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.     

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.     

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.     

Spatial heterogeneity of plant–soil feedbacks increases per capita reproductive biomass of species at an establishment disadvantage

Plant–soil feedbacks have been widely implicated as a driver of plant community diversity, and the coexistence prediction generated by a negative plant–soil feedback can be tested using the mutual invasibility criterion: if two populations are able to invade one another, this result is consistent with stable coexistence. We previously showed that two co-occurring Rumex species exhibit negative pairwise plant–soil feedbacks, predicting that plant–soil feedbacks could lead to their coexistence. However, whether plants are able to reproduce when at an establishment disadvantage (“invasibility”), or what drivers in the soil might correlate with this pattern, are unknown. To address these questions, we created experimental plots with heterogeneous and homogeneous soils using field-collected conditioned soils from each of these Rumex species. We then allowed resident plants of each species to establish and added invader seeds of the congener to evaluate invasibility. Rumex congeners were mutually invasible, in that both species were able to establish and reproduce in the other’s resident population. Invaders of both species had twice as much reproduction in heterogeneous compared to homogeneous soils; thus the spatial arrangement of plant–soil feedbacks may influence coexistence. Soil mixing had a non-additive effect on the soil bacterial and fungal communities, soil moisture, and phosphorous availability, suggesting that disturbance could dramatically alter soil legacy effects. Because the spatial arrangement of soil patches has coexistence implications, plant–soil feedback studies should move beyond studies of mean effects of single patch types, to consider how the spatial arrangement of patches in the field influences plant communities.     

Spatial heterogeneity, source-sink dynamics, and the local coexistence of competing species

Patch occupancy theory predicts that a trade-off between competition and dispersal should lead to regional coexistence of competing species. Empirical investigations, however, find local coexistence of superior and inferior competitors, an outcome that cannot be explained within the patch occupancy framework because of the decoupling of local and spatial dynamics. We develop two-patch metapopulation models that explicitly consider the interaction between competition and dispersal. We show that a dispersal-competition trade-off can lead to local coexistence provided the inferior competitor is superior at colonizing empty patches as well as immigrating among occupied patches. Immigration from patches that the superior competitor cannot colonize rescues the inferior competitor from extinction in patches that both species colonize. Too much immigration, however, can be detrimental to coexistence. When competitive asymmetry between species is high, local coexistence is possible only if the dispersal rate of the inferior competitor occurs below a critical threshold. If competing species have comparable colonization abilities and the environment is otherwise spatially homogeneous, a superior ability to immigrate among occupied patches cannot prevent exclusion of the inferior competitor. If, however, biotic or abiotic factors create spatial heterogeneity in competitive rankings across the landscape, local coexistence can occur even in the absence of a dispersal-competition trade-off. In fact, coexistence requires that the dispersal rate of the overall inferior competitor not exceed a critical threshold. Explicit consideration of how dispersal modifies local competitive interactions shifts the focus from the patch occupancy approach with its emphasis on extinction-colonization dynamics to the realm of source-sink dynamics. The key to coexistence in this framework is spatial variance in fitness. Unlike in the patch occupancy framework, high rates of dispersal can undermine coexistence, and hence diversity, by reducing spatial variance in fitness.     

Competition between similar invasive species: modeling invasional interference across a landscape

As the number of biological invasions increases, interactions between different invasive species will become increasingly important. Several studies have examined facilitative invader–invader interactions, potentially leading to invasional meltdown. However, if invader interactions are negative, invasional interference may lead to lower invader abundance and spread. To explore this possibility, we develop models of two competing invaders. A landscape simulation model examines the patterns created by two such species invading into the same region. We then apply the model to a case study of Carduus nutans L. and C. acanthoides L., two economically important invasive weeds that exhibit a spatially segregated distribution in central Pennsylvania, USA. The results of these spatially-explicit models are generally consistent with the results of classic Lotka–Volterra competition models, with widespread coexistence predicted if interspecific effects are weaker than intraspecific effects for both species. However, spatial segregation of the two species (with lower net densities and no further spread) may arise, particularly when interspecific competition is stronger than intraspecific competition. A moving area of overlap may result when one species is a superior competitor. In the Carduus system, our model suggests that invasional interference will lead to lower levels of each species when together, but a similar net level of thistle invasion due to the similarity of intra- and interspecific competition. Thus, invasional interference may have important implications for the distribution and management of invasive species.     

