Ecological Invasion,Roughened Fronts,and a Competitor’s Extreme Advance: Integrating Stochastic Spatial-Growth Models

Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An ecologically superior invader and a resident species compete for space preemptively. Our general model includes the basic contact process and a variant of the Eden model as special cases. We employ the concept of a “roughened” front to quantify effects of discreteness and stochasticity on invasion; we emphasize the probability distribution of the front-runner’s relative position. That is, we analyze the location of the most advanced invader as the extreme deviation about the front’s mean position. We find that a class of models with different assumptions about neighborhood interactions exhibits universal characteristics. That is, key features of the invasion dynamics span a class of models, independently of locally detailed demographic rules. Our results integrate theories of invasive spatial growth and generate novel hypotheses linking habitat or landscape size (length of the invading front) to invasion velocity, and to the relative position of the most advanced invader.     

Coexistence and Spread of Competitors in Heterogeneous Landscapes

Competition between species is ubiquitous in nature and therefore widely studied in ecology through experiment and theory. One of the central questions is under which conditions a (rare) invader can establish itself in a landscape dominated by a resident species at carrying capacity. Applying the same question with the roles of the invader and resident reversed leads to the principle that “mutual invasibility implies coexistence.” A related but different question is how fast a locally introduced invader spreads into a landscape (with or without competing resident), provided it can invade. We explore some aspects of these questions in a deterministic, spatially explicit model for two competing species with discrete non-overlapping generations in a patchy periodic environment. We obtain threshold values for fragmentation levels and dispersal distances that allow for mutual invasion and coexistence even if the non-spatial competition model predicts competitive exclusion. We obtain exact results when dispersal is governed by a Laplace kernel. Using the average dispersal success, we develop a mathematical framework to obtain approximate results that are independent of the exact dispersal patterns, and we show numerically that these approximations are very accurate.     

Facilitation promotes invasions in plant‐associated microbial communities

While several studies have established a positive correlation between community diversity and invasion resistance, it is less clear how species interactions within resident communities shape this process. Here, we experimentally tested how antagonistic and facilitative pairwise interactions within resident model microbial communities predict invasion by the plant–pathogenic bacterium Ralstonia solanacearum. We found that facilitative resident community interactions promoted and antagonistic interactions suppressed invasions both in the lab and in the tomato plant rhizosphere. Crucially, pairwise interactions reliably explained observed invasion outcomes also in multispecies communities, and mechanistically, this was linked to direct inhibition of the invader by antagonistic communities (antibiosis), and to a lesser degree by resource competition between members of the resident community and the invader. Together, our findings suggest that the type and strength of pairwise interactions can reliably predict the outcome of invasions in more complex multispecies communities.     

Species diversity reduces invasion success in pathogen‐regulated communities

The loss of natural enemies is thought to explain why certain invasive species are so spectacularly successful in their introduced range. However, if losing natural enemies leads to unregulated population growth, this implies that native species are themselves normally subject to natural enemy regulation. One possible widespread mechanism of natural enemy regulation is negative soil feedbacks, in which resident species growing on home soils are disadvantaged because of a build‐up of species‐specific soil pathogens. Here we construct simple models in which pathogens cause resident species to suffer reduced competitive ability on home soils and consider the consequences of such pathogen regulation for potential invading species. We show that the probability of successful invasion and its timescale depend strongly on the competitive ability of the invader on resident soils, but are unaffected by whether or not the invader also suffers reduced competitive ability on home soils (i.e. pathogen regulation). This is because, at the start of an invasion, the invader is rare and hence mostly encounters resident soils. However, the lack of pathogen regulation does allow the invader to achieve an unusually high population density. We also show that increasing resident species diversity in a pathogen‐regulated community increases invasion resistance by reducing the frequency of home‐site encounters. Diverse communities are more resistant to invasion than monocultures of the component species: they preclude a greater range of potential invaders, slow the timescale of invasion and reduce invader population size. Thus, widespread pathogen regulation of resident species is a potential explanation for the empirical observation that diverse communities are more invasion resistant.     

