale-invariant spatial dynamics may be limited by the form of the organisms’ dispersal kernel and by the connectivity of the habitat. Recognition of this self-similar pattern suggests that certain concepts for understanding and managing invasions might be widely transferable across spatial scales.

Positive association between COVID-19 deaths and influenza vaccination rates in elderly people worldwide

Background

The coronavirus disease 2019 (COVID-19) pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is an ongoing global health crisis, directly and indirectly impacting all spheres of human life. Some pharmacological measures have been proposed to prevent COVID-19 or reduce its severity, such as vaccinations. Previous reports indicate that influenza vaccination appears to be negatively correlated with COVID-19-associated mortality, perhaps as a result of heterologous immunity or changes in innate immunity. The understanding of such trends in correlations could prevent deaths from COVID-19 in the future. The aim of this study was therefore to analyze the association between COVID-19 related deaths and influenza vaccination rate (IVR) in elderly people worldwide.

Methods

To determine the association between COVID-19 deaths and influenza vaccination, available data sets from countries with more than 0.5 million inhabitants were analyzed (in total 39 countries). To accurately estimate the influence of IVR on COVID-19 deaths and mitigate effects of confounding variables, a sophisticated ranking of the importance of different variables was performed, including as predictor variables IVR and some potentially important geographical and socioeconomic variables as well as variables related to non-pharmaceutical intervention. The associations were measured by non-parametric Spearman rank correlation coefficients and random forest functions.

Results

The results showed a positive association between COVID-19 deaths and IVR of people ≥65 years-old. There is a significant increase in COVID-19 deaths from eastern to western regions in the world. Further exploration is needed to explain these findings, and additional work on this line of research may lead to prevention of deaths associated with COVID-19.

The macroecology of the COVID-19 pandemic in the Anthropocene

Severe acute respiratory syndrome coronavirus 2, the virus that causes coronavirus disease 2019 (COVID-19), has expanded rapidly throughout the world. Thus, it is important to understand how global factors linked with the functioning of the Anthropocene are responsible for the COVID-19 outbreak. We tested hypotheses that the number of COVID-19 cases, number of deaths and growth rate of recorded infections: (1) are positively associated with population density as well as (2) proportion of the human population living in urban areas as a proxies of interpersonal contact rate, (3) age of the population in a given country as an indication of that population's susceptibility to COVID-19; (4) net migration rate and (5) number of tourists as proxies of infection pressure, and negatively associated with (5) gross domestic product which is a proxy of health care quality. Data at the country level were compiled from publicly available databases and analysed with gradient boosting regression trees after controlling for confounding factors (e.g. geographic location). We found a positive association between the number of COVID-19 cases in a given country and gross domestic product, number of tourists, and geographic longitude. The number of deaths was positively associated with gross domestic product, number of tourists in a country, and geographic longitude. The effects of gross domestic product and number of tourists were non-linear, with clear thresholds above which the number of COVID-19 cases and deaths increased rapidly. The growth rate of COVID-19 cases was positively linked to the number of tourists and gross domestic product. The growth rate of COVID-19 cases was negatively associated with the mean age of the population and geographic longitude. Growth was slower in less urbanised countries. This study demonstrates that the characteristics of the human population and high mobility, but not population density, may help explain the global spread of the virus. In addition, geography, possibly via climate, may play a role in the pandemic. The unexpected positive and strong association between gross domestic product and number of cases, deaths, and growth rate suggests that COVID-19 may be a new civilisation disease affecting rich economies.

Stabilization of extensive fine-scale diversity by ecologically driven spatiotemporal chaos