Coexistence in a fluctuating environment by the effect of relative nonlinearity: A minimal model

The minimal model of the “relative nonlinearity” type fluctuation-maintained coexistence is investigated. The competing populations are affected by an environmental white noise. With quadratic density dependence, the long-term growth rates of the populations are determined by the average and the variance of the (fluctuating) total density. At most two species can coexist on these two “regulating” variables; competitive exclusion would ensue in a constant environment. A numerical study of the expected time until extinction of any of the two species reveals that the criterion of mutual invasibility predicts the parameter range of long-term coexistence correctly in the limit of zero extinction threshold. However, any extinction threshold consistent with a realistic population size will allow only short-term coexistence. Therefore, our simulations question the biological relevance of mutual invasibility, as a sufficient condition of coexistence, for large density fluctuations. We calculate the average and the variance of the fluctuating density of the coexisting populations analytically via the moment-closure approximation; the results are reasonably close to the simulated behavior. Based on this treatment, robustness of coexistence is studied in the limit of infinite population size. We interpret the results of this analysis in the context of necessity of niche segregation with respect to the regulating variables using a framework theory published earlier.     

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     

Transient dynamics limit the effectiveness of keystone predation in bringing about coexistence

We analyze the transient dynamics of simple models of keystone predation, in which a predator preferentially consumes the dominant of two (or more) competing prey species. We show that coexistence is unlikely in many systems characterized both by successful invasion of either prey species into the food web that lacks it and by a stable equilibrium with high densities of all species. Invasion of the predator-resistant consumer species often causes the resident, more vulnerable prey to crash to such low densities that extinction would occur for many realistic population sizes. Subsequent transient cycles may entail very low densities of the predator or of the initially successful invader, which may also preclude coexistence of finite populations. Factors causing particularly low minimum densities during the transient cycles include biotic limiting resources for the prey, limited resource partitioning between the prey, a highly efficient predator with relatively slow dynamics, and a vulnerable prey whose population dynamics are rapid relative to the less vulnerable prey. Under these conditions, coexistence of competing prey via keystone predation often requires that the prey's competitive or antipredator characteristics fall within very narrow ranges. Similar transient crashes are likely to occur in other food webs and food web models.     

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     

Dynamical mechanism for coexistence of dispersing species.

Dispersal of organisms may play an essential role in the coexistence of species. Recent studies of the evolution of dispersal in temporally varying environments suggest that clones differing in dispersal rates can coexist indefinitely. In this work, we explore the mechanism permitting such coexistence for a model of dispersal in a patchy environment, where temporal heterogeneity arises from endogenous chaotic dynamics. We show that coexistence arises from an extreme type of intermittent behavior, namely the phenomenon known as on-off intermittency. In effect, coexistence arises because of an alternation between synchronized and de-synchronized dynamical behaviors. Our analysis of the dynamical mechanism for on-off intermittency lends strong credence to the proposition that chaotic synchronism may be a general feature of species coexistence, where competing species differ only in dispersal rate.     

Predicting dispersal and recruitment of <Emphasis Type="Italic">Miconia calvescens</Emphasis> (Melastomataceae) in Australian tropical rainforests

Miconia calvescens (Melastomataceae) is a serious invader in the tropical Pacific, including the Hawaiian and Tahitian Islands, and currently poses a major threat to native biodiversity in the Wet Tropics of Australia. The species is fleshy-fruited, small-seeded and shade tolerant, and thus has the potential to be dispersed widely and recruit in relatively intact rainforest habitats, displacing native species. Understanding and predicting the rate of spread is critical for the design and implementation of effective management actions. We used an individual-based model incorporating a dispersal function derived from dispersal curves for similar berry-fruited native species, and life-history parameters of fecundity and mortality to predict the spatial structure of a Miconia population after a 30 year time period. We compared the modelled population spatial structure to that of an actual infestation in the rainforests of north Queensland. Our goal was to assess how well the model predicts actual dispersion and to identify potential barriers and conduits to seed movement and seedling establishment. The model overpredicts overall population size and the spatial extent of the actual infestation, predicting individuals to occur at a maximum 1,750 m from the source compared with the maximum distance of any detected individual in the actual infestation of 1,191 m. We identify several characteristic features of managed invasive populations that make comparisons between modelled outcomes and actual infestations difficult. Our results suggest that the model’s ability to predict both spatial structure and spread of the population will be improved by incorporating a spatially explicit element, with dispersal and recruitment probabilities that reflect the relative suitability of different parts of the landscape for these processes.     

Demographic stochasticity versus spatial variation in the competition between fast and slow dispersers

Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population models predict that a species with a lower dispersal rate always drives a competing species to extinction in the presence of spatial variation of resources. However, the introduction of intrinsic demographic stochasticity can reverse this conclusion. We present a simple model in which competition between the exploitation of resources and stochastic fluctuations leads to victory by either the faster or slower of two species depending on the environmental parameters. A simplified limiting case of the model, analyzed by closing the moment and correlation hierarchy, quantitatively predicts which species will win in the complete model under given parameters of spatial variation and average carrying capacity.     

Difference Inadaptive Dispersal Ability Can Promote Species Coexistence in Fluctuating Environments

Theories and empirical evidence suggest that random dispersal of organisms promotes species coexistence in spatially structured environments. However, directed dispersal, where movement is adjusted with fitness-related cues, is less explored in studies of dispersal-mediated coexistence. Here, we present a metacommunity model of two consumers exhibiting directed dispersal and competing for a single resource. Our results indicated that directed dispersal promotes coexistence through two distinct mechanisms, depending on the adaptiveness of dispersal. Maladaptive directed dispersal may promote coexistence similar to random dispersal. More importantly, directed dispersal is adaptive when dispersers track patches of increased resources in fluctuating environments. Coexistence is promoted under increased adaptive dispersal ability of the inferior competitor relative to the superior competitor. This newly described dispersal-mediated coexistence mechanism is likely favored by natural selection under the trade-off between competitive and adaptive dispersal abilities.     

Evolutionary Convergence to Ideal Free Dispersal Strategies and Coexistence

We study a two species competition model in which the species have the same population dynamics but different dispersal strategies and show how these dispersal strategies evolve. We introduce a general dispersal strategy which can result in the ideal free distributions of both competing species at equilibrium and generalize the result of Averill et al. (2011). We further investigate the convergent stability of this ideal free dispersal strategy by varying random dispersal rates, advection rates, or both of these two parameters simultaneously. For monotone resource functions, our analysis reveals that among two similar dispersal strategies, selection generally prefers the strategy which is closer to the ideal free dispersal strategy. For nonmonotone resource functions, our findings suggest that there may exist some dispersal strategies which are not ideal free, but could be locally evolutionarily stable and/or convergent stable, and allow for the coexistence of more than one species.     

The impact of transportation and translocation on dispersal behaviour in the invasive cane toad

Biological invasions transport organisms to novel environments; but how does the translocation process influence movement patterns of the invader? Plausibly, the stress of encountering a novel environment, or of the transport process, might induce rapid dispersal from the release site—potentially enhancing (or reducing) invader success and spread. We investigated the effect of transportation and release to novel environments on dispersal-relevant traits of one of the world’s most notorious invaders, the cane toad (Rhinella marina). We collected toads in northern New South Wales from heath and woodland habitats, manipulated the level of transport stress and either returned toads to their exact collection point (residents) or reciprocally translocated them to a novel site. Both translocation and the level of transport stress drastically altered toad dispersal rates for at least 5 days post-release. Translocated toads (depending on their level of transport stress and release habitat) moved on average two to five times further per day (mean range 67–148 m) than did residents (mean range 22–34 m). Translocated toads also moved on more days, and moved further from their release point than did resident toads, but did not move in straighter lines. A higher level of transport stress (simulating long-distance translocation) had no significant effect on movements of resident toads but amplified the dispersal of translocated toads only when released into woodland habitat. These behavioural shifts induced by translocation and transportation may affect an invader’s ability to colonise novel sites, and need to be incorporated into plans for invader control.     

