Allee effect promotes diversity in traveling waves of colonization

Mutualism at the leading edge: insights into the eco-evolutionary dynamics of host-symbiont communities during range expansion

The evolution of mutualism between host and symbiont communities plays an essential role in maintaining ecosystem function and should therefore have a profound effect on their range expansion dynamics. In particular, the presence of mutualistic symbionts at the leading edge of a host-symbiont community should enhance its propagation in space. We develop a theoretical framework that captures the eco-evolutionary dynamics of host-symbiont communities, to investigate how the evolution of resource exchange may shape community structure during range expansion. We consider a community with symbionts that are mutualistic or parasitic to various degrees, where parasitic symbionts receive the same amount of resource from the host as mutualistic symbionts, but at a lower cost. The selective advantage of parasitic symbionts over mutualistic ones is increased with resource availability (i.e. with host density), promoting mutualism at the range edges, where host density is low, and parasitism at the population core, where host density is higher. This spatial selection also influences the speed of spread. We find that the host growth rate (which depends on the average benefit provided by the symbionts) is maximal at the range edges, where symbionts are more mutualistic, and that host-symbiont communities with high symbiont density at their core (e.g. resulting from more mutualistic hosts) spread faster into new territories. These results indicate that the expansion of host-symbiont communities is pulled by the hosts but pushed by the symbionts, in a unique push-pull dynamic where both the host and symbionts are active and tightly-linked players.

Anti-predator defences are linked with high levels of genetic differentiation in frogs

Predator-prey interactions have been suggested as drivers of diversity in different lineages, and the presence of anti-predator defences in some clades is linked to higher rates of diversification. Warning signals are some of the most widespread defences in the animal world, and there is evidence of higher diversification rates in aposematic lineages. The mechanisms behind such species richness, however, are still unclear. Here, we test whether lineages that use aposematism as anti-predator defence exhibit higher levels of genetic differentiation between populations, leading to increased opportunities for divergence. We collated from the literature more than 3000 pairwise genetic differentiation values across more than 700 populations from over 60 amphibian species. We find evidence that over short geographical distances, populations of species of aposematic lineages exhibit greater genetic divergence relative to species that are not aposematic. Our results support a scenario where the use of warning signals could restrict gene flow, and suggest that anti-predator defences could impact divergence between populations and potentially have effects at a macro-evolutionary scale.

Looking forwards and backwards: dynamics and genealogies of locally regulated populations

We introduce a broad class of mechanistic spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial position and local population density, defined at a location to be the convolution of the point measure with a suitable non-negative integrable kernel centred on that location. We pass to three different scaling limits: an interacting superprocess, a nonlocal partial differential equation (PDE), and a classical PDE. The classical PDE is obtained both by a two-step convergence argument, in which we first scale time and population size and pass to the nonlocal PDE, and then scale the kernel that determines local population density; and in the important special case in which the limit is a reaction-diffusion equation, directly by simultaneously scaling the kernel width, timescale and population size in our individual based model. A novelty of our model is that we explicitly model a juvenile phase. The number of juveniles produced by an individual depends on local population density at the location of the parent; these juvenile offspring are thrown off in a (possibly heterogeneous, anisotropic) Gaussian distribution around the location of the parent; they then reach (instant) maturity with a probability that can depend on the local population density at the location at which they land. Although we only record mature individuals, a trace of this two-step description remains in our population models, resulting in novel limits in which the spatial dynamics are governed by a nonlinear diffusion. Using a lookdown representation, we are able to retain information about genealogies relating individuals in our population and, in the case of deterministic limiting models, we use this to deduce the backwards in time motion of the ancestral lineage of an individual sampled from the population. We observe that knowing the history of the population density is not enough to determine the motion of ancestral lineages in our model. We also investigate (and contrast) the behaviour of lineages for three different deterministic models of a population expanding its range as a travelling wave: the Fisher-KPP equation, the Allen-Cahn equation, and a porous medium equation with logistic growth.

Interplay between morphology and competition in two-dimensional colony expansion

In growing populations, the fate of mutations depends on their competitive ability against the ancestor and their ability to colonize new territory. Here we present a theory that integrates both aspects of mutant fitness by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (Kardar-Parisi-Zhang equation). We solve these equations and find three regimes, which are controlled solely by the expansion rates, solely by the competitive abilities, or by both. Collectively, our results provide a simple framework to study spatial competition.

Seed predation-induced Allee effects, seed dispersal and masting jointly drive the diversity of seed sources during population expansion

The environmental factors affecting plant reproduction and effective dispersal, in particular biotic interactions, have a strong influence on plant expansion dynamics, but their demographic and genetic consequences remain an understudied body of theory. Here, we use a mathematical model in a one-dimensional space and on a single reproductive period to describe the joint effects of predispersal seed insect predators foraging strategy and plant reproduction strategy (masting) on the spatio-temporal dynamics of seed sources diversity in the colonisation front of expanding plant populations. We show that certain foraging strategies can result in a higher seed predation rate at the colonisation front compared to the core of the population, leading to an Allee effect. This effect promotes the contribution of seed sources from the core to the colonisation front, with long-distance dispersal further increasing this contribution. As a consequence, our study reveals a novel impact of the predispersal seed predation-induced Allee effect, which mitigates the erosion of diversity in expanding populations. We use rearrangement inequalities to show that masting has a buffering role: it mitigates this seed predation-induced Allee effect. This study shows that predispersal seed predation, plant reproductive strategies and seed dispersal patterns can be intermingled drivers of the diversity of seed sources in expanding plant populations, and opens new perspectives concerning the analysis of more complex models such as integro-difference or reaction-diffusion equations.

