Dispersal polymorphism and the speed of biological invasions

Travelling waves for a fast reaction limit of a discrete coagulation-fragmentation model with diffusion and proliferation

We study traveling wave solutions for a reaction-diffusion model, introduced in the article Calvez et al. (Regime switching on the propagation speed of travelling waves of some size-structured myxobacteriapopulation models, 2023), describing the spread of the social bacterium Myxococcus xanthus. This model describes the spatial dynamics of two different cluster sizes: isolated bacteria and paired bacteria. Two isolated bacteria can coagulate to form a cluster of two bacteria and conversely, a pair of bacteria can fragment into two isolated bacteria. Coagulation and fragmentation are assumed to occur at a certain rate denoted by k. In this article we study theoretically the limit of fast coagulation fragmentation corresponding mathematically to the limit when the value of the parameter k tends to + ∞ . For this regime, we demonstrate the existence and uniqueness of a transition between pulled and pushed fronts for a certain critical ratio θ ⋆ between the diffusion coefficient of isolated bacteria and the diffusion coefficient of paired bacteria. When the ratio is below θ ⋆ , the critical front speed is constant and corresponds to the linear speed. Conversely, when the ratio is above the critical threshold, the critical spreading speed becomes strictly greater than the linear speed.

Integrodifference models for evolutionary processes in biological invasions

Individual variability in dispersal and reproduction abilities can lead to evolutionary processes that may have significant effects on the speed and shape of biological invasions. Spatial sorting, an evolutionary process through which individuals with the highest dispersal ability tend to agglomerate at the leading edge of an invasion front, and spatial selection, spatially heterogeneous forces of selection, are among the fundamental evolutionary forces that can change range expansions. Most mathematical models for these processes are based on reaction-diffusion equations, i.e., time is continuous and dispersal is Gaussian. We develop novel theory for how evolution shapes biological invasions with integrodifference equations, i.e., time is discrete and dispersal can follow a variety of kernels. Our model tracks how the distribution of growth rates and dispersal ability in the population changes from one generation to the next in continuous space. We include mutation between types and a potential trade-off between dispersal ability and growth rate. We perform the analysis of such models in continuous and discrete trait spaces, i.e., we determine the existence of travelling wave solutions, asymptotic spreading speeds and their linear determinacy, as well as the population distributions at the leading edge. We also establish the relation between asymptotic spreading speeds and mutation probabilities. We observe conditions for when spatial sorting emerges and when it does not and also explore conditions where anomalous spreading speeds occur, as well as possible effects of deleterious mutations in the population.

Boldness and physiological variation in round goby populations along their Baltic Sea invasion front

The round goby (Neogobius melanostomus) is a fish native to the Ponto-Caspian region that is highly invasive through freshwater and brackish habitats in northern Europe and North America. Individual behavioural variation appears to be an important factor in their spread, for example a round goby's personality traits can influence their dispersal tendency, which may also produce variation in the behavioural composition of populations at different points along their invasion fronts. To further analyze the drivers of behavioural variation within invasive round goby populations, we focused on two populations along the Baltic Sea invasion front with closely comparable physical and community characteristics. Specifically, this study measured personality within a novel environment and predator response context (i.e., boldness), and directly analyzed links between individuals' personality traits and their physiological characteristics and stress responses (i.e., blood cortisol and lactate, brain neurotransmitters). In contrast to previous findings, the more recently established population had similar activity levels but were less bold in response to a predator cue than the older population, which suggests that behavioural compositions within our study populations may be more driven by local environmental conditions rather than being a result of personality-biased dispersal. Furthermore, we found that both populations showed similar physiological stress responses, and there also appeared to be no detectable relationship between physiological parameters and behavioural responses to predator cues. Instead, body size and body condition were important factors influencing individual behavioural responses. Overall, our results reinforce the importance of boldness traits as a form of phenotypic variation in round goby populations in the Baltic Sea. We also highlight the importance of these traits for future studies specifically testing for effects of invasion processes on phenotypic variation in the species. Nonetheless, our results also highlight that the physiological mechanisms underpinning behavioural variation in these populations remain unclear.

Anomalous invasion dynamics due to dispersal polymorphism and dispersal-reproduction trade-offs

Dispersal polymorphism and mutation play significant roles during biological invasions, potentially leading to evolution and complex behaviour such as accelerating or decelerating invasion fronts. However, life-history theory predicts that reproductive fitness-another key determinant of invasion dynamics-may be lower for more dispersive strains. Here, we use a mathematical model to show that unexpected invasion dynamics emerge from the combination of heritable dispersal polymorphism, dispersal-fitness trade-offs, and mutation between strains. We show that the invasion dynamics are determined by the trade-off relationship between dispersal and population growth rates of the constituent strains. We find that invasion dynamics can be 'anomalous' (i.e. faster than any of the strains in isolation), but that the ultimate invasion speed is determined by the traits of, at most, two strains. The model is simple but generic, so we expect the predictions to apply to a wide range of ecological, evolutionary, or epidemiological invasions.

Individual variation in dispersal and fecundity increases rates of spatial spread

Dispersal and fecundity are two fundamental traits underlying the spread of populations. Using integral difference equation models, we examine how individual variation in these fundamental traits and the heritability of these traits influence rates of spatial spread of populations along a one-dimensional transect. Using a mixture of analytic and numerical methods, we show that individual variation in dispersal rates increases spread rates and the more heritable this variation, the greater the increase. In contrast, individual variation in lifetime fecundity only increases spread rates when some of this variation is heritable. The highest increases in spread rates occur when variation in dispersal positively co-varies with fecundity. Our results highlight the importance of estimating individual variation in dispersal rates, dispersal syndromes in which fecundity and dispersal co-vary positively and heritability of these traits to predict population rates of spatial spread.

The interplay between movement, morphology and dispersal in Tetrahymena ciliates

Understanding how and why individual movement translates into dispersal between populations is a long-term goal in ecology. Movement is broadly defined as ‘any change in the spatial location of an individual’, whereas dispersal is more narrowly defined as a movement that may lead to gene flow. Because the former may create the condition for the latter, behavioural decisions that lead to dispersal may be detectable in underlying movement behaviour. In addition, dispersing individuals also have specific sets of morphological and behavioural traits that help them coping with the costs of movement and dispersal, and traits that mitigate costs should be under selection and evolve if they have a genetic basis. Here, we experimentally study the relationships between movement behaviour, morphology and dispersal across 44 genotypes of the actively dispersing unicellular, aquatic model organism Tetrahymena thermophila. We used two-patch populations to quantify individual movement trajectories, as well as activity, morphology and dispersal rate. First, we studied variation in movement behaviour among and within genotypes (i.e. between dispersers and residents) and tested whether this variation can be explained by morphology. Then, we addressed how much the dispersal rate is driven by differences in the underlying movement behaviour. Genotypes revealed clear differences in terms of movement speed and linearity. We also detected marked movement differences between resident and dispersing individuals, mediated by the genotype. Movement variation was partly explained by morphological properties such as cell size and shape, with larger cells consistently showing higher movement speed and higher linearity. Genetic differences in activity and movement were positively related to the observed dispersal and jointly explained 47% of the variation in dispersal rate. Our study shows that a detailed understanding of the interplay between morphology, movement and dispersal may have potential to improve dispersal predictions over broader spatio-temporal scales.

Individual Variability in Dispersal and Invasion Speed

We model the growth, dispersal and mutation of two phenotypes of a species using reaction–diffusion equations, focusing on the biologically realistic case of small mutation rates. Having verified that the addition of a small linear mutation term to a Lotka–Volterra system limits it to only two steady states in the case of weak competition, an unstable extinction state and a stable coexistence state, we exploit the fact that the spreading speed of the system is known to be linearly determinate to show that the spreading speed is a nonincreasing function of the mutation rate, so that greater mixing between phenotypes leads to slower propagation. We also find the ratio at which the phenotypes occur at the leading edge in the limit of vanishing mutation.

