A simulation model of plant invasion: long-distance dispersal determines the pattern of spread

Mechanisms and consequences of biological invasions are a global issue. Yet, one of the key aspects, the initial phase of invasion, is rarely observed in detail. Data from aerial photographs covering the spread of Heracleum mantegazzianum (Apiaceae, native to Caucasus) on a local scale of hectares in the Czech Republic from the beginning of invasion were used as an input for an individual-based model (IBM), based on small-scale and short-time data. To capture the population development inferred from the photographs, long-distance seed dispersal, changes in landscape structures and suitability of landscape elements to invasion by H. mantegazzianum were implemented in the model. The model was used to address (1) the role of long-distance dispersal in regional invasion dynamics, and (2) the effect of land-use changes on the progress of the invasion. Simulations showed that already small fractions of seed subjