Invasion Speed Research Articles

Deformations of acid-mediated invasive tumors in a model with Allee effect

We consider a Gatenby–Gawlinski-type model of invasive tumors in the presence of an Allee effect. We describe the construction of bistable one-dimensional traveling fronts using singular perturbation techniques in different parameter regimes corresponding to tumor interfaces with, or without, an acellular gap. By extending the front as a planar interface, we perform a stability analysis to long wavelength perturbations transverse to the direction of front propagation and derive a simple stability criterion for the front in two spatial dimensions. In particular we find that in general the presence of the acellular gap indicates transversal instability of the associated planar front, which can lead to complex interfacial dynamics such as the development of finger-like protrusions and/or different invasion speeds.

Spatio-temporal dynamics of a lattice prey–predator system with non-local diffusion in a periodic habitat

This article is concerned with the spreading speed and traveling waves of a lattice prey–predator system with non-local diffusion in a periodic habitat. With the help of an associated scalar lattice equation, we derive the invasion speed for the predator. More specifically, when the dispersal kernel of the predator is exponentially bounded, the invasion speed is finite and can be characterized in terms of principal eigenvalues; while the dispersal kernel is algebraically decaying, the invasion speed is infinite and the accelerated spreading rate is obtained. Furthermore, the existence and non-existence of traveling waves connecting the semi-equilibrium point to a uniformly persistent state are established.

Biological invasions and epidemics with nonlocal diffusion along a line.

To James D. Murray, with our admiration. The goal of this work is to understand and quantify how a line with nonlocal diffusion given by an integral enhances a reaction-diffusion process occurring in the surrounding plane. This is part of a long-term programme where we aim at modelling, in a mathematically rigorous way, the effect of transportation networks on the speed of biological invasions or propagation of epidemics. We prove the existence of a global propagation speed and characterize in terms of the parameters of the system the situations where such a speed is boosted by the presence of the line. In the course of the study we also uncover unexpected regularity properties of the model. On the quantitative side, the two main parameters are the intensity of the diffusion kernel and the characteristic size of its support. One outcome of this work is that the propagation speed will significantly be enhanced even if only one of the two is large, thus broadening the picture that we have already drawn in our previous works on the subject, with local diffusion modelled by a standard Laplacian. We further investigate the role of the other parameters, enlightening some subtle effects due to the interplay between the diffusion in the half plane and that on the line. Lastly, in the context of propagation of epidemics, we also discuss the model where, instead of a diffusion, displacement on the line comes from a pure transport term.

Modelling the effect of cell motility on mixing and invasion in epithelial monolayers

Collective cell invasion underlies several biological processes such as wound healing, embryonic development, and cancerous invasion. Here, we investigate the impact of cell motility on invasion in epithelial monolayers and its coupling to cellular mechanical properties, such as cell-cell adhesion and cortex contractility. We develop a two-dimensional computational model for cells with active motility based on the cellular Potts model, which predicts that the cellular invasion speed is mainly determined by active cell motility and is independent of the biological and mechanical properties of the cells. We also find that, in general, motile cells out-compete and invade non-motile cells, however, this can be reversed by differential cell proliferation. Stable coexistence of motile and static cell types is also possible for certain parameter regimes.

Environmental gradients mediate dispersal evolution during biological invasions.

Rapid evolution of increased dispersal at the edge of a range expansion can accelerate invasions. However, populations expanding across environmental gradients often face challenging environments that reduce fitness of dispersing individuals. We used an eco-evolutionary model to explore how environmental gradients influence dispersal evolution and, in turn, modulate the speed and predictability of invasion. Environmental gradients opposed evolution of increased dispersal during invasion, even leading to evolution of reduced dispersal along steeper gradients. Counterintuitively, reduced dispersal could allow for faster expansion by minimizing maladaptive gene flow and facilitating adaptation. While dispersal evolution across homogenous landscapes increased both the mean and variance of expansion speed, these increases were greatly dampened by environmental gradients. We illustrate our model's potential application to prediction and management of invasions by parameterizing it with data from a recent invertebrate range expansion. Overall, we find that environmental gradients strongly modulate the effect of dispersal evolution on invasion trajectories.

Age and Density of Mated Females Affect Dispersal Strategies in Spider Mite Tetranychus ludeni Zacher.

The dispersal strategies of a species can affect its invasion success. Investigations into the dispersal strategies of invasive species in relation to different factors help improve our understanding of invasion mechanisms and provide knowledge for population management and invasion evaluation. Tetranychus ludeni Zacher (Acari: Tetranychidae) is an invasive species which is native to Europe but is now cosmopolitan. Here, we examined the effects of age and density on dispersal in mated females. Our results show that older females that are capable of producing more eggs within 24 h were more likely to disperse and moved longer distances than younger ones with fewer eggs. Older females spread most of their eggs out of their natal habitats and over longer distances, which reduced competition and increased offspring fitness. Females exhibited significantly increased dispersal probability and distances with an increase in population density to avoid crowding. The synchronization of dispersal and reproduction, along with the positive density-dependent dispersal strategy, may facilitate the habitat colonization and invasion speed of T. ludeni.

River hydrology mediates fish invasions in Addo Elephant National Park, South Africa

Invasive freshwater fish can often have severe negative effects on native fishes in river systems. The interactions between hydrology and habitat variability can mediate the speed and success of individual invasions and the consequent impact on biodiversity. The rivers within Addo Elephant National Park (AENP) in the Eastern Cape, South Africa experience cyclical droughts and wet periods and as a result are naturally episodic. These rivers were recently invaded by three non-native species, the invasive largemouth bass (Micropterus salmoides) as well as the extralimital sharptooth catfish (Clarias gariepinus) and Mozambique tilapia (Oreochromis mossambicus). Monitoring of key sampling sites along two rivers over a 12-year period that included two major droughts revealed unexpected patterns in the spread of these species and their interactions with native fishes. On the Coerney River, C. gariepinus repeatedly invaded and was extirpated from a seasonal reach of the river, wherein O. mossambicus was only occasionally captured. On the Wit River, two apparently independent introductions of M. salmoides in the lower and upper reaches of the river resulted in patchy habitat occupancy over the course of 12 years. While C. gariepinus regularly co-occurred with native species, M. salmoides appeared to locally extirpate the endangered Eastern Cape redfin (Pseudobarbus afer). During drought, both species persisted in close but disconnected pools, suggesting that the episodic hydrology and geomorphology of these rivers may offer temporary predation refugia for native species during drought.Conservation implications: Drought in episodic rivers can mitigate against the impact and spread of freshwater invasions within protected areas. Effects of drying on invasion corridors and spatial interactions with native species should be taken into consideration when managing such invasions. Severe droughts also offer an opportunity to actively control invasive species when they are confined to accessible drought refugia within the protected area.

Early development of Acacia longifolia is more severely impacted by water and nutrient stress in invasive than native seedlings

Acacia longifolia (Andrews) Willd. is a legume native to southeast mainland Australia and Tasmania and has two described subspecies: A. l. subsp. longifolia and A. l. subsp. sophorae. The species has been introduced around the world and is considered invasive in several Mediterranean-type climate regions, including in South America, South Africa, and southern Europe. Previous studies comparing native and invasive populations of A. longifolia have focused on its reproductive ecology and population genetics, and little information exists on the species’ early life development and how abiotic factors influence it. Here, we performed a glasshouse experiment to compare the phenotypic responses of native and invasive (in Portugal) A. longifolia seedlings to different levels of water and nutrient availability. We found that seedlings of both subspecies responded similarly to different water and nutrient availability conditions in terms of biomass accumulation, root length, the number of phyllodes produced, phyllode water content, and root-to-shoot ratio. However, compared to native seedlings, invasive seedlings had limited capacity for stress responses. We found that invasive seedlings had lower drought tolerance than native seedlings, and thus the speed of invasion by A. longifolia into drier parts of Portugal may be hindered. Our results also hint of a possible role of seed “imprinting” in this species’ early growth responses, resulting in different resource allocation strategies such as favouring early growth and development over drought resistance in the invaded range. Further studies are required to better understand the species’ abiotic stress responses at the intraspecific level and their relation to its invasiveness.