It has recently become apparent that the diversity of microbial life extends far below the species level to the finest scales of genetic differences. Remarkably, extensive fine-scale diversity can coexist spatially. How is this diversity stable on long timescales, despite selective or ecological differences and other evolutionary processes? Most work has focused on stable coexistence or assumed ecological neutrality. We present an alternative: extensive diversity maintained by ecologically driven spatiotemporal chaos, with no assumptions about niches or other specialist differences between strains. We study generalized Lotka-Volterra models with antisymmetric correlations in the interactions inspired by multiple pathogen strains infecting multiple host strains. Generally, these exhibit chaos with increasingly wild population fluctuations driving extinctions. But the simplest spatial structure, many identical islands with migration between them, stabilizes a diverse chaotic state. Some strains (subspecies) go globally extinct, but many persist for times exponentially long in the number of islands. All persistent strains have episodic local blooms to high abundance, crucial for their persistence as, for many, their average population growth rate is negative. Snapshots of the abundance distribution show a power law at intermediate abundances that is essentially indistinguishable from the neutral theory of ecology. But the dynamics of the large populations are much faster than birth-death fluctuations. We argue that this spatiotemporally chaotic "phase" should exist in a wide range of models, and that even in rapidly mixed systems, longer-lived spores could similarly stabilize a diverse chaotic phase.

Operator Lévy Flight: Light Cones in Chaotic Long-Range Interacting Systems

We argue that chaotic power-law interacting systems have emergent limits on information propagation, analogous to relativistic light cones, which depend on the spatial dimension d and the exponent α governing the decay of interactions. Using the dephasing nature of quantum chaos, we map the problem to a stochastic model with a known phase diagram. A linear light cone results for α≥d+1/2. We also provide a Lévy flight (long-range random walk) interpretation of the results and show consistent numerical data for 1D long-range spin models with 200 sites.

The impact of long-range dispersal on gene surfing

Range expansions lead to distinctive patterns of genetic variation in populations, even in the absence of selection. These patterns and their genetic consequences have been well studied for populations advancing through successive short-ranged migration events. However, most populations harbor some degree of long-range dispersal, experiencing rare yet consequential migration events over arbitrarily long distances. Although dispersal is known to strongly affect spatial genetic structure during range expansions, the resulting patterns and their impact on neutral diversity remain poorly understood. Here, we systematically study the consequences of long-range dispersal on patterns of neutral variation during range expansion in a class of dispersal models which spans the extremes of local (effectively short-ranged) and global (effectively well-mixed) migration. We find that sufficiently long-ranged dispersal leaves behind a mosaic of monoallelic patches, whose number and size are highly sensitive to the distribution of dispersal distances. We develop a coarse-grained model which connects statistical features of these spatial patterns to the evolution of neutral diversity during the range expansion. We show that growth mechanisms that appear qualitatively similar can engender vastly different outcomes for diversity: Depending on the tail of the dispersal distance distribution, diversity can be either preserved (i.e., many variants survive) or lost (i.e., one variant dominates) at long times. Our results highlight the impact of spatial and migratory structure on genetic variation during processes as varied as range expansions, species invasions, epidemics, and the spread of beneficial mutations in established populations.

Impact of consumer-resource dynamics on C. elegans-E. coli system exposed to nano zero-valent iron (nZVI)

Nano zero-valent iron (nZVI) is one of the most paramount nanoparticles (NPs) applied in environmental remediation, leading to great concerns for the potential impacts on soil ecosystem health. The objective of this study was to link toxicokinetics and consumer-resource dynamics in the Caenorhabditis elegans-Escherichia coli (worm-bacteria) ecosystem. The biokinetic parameters of bacteria and worms were obtained from toxicokinetic experiments and related published literature. Biomass dynamics of bacteria and worms were estimated by employing the modified Lotka-Volterra model. Dynamics of bacteria and worm biomass, internal concentrations of nZVI, bioconcentration factors (BCFs), and biomagnification factors (BMFs) were simulated based on the consumer-resource dynamics. Results showed that the biomass of worms steadily increased from 22.25 to 291.49 g L^-1, whereas the biomass of bacteria decreased from 17.17 to 4.70 × 10^-8 g L^-1 after 96-h exposures of nZVI. We also observed ratios of nZVI concentrations in worms and bacteria increased from 0.06 to 26.60 after 96 h. Moreover, decrements of the bioconcentration factor of E. coli (BCF_E) values from 0.82 to 0.03 after 96 h were observed, whereas values of BMFs increased from 0.06 to 57.62 after 96 h. Internal concentrations of nZVI in worms were found to be mainly influenced by the ingestion rate of bacteria by worms, and the biomass conversion of bacteria had the lowest effect. Implementation of the integrated bioaccumulation-consumer-resource model supports the hypothesis that the C. elegans-E. coli dynamics of internal nZVI concentrations could be effectively associated with the predator-prey behavior and was dominated by the same physiological parameter in the two biological systems.

