The genetic signature of rapid range expansions: How dispersal,growth and invasion speed impact heterozygosity and allele surfing

As researchers collect spatiotemporal population and genetic data in tandem, models that connect demography and dispersal to genetics are increasingly relevant. The dominant spatiotemporal model of invasion genetics is the stepping-stone model which represents a gradual range expansion in which individuals jump to uncolonized locations one step at a time. However, many range expansions occur quickly as individuals disperse far from currently colonized regions. For these types of expansion, stepping-stone models are inappropriate. To more accurately reflect wider dispersal in many organisms, we created kernel-based models of invasion genetics based on integrodifference equations. Classic theory relating to integrodifference equations suggests that the speed of range expansions is a function of population growth and dispersal. In our simulations, populations that expanded at the same speed but with spread rates driven by dispersal retained more heterozygosity along axes of expansion than range expansions with rates of spread that were driven primarily by population growth. To investigate surfing we introduced mutant alleles in wave fronts of simulated range expansions. In our models based on random mating, surfing alleles remained at relatively low frequencies and surfed less often compared to previous results based on stepping-stone simulations with asexual reproduction.     

Recolonisation by diffusion can generate increasing rates of spread

Diffusion is one of the most frequently used assumptions to explain dispersal. Diffusion models and in particular reaction-diffusion equations usually lead to solutions moving at constant speeds, too slow compared to observations. As early as 1899, Reid had found that the rate of spread of tree species migrating to northern environments at the beginning of the Holocene was too fast to be explained by diffusive dispersal. Rapid spreading is generally explained using long distance dispersal events, modelled through integro-differential equations (IDEs) with exponentially unbounded (EU) kernels, i.e. decaying slower than any exponential. We show here that classical reaction-diffusion models of the Fisher-Kolmogorov-Petrovsky-Piskunov type can produce patterns of colonisation very similar to those of IDEs, if the initial population is EU at the beginning of the considered colonisation event. Many similarities between reaction-diffusion models with EU initial data and IDEs with EU kernels are found; in particular comparable accelerating rates of spread and flattening of the solutions. There was previously no systematic mathematical theory for such reaction-diffusion models with EU initial data. Yet, EU initial data can easily be understood as consequences of colonisation-retraction events and lead to fast spreading and accelerating rates of spread without the long distance hypothesis.     

Accelerating invasion rates result from the evolution of density-dependent dispersal

Evolutionary processes play an important role in shaping the dynamics of range expansions, and selection on dispersal propensity has been demonstrated to accelerate rates of advance. Previous theory has considered only the evolution of unconditional dispersal rates, but dispersal is often more complex. For example, many species emigrate in response to crowding. Here, we use an individual-based model to investigate the evolution of density dependent dispersal into empty habitat, such as during an invasion. The landscape is represented as a lattice and dispersal between populations follows a stepping-stone pattern. Individuals carry three ‘genes’ that determine their dispersal strategy when experiencing different population densities. For a stationary range we obtain results consistent with previous theoretical studies: few individuals emigrate from patches that are below equilibrium density. However, during the range expansion of a previously stationary population, we observe evolution towards dispersal strategies where considerable emigration occurs well below equilibrium density. This is true even for moderate costs to dispersal, and always results in accelerating rates of range expansion. Importantly, the evolution we observe at an expanding front depends upon fitness integrated over several generations and cannot be predicted by a consideration of lifetime reproductive success alone. We argue that a better understanding of the role of density dependent dispersal, and its evolution, in driving population dynamics is required especially within the context of range expansions.     

Invasion by extremes: population spread with variation in dispersal and reproduction

For populations having dispersal described by fat-tailed kernels (kernels with tails that are not exponentially bounded), asymptotic population spread rates cannot be estimated by traditional models because these models predict continually accelerating (asymptotically infinite) invasion. The impossible predictions come from the fact that the fat-tailed kernels fitted to dispersal data have a quality (nondiscrete individuals and, thus, no moment-generating function) that never applies to data. Real organisms produce finite (and random) numbers of offspring; thus, an empirical moment-generating function can always be determined. Using an alternative method to estimate spread rates in terms of extreme dispersal events, we show that finite estimates can be derived for fat-tailed kernels, and we demonstrate how variable reproduction modifies these rates. Whereas the traditional models define spread rate as the speed of an advancing front describing the expected density of individuals, our alternative definition for spread rate is the expected velocity for the location of the furthest-forward individual in the population. The asymptotic wave speed for a constant net reproductive rate R0 is approximated as (1/T)(piuR)/2)(1/2) m yr(-1), where T is generation time, and u is a distance parameter (m2) of Clark et al.'s 2Dt model having shape parameter p = 1. From fitted dispersal kernels with fat tails and infinite variance, we derive finite rates of spread and a simple method for numerical estimation. Fitted kernels, with infinite variance, yield distributions of rates of spread that are asymptotically normal and, thus, have finite moments. Variable reproduction can profoundly affect rates of spread. By incorporating the variance in reproduction that results from variable life span, we estimate much lower rates than predicted by the standard approach, which assumes a constant net reproductive rate. Using basic life-history data for trees, we show these estimated rates to be lower than expected from previous analytical models and as interpreted from paleorecords of forest spread at the end of the Pleistocene. Our results suggest reexamination of past rates of spread and the potential for future response to climate change.     

Spatial Assortment of Mixed Propagules Explains the Acceleration of Range Expansion

Range expansion of spreading organisms has been found to follow three types: (i) linear expansion with a constant rate of spread; (ii) bi-phase expansion with a faster linear expansion following a slower linear expansion; and (iii) accelerating expansion with a continuously increasing rate of spread. To date, no overarching formula exists that can be applied to all three types of range expansion. We investigated how propagule pressure, i.e., the initial number of individuals and their composition in terms of dispersal ability, affects the spread of a population. A system of integrodifference equations was then used to model the spatiotemporal dynamics of the population. We studied the dynamics of dispersal ability as well as the instantaneous and asymptotic rate of spread. We found that individuals with different dispersal abilities were spatially sorted with the stronger dispersers situated at the expanding range front, causing the velocity of expansion to accelerate. The instantaneous rate of spread was found to be fully determined by the growth and dispersal abilities of the population at the advancing edge of the invasion. We derived a formula for the asymptotic rate of spread under different scenarios of propagule pressure. The results suggest that data collected from the core of the invasion may underestimate the spreading rate of the population. Aside from better managing of invasive species, the derived formula could conceivably also be applied to conservation management of relocated, endangered or extra-limital species.     

A toad more traveled: the heterogeneous invasion dynamics of cane toads in Australia

To predict the spread of invasive species, we need to understand the mechanisms that underlie their range expansion. Assuming random diffusion through homogeneous environments, invasions are expected to progress at a constant rate. However, environmental heterogeneity is expected to alter diffusion rates, especially by slowing invasions as populations encounter suboptimal environmental conditions. Here, we examine how environmental and landscape factors affect the local invasion speeds of cane toads (Chaunus [Bufo] marinus) in Australia. Using high-resolution cane toad data, we demonstrate heterogeneous regional invasion dynamics that include both decelerating and accelerating range expansions. Toad invasion speed increased in regions characterized by high temperatures, heterogeneous topography, low elevations, dense road networks, and high patch connectivity. Regional increases in the toad invasion rate might be caused by environmental conditions that facilitate toad reproduction and movement, by the evolution of long-distance dispersal ability, or by some combination of these factors. In any case, theoretical predictions that neglect environmental influences on dispersal at multiple spatial scales may prove to be inaccurate. Early predictions of cane toad range expansion rates that assumed constant diffusion across homogeneous landscapes already have been proved wrong. Future attempts to predict range dynamics for invasive species should consider heterogeneity in (1) the environmental factors that determine dispersal rates and (2) the mobility of invasive populations because dispersal-relevant traits can evolve in exotic habitats. As an invasive species spreads, it is likely to encounter conditions that influence dispersal rates via one or both of these mechanisms.     

A spatial model for the spread of invading organisms subject to competition

 A spatially explicit integrodifference equation model is studied for the spread of an invading organism against an established competitor. Provided the invader is initially confined to a bounded region, the invasion spreads asymptotically as a travelling wave whose speed depends on the strength of the competitive interaction and on the dispersal characteristics of the invader. Even an inferior, but established, competitor can significantly reduce the invasion speed. The invasion speed is also influenced by the exact shape of the dispersal kernel (especially the thickness of the tail) as well as the mean dispersal distance for each generation. Received 10 April 1996; received in revised form 21 August 1996     

Reid's paradox revisited: the evolution of dispersal kernels during range expansion

Current approaches to modeling range advance assume that the distribution describing dispersal distances in the population (the "dispersal kernel") is a static entity. We argue here that dispersal kernels are in fact highly dynamic during periods of range advance because density effects and spatial assortment by dispersal ability ("spatial selection") drive the evolution of increased dispersal on the expanding front. Using a spatially explicit individual-based model, we demonstrate this effect under a wide variety of population growth rates and dispersal costs. We then test the possibility of an evolved shift in dispersal kernels by measuring dispersal rates in individual cane toads (Bufo marinus) from invasive populations in Australia (historically, toads advanced their range at 10 km/year, but now they achieve >55 km/year in the northern part of their range). Under a common-garden design, we found a steady increase in dispersal tendency with distance from the invasion origin. Dispersal kernels on the invading front were less kurtotic and less skewed than those from origin populations. Thus, toads have increased their rate of range expansion partly through increased dispersal on the expanding front. For accurate long-range forecasts of range advance, we need to take into account the potential for dispersal kernels to be evolutionarily dynamic.     

Dispersal polymorphism and the speed of biological invasions

The speed at which biological range expansions occur has important consequences for the conservation management of species experiencing climate change and for invasion by exotic organisms. Rates of dispersal and population growth are known to affect the speed of invasion, but little is known about the effect of having a community of dispersal phenotypes on the rate of range expansion. We use reaction-diffusion equations to model the invasion of a species with two dispersal phenotypes into a previously unoccupied landscape. These phenotypes differ in both their dispersal rate and population growth rate. We find that the presence of both phenotypes can result in faster range expansions than if only a single phenotype were present in the landscape. For biologically realistic parameters, the invasion can occur up to twice as fast as a result of this polymorphism. This has implications for predicting the speed of biological invasions, suggesting that speeds cannot just be predicted from looking at a single phenotype and that the full community of phenotypes needs to be taken into consideration.     

From introduction to equilibrium: reconstructing the invasive pathways of the Argentine ant in a Mediterranean region

Determining the geographical range of invasive species is an important component of formulating effective management strategies. In the absence of detailed distributional data, species distribution models can provide estimates of an invasion range and increase our understanding of the ecological processes acting at various spatial scales. We used two complementary approaches to evaluate the influence of historical and environmental factors in shaping the distribution of the Argentine ant ( Linepithema humile ), a widespread, highly invasive species native to South America. Occurrence data were combined with environmental data at incremental spatial scales (extent and resolution) to predict the suitable range of the ant invasion using ecological niche models. In addition, we also used a spread model that simulated the jump dispersal of the species to identify the most plausible scenarios of arrival of L. humile in the NE Iberian Peninsula at local scales. Based on the results of both modelling practices, we suggest that L. humile might have reached its maximum geographic range at regional scales in the NE Iberian Peninsula. However, the species does not appear in equilibrium with the environment at small spatial scales, and further expansions are expected along coastal and inland localities of the Costa Brava. Long-distance jumps are ultimately responsible for the spread of the Argentine ant in the area. Overall, our study shows the utility of combining niche based models with spread models to understand the dynamics of species' invasions.     

Evolution of dispersal and life history interact to drive accelerating spread of an invasive species

Populations on the edge of an expanding range are subject to unique evolutionary pressures acting on their life‐history and dispersal traits. Empirical evidence and theory suggest that traits there can evolve rapidly enough to interact with ecological dynamics, potentially giving rise to accelerating spread. Nevertheless, which of several evolutionary mechanisms drive this interaction between evolution and spread remains an open question. We propose an integrated theoretical framework for partitioning the contributions of different evolutionary mechanisms to accelerating spread, and we apply this model to invasive cane toads in northern Australia. In doing so, we identify a previously unrecognised evolutionary process that involves an interaction between life‐history and dispersal evolution during range shift. In roughly equal parts, life‐history evolution, dispersal evolution and their interaction led to a doubling of distance spread by cane toads in our model, highlighting the potential importance of multiple evolutionary processes in the dynamics of range expansion.     

Evolutionarily accelerated invasions: the rate of dispersal evolves upwards during the range advance of cane toads

Human activities are changing habitats and climates and causing species' ranges to shift. Range expansion brings into play a set of powerful evolutionary forces at the expanding range edge that act to increase dispersal rates. One likely consequence of these forces is accelerating rates of range advance because of evolved increases in dispersal on the range edge. In northern Australia, cane toads have increased their rate of spread fivefold in the last 70 years. Our breeding trials with toads from populations spanning the species' invasion history in Australia suggest a genetic basis to dispersal rates and interpopulation genetic variation in such rates. Toads whose parents were from the expanding range front dispersed faster than toads whose parents were from the core of the range. This difference reflects patterns found in their field-collected mothers and fathers and points to heritable variance in the traits that have accelerated the toads' rate of invasion across tropical Australia over recent decades. Taken together with demonstrated spatial assortment by dispersal ability occurring on the expanding front, these results point firmly to ongoing evolution as a driving force in the accelerated expansion of toads across northern Australia.     