Spreading speeds for time heterogeneous prey-predator systems with nonlocal diffusion on a lattice

Spreading speeds for time heterogeneous prey-predator systems with nonlocal diffusion on a lattice

Increasing planting density increases fruit mass and reduces the dispersal ability of a range‐expanding invasive plant, Mikania micrantha

AbstractAimInvasive plants may evolve a suite of distinctive traits during spread in the new range. Among these traits, dispersal ability is an important trait determining the invasion speed of exotic plants. There is evidence that higher dispersal ability is favoured at the invasion front, where population density may be low. However, no study has explicitly tested how planting density in a common garden affects the dispersal ability of invasive plants.LocationHainan island of China.MethodsIn this study, using 27 populations of an invasive plant, Mikania micrantha, which is expanding its range on Hainan island of China, we examine how three dispersal‐related traits (i.e. dispersal ability, fruit mass, and pappus radius) change with distance from invasion centre and field population density, and how planting density in a common garden affects dispersal traits.ResultsDispersal traits did not change with distance from the invasion centre and field population cover either in the natural environment or in the common garden. In the common garden, increasing planting density from one to five plants per pot increased fruit mass and decreased dispersal ability, indicating that the effect of density on dispersal traits could not be detected in the field. The relationship between dispersal ability in the natural environment and that in the common garden was positive but significant only under the five plants per pot treatment, possibly because dispersal traits in natural conditions were selected under high‐density growth conditions.Main ConclusionsOur results indicate that increasing population density may increase fruit mass and reduce the dispersal ability of range‐expanding invasive plants. We suggest that further studies exploring the patterns of dispersal traits in range‐expanding invasive plants in a common garden should consider intraspecific competition.

Defect turbulence in a dense suspension of polar, active swimmers.

We study the effects of inertia in dense suspensions of polar swimmers. The hydrodynamic velocity field and the polar order parameter field describe the dynamics of the suspension. We show that a dimensionless parameter R (ratio of the swimmer self-advection speed to the active stress invasion speed [Phys. Rev. X 11, 031063 (2021)2160-330810.1103/PhysRevX.11.031063]) controls the stability of an ordered swimmer suspension. For R smaller than a threshold R_{1}, perturbations grow at a rate proportional to their wave number q. Beyond R_{1} we show that the growth rate is O(q^{2}) until a second threshold R=R_{2} is reached. The suspension is stable for R>R_{2}. We perform direct numerical simulations to characterize the steady-state properties and observe defect turbulence for R<R_{2}. An investigation of the spatial organization of defects unravels a hidden transition: for small R≈0 defects are uniformly distributed and cluster as R→R_{1}. Beyond R_{1}, clustering saturates and defects are arranged in nearly stringlike structures.

Clonal alien plants in the mountains spread upward more extensively and faster than non-clonal