Spatial dynamics of invasion: the geometry of introduced species

Many exotic species combine low probability of establishment at each introduction with rapid population growth once introduction does succeed. To analyse this phenomenon, we note that invaders often cluster spatially when rare, and consequently an introduced exotic's population dynamics should depend on locally structured interactions. Ecological theory for spatially structured invasion relies on deterministic approximations, and determinism does not address the observed uncertainty of the exotic-introduction process. We take a new approach to the population dynamics of invasion and, by extension, to the general question of invasibility in any spatial ecology. We apply the physical theory for nucleation of spatial systems to a lattice-based model of competition between plant species, a resident and an invader, and the analysis reaches conclusions that differ qualitatively from the standard ecological theories. Nucleation theory distinguishes between dynamics of single- and multi-cluster invasion. Low introduction rates and small system size produce single-cluster dynamics, where success or failure of introduction is inherently stochastic. Single-cluster invasion occurs only if the cluster reaches a critical size, typically preceded by a number of failed attempts. For this case, we identify the functional form of the probability distribution of time elapsing until invasion succeeds. Although multi-cluster invasion for sufficiently large systems exhibits spatial averaging and almost-deterministic dynamics of the global densities, an analytical approximation from nucleation theory, known as Avrami's law, describes our simulation results far better than standard ecological approximations.     

Spreading speed and linear determinacy for two-species competition models

 One crucial measure of a species' invasiveness is the rate at which it spreads into a competitor's environment. A heuristic spread rate formula for a spatially explicit, two-species competition model relies on `linear determinacy' which equates spread rate in the full nonlinear model with spread rate in the system linearized about the leading edge of the invasion. However, linear determinacy is not always valid for two-species competition; it has been shown numerically that the formula only works for certain values of model parameters when the model is diffusive Lotka-Volterra competition [2]. This paper derives a set of sufficient conditions for linear determinacy in spatially explicit two-species competition models. These conditions can be interpreted as requiring sufficiently large dispersal of the invader relative to dispersal of the out-competed resident and sufficiently weak interactions between the resident and the invader. When these conditions are not satisfied, spread rate may exceed linearly determined predictions. The mathematical methods rely on the application of results established in a companion paper [11]. Received: 7 August 2000 / Revised version: 5 January 2002 / Published online: 17 July 2002     

Siderophores drive invasion dynamics in bacterial communities through their dual role as public good versus public bad

Microbial invasions can compromise ecosystem services and spur dysbiosis and disease in hosts. Nevertheless, the mechanisms determining invasion outcomes often remain unclear. Here, we examine the role of iron-scavenging siderophores in driving invasions of Pseudomonas aeruginosa into resident communities of environmental pseudomonads. Siderophores can be ‘public goods’ by delivering iron to individuals possessing matching receptors; but they can also be ‘public bads’ by withholding iron from competitors lacking these receptors. Accordingly, siderophores should either promote or impede invasion, depending on their effects on invader and resident growth. Using supernatant feeding and invasion assays, we show that invasion success indeed increased when the invader could use its siderophores to inhibit (public bad) rather than stimulate (public good) resident growth. Conversely, invasion success decreased the more the invader was inhibited by the residents’ siderophores. Our findings identify siderophores as a major driver of invasion dynamics in bacterial communities under iron-limited conditions.     

Phase control of resonant systems: interference, chaos and high periodicity

Much progress has been made in understanding the effect of periodic forcing on epidemiological and ecological systems when that forcing acts on just one part of the system. Much less is known about situations in which several parts of the system are affected. In this case the interaction between the impacts of the different forcing components can lead to reinforcement of system responses or to their interference. This interference phenomenon is significant if some forcing components are anthropogenic for then management might be able to exercise sufficient control to bring about suppression of undesirable aspects of the forcing, for example resonant amplification and the problems this can cause. We set out the algebraic theory when forcing is weak and illustrate by example what can happen when forcing is strong enough to create subharmonics and chaotic states. Phase is the key control variable that can bring about interference, advantageously shift nonlinear response curves and create periodic states out of chaos. The phenomenon in which high period fluctuations appear to be generated by low period forcing is examined and different mechanisms compared in a two-strain epidemiological model. The effect of noise as a source of high period fluctuations is also considered.     