Adaptive Patch Searching Strategies in Fragmented Landscapes

The search strategies dispersers employ to search for new habitat patches affect individuals’ search success and subsequently landscape connectivity and metapopulation viability. Some evidence indicates that individuals within the same species may display a variety of behavioural patch searching strategies rather than one species-specific strategy. This may result from landscape heterogeneity. We modelled the evolution of individual patch searching strategies in different landscapes. Specifically, we analysed whether evolution can favour different, co-existing, behavioural search strategies within one population and to what extent this coexistence of multiple strategies was dependent on landscape configuration. Using an individual-based simulation model, we studied the evolution of patch searching strategies in three different landscape configurations: uniform, random and clumped. We found that landscape configuration strongly influenced the evolved search strategy. In uniform landscapes, one fixed search strategy evolved for the entire spatially structured population, while in random and clumped landscapes, a set of different search strategies emerged. The coexistence of several search strategies also strongly depended on the dispersal mortality. We show that our result can affect landscape connectivity and metapopulation dynamics. Co-ordinating editor: N. Yamamura     

<Emphasis Type="Italic">PRUNUS</Emphasis>: a spatially explicit demographic model to study plant invasions in stochastic,heterogeneous environments

To model the invasion of Prunus serotina invasion within a real forest landscape we built a spatially explicit, non-linear Markov chain which incorporated a stage-structured population matrix and dispersal functions. Sensitivity analyses were subsequently conducted to identify key processes controlling the spatial spread of the invader, testing the hypothesis that the landscape invasion patterns are driven in the most part by disturbance patterns, local demographical processes controlling propagule pressure, habitat suitability, and long-distance dispersal. When offspring emigration was considered as a density-dependent phenomenon, local demographic factors generated invasion patterns at larger spatial scales through three factors: adult longevity; adult fecundity; and the intensity of self-thinning during stand development. Three other factors acted at the landscape scale: habitat quality, which determined the proportion of the landscape mosaic which was potentially invasible; disturbances, which determined when suitable habitats became temporarily invasible; and the existence of long distance dispersal events, which determined how far from the existing source populations new founder populations could be created. As a flexible “all-in-one” model, PRUNUS offers perspectives for generalization to other plant invasions, and the study of interactions between key processes at multiple spatial scales.     

Markov models of territory occupancy: implications for the management and conservation of competing species

Markov chains have been frequently used in community ecology to model successional changes, but little attention has been paid to its application in population ecology as a tool to explore the outcomes of species interactions. Markov models can be regarded as “null models” that provide predicted values under a no-change scenario against which the consequences of changes in variables of interest can be assessed. Here we explore Markov chains’ potential to project population trends of competing species and derive sensible management strategies. To do that we use six years of field data on territory occupancy and turn-over of two competing top predators in a Mediterranean landscape: the golden and Bonelli’s eagles. The results suggest that long-term coexistence of both species in the study area is likely, with the main limitation for their coexistence being the difficulties Bonelli’s eagles have in colonising new territories that become available. To avoid future declines in the population of Bonelli’s eagle, it is important to take into account that the positive effects of conservation strategies focused on encouraging colonization (e.g. decreasing disperser mortality) are likely to be larger than those focused on avoiding territory abandonment (e.g. decreasing adult mortality). Markov chains are likely to be useful to evaluate the relative merit of alternative management options in other territorial species when patterns of territory occupancy are the only reliable data available, as often happens with large predators.     

Movement behaviour determines competitive outcome and spread rates in strongly heterogeneous landscapes

Classical models for biological invasions were single-species models in homogeneous landscapes, but most invasions happen in the presence of interacting species and in heterogeneous environments. The combination of spatial variation and species interaction could alter the spreading process significantly. For example, the ‘environmental heterogeneity hypothesis of invasions’ posits that heterogeneity offers more opportunities for invaders and reduces the negative impact on native species. Environmental heterogeneity offers an obvious coexistence mechanism on the regional scale if two or more competing species have different spatial niches, i.e. if the local competitive advantage changes in space. We consider a more subtle mechanism of space use through individual movement behaviour when the local competitive advantage remains with the same species. Specifically, we model the densities of two species, diffusing and competing in an infinite landscape consisting of two types of patches. We include individual behaviour in terms of movement rate and patch preference. We consider the scenario that one of the species is the stronger local competitor in both patch types. We then uncover a number of mechanisms—based solely on movement behaviour—through which these two species can coexist regionally, how the inferior competitor can replace the superior competitor globally, or how a bistable situation can arise between the two. We calculate mutual invasion conditions as well as mutual spatial spread rates, and we show that spread rates may depend on movement parameters in unexpected ways.