Seed rain and environmental controls on invasion of <Emphasis Type="Italic">Picea abies</Emphasis> into grassland

Although changes in land-use, climate, and the spread of introduced tree species have increased the global importance of tree invasions into grasslands, our ability to predict any particular invasion is limited. To elucidate mechanisms driving tree invasions of grasslands, we studied in detail how seed dispersal and fine-scale environment control the expansion of an introduced Picea abies Karst. (Norway spruce) population into Western Carpathian grassland. We mapped invading trees and measured tree size, fecundity, seed rain, seedling density, plant community composition, and light and soil environment within a 200 × 60 m belt across the invasion front. Maximum likelihood estimates of dispersal kernels suggested peak seed deposition directly underneath tree crowns where germination was poor, but mean dispersal distances were sufficiently large to generate overlapping seed shadows from multiple trees that saturated the invasion front with seeds further away from seed-dispersing trees. Partial Mantel tests indicated that germinant density was affected considerably less by seed rain than by moss cover (r = 0.54), overstory tree influence (r = −0.32), soil moisture (r = 0.21), grass cover (r = −0.15), and diffuse radiation (r = 0.13). However, these variables were not independent but formed complex multivariate gradients within the invasion front. Moss cover and soil moisture were negatively correlated with overstory tree influence and the resulting gradient clearly affected germinant density (partial Mantel r = 0.45). In contrast, positively correlated light and grass cover defined a gradient related weakly to germinant density (partial Mantel r = 0.05) as it integrated opposing effects of these variables on germinants. Seedlings had similar environmental associations, but except for the lasting positive effects of moss these tended to weaken with seedling size. Although a few seedlings may establish and survive in the more adverse environment of the outer edges of the invasion front, a significant population expansion may require a gradual build-up of the critical density of invading trees to reduce grass cover and facilitate germination on moist mossy seedbeds within uncolonized areas. Thus, Picea abies appears more likely to spread within temperate grasslands by gradual expansion of its population frontier rather than by advanced groups.     

Sex and stochasticity affect range expansion of experimental invasions

Understanding and predicting range expansion are key objectives in many basic and applied contexts. Among dioecious organisms, there is strong evidence for sex differences in dispersal, which could alter the sex ratio at the expansion's leading edge. However, demographic stochasticity could also affect leading‐edge sex ratios, perhaps overwhelming sex‐biased dispersal. We used insects in laboratory mesocosms to test the effects of sex‐biased dispersal on range expansion, and a simulation model to explore interactive effects of sex‐biased dispersal and demographic stochasticity. Sex‐biased dispersal created spatial clines in the sex ratio, which influenced offspring production at the front and altered invasion velocity. Increasing female dispersal relative to males accelerated spread, despite the prediction that demographic stochasticity would weaken a signal of sex‐biased dispersal. Our results provide the first experimental evidence for an influence of sex‐biased dispersal on invasion velocity, highlighting the value of accounting for sex structure in studies of range expansion.     

Evolution of dispersal in explicitly spatial metacommunities

We apply an evolutionary game theoretic approach to the evolution of dispersal in explicitly spatial metacommunities, using a flexible parametric class of dispersal kernels, namely 2Dt kernels, and study the resulting evolutionary dynamics and outcomes. We observe strong selective pressure on mean dispersal distance (i.e., the first moment), and weaker, but significant, one on the shape of dispersal kernel (i.e., higher moments). We investigate the effects of landscape topology and spatial heterogeneity on the resulting ‘optimal’ dispersal kernels. The shape—importantly the tail structure—and stability of evolutionarily optimal dispersal strategies are strongly affected by landscape topology or connectivity. Specifically, the results suggest that the optimal dispersal kernels in the river network topology have heavier tails and are stable, while those in the direct topology, where organisms are allowed to travel directly from one location to another, have relatively thin tails and may be unstable. We also find that habitat spatial heterogeneity enables coexistence and controls spatial distribution of distinct groups of dispersal strategies and that alteration in topology alone may not be sufficient to change such coexistence. This work provides a tool to translate environmental changes such as global climate change and human intervention into changes in dispersal behavior, which in turn may lead to important alterations of biodiversity and biological invasion patterns.     