Spatial Population Genetics: It's About Time

Many important questions about the history and dynamics of organisms have a geographical component: How many are there, and where do they live? How do they move and interbreed across the landscape? How were they moving a thousand years ago, and where were the ancestors of a particular individual alive today? Answers to these questions can have profound consequences for our understanding of history, ecology, and the evolutionary process. In this review, we discuss how geographic aspects of the distribution, movement, and reproduction of organisms are reflected in their pedigree across space and time. Because the structure of the pedigree is what determines patterns of relatedness in modern genetic variation, our aim is to thus provide intuition for how these processes leave an imprint in genetic data. We also highlight some current methods and gaps in the statistical toolbox of spatial population genetics.

Epidemic growth rates and host movement patterns shape management performance for pathogen spillover at the wildlife-livestock interface

Managing pathogen spillover at the wildlife-livestock interface is a key step towards improving global animal health, food security and wildlife conservation. However, predicting the effectiveness of management actions across host-pathogen systems with different life histories is an on-going challenge since data on intervention effectiveness are expensive to collect and results are system-specific. We developed a simulation model to explore how the efficacies of different management strategies vary according to host movement patterns and epidemic growth rates. The model suggested that fast-growing, fast-moving epidemics like avian influenza were best-managed with actions like biosecurity or containment, which limited and localized overall spillover risk. For fast-growing, slower-moving diseases like foot-and-mouth disease, depopulation or prophylactic vaccination were competitive management options. Many actions performed competitively when epidemics grew slowly and host movements were limited, and how management efficacy related to epidemic growth rate or host movement propensity depended on what objective was used to evaluate management performance. This framework offers one means of classifying and prioritizing responses to novel pathogen spillover threats, and evaluating current management actions for pathogens emerging at the wildlife-livestock interface. This article is part of the theme issue 'Dynamic and integrative approaches to understanding pathogen spillover'.

Evolution at the Edge of Expanding Populations

Predicting the evolution of expanding populations is critical to controlling biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of evolution where organisms pay a reproductive cost to disperse faster. When does selection favor this "survival of the fastest"? We searched for a simple rule, motivated by evolution experiments where swarming bacteria evolved into a hyperswarmer mutant that disperses ∼100% faster but pays a growth cost of ∼10% to make many copies of its flagellum. We analyzed a two-species model based on the Fisher equation to explain this observation: the population expansion rate (v) results from an interplay of growth (r) and dispersal (D) and is independent of the carrying capacity: v = 2 ( rD ) 1 / 2 . A mutant can take over the edge only if its expansion rate (v2) exceeds the expansion rate of the established species (v1); this simple condition ( v 2 > v 1 ) determines the maximum cost in slower growth that a faster mutant can pay and still be able to take over. Numerical simulations and time-course experiments where we tracked evolution by imaging bacteria suggest that our findings are general: less favorable conditions delay but do not entirely prevent the success of the fastest. Thus, the expansion rate defines a traveling wave fitness, which could be combined with trade-offs to predict evolution of expanding populations.

Seasonal host life-history processes fuel disease dynamics at different spatial scales

Understanding the drivers underlying disease dynamics is still a major challenge in disease ecology, especially in the case of long-term disease persistence. Even though there is a strong consensus that density-dependent factors play an important role for the spread of diseases, the main drivers are still discussed and, more importantly, might differ between invasion and persistence periods. Here, we analysed long-term outbreak data of classical swine fever, an important disease in both wild boar and livestock, prevalent in the wild boar population from 1993 to 2000 in Mecklenburg-Vorpommern, Germany. We report outbreak characteristics and results from generalized linear mixed models to reveal what factors affected infection risk on both the landscape and the individual level. Spatiotemporal outbreak dynamics showed an initial wave-like spread with high incidence during the invasion period followed by a drop of incidence and an increase in seroprevalence during the persistence period. Velocity of spread increased with time during the first year of outbreak and decreased linearly afterwards, being on average 7.6 km per quarter. Landscape- and individual-level analyses of infection risk indicate contrasting seasonal patterns. During the persistence period, infection risk on the landscape level was highest during autumn and winter seasons, probably related to spatial behaviour such as increased long-distance movements and contacts induced by rutting and escaping movements. In contrast, individual-level infection risk peaked in spring, probably related to the concurrent birth season leading to higher densities, and was significantly higher in piglets than in reproductive animals. Our findings highlight that it is important to investigate both individual- and landscape-level patterns of infection risk to understand long-term persistence of wildlife diseases and to guide respective management actions. Furthermore, we highlight that exploring different temporal aggregation of the data helps to reveal important seasonal patterns, which might be masked otherwise.