Pulled, pushed or failed: the demographic impact of a gene drive can change the nature of its spatial spread

Understanding the temporal spread of gene drive alleles-alleles that bias their own transmission-through modeling is essential before any field experiments. In this paper, we present a deterministic reaction-diffusion model describing the interplay between demographic and allelic dynamics, in a one-dimensional spatial context. We focused on the traveling wave solutions, and more specifically, on the speed of gene drive invasion (if successful). We considered various timings of gene conversion (in the zygote or in the germline) and different probabilities of gene conversion (instead of assuming 100[Formula: see text] conversion as done in a previous work). We compared the types of propagation when the intrinsic growth rate of the population takes extreme values, either very large or very low. When it is infinitely large, the wave can be either successful or not, and, if successful, it can be either pulled or pushed, in agreement with previous studies (extended here to the case of partial conversion). In contrast, it cannot be pushed when the intrinsic growth rate is vanishing. In this case, analytical results are obtained through an insightful connection with an epidemiological SI model. We conducted extensive numerical simulations to bridge the gap between the two regimes of large and low growth rate. We conjecture that, if it is pulled in the two extreme regimes, then the wave is always pulled, and the wave speed is independent of the growth rate. This occurs for instance when the fitness cost is small enough, or when there is stable coexistence of the drive and the wild-type in the population after successful drive invasion. Our model helps delineate the conditions under which demographic dynamics can affect the spread of a gene drive.

Ancestral Lineages in Mutation Selection Equilibria with Moving Optimum

Many populations can somehow adapt to rapid environmental changes. To understand this fast evolution, we investigate the genealogy of individuals inside those populations. More precisely, we use a deterministic model to describe the phenotypic density of a population under selection when the fitness optimum moves at constant speed. We study the inside dynamics of this population using the neutral fractions approach. We then define a Markov process characterizing the distribution of ancestral phenotypic lineages inside the equilibrium. This construction yields qualitative as well as quantitative properties on the phenotype of typical ancestors. In particular, we show that in asexual populations typical ancestors of present individuals carried traits much closer to the fitness optimum than most individuals alive at the same time. We also investigate more deeply the asymptotic regime of small mutation effects. In this regime, we obtain an explicit formula for the typical ancestral lineage using the description of the solutions of the Hamilton Jacobi equation as a minimizer of an optimization problem. In addition, we compare our deterministic results on lineages with the lineages of stochastic models.

Life history traits and dispersal shape neutral genetic diversity in metapopulations

Genetic diversity at population scale, depends on species life-history traits, population dynamics and local and global environmental factors. We first investigate the effect of life-history traits on the neutral genetic diversity of a single population using a deterministic mathematical model. When the population is stable, we show that semelparous species with precocious maturation and iteroparous species with delayed maturation exhibit higher diversity because their life history traits tend to balance the lifetimes of non reproductive individuals (juveniles) and adults which reproduce. Then, we extend our model to a metapopulation to investigate the additional effect of dispersal on diversity. We show that dispersal may truly modify the local effect of life history on diversity. As a result, the diversity at the global scale of the metapopulation differ from the local diversity which is only described through local life history traits of the populations. In particular, dispersal usually promotes diversity at the global metapopulation scale.

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.

A missing cog in the wheel: an Allee effects perspective in biological invasion paradigm

Environmental stochasticity and invasive species demographical factors are considered to be fundamental aspects of species invasion. Population size, density, and intraspecific competition are the important determinants of species range expansion. Allee effects, interesting density-dependent phenomena, act as 'mechanism of population regulation' during species expansion. The study intends to understand the trend of published researches and identify research gaps pertaining to biological invasions and Allee effects with the help of bibliometric analysis. Content and citation analysis using key words 'Allee effects' AND 'biological invasion' was conducted on research articles published over a period of two and a half decades from Scopus database for global and Indian context. Understanding of Allee effects dynamics in context of biological invasion is limited, especially in India. Integrating the emerging trends pertaining to Allee effects in the biological invasion framework will strengthen the understanding on species range expansion. It is emphasized that Allee effects can emerge as an important tool to manage invasive species range expansion.

Weak spatial-genetic structure in a native invasive, the southern pine beetle (Dendroctonus frontalis), across the eastern United States

The southern pine beetle, Dendroctonus frontalis, is a native pest of pine trees that has recently expanded its range into the northeastern United States. Understanding its colonization, dispersal, and connectivity will be critical for mitigating negative economic and ecological impacts in the newly invaded areas. Characterization of spatial-genetic structure can contribute to this; however, previous studies have reached different conclusions about regional population genetic structure, with one study reporting a weak east-west pattern, and the most recent reporting an absence of structure. Here we systematically assessed several explanations for the absence of spatial-genetic structure. To do this, we developed nine new microsatellite markers and combined them with an existing 24-locus data matrix for the same individuals. We then reanalyzed this full dataset alongside datasets in which certain loci were omitted with the goal of creating more favorable signal to noise ratios. We also partitioned the data based on the sex of D. frontalis individuals, and then employed a broad suite of genotypic clustering and isolation-by-distance (IBD) analyses. We found that neither inadequate information content in the molecular marker set, nor unfavorable signal-to-noise ratio, nor insensitivity of the analytical approaches could explain the absence of structure. Regardless of dataset composition, there was little evidence for clusters (i.e., distinct geo-genetic groups) or clines (i.e., gradients of increasing allele frequency differences over larger geographic distances), with one exception: significant IBD was repeatedly detected using an individual-based measure of relatedness whenever datasets included males (but not for female-only datasets). This is strongly indicative of broad-scale female-biased dispersal, which has not previously been reported for D. frontalis, in part owing to logistical limitations of direct approaches (e.g., capture-mark-recapture). Weak spatial-genetic structure suggests long-distance connectivity and that gene flow is high, but additional research is needed to understand range expansion and outbreak dynamics in this species using alternate approaches.

Genealogical structure changes as range expansions transition from pushed to pulled

Range expansions accelerate evolution through multiple mechanisms, including gene surfing and genetic drift. The inference and control of these evolutionary processes ultimately rely on the information contained in genealogical trees. Currently, there are two opposing views on how range expansions shape genealogies. In invasion biology, expansions are typically approximated by a series of population bottlenecks producing genealogies with only pairwise mergers between lineages-a process known as the Kingman coalescent. Conversely, traveling wave models predict a coalescent with multiple mergers, known as the Bolthausen-Sznitman coalescent. Here, we unify these two approaches and show that expansions can generate an entire spectrum of coalescent topologies. Specifically, we show that tree topology is controlled by growth dynamics at the front and exhibits large differences between pulled and pushed expansions. These differences are explained by the fluctuations in the total number of descendants left by the early founders. High growth cooperativity leads to a narrow distribution of reproductive values and the Kingman coalescent. Conversely, low growth cooperativity results in a broad distribution, whose exponent controls the merger sizes in the genealogies. These broad distribution and non-Kingman tree topologies emerge due to the fluctuations in the front shape and position and do not occur in quasi-deterministic simulations. Overall, our results show that range expansions provide a robust mechanism for generating different types of multiple mergers, which could be similar to those observed in populations with strong selection or high fecundity. Thus, caution should be exercised in making inferences about the origin of non-Kingman genealogies.

Hypoxia triggers collective aerotactic migration in Dictyostelium discoideum

Using a self-generated hypoxic assay, we show that the amoeba Dictyostelium discoideum displays a remarkable collective aerotactic behavior. When a cell colony is covered, cells quickly consume the available oxygen (O₂) and form a dense ring moving outwards at constant speed and density. To decipher this collective process, we combined two technological developments: porphyrin-based O₂ -sensing films and microfluidic O₂ gradient generators. We showed that Dictyostelium cells exhibit aerotactic and aerokinetic response in a low range of O₂ concentration indicative of a very efficient detection mechanism. Cell behaviors under self-generated or imposed O₂ gradients were modeled using an in silico cellular Potts model built on experimental observations. This computational model was complemented with a parsimonious ‘Go or Grow’ partial differential equation (PDE) model. In both models, we found that the collective migration of a dense ring can be explained by the interplay between cell division and the modulation of aerotaxis.

Genetic signatures of divergent selection in European beech (Fagus sylvatica L.) are associated with the variation in temperature and precipitation across its distribution range

High genetic variation and extensive gene flow may help forest trees with adapting to ongoing climate change, yet the genetic bases underlying their adaptive potential remain largely unknown. We investigated range-wide patterns of potentially adaptive genetic variation in 64 populations of European beech (Fagus sylvatica L.) using 270 SNPs from 139 candidate genes involved either in phenology or in stress responses. We inferred neutral genetic structure and processes (drift and gene flow) and performed differentiation outlier analyses and gene-environment association (GEA) analyses to detect signatures of divergent selection. Beech range-wide genetic structure was consistent with the species' previously identified postglacial expansion scenario and recolonization routes. Populations showed high diversity and low differentiation along the major expansion routes. A total of 52 loci were found to be putatively under selection and 15 of them turned up in multiple GEA analyses. Temperature and precipitation related variables were equally represented in significant genotype-climate associations. Signatures of divergent selection were detected in the same proportion for stress response and phenology-related genes. The range-wide adaptive genetic structure of beech appears highly integrated, suggesting a balanced contribution of phenology and stress-related genes to local adaptation, and of temperature and precipitation regimes to genetic clines. Our results imply a best-case scenario for the maintenance of high genetic diversity during range shifts in beech (and putatively other forest trees) with a combination of gene flow maintaining within-population neutral diversity and selection maintaining between-population adaptive differentiation.

Emerging strains of watermelon mosaic virus in Southeastern France: model-based estimation of the dates and places of introduction

Where and when alien organisms are successfully introduced are central questions to elucidate biotic and abiotic conditions favorable to the introduction, establishment and spread of invasive species. We propose a modelling framework to analyze multiple introductions by several invasive genotypes or genetic variants, in competition with a resident population, when observations provide knowledge on the relative proportions of each variant at some dates and places. This framework is based on a mechanistic-statistical model coupling a reaction–diffusion model with a probabilistic observation model. We apply it to a spatio-temporal dataset reporting the relative proportions of five genetic variants of watermelon mosaic virus (WMV, genus Potyvirus, family Potyviridae) in infections of commercial cucurbit fields. Despite the parsimonious nature of the model, it succeeds in fitting the data well and provides an estimation of the dates and places of successful introduction of each emerging variant as well as a reconstruction of the dynamics of each variant since its introduction.

Dioecy Is Associated with High Genetic Diversity and Adaptation Rates in the Plant Genus Silene

About 15,000 angiosperm species (∼6%) have separate sexes, a phenomenon known as dioecy. Why dioecious taxa are so rare is still an open question. Early work reported lower species richness in dioecious compared with nondioecious sister clades, raising the hypothesis that dioecy may be an evolutionary dead-end. This hypothesis has been recently challenged by macroevolutionary analyses that detected no or even positive effect of dioecy on diversification. However, the possible genetic consequences of dioecy at the population level, which could drive the long-term fate of dioecious lineages, have not been tested so far. Here, we used a population genomics approach in the Silene genus to look for possible effects of dioecy, especially for potential evidence of evolutionary handicaps of dioecy underlying the dead-end hypothesis. We collected individual-based RNA-seq data from several populations in 13 closely related species with different sexual systems: seven dioecious, three hermaphroditic, and three gynodioecious species. We show that dioecy is associated with increased genetic diversity, as well as higher selection efficacy both against deleterious mutations and for beneficial mutations. The results hold after controlling for phylogenetic inertia, differences in species census population sizes and geographic ranges. We conclude that dioecious Silene species neither show signs of increased mutational load nor genetic evidence for extinction risk. We discuss these observations in the light of the possible demographic differences between dioecious and self-compatible hermaphroditic species and how this could be related to alternatives to the dead-end hypothesis to explain the rarity of dioecy.

Weak founder effects but significant spatial genetic imprint of recent contraction and expansion of European beech populations

Understanding the ecological and evolutionary processes occurring during species range shifts is important in the current context of global change. Here, we investigate the interplay between recent expansion, gene flow and genetic drift, and their consequences for genetic diversity and structure at landscape and local scales in European beech (Fagus sylvatica L.) On Mont Ventoux, South-Eastern France, we located beech forest refugia at the time of the most recent population minimum, ~150 years ago, and sampled 71 populations (2042 trees) in both refugia and expanding populations over an area of 15,000 ha. We inferred patterns of gene flow and genetic structure using 12 microsatellite markers. We identified six plots as originating from planting, rather than natural establishment, mostly from local genetic material. Comparing genetic diversity and structure in refugia versus recent populations did not support the existence of founder effects: heterozygosity (He = 0.667) and allelic richness (Ar = 4.298) were similar, and FST was low (0.031 overall). Still, significant spatial evidence of colonization was detected, with He increasing along the expansion front, while genetic differentiation from the entire pool (βWT) decreased. Isolation by distance was found in refugia but not in recently expanding populations. Our study indicates that beech capacities for colonization and gene flow were sufficient to preserve genetic diversity despite recent forest contraction and expansion. Because beech has long distance pollen and seed dispersal, these results illustrate a 'best case scenario' for the maintenance of high genetic diversity and adaptive potential under climate-change-related range change.

Dispersal and Good Habitat Quality Promote Neutral Genetic Diversity in Metapopulations

Dispersal is a fundamental and crucial ecological process for a metapopulation to survive in heterogeneous or changing habitats. In this paper, we investigate the effect of the habitat quality and the dispersal on the neutral genetics diversity of a metapopulation. We model the metapopulation dynamics on heterogeneous habitats using a deterministic system of ordinary differential equations. We decompose the metapopulation into several neutral genetic fractions seeing as they could be located in different habitats. By using a mathematical model which describes their temporal dynamics inside the metapopulation, we provide the analytical results of their transient dynamics, as well as their asymptotic proportion in the different habitats. The diversity indices show how the genetic diversity at a global metapopulation scale is preserved by the correlation of two factors: the dispersal of the population, as well as the existence of adequate and sufficiently large habitats. The diversity indices show how the genetic diversity at a global metapopulation scale is preserved by the correlation of two factors: the dispersal of the population as well as the existence of adequate and sufficiently large habitats. Moreover, they ensure genetic diversity at the local habitat scale. In a source-sink metapopulation, we demonstrate that the diversity of the sink can be rescued if the condition of the sink is not too deteriorated and the migration from the source is larger than the migration from the sink. Furthermore, our study provides an analytical insight into the dynamics of the solutions of the systems of ordinary differential equations.

Anthropogenic hybridization at sea: three evolutionary questions relevant to invasive species management

Species introductions promote secondary contacts between taxa with long histories of allopatric divergence. Anthropogenic contact zones thus offer valuable contrasts to speciation studies in natural systems where past spatial isolations may have been brief or intermittent. Investigations of anthropogenic hybridization are rare for marine animals, which have high fecundity and high dispersal ability, characteristics that contrast to most terrestrial animals. Genomic studies indicate that gene flow can still occur after millions of years of divergence, as illustrated by invasive mussels and tunicates. In this context, we highlight three issues: (i) the effects of high propagule pressure and demographic asymmetries on introgression directionality, (ii) the role of hybridization in preventing introduced species spread, and (iii) the importance of postzygotic barriers in maintaining reproductive isolation. Anthropogenic contact zones offer evolutionary biologists unprecedented large scale hybridization experiments. In addition to breaking the highly effective reproductive isolating barrier of spatial segregation, they allow researchers to explore unusual demographic contexts with strong asymmetries. The outcomes are diverse, from introgression swamping to strong barriers to gene flow, and lead to local containment or widespread invasion. These outcomes should not be neglected in management policies of marine invasive species. This article is part of the theme issue 'Towards the completion of speciation: the evolution of reproductive isolation beyond the first barriers'.

Analysis of the Fisher-KPP equation with a time-dependent Allee effect

In this short note, we study the Fisher-KPP population model with a time-dependent Allee threshold. We consider the time dependence as sinusoidal functions and rational functions as they relate to varying environmental situations of the model. Employing the generalized Riccati equation mapping method, we obtain exact traveling wave solutions. Also, when the time-dependent Allee threshold decays to a constant value, we recover the traveling wave solution of the degenerate Fitzhugh-Nagumo equation from our general solution.

The spatial Muller's ratchet: Surfing of deleterious mutations during range expansion

During a range expansion, deleterious mutations can "surf" on the colonization front. The resultant decrease in fitness is known as expansion load. An Allee effect is known to reduce the loss of genetic diversity of expanding populations, by changing the nature of the expansion from "pulled" to "pushed". We study the impact of an Allee effect on the formation of an expansion load with a new model, in which individuals have the genetic structure of a Muller's ratchet. A key feature of Muller's ratchet is that the population fatally accumulates deleterious mutations due to the stochastic loss of the fittest individuals, an event called a click of the ratchet. We observe fast clicks of the ratchet at the colonization front owing to small population size, followed by a slow fitness recovery due to migration of fit individuals from the bulk of the population, leading to a transient expansion load. For large population size, we are able to derive quantitative features of the expansion wave, such as the wave speed and the frequency of individuals carrying a given number of mutations. Using simulations, we show that the presence of an Allee effect reduces the rate at which clicks occur at the front, and thus reduces the expansion load.

A Non-local Cross-Diffusion Model of Population Dynamics II: Exact, Approximate, and Numerical Traveling Waves in Single- and Multi-species Populations

We study traveling waves in a non-local cross-diffusion-type model, where organisms move along gradients in population densities. Such models are valuable for understanding waves of migration and invasion and how directed motion can impact such scenarios. In this paper, we demonstrate the emergence of traveling wave solutions, studying properties of both planar and radial wave fronts in one- and two-species variants of the model. We compute exact traveling wave solutions in the purely diffusive case and then perturb these solutions to analytically capture the influence directed motion has on these exact solutions. Using linear stability analysis, we find that the minimum wavespeeds correspond to the purely diffusive case, but numerical simulations suggest that advection can in general increase or decrease the observed wavespeed substantially, which allows a single species to more rapidly move into unoccupied resource-rich spatial regions or modify the speed of an invasion for two populations. We also find interesting effects from the non-local interactions in the model, suggesting that single species invasions can be enhanced with stronger non-locality, but that invasion of a competitive species may be slowed due to this non-local effect. Finally, we simulate pattern formation behind waves of invasion, showing that directed motion can have substantial impacts not only on wavespeed but also on the existence and structure of emergent patterns, as predicted in the first part of our study (Taylor et al. in Bull Math Biol, 2020).

Dispersal evolution diminishes the negative density dependence in dispersal

In many organisms, dispersal varies with the local population density. Such patterns of density-dependent dispersal (DDD) are expected to shape the dynamics, spatial spread, and invasiveness of populations. Despite their ecological importance, empirical evidence for the evolution of DDD patterns remains extremely scarce. This is especially relevant because rapid evolution of dispersal traits has now been empirically confirmed in several taxa. Changes in DDD of dispersing populations could help clarify not only the role of DDD in dispersal evolution, but also the possible pattern of subsequent range expansion. Here, we investigate the relationship between dispersal evolution and DDD using a long-term experimental evolution study on Drosophila melanogaster. We compared the DDD patterns of four dispersal-selected populations and their non-selected controls. The control populations showed negative DDD, which was stronger in females than in males. In contrast, the dispersal-selected populations showed DDD, where neither males nor females exhibited DDD. We compare our results with previous evolutionary predictions that focused largely on positive DDD, and highlight how the direction of evolutionary change depends on the initial DDD pattern of a population. Finally, we discuss the implications of DDD evolution for spatial ecology and evolution.