Demography and dispersal: invasion speeds and sensitivity analysis in periodic and stochastic environments

Invasion speeds can be calculated from matrix integrodifference equation models that incorporate stage-specific demography and dispersal. These models also permit the calculation of the sensitivity and elasticity of invasion speed to changes in demographic and dispersal parameters. Such calculations have been used to understand the factors determining invasion speed and to explore possible tactics to manage invasive species. In this paper, we extend these calculations to temporally varying environments. We present formulas for the invasion speed and its sensitivity and elasticity in both periodic and stochastic environments. Periodic models can describe seasonal variation within a year, or can be used to study the frequency of occurrence of events (e.g., floods, fires) on interannual time scales. Stochastic models can incorporate variances, covariances, and temporal autocorrelation of parameters. We show that the invasion speed is calculated from a growth rate which is in turn calculated from a periodic or stochastic product of moment-generating function matrices. We present a new formulation of sensitivity analysis, using matrix calculus, that applies equally to constant, periodic, and stochastic environments.     

Modelling invasibility in endogenously oscillating tree populations: timing of invasion matters

The timing of introduction of a new species into an ecosystem can be critical in determining the invasibility (i.e. the sensitivity to invasion) of a resident population. Here, we use an individual-based model to test how (1) the type of competition (symmetric versus asymmetric) and (2) seed masting influence the success of invasion by producing oscillatory dynamics in resident tree populations. We focus on a case where two species (one resident, one invader introduced at low density) do not differ in terms of competitive abilities. By varying the time of introduction of the invader, we show that oscillations in the resident population favour invasion, by creating “invasibility windows” during which resource is available for the invader due to transiently depressed resident population density. We discuss this result in the context of current knowledge on forest dynamics and invasions, emphasizing the importance of variability in population dynamics.     

Rate of forcing and the forecastability of critical transitions

Critical transitions are qualitative changes of state that occur when a stochastic dynamical system is forced through a critical point. Many critical transitions are preceded by characteristic fluctuations that may serve as model‐independent early warning signals, implying that these events may be predictable in applications ranging from physics to biology. In nonbiological systems, the strength of such early warning signals has been shown partly to be determined by the speed at which the transition occurs. It is currently unknown whether biological systems, which are inherently high dimensional and typically display low signal‐to‐noise ratios, also exhibit this property, which would have important implications for how ecosystems are managed, particularly where the forces exerted on a system are anthropogenic. We examine whether the rate of forcing can alter the strength of early warning signals in (1) a model exhibiting a fold bifurcation where a state shift is driven by the harvesting of individuals, and (2) a model exhibiting a transcritical bifurcation where a state shift is driven by increased grazing pressure. These models predict that the rate of forcing can alter the detectability of early warning signals regardless of the underlying bifurcation the system exhibits, but that this result may be more pronounced in fold bifurcations. These findings have important implications for the management of biological populations, particularly harvested systems such as fisheries, and suggest that knowing the class of bifurcations a system will manifest may help discriminate between true‐positive and false‐positive signals.     

The impact of interactions on invasion and colonization resistance in microbial communities

In human microbiota, the prevention or promotion of invasions can be crucial to human health. Invasion outcomes, in turn, are impacted by the composition of resident communities and interactions of resident members with the invader. Here we study how interactions influence invasion outcomes in microbial communities, when interactions are primarily mediated by chemicals that are released into or consumed from the environment. We use a previously developed dynamic model which explicitly includes species abundances and the concentrations of chemicals that mediate species interaction. Using this model, we assessed how species interactions impact invasion by simulating a new species being introduced into an existing resident community. We classified invasion outcomes as resistance, augmentation, displacement, or disruption depending on whether the richness of the resident community was maintained or decreased and whether the invader was maintained in the community or went extinct. We found that as the number of invaders introduced into the resident community increased, disruption rather than augmentation became more prevalent. With more facilitation of the invader by the resident community, resistance outcomes were replaced by displacement and augmentation. By contrast, with more facilitation among residents, displacement outcomes shifted to resistance. When facilitation of the resident community by the invader was eliminated, the majority of augmentation outcomes turned into displacement, while when inhibition of residents by invaders was eliminated, invasion outcomes were largely unaffected. Our results suggest that a better understanding of interactions within resident communities and between residents and invaders is crucial to predicting the success of invasions into microbial communities.     