Dynamic expansion in recently introduced populations of fire ant parasitoids (Diptera: Phoridae)

Combating invasive species requires a detailed, mechanistic understanding of the manner and speed with which organisms expand their ranges. Biological control efforts provide an opportunity to study the process of species invasions and range expansions under known initial conditions. This study examines the rate, pattern and mechanisms of spread for two populations of the biological control agent Pseudacteon tricuspis, phorid-fly parasitoids of imported fire ants. We employ a trap-based survey method that detects phorid flies in low-density populations, and provides data on abundance. This technique allows us to differentiate between continuous population spread and effective long-distance dispersal and to examine density gradients of phorid flies across the expanding population front. We find that occupied sites in front of the leading edge of continuous populations were common; forming small populations we refer to as satellite populations. Satellite populations are tens of kilometers from the nearest possible source. Wind governs the dynamics of spread in these two central Texas populations. Population edges expanding with the wind exhibited a higher frequency of effective long-distance dispersal than did populations expanding into the wind. This enhanced effective long-distance dispersal rate translated into a five times faster rate of spread for population edges traveling with the wind. This planned invasion shares many characteristics in common with unplanned species invasions including: protracted establishment phase during which densities were below detection thresholds, and slow initial spread immediately after establishment followed by rapid, accelerating spread rates as population sizes grew.     

40年间红耳鹎在中国的分布变化探讨

红耳鹎(Pycnonotus jocosus)为华南区常见鸟类。我们在整理中国鹎科鸟类分布区变化情况时发现,2006年以来红耳鹎的地理分布范围发生较大的变化。本文收集整理了中国1976至2016年期间红耳鹎的分布信息,并利用GIS技术详细地描述分析了该物种的地理分布变化情况。结果显示,红耳鹎jocosus亚种的分布范围呈现一个辐射状的扩散趋势,且向北方地区迁移。除少数扩散属人为因素造成外,基本上都是自然扩散。本研究还初步讨论了生境选择、繁殖习性以及食性等生态特征对红耳鹎扩散的影响,并对该物种地理分布扩散可能造成的影响进行讨论。     

Shifting dispersal modes at an expanding species’ range margin

While it is generally recognized that noncontiguous (long‐distance) dispersal of small numbers of individuals is important for range expansion over large geographic areas, it is often assumed that colonization on more local scales proceeds by population expansion and diffusion dispersal (larger numbers of individuals colonizing adjacent sites). There are few empirical studies of dispersal modes at the front of expanding ranges, and very little information is available on dispersal dynamics at smaller geographic scales where we expect contiguous (diffusion) dispersal to be prevalent. We used highly polymorphic genetic markers to characterize dispersal modes at a local geographic scale for populations at the edge of the range of a newly invasive grass species (Brachypodium sylvaticum) that is undergoing rapid range expansion in the Pacific Northwest of North America. Comparisons of Bayesian clustering of populations, patterns of genetic diversity, and gametic disequilibrium indicate that new populations are colonized ahead of the invasion front by noncontiguous dispersal from source populations, with admixture occurring as populations age. This pattern of noncontiguous colonization was maintained even at a local scale. Absence of evidence for dispersal among adjacent pioneer sites at the edge of the expanding range of this species suggests that pioneer populations undergo an establishment phase during which they do not contribute emigrants for colonization of neighbouring sites. Our data indicate that dispersal modes change as the invasion matures: initial colonization processes appear to be dominated by noncontiguous dispersal from only a few sources, while contiguous dispersal may play a greater role once populations become established.     

Integrodifference model for blowfly invasion

We propose a stage-structured integrodifference model for blowflies’ growth and dispersion taking into account the density dependence of fertility and survival rates and the non-overlap of generations. We assume a discrete-time, stage-structured, model. The spatial dynamics is introduced by means of a redistribution kernel. We treat one and two dimensional cases, the latter on the semi-plane, with a reflexive boundary. We analytically show that the upper bound for the invasion front speed is the same as in the one-dimensional case. Using laboratory data for fertility and survival parameters and dispersal data of a single generation from a capture-recapture experiment in South Africa, we obtain an estimate for the velocity of invasion of blowflies of the species Chrysomya albiceps. This model predicts a speed of invasion which was compared to actual observational data for the invasion of the focal species in the Neotropics. Good agreement was found between model and observations.