Inside Dynamics of Integrodifference Equations with Mutations

The method of inside dynamics provides a theory that can track the dynamics of neutral gene fractions in spreading populations. However, the role of mutations has so far been absent in the study of the gene flow of neutral fractions via inside dynamics. Using integrodifference equations, we develop a neutral genetic mutation model by extending a previously established scalar inside dynamics model. To classify the mutation dynamics, we define a mutation class as the set of neutral fractions that can mutate into one another. We show that the spread of neutral genetic fractions is dependent on the leading edge of population as well as the structure of the mutation matrix. Specifically, we show that the neutral fractions that contribute to the spread of the population must belong to the same mutation class as the neutral fraction found in the leading edge of the population. We prove that the asymptotic proportion of individuals at the leading edge of the population spread is given by the dominant right eigenvector of the associated mutation matrix, independent of growth and dispersal parameters. In addition, we provide numerical simulations to demonstrate our mathematical results, to extend their generality and to develop new conjectures about our model.

Dynamic range expansion leads to establishment of a new, genetically distinct wolf population in Central Europe

Local extinction and recolonization events can shape genetic structure of subdivided animal populations. The gray wolf (Canis lupus) was extirpated from most of Europe, but recently recolonized big part of its historical range. An exceptionally dynamic expansion of wolf population is observed in the western part of the Great European Plain. Nonetheless, genetic consequences of this process have not yet been fully understood. We aimed to assess genetic diversity of this recently established wolf population in Western Poland (WPL), determine its origin and provide novel data regarding the population genetic structure of the grey wolf in Central Europe. We utilized both spatially explicit and non-explicit Bayesian clustering approaches, as well as a model-independent, multivariate method DAPC, to infer genetic structure in large dataset (881 identified individuals) of wolf microsatellite genotypes. To put the patterns observed in studied population into a broader biogeographic context we also analyzed a mtDNA control region fragment widely used in previous studies. In comparison to a source population, we found slightly reduced allelic richness and heterozygosity in the newly recolonized areas west of the Vistula river. We discovered relatively strong west-east structuring in lowland wolves, probably reflecting founder-flush and allele surfing during range expansion, resulting in clear distinction of WPL, eastern lowland and Carpathian genetic groups. Interestingly, wolves from recently recolonized mountainous areas (Sudetes Mts, SW Poland) clustered together with lowland, but not Carpathian wolf populations. We also identified an area in Central Poland that seems to be a melting pot of western, lowland eastern and Carpathian wolves. We conclude that the process of dynamic recolonization of Central European lowlands lead to the formation of a new, genetically distinct wolf population. Together with the settlement and establishment of packs in mountains by lowland wolves and vice versa, it suggests that demographic dynamics and possibly anthropogenic barriers rather than ecological factors (e.g. natal habitat-biased dispersal patterns) shape the current wolf genetic structure in Central Europe.

Cooperation mitigates diversity loss in a spatially expanding microbial population

Spatially expanding populations lose genetic diversity rapidly because of repeated bottlenecks formed at the colonization front. However, the rate of diversity loss depends on the specifics of the expanding population, such as its growth and dispersal dynamics. We have previously demonstrated that changing the amount of within-species cooperation leads to a qualitative transition in the nature of expansion from pulled (driven by growth at the low-density tip) to pushed (driven by migration from the high-density region at the front, but behind the tip). Here we demonstrate experimentally that pushed waves result in strongly reduced genetic drift during range expansions, thus preserving genetic diversity in the newly colonized region.

The evolution and potentially even the survival of a spatially expanding population depends on its genetic diversity, which can decrease rapidly due to a serial founder effect. The strength of the founder effect is predicted to depend strongly on the details of the growth dynamics. Here, we probe this dependence experimentally using a single microbial species, Saccharomyces cerevisiae, expanding in multiple environments that induce varying levels of cooperativity during growth. We observe a drastic reduction in diversity during expansions when yeast grows noncooperatively on simple sugars, but almost no loss of diversity when cooperation is required to digest complex metabolites. These results are consistent with theoretical expectations: When cells grow independently from each other, the expansion proceeds as a pulled wave driven by growth at the low-density tip of the expansion front. Such populations lose diversity rapidly because of the strong genetic drift at the expansion edge. In contrast, diversity loss is substantially reduced in pushed waves that arise due to cooperative growth. In such expansions, the low-density tip of the front grows much more slowly and is often reseeded from the genetically diverse population core. Additionally, in both pulled and pushed expansions, we observe a few instances of abrupt changes in allele fractions due to rare fluctuations of the expansion front and show how to distinguish such rapid genetic drift from selective sweeps.

The ecology of predispersal insect herbivory on tree reproductive structures in natural forest ecosystems

Plant-insect interactions are key model systems to assess how some species affect the distribution, the abundance, and the evolution of others. Tree reproductive structures represent a critical resource for many insect species, which can be likely drivers of demography, spatial distribution, and trait diversification of plants. In this review, we present the ecological implications of predispersal herbivory on tree reproductive structures by insects (PIHR) in forest ecosystems. Both insect's and tree's perspectives are addressed with an emphasis on how spatiotemporal variation and unpredictability in seed availability can shape such particular plant-animal interactions. Reproductive structure insects show strong trophic specialization and guild diversification. Insects evolved host selection and spatiotemporal dispersal strategies in response to variable and unpredictable abundance of reproductive structures in both space and time. If PIHR patterns have been well documented in numerous systems, evidences of the subsequent demographic and evolutionary impacts on tree populations are still constrained by time-scale challenges of experimenting on such long-lived organisms, and modeling approaches of tree dynamics rarely consider PIHR when including biotic interactions in their processes. We suggest that spatially explicit and mechanistic approaches of the interactions between individual tree fecundity and insect dynamics will clarify predictions of the demogenetic implications of PIHR in tree populations. In a global change context, further experimental and theoretical contributions to the likelihood of life-cycle disruptions between plants and their specialized herbivores, and to how these changes may generate novel dynamic patterns in each partner of the interaction are increasingly critical.