Spatial soft sweeps: Patterns of adaptation in populations with long-range dispersal

Adaptation in extended populations often occurs through multiple independent mutations responding in parallel to a common selection pressure. As the mutations spread concurrently through the population, they leave behind characteristic patterns of polymorphism near selected loci—so-called soft sweeps—which remain visible after adaptation is complete. These patterns are well-understood in two limits of the spreading dynamics of beneficial mutations: the panmictic case with complete absence of spatial structure, and spreading via short-ranged or diffusive dispersal events, which tessellates space into distinct compact regions each descended from a unique mutation. However, spreading behaviour in most natural populations is not exclusively panmictic or diffusive, but incorporates both short-range and long-range dispersal events. Here, we characterize the spatial patterns of soft sweeps driven by dispersal events whose jump distances are broadly distributed, using lattice-based simulations and scaling arguments. We find that mutant clones adopt a distinctive structure consisting of compact cores surrounded by fragmented “haloes” which mingle with haloes from other clones. As long-range dispersal becomes more prominent, the progression from diffusive to panmictic behaviour is marked by two transitions separating regimes with differing relative sizes of halo to core. We analyze the implications of the core-halo structure for the statistics of soft sweep detection in small genomic samples from the population, and find opposing effects of long-range dispersal on the expected diversity in global samples compared to local samples from geographic subregions of the range. We also discuss consequences of the standing genetic variation induced by the soft sweep on future adaptation and mixing.

When a species is spread out over a large geographic range, different regions may adapt to the same selection pressure by acquiring distinct beneficial mutations. The resulting pattern of genetic variation in the population is called a soft sweep. Dispersal strongly influences soft sweep patterns, as it determines how a mutation that arose in one region might spread to others. Although most plant and animal populations experience some amount of dispersal over very long distances, the impact of such long-range dispersal events on soft sweep patterns remains poorly understood. We use computer simulations and mathematical analysis to study patterns of genetic variation in a model of soft sweeps including long-range dispersal. We show that long-range dispersal leaves distinct signatures in the genetic makeup of the population, which can be detected in genetic samples from individuals across the range. Our results are important for correctly interpreting patterns of genetic diversity in populations that have undergone recent adaptation.

Reaction fronts in persistent random walks with demographic stochasticity

Standard reaction-diffusion systems are characterized by infinite velocities and no persistence in the movement of individuals, two conditions that are violated when considering living organisms. Here we consider a discrete particle model in which individuals move following a persistent random walk with finite speed and grow with logistic dynamics. We show that, when the number of individuals is very large, the individual-based model is well described by the continuous reactive Cattaneo equation (RCE), but for smaller values of the carrying capacity important finite-population effects arise. The effects of fluctuations on the propagation speed are investigated both considering the RCE with a cutoff in the reaction term and by means of numerical simulations of the individual-based model. Finally, a more general Lévy walk process for the transport of individuals is examined and an expression for the front speed of the resulting traveling wave is proposed.

Spatial constraints on the diffusion of religious innovations: The case of early Christianity in the Roman Empire

Christianity emerged as a small and marginal movement in the first century Palestine and throughout the following three centuries it became highly visible in the whole Mediterranean. Little is known about the mechanisms of spreading innovative ideas in past societies. Here we investigate how well the spread of Christianity can be explained as a diffusive process constrained by physical travel in the Roman Empire. First, we combine a previously established model of the transportation network with city population estimates and evaluate to which extent the spatio-temporal pattern of the spread of Christianity can be explained by static factors. Second, we apply a network-theoretical approach to analyze the spreading process utilizing effective distance. We show that the spread of Christianity in the first two centuries closely follows a gravity-guided diffusion, and is substantially accelerated in the third century. Using the effective distance measure, we are able to suggest the probable path of the spread. Our work demonstrates how the spatio-temporal patterns we observe in the data can be explained using only spatial constraints and urbanization structure of the empire. Our findings also provide a methodological framework to be reused for studying other cultural spreading phenomena.