Landscape permeability and individual variation in a dispersal-linked gene jointly determine genetic structure in the Glanville fritillary butterfly

There is now clear evidence that species across a broad range of taxa harbor extensive heritable variation in dispersal. While studies suggest that this variation can facilitate demographic outcomes such as range expansion and invasions, few have considered the consequences of intraspecific variation in dispersal for the maintenance and distribution of genetic variation across fragmented landscapes. Here, we examine how landscape characteristics and individual variation in dispersal combine to predict genetic structure using genomic and spatial data from the Glanville fritillary butterfly. We used linear and latent factor mixed models to identify the landscape features that best predict spatial sorting of alleles in the dispersal-related gene phosphoglucose isomerase (Pgi). We next used structural equation modeling to test if variation in Pgi mediated gene flow as measured by Fst at putatively neutral loci. In a year when the population was recovering following a large decline, individuals with a genotype associated with greater dispersal ability were found at significantly higher frequencies in populations isolated by water and forest, and these populations showed lower levels of genetic differentiation at neutral loci. These relationships disappeared in the next year when metapopulation density was high, suggesting that the effects of individual variation are context dependent. Together our results highlight that (1) more complex aspects of landscape structure beyond just the configuration of habitat can be important for maintaining spatial variation in dispersal traits and (2) that individual variation in dispersal plays a key role in maintaining genetic variation across fragmented landscapes.

The invasion speed of cell migration models with realistic cell cycle time distributions

Cell proliferation is typically incorporated into stochastic mathematical models of cell migration by assuming that cell divisions occur after an exponentially distributed waiting time. Experimental observations, however, show that this assumption is often far from the real cell cycle time distribution (CCTD). Recent studies have suggested an alternative approach to modelling cell proliferation based on a multi-stage representation of the CCTD. In this paper we investigate the connection between the CCTD and the speed of the collective invasion. We first state a result for a general CCTD, which allows the computation of the invasion speed using the Laplace transform of the CCTD. We use this to deduce the range of speeds for the general case. We then focus on the more realistic case of multi-stage models, using both a stochastic agent-based model and a set of reaction-diffusion equations for the cells' average density. By studying the corresponding travelling wave solutions, we obtain an analytical expression for the speed of invasion for a general N-stage model with identical transition rates, in which case the resulting cell cycle times are Erlang distributed. We show that, for a general N-stage model, the Erlang distribution and the exponential distribution lead to the minimum and maximum invasion speed, respectively. This result allows us to determine the range of possible invasion speeds in terms of the average proliferation time for any multi-stage model.

Low genetic diversity contrasts with high phenotypic variability in heptaploid Spartina densiflora populations invading the Pacific coast of North America

Species can respond to environmental pressures through genetic and epigenetic changes and through phenotypic plasticity, but few studies have evaluated the relationships between genetic differentiation and phenotypic plasticity of plant species along changing environmental conditions throughout wide latitudinal ranges. We studied inter‐ and intrapopulation genetic diversity (using simple sequence repeats and chloroplast DNA sequencing) and inter‐ and intrapopulation phenotypic variability of 33 plant traits (using field and common‐garden measurements) for five populations of the invasive cordgrass Spartina densiflora Brongn. along the Pacific coast of North America from San Francisco Bay to Vancouver Island. Studied populations showed very low genetic diversity, high levels of phenotypic variability when growing in contrasted environments and high intrapopulation phenotypic variability for many plant traits. This intrapopulation phenotypic variability was especially high, irrespective of environmental conditions, for those traits showing also high phenotypic plasticity. Within‐population variation represented 84% of the total genetic variation coinciding with certain individual plants keeping consistent responses for three plant traits (chlorophyll b and carotenoid contents, and dead shoot biomass) in the field and in common‐garden conditions. These populations have most likely undergone genetic bottleneck since their introduction from South America; multiple introductions are unknown but possible as the population from Vancouver Island was the most recent and one of the most genetically diverse. S. densiflora appears as a species that would not be very affected itself by climate change and sea‐level rise as it can disperse, establish, and acclimate to contrasted environments along wide latitudinal ranges.

Comparing the consequences of natural selection, adaptive phenotypic plasticity, and matching habitat choice for phenotype-environment matching, population genetic structure, and reproductive isolation in meta-populations

Organisms commonly experience significant spatiotemporal variation in their environments. In response to such heterogeneity, different mechanisms may act that enhance ecological performance locally. However, depending on the nature of the mechanism involved, the consequences for populations may differ greatly. Building on a previous model that investigated the conditions under which different adaptive mechanisms (co)evolve, this study compares the ecological and evolutionary population consequences of three very different responses to environmental heterogeneity: matching habitat choice (directed gene flow), adaptive plasticity (associated with random gene flow), and divergent natural selection. Using individual‐based simulations, we show that matching habitat choice can have a greater adaptive potential than plasticity or natural selection: it allows for local adaptation while protecting genetic polymorphism despite global mating or strong environmental changes. Our simulations further reveal that increasing environmental fluctuations and unpredictability generally favor the emergence of specialist genotypes but that matching habitat choice is better at preventing local maladaptation by individuals. This confirms that matching habitat choice can speed up the genetic divergence among populations, cause indirect assortative mating via spatial clustering, and hence even facilitate sympatric speciation. This study highlights the potential importance of directed dispersal in local adaptation and speciation, stresses the difficulty of deriving its operation from nonexperimental observational data alone, and helps define a set of ecological conditions which should favor its emergence and subsequent detection in nature.