Species diversity, invasion, and alternative community states in sequentially assembled communities

The relationship between resident species diversity and invasion is generally negative in experimental studies but takes various forms in observational studies of natural communities. We hypothesized that stochastic species colonization, which applies to natural communities but not to experimental communities generally assembled through simultaneous species introduction, may lead to nonnegative diversity-invasion relationships via incurring priority effects. To test this hypothesis, we manipulated both resident species diversity and colonization history in sequentially assembled communities of bacterivorous protist species. We found that, despite a significant effect of assembly history on invader abundance, invader abundance decreased with diversity. This result was largely driven by positive selection effects associated with the dominant influence of an invasion-resistant species, which shared the most similar resource use pattern with the invader, and by the overall weak priority effects observed for the resident communities. Increasing species diversity, however, significantly strengthened priority effects, providing the first experimental support for the idea that larger species pools promote alternative community states. We suggest that elucidating mechanisms regulating the strength of priority effects may help in understanding variation in diversity-invasion relationships among natural communities.     

The resident strikes back: invader-induced switching of resident attractor

The aim of this paper is two-fold: (a) by way of example, we elucidate the phenomenon of invader-induced switches in a resident attractor; (b) we expose in detail how resonance and phase have a strong impact when semelparous organisms (as, e.g. Pacific salmon) with different life-cycle lengths compete in a self-induced periodically fluctuating environment. We analyse a simple model for the competition between annuals and biennials, focusing on the situation that the annual population in isolation converges to a two-cycle. Well-timed biennial mutants sample the periodically varying environment more efficiently than the annual resident. They can invade successfully even when they are inferior to the resident, in the sense that they have lower viability and/or fertility. Successful invasion can lead to resonance-mediated coexistence if the invader is rather inferior to the resident. Remarkably, for mutants that are less inferior to the resident, successful invasion by a mutant strategy will inevitably be followed by the extinction of the former invader and concurrent re-establishment of the resident. The expulsion of the invader is brought about by an invasion-induced phase shift or attractor switch. We call this phenomenon "the resident strikes back" and say that the resident strategy is invasible, yet invincible. After the resident has struck back, other mutants can successfully invade again. On a longer time-scale, this might lead to an intermittent occurrence of ultimately inferior strategies. The results show that even in a deterministic setting, successful invasion does not necessarily lead to establishment and that mutual invasibility is not always sufficient for coexistence.     

Extended leaf phenology may drive plant invasion through direct and apparent competition

Invasive plants can inflict great harm, yet drivers of successful invasion remain unclear. Many invaders of North American deciduous forests exhibit extended leaf phenology (ELP), or longer growing season relative to natives. ELP may grant invaders competitive advantages, but we argue that ELP more potently drives invasion in the presence of herbivores. ELP invaders can support herbivores by lessening starvation during winter; consequently, native plants may suffer when attacked later through apparent competition. As modeled here, even short ELP can promote competitive success of invaders, and apparent competition sharply enhances ELP invader dominance. In ‘partial enemy escape’ scenarios, a less palatable ELP invader nearly excludes a preferred native where an invader without ELP could not. Together, ELP and apparent competition enhance invasion even when biotic resistance should suppress it, i.e. when the invader competes weakly or provides preferred forage. Thus, ELP‐apparent competition interactions grant invaders considerable success while challenging core tenets of invasion ecology.     

Does disturbance,competition or resource limitation underlie Hieracium lepidulum invasion in New Zealand? Mechanisms of establishment and persistence,and functional differentiation among invasive and native species