Selection-Like Biases Emerge in Population Models with Recurrent Jackpot Events

Evolutionary dynamics driven out of equilibrium by growth, expansion, or adaptation often generate a characteristically skewed distribution of descendant numbers: the earliest, the most advanced, or the fittest ancestors have exceptionally large number of descendants, which Luria and Delbrück called "jackpot" events. Here, I show that recurrent jackpot events generate a deterministic median bias favoring majority alleles, which is akin to positive frequency-dependent selection (proportional to the log ratio of the frequencies of mutant and wild-type alleles). This fictitious selection force results from the fact that majority alleles tend to sample deeper into the tail of the descendant distribution. The flip side of this sampling effect is the rare occurrence of large frequency hikes in favor of minority alleles, which ensures that the allele frequency dynamics remains neutral in expectation, unless genuine selection is present. The resulting picture of a selection-like bias compensated by rare big jumps allows for an intuitive understanding of allele frequency trajectories and enables the exact calculation of transition densities for a range of important scenarios, including population-size variations and different forms of natural selection. As a general signature of evolution by rare events, fictitious selection hampers the establishment of new beneficial mutations, counteracts balancing selection, and confounds methods to infer selection from data over limited timescales.

Effective models and the search for quantitative principles in microbial evolution

Microbes evolve rapidly. Yet they do so in idiosyncratic ways, which depend on the specific mutations that are beneficial or deleterious in a given situation. At the same time, some population-level patterns of adaptation are strikingly similar across different microbial systems, suggesting that there may also be simple, quantitative principles that unite these diverse scenarios. We review the search for simple principles in microbial evolution, ranging from the biophysical level to emergent evolutionary dynamics. A key theme has been the use of effective models, which coarse-grain over molecular and cellular details to obtain a simpler description in terms of a few effective parameters. Collectively, these theoretical approaches provide a set of quantitative principles that facilitate understanding, prediction, and potentially control of evolutionary phenomena, though formidable challenges remain due to the ecological complexity of natural populations.

Reaction-diffusion on random spatial networks with scale-free jumping rates via effective medium theory

We study epidemic processes using a metapopulation approach on the line featuring random transport rates between arbitrarily distant sites. An average transport network is found using a recently developed variant of the effective medium approximation (EMA) that is capable of dealing with these long-range connections. Using a Feynman-Kac argument in the effective medium, we derive an estimate on the size of the infected domain, and reproduce the known result of its exponential growth in time. We hereby demonstrate the applicability of long-range EMA to dynamical processes on networks more intricate than simple diffusion.

Spatial mutation patterns as markers of early colorectal tumor cell mobility

A growing body of evidence suggests that a subset of human cancers grows as single clonal expansions. In such a nearly neutral evolution scenario, it is possible to infer the early ancestral tree of a full-grown tumor. We hypothesized that early tree reconstruction can provide insights into the mobility phenotypes of tumor cells during their first few cell divisions. We explored this hypothesis by means of a computational multiscale model of tumor expansion incorporating the glandular structure of colorectal tumors. After calibrating the model to multiregional and single gland data from 19 human colorectal tumors using approximate Bayesian computation, we examined the role of early tumor cell mobility in shaping the private mutation patterns of the final tumor. The simulations showed that early cell mixing in the first tumor gland can result in side-variegated patterns where the same private mutations could be detected on opposite tumor sides. In contrast, absence of early mixing led to nonvariegated, sectional mutation patterns. These results suggest that the patterns of detectable private mutations in colorectal tumors may be a marker of early cell movement and hence the invasive and metastatic potential of the tumor at the start of the growth. In alignment with our hypothesis, we found evidence of early abnormal cell movement in 9 of 15 invasive colorectal carcinomas ("born to be bad"), but in none of 4 benign adenomas. If validated with a larger dataset, the private mutation patterns may be used for outcome prediction among screen-detected lesions with unknown invasive potential.