Alien species are colonizing mountain ecosystems and increasing their elevation ranges in response to ongoing climate change and anthropogenic disturbances, posing increasing threats to native species. However, how quickly alien species spread upward and what drives their invasion remains insufficiently understood. Here, using 26,952 occurrence records of 58 alien plant species collected over two centuries in the Czech Republic, we explored the elevation range and invasion speed of each alien species and the underlying factors driving these variables. We collected species traits relevant for invasion (e.g., clonality, flowering time, life span, invasion status, height, mycorrhizal type, native range, naturalized range, monoploid genome size, and Ellenberg-type indicator values for light, temperature, and nitrogen), human-associated factors (e.g., introduction pathways and the sum of economic use types), and minimum residence time. We explored the relationships between these factors and species’ elevation range and invasion speed using phylogenetic regressions. Our results showed that 58 alien species have been expanding upward along mountain elevations in the Czech Republic over the past two centuries. A stronger effect of species’ traits than human-associated factors has been revealed, e.g., clonality was a key trait supporting the invasion of alien species into the mountains, while human-associated factors showed no effect. Our findings highlight that the characteristics associated with rapid reproduction and spread are crucial for alien species’ invasion into montane regions. Identifying key drivers of this process is important for predicting the spatiotemporal dynamics of alien species in high-altitude ecosystems and thus employing apposite measures to reduce the threat to native plant species.

Translational medical bioengineering research of traumatic brain injury among Chinese and American pedestrians caused by vehicle collision based on human body finite element modeling

Based on the average human body size in China and the THUMS AM50 finite element model of the human body, the Kriging interpolation algorithm was used to model the Chinese 50th percentile human body, and the biological fidelity of the model was verified. We built three different types of passenger vehicle models, namely, sedan, sports utility vehicle (SUV), and multi-purpose vehicle (MPV), and used mechanical response analysis and finite element simulation to compare and analyze the dynamic differences and head injury differences between the Chinese 50th percentile human body and the THUMS AM50 model during passenger vehicle collisions. The results showed that there are obvious differences between the Chinese mannequin and THUMS in terms of collision time, collision position, invasion speed, and angle. When a sedan collided with the mannequins, the skull damage to the Chinese human body model was more severe, and when a sedan or SUV collided, the brain damage to the Chinese human body was more severe. The abovementioned results suggest that the existing C-NCAP pedestrian protection testing regulations may not provide the best protection for Chinese human bodies, and that the regulations need to be improved by combining collision damage mechanisms and the physical characteristics of Chinese pedestrians. This thorough investigation is positioned to shed light on the fundamental biomechanics and injury mechanisms at play. Furthermore, the amalgamation of clinically rooted translational and engineering research in the realm of traumatic brain injury has the potential to establish a solid foundation for discerning preventive methodologies. Ultimately, this endeavor holds the potential to introduce effective strategies aimed at preventing and safeguarding against traumatic brain injuries.

The minimal invasion speed of two competing species in homogeneous environment

Biological invasion has become an important element of global changes. In this paper, we use a reaction-diffusion system to discuss the minimal invasion speed of two competing species in the homogeneous environment. The general condition for the minimum invasion speed is obtained by applying the theory of propagation dynamics. Then the explicit conditions are derived by constructing upper solutions. The analytical results are corroborated by simulations of the considered reaction-diffusion system. Our results reveal the impact of the diffusion rate, growth rate, competitiveness of the species, as well as the carrying capacity of the environment, on the invasion speed, which provides an effective method for preventing biological invasion and controlling existing biological invasion.

The speed of invasion in an advancing population

We derive rigorous estimates on the speed of invasion of an advantageous trait in a spatially advancing population in the context of a system of one-dimensional F-KPP equations. The model was introduced and studied heuristically and numerically in a paper by Venegas-Ortiz et al. (Genetics 196:497–507, 2014). In that paper, it was noted that the speed of invasion by the mutant trait is faster when the resident population is expanding in space compared to the speed when the resident population is already present everywhere. We use the Feynman–Kac representation to provide rigorous estimates that confirm these predictions.

Spatial spread of epidemic with Allee effect.

The spatial spread of an epidemic is investigated in the case of a bistable dynamics, where the effective transmission rate depends on the fraction of infected and the state of no epidemic is linearly stable. The front propagation phenomenon is investigated both numerically and theoretically, by an analysis in a four-dimensional phase plane. A good agreement between numerical and theoretical results has been found both for the front profiles and for the speed of invasion. We discovered a novel phenomenon of front stoppage: In some regime of parameters, the front solution ceases to exist, and the propagating pulse of infection decays despite the initial outbreak.