The processes underlying plant invasions have been the subject of much ecological research. Understanding mechanisms of plant invasions are difficult to elucidate from observations, yet are crucial for ecological management of invasions. Hieracium lepidulum, an asteraceous invader in New Zealand, is a species for which several explanatory mechanisms can be raised. Alternative mechanisms, including competitive dominance, disturbance of resident vegetation allowing competitive release or nutrient resource limitation reducing competition with the invader are raised to explain invasion. We tested these hypotheses in two field experiments which manipulated competitive, disturbance and nutrient environments in pre‐invasion and post‐invasion vegetation. H. lepidulum and resident responses to environmental treatments were measured to allow interpretation of underlying mechanisms of establishment and persistence. We found that H. lepidulum differed in functional response profile from native species. We also found that other exotic invaders at the sites were functionally different to H. lepidulum in their responses. These data support the hypothesis that different invaders use different invasion mechanisms from one another. These data also suggest that functional differentiation between invaders and native resident vegetation may be an important contributing factor allowing invasion. H. lepidulum appeared to have little direct competitive effect on post‐invasion vegetation, suggesting that competition was not a dominant mechanism maintaining its persistence. There was weak support for disturbance allowing initial establishment of H. lepidulum in pre‐invasion vegetation, but disturbance did not lead to invader dominance. Strong support for nutrient limitation of resident species was provided by the rapid competitive responses with added nutrients despite presence of H. lepidulum. Rapid competitive suppression of H. lepidulum once nutrient limitation was alleviated suggests that nutrient limitation may be an important process allowing the invader to dominate. Possible roles of historical site degradation and/or invader‐induced soil chemical/microbial changes in nutrient availability are discussed.     

Diversity decreases invasion via both sampling and complementarity effects

Complementarity and sampling effects may both contribute to increased invasion resistance at higher diversity. We measured plant invader biomass across a long-term experimental plant diversity gradient. Invader species' biomass was inhibited in more diverse plots, largely because of the presence of strongly competitive C₄ bunchgrasses, consistent with a sampling effect. Invader biomass was negatively correlated with resident root biomass, and positively correlated with soil nitrate concentrations, suggesting that competition for nitrogen limited invader success. Resident root biomass increased and soil nitrate concentrations decreased with the presence of C₄ grasses and also across the diversity gradient, suggesting that diverse plots are more competitive because of the presence of C₄ grasses. In addition to this evidence for a sampling effect, we also found evidence for a complementarity effect. Specifically, the percentage of plots that had lower invader biomass than did the best resident monoculture (i.e. that had invader 'underyielding') increased across the species richness gradient. This pattern cannot be explained by a sampling effect and is a unique signature of complementarity effects. Our results demonstrate the importance of multiple mechanisms by which diversity can increase invasion resistance.     

Consumer diversity mediates invasion dynamics at multiple trophic levels

Theory and recent experiments, mostly focused on plants, indicate that biodiversity can reduce invasion success, but diversity effects on mobile animal invasion have received little attention. We tested effects of mobile crustacean grazer diversity (species richness) on the establishment of invaders at multiple trophic levels in flow-through seagrass mesocosms. On average, increasing diversity of resident grazers reduced population growth and biomass of experimentally introduced grazers. This increase in invasion resistance was concurrent with reductions in food and habitat availability and increases in resident density, paralleling previous results with plants. In many cases, mixtures of resident species resisted invasion better than did any single resident species, arguing that interactions among residents, rather than a sampling mechanism, explained diversity effects on invasion. Higher grazer diversity also generally reduced biomass of naturally recruiting invertebrates and algae and shifted epiphytic community dominance from algae to sessile invertebrates. Exploitation competition, then, appears to contribute to the diversity effect on invasion in both plant and animal systems. Our results further suggest that resident competitive advantage may also be at work in multi-trophic level systems. Thus, negative effects of local diversity on invasion appear general, and trophically mediated processes can also strongly influence invader success and identity in multi-trophic level systems.     

Analysis of linear determinacy for spread in cooperative models

 The discrete-time recursion system $\u_{n+1}=Q[\u_n]$ with $\u_n(x)$ a vector of population distributions of species and $Q$ an operator which models the growth, interaction, and migration of the species is considered. Previously known results are extended so that one can treat the local invasion of an equilibrium of cooperating species by a new species or mutant. It is found that, in general, the resulting change in the equilibrium density of each species spreads at its own asymptotic speed, with the speed of the invader the slowest of the speeds. Conditions on $Q$ are given which insure that all species spread at the same asymptotic speed, and that this speed agrees with the more easily calculated speed of a linearized problem for the invader alone. If this is true we say that the recursion has a single speed and is linearly determinate. The conditions are such that they can be verified for a class of reaction-diffusion models. Received: 7 August 2000 / Revised version: 5 January 2002 / Published online: 17 July 2002