Epidemics on plants: Modeling long-range dispersal on spatially embedded networks

Here we develop an epidemic model that accounts for long-range dispersal of pathogens between plants. This model generalizes the classical compartmental models-Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered (SIR)-to take into account those factors that are key to understand epidemics in real plant populations. These ingredients are the spatial characteristics of the plots and fields in which plants are embedded and the effect of long-range dispersal of pathogens. The spatial characteristics are included through the use of random rectangular graphs which allow to consider the effects of the elongation of plots and fields, while the long-range dispersal is implemented by considering transformations, such as the Mellin and Laplace transforms, of a generalization of the adjacency matrix of the geometric graph. Our results point out that long-range dispersal favors the propagation of pathogens while the elongation of plant plots increases the epidemic threshold and decreases dramatically the number of affected plants. Interestingly, our model is able of reproducing the existence of patchy regions of infected plants and the absence of a clear propagation front centered in the initial infected plants, as it is observed in real plant epidemics.

Hitchhiking in space: Ancestry in adapting, spatially extended populations

Selective sweeps reduce neutral genetic diversity. In sexual populations, this "hitchhiking" effect is thought to be limited to the local genomic region of the sweeping allele. While this is true in panmictic populations, we find that in spatially extended populations the combined effects of many unlinked sweeps can affect patterns of ancestry (and therefore neutral genetic diversity) across the whole genome. Even low rates of sweeps can be enough to skew the spatial locations of ancestors such that neutral mutations that occur in an individual living outside a small region in the center of the range have virtually no chance of fixing in the population. The fact that nearly all ancestry rapidly traces back to a small spatial region also means that relatedness between individuals falls off very slowly as a function of the spatial distance between them.

CRISPR-based herd immunity can limit phage epidemics in bacterial populations

Herd immunity, a process in which resistant individuals limit the spread of a pathogen among susceptible hosts has been extensively studied in eukaryotes. Even though bacteria have evolved multiple immune systems against their phage pathogens, herd immunity in bacteria remains unexplored. Here we experimentally demonstrate that herd immunity arises during phage epidemics in structured and unstructured Escherichia coli populations consisting of differing frequencies of susceptible and resistant cells harboring CRISPR immunity. In addition, we develop a mathematical model that quantifies how herd immunity is affected by spatial population structure, bacterial growth rate, and phage replication rate. Using our model we infer a general epidemiological rule describing the relative speed of an epidemic in partially resistant spatially structured populations. Our experimental and theoretical findings indicate that herd immunity may be important in bacterial communities, allowing for stable coexistence of bacteria and their phages and the maintenance of polymorphism in bacterial immunity.

The future distribution of river fish: The complex interplay of climate and land use changes, species dispersal and movement barriers

The future distribution of river fishes will be jointly affected by climate and land use changes forcing species to move in space. However, little is known whether fish species will be able to keep pace with predicted climate and land use-driven habitat shifts, in particular in fragmented river networks. In this study, we coupled species distribution models (stepwise boosted regression trees) of 17 fish species with species-specific models of their dispersal (fish dispersal model FIDIMO) in the European River Elbe catchment. We quantified (i) the extent and direction (up- vs. downstream) of predicted habitat shifts under coupled "moderate" and "severe" climate and land use change scenarios for 2050, and (ii) the dispersal abilities of fishes to track predicted habitat shifts while explicitly considering movement barriers (e.g., weirs, dams). Our results revealed median net losses of suitable habitats of 24 and 94 river kilometers per species for the moderate and severe future scenarios, respectively. Predicted habitat gains and losses and the direction of habitat shifts were highly variable among species. Habitat gains were negatively related to fish body size, i.e., suitable habitats were projected to expand for smaller-bodied fishes and to contract for larger-bodied fishes. Moreover, habitats of lowland fish species were predicted to shift downstream, whereas those of headwater species showed upstream shifts. The dispersal model indicated that suitable habitats are likely to shift faster than species might disperse. In particular, smaller-bodied fish (<200 mm) seem most vulnerable and least able to track future environmental change as their habitat shifted most and they are typically weaker dispersers. Furthermore, fishes and particularly larger-bodied species might substantially be restricted by movement barriers to respond to predicted climate and land use changes, while smaller-bodied species are rather restricted by their specific dispersal ability.