Stand biomass decreases towards the edge of a range expanding invasive plant, Mikania micrantha, but only on thick soil layers

During spread in the new range, invasive plants may evolve distinctive traits that make them rapidly occupy the suitable and empty sites at the invasion front, such as rapid growth rate and high seed dispersal ability. However, less is known about how competitive ability evolves during range expansion, and no study has examined whether stand biomass (i.e. biomass production of dense monocultural stands, which may indicate the invasion speed and impacts of invasive plants) changes during range expansion. In this study, using 27 populations of an invasive plant, Mikania micrantha, which is expanding its range on Hainan island of China, we examined how competitive ability and stand biomass change along the invasion route. We grew plants of M. micrantha either singly or with common intraspecific competitors originating from different populations in 3 liter pots to evaluate competitive ability, and grew six plants from the same population together in 3 or 11 liter pots to evaluate stand biomass. When grown alone or with competitors, plant biomass and competitive ability did not correlate with distance from invasion center. Stand biomass was negatively correlated with distance from invasion center in 11 liter pots with a thick soil layer, but not in 3 liter pots with a thin soil layer. Stand biomass was negatively correlated with root to shoot ratio (RSR) in 3 liter pots but not in 11 liter pots, possibly because excessive allocation to roots for belowground competition reduced the overall performance at the stand level when soil space was highly limited. Stand biomass was unrelated to competitive ability. Our results indicate that edge populations of invasive plants may have reduced stand level performance in habitats with thick soil layers. In habitats with shallow soil layers, populations of invasive plants may evolve greater allocation to roots and reduced stand level performance.

Mechanistic movement models to predict geographic range expansions of ticks and tick-borne pathogens: Case studies with Ixodes scapularis and Amblyomma americanum in eastern North America

Mechanistic movement models to predict geographic range expansions of ticks and tick-borne pathogens: Case studies with Ixodes scapularis and Amblyomma americanum in eastern North America

Spatial ecology of the invasive Asian common toad in Madagascar and its implications for invasion dynamics

Invasion dynamics are determined, among other aspects, by the spatial behaviour of invasive populations. The invasive toad Duttaphrynus melanostictus is spreading inland from the eastern coast of Madagascar, causing considerable ecological impacts. Understanding the basic factors determining the spread dynamics can inform management strategies and provide insights into spatial evolutionary processes. We radio-tracked 91 adult toads in three localities along the invasion gradient to determine whether spatial sorting of dispersive phenotypes is occurring, and investigate intrinsic and extrinsic determinants of spatial behaviour. Overall, toads in our study appeared as habitat generalists, and their sheltering behaviour was tied to water proximity, with toads changing shelter more frequently closer to waterbodies. Toads showed low displacement rates (mean = 4.12 m/day) and quite a philopatric behaviour but were able to perform daily movements of over 50 m. We did not detect any spatial sorting of dispersal-relevant traits nor sex- or size-biased dispersal. Our results suggest that toads are more likely to expand their range during the wet season, and that the range expansion is probably dominated by short-distance dispersal at this stage of the invasion, although a future increase in invasion speed is expected, due to the capacity for long-distance movements of this species.

Modelling of Tissue Invasion in Epithelial Monolayers

Mathematical and computational models are used to describe biomechanical processes in multicellular systems. Here, we develop a model to analyse how two types of epithelial cell layers interact during tissue invasion depending on their cellular properties, i.e., simulating cancer cells expanding into a region of normal cells. We model the tissue invasion process using the cellular Potts model and implement our two-dimensional computational simulations in the software package CompuCell3D. The model predicts that differences in mechanical properties of cells can lead to tissue invasion, even if the division rates and death rates of the two cell types are the same. We also show how the invasion speed varies depending on the cell division and death rates and the mechanical properties of the cells.