Long-distance pollen dispersal during recent colonization favors a rapid but partial recovery of genetic diversity in Picea sitchensis

Tree species in the northern hemisphere are currently subject to rapid anthropogenic climate change and are shifting their ranges in response. This prompts questions about the mechanisms allowing tree populations to respond quickly to selection pressures when establishing into new areas. Focusing on the northern expanding range edge of Picea sitchensis, a widespread conifer of western North America, we ask how genetic structure and diversity develop during colonization, and assess the role of demographic history in shaping the evolutionary trajectory of an establishing population. We combined 500 yr of tree-ring and genotyping-by-sequencing data in 639 trees at the expansion front on the Kodiak Archipelago. We show that alleles accumulated rapidly during an increase in recruitment rate in the early 1700s. A shift from foreign to local pollen flow subsequently homogenized genetic structure at the expansion front. Taking advantage of the exceptional longevity of conifers, we highlight the major role of long-distance pollen dispersal in the rapid but incomplete recovery of genetic diversity during the initial stages of colonization. We also warn that slow initial population growth as well as long-lasting dominance of local gene flow by early founders could increase evolutionary load under a rapidly changing climate.

Local adaptation, dispersal evolution, and the spatial eco-evolutionary dynamics of invasion

Local adaptation and dispersal evolution are key evolutionary processes shaping the invasion dynamics of populations colonizing new environments. Yet their interaction is largely unresolved. Using a single-species population model along a one-dimensional environmental gradient, we show how local competition and dispersal jointly shape the eco-evolutionary dynamics and speed of invasion. From a focal introduction site, the generic pattern predicted by our model features a temporal transition from wave-like to pulsed invasion. Each regime is driven primarily by local adaptation, while the transition is caused by eco-evolutionary feedbacks mediated by dispersal. The interaction range and cost of dispersal arise as key factors of the duration and speed of each phase. Our results demonstrate that spatial eco-evolutionary feedbacks along environmental gradients can drive strong temporal variation in the rate and structure of population spread, and must be considered to better understand and forecast invasion rates and range dynamics.

Loss of genetic diversity, recovery and allele surfing in a colonizing parasite, Geomydoecus aurei

Understanding the genetic consequences of changes in species distributions has wide-ranging implications for predicting future outcomes of climate change, for protecting threatened or endangered populations and for understanding the history that has led to current genetic patterns within species. Herein, we examine the genetic consequences of range expansion over a 25-year period in a parasite (Geomydoecus aurei) that is in the process of expanding its geographic range via invasion of a novel host. By sampling the genetics of 1,935 G. aurei lice taken from 64 host individuals collected over this time period using 12 microsatellite markers, we test hypotheses concerning linear spatial expansion, genetic recovery time and allele surfing. We find evidence of decreasing allelic richness (AR) with increasing distance from the source population, supporting a linear, stepping stone model of spatial expansion that emphasizes the effects of repeated bottleneck events during colonization. We provide evidence of post-bottleneck genetic recovery, with average AR of infrapopulations increasing about 30% over the 225-generation span of time observed directly in this study. Our estimates of recovery rate suggest, however, that recovery has plateaued and that this population may not reach genetic diversity levels of the source population without further immigration from the source population. Finally, we employ a grid-based sampling scheme in the region of ongoing population expansion and provide empirical evidence for the power of allele surfing to impart genetic structure on a population, even under conditions of selective neutrality and in a place that lacks strong barriers to gene flow.

Its all about connections: hubs and invasion in habitat networks

During the early stages of invasion, the interaction between the features of the invaded landscape, notably its spatial structure, and the internal dynamics of an introduced population has a crucial impact on establishment and spread. By approximating introduction areas as networks of patches linked by dispersal, we characterised their spatial structure with specific metrics and tested their impact on two essential steps of the invasion process: establishment and spread. By combining simulations with experimental introductions of Trichogramma chilonis (Hymenoptera: Trichogrammatidae) in artificial laboratory microcosms, we demonstrated that spread was hindered by clusters and accelerated by hubs but was also affected by small-population mechanisms prevalent for invasions, such as Allee effects. Establishment was also affected by demographic mechanisms, in interaction with network metrics. These results highlight the importance of considering the demography of invaders as well as the structure of the invaded area to predict the outcome of invasions.