Programmed Allee effect in bacteria causes a tradeoff between population spread and survival

Dispersal is necessary for spread into new habitats, but it has also been shown to inhibit spread. Theoretical studies have suggested that the presence of a strong Allee effect may account for these counterintuitive observations. Experimental demonstration of this notion is lacking due to the difficulty in quantitative analysis of such phenomena in a natural setting. We engineered Escherichia coli to exhibit a strong Allee effect and examined how the Allee effect would affect the spread of the engineered bacteria. We showed that the Allee effect led to a biphasic dependence of bacterial spread on the dispersal rate: spread is promoted for intermediate dispersal rates but inhibited at low or high dispersal rates. The shape of this dependence is contingent upon the initial density of the source population. Moreover, the Allee effect led to a tradeoff between effectiveness of population spread and survival: increasing the number of target patches during dispersal allows more effective spread, but it simultaneously increases the risk of failing to invade or of going extinct. We also observed that total population growth is transiently maximized at an intermediate number of target patches. Finally, we demonstrate that fluctuations in cell growth may contribute to the paradoxical relationship between dispersal and spread. Our results provide direct experimental evidence that the Allee effect can explain the apparently paradoxical effects of dispersal on spread and have implications for guiding the spread of cooperative organisms.

The polyploid nature of Cenchrus ciliaris L. (Poaceae) has been overlooked: new insights for the conservation and invasion biology of this species – a review

Climate change, associated with increased aridity, and high grazing pressure by livestock results in the scarcity and loss of perennial Poaceae in arid ecosystems. The species threatened by this include Cenchrus ciliaris L., a native perennial grass of the tropical and sub-tropical arid rangelands of Africa and Western Asia and now introduced in Central and South America, and Australia. This species reproduces predominantly through aposporous apomixis although sexual individuals have been occasionally identified. Cenchrus ciliaris is characterised by a significant, heritable, phenotypic polymorphism and three ploidy levels including tetraploids (2n = 4x = 36), pentaploids (2n = 5x = 45) and hexaploids (2n = 6x = 54). Under water-deficit conditions, C. ciliaris shows plasticity in growth characteristics and aboveground biomass. This phenotypic plasticity has led to the identification of genotypic-associated responses conferring more productivity. This underlines the importance of conserving the genetic diversity of C. ciliaris in order to ensure the persistence of the vegetation cover in the arid ecosystems in which it occurs. Observations from cytogenetic and molecular data converge to underline the possibility of sexual reproduction, recombination and gene flow within and between populations of C. ciliaris. Genetic mechanisms, such as polyploidy, hybridisation between ploidy levels and apomixes, are generating and then maintaining the diversity of C. ciliaris. This review emphasises the role of polyploidy in the evolutionary development of C. ciliaris and how it may be a crucial factor for its conservation in some countries and its weedy nature in others.

Are anomalous invasion speeds robust to demographic stochasticity?

Two important issues for conservation are the range expansion of species as a result of climate change and the invasion of exotic species. Being able to predict the rate at which species spread is key for successful management. In deterministic models, the invasion speed of a polymorphic population can be faster than that of any of the component phenotypes, and these “anomalous” invasion speeds persist even when the mutation rate between phenotypes is vanishingly small. Here we investigate whether the same phenomenon is observed in a model with demographic stochasticity. The model that we use is discrete in time and space and we carry out numerical simulations to determine the invasion speed of a population that has two morphs which differ in their dispersal abilities. We find that anomalous speeds are observed in the stochastic model, but only when the carrying capacity of the population is large or the mutation rate between morphs is high enough. These results suggest that only species with large population sizes, such as many insect species, may be able to invade faster if they are polymorphic than if there is only a single morph present in the population.