Causes and Consequences of Spatial Within-Host Viral Spread

The spread of viral pathogens both between and within hosts is inherently a spatial process. While the spatial aspects of viral spread at the epidemiological level have been increasingly well characterized, the spatial aspects of viral spread within infected hosts are still understudied. Here, with a focus on influenza A viruses (IAVs), we first review experimental studies that have shed light on the mechanisms and spatial dynamics of viral spread within hosts. These studies provide strong empirical evidence for highly localized IAV spread within hosts. Since mathematical and computational within-host models have been increasingly used to gain a quantitative understanding of observed viral dynamic patterns, we then review the (relatively few) computational modeling studies that have shed light on possible factors that structure the dynamics of spatial within-host IAV spread. These factors include the dispersal distance of virions, the localization of the immune response, and heterogeneity in host cell phenotypes across the respiratory tract. While informative, we find in these studies a striking absence of theoretical expectations of how spatial dynamics may impact the dynamics of viral populations. To mitigate this, we turn to the extensive ecological and evolutionary literature on range expansions to provide informed theoretical expectations. We find that factors such as the type of density dependence, the frequency of long-distance dispersal, specific life history characteristics, and the extent of spatial heterogeneity are critical factors affecting the speed of population spread and the genetic composition of spatially expanding populations. For each factor that we identified in the theoretical literature, we draw parallels to its analog in viral populations. We end by discussing current knowledge gaps related to the spatial component of within-host IAV spread and the potential for within-host spatial considerations to inform the development of disease control strategies.

Heterogeneity in local density allows a positive evolutionary relationship between self-fertilisation and dispersal

Despite empirical evidence for a positive relationship between dispersal and self-fertilization (selfing), theoretical work predicts that these traits should always be negatively correlated, and the Good Coloniser Syndrome of high dispersal and selfing (Cf. Baker's Law) should not evolve. Critically, previous work assumes that adult density is spatiotemporally homogeneous, so selfing results in identical offspring production for all patches, eliminating the benefit of dispersal for escaping from local resource competition. We investigate the joint evolution of dispersal and selfing in a demographically structured metapopulation model where local density is spatiotemporally heterogeneous due to extinction-recolonization dynamics. Selfing alleviates outcrossing failure due to low local density (an Allee effect) while dispersal alleviates competition through dispersal of propagules from high- to low-density patches. Because local density is spatiotemporally heterogeneous in our model, selfing does not eliminate heterogeneity in competition, so dispersal remains beneficial even under full selfing. Hence the Good Coloniser Syndrome is evolutionarily stable under a broad range of conditions, and both negative and positive relationships between dispersal and selfing are possible, depending on the environment. Our model thus accommodates positive empirical relationships between dispersal and selfing not predicted by previous theoretical work and provides additional explanations for negative relationships.

Invoking adaptation to decipher the genetic legacy of past climate change

Persistence of natural populations during periods of climate change is likely to depend on migration (range shifts) or adaptation. These responses were traditionally considered discrete processes and conceptually divided into the realms of ecology and evolution. In a milestone paper, Davis and Shaw (2001) Science 292:673 argued that the interplay of adaptation and migration was central to biotic responses to Quaternary climate, but since then there has been no synthesis of efforts made to set up this research program. Here we review some of the salient findings from molecular genetic studies assessing ecological and evolutionary responses to Quaternary climate change. These studies have revolutionized our understanding of population processes associated with past species migration. However, knowledge remains limited about the role of natural selection for local adaptation of populations to Quaternary environmental fluctuations and associated range shifts, and for the footprints this might have left on extant populations. Next-generation sequencing technologies, high-resolution paleoclimate analyses, and advances in population genetic theory offer an unprecedented opportunity to test hypotheses about adaptation through time. Recent population genomics studies have greatly improved our understanding of the role of contemporary adaptation to local environments in shaping spatial patterns of genetic diversity across modern-day landscapes. Advances in this burgeoning field provide important conceptual and methodological bases to decipher the historical role of natural selection and assess adaptation to past environmental variation. We suggest that a process called "temporal conditional neutrality" has taken place: some alleles favored in glacial environments become selectively neutral in modern-day conditions, whereas some alleles that had been neutral during glacial periods become under selection in modern environments. Building on this view, we present a new integrative framework for addressing the interplay of demographic and adaptive evolutionary responses to Quaternary climate dynamics, the research agenda initially envisioned by Davis and Shaw (2001) Science 292:673.

Fluctuations uncover a distinct class of traveling waves

Epidemics, flame propagation, and cardiac rhythms are classic examples of reaction-diffusion waves that describe a switch from one alternative state to another. Only two types of waves are known: pulled, driven by the leading edge, and pushed, driven by the bulk of the wave. Here, we report a distinct class of semipushed waves for which both the bulk and the leading edge contribute to the dynamics. These hybrid waves have the kinetics of pushed waves, but exhibit giant fluctuations similar to pulled waves. The transitions between pulled, semipushed, and fully pushed waves occur at universal ratios of the wave velocity to the Fisher velocity. We derive these results in the context of a species invading a new habitat by examining front diffusion, rate of diversity loss, and fluctuation-induced corrections to the expansion velocity. All three quantities decrease as a power law of the population density with the same exponent. We analytically calculate this exponent, taking into account the fluctuations in the shape of the wave front. For fully pushed waves, the exponent is -1, consistent with the central limit theorem. In semipushed waves, however, the fluctuations average out much more slowly, and the exponent approaches 0 toward the transition to pulled waves. As a result, a rapid loss of genetic diversity and large fluctuations in the position of the front occur, even for populations with cooperative growth and other forms of an Allee effect. The evolutionary outcome of spatial spreading in such populations could therefore be less predictable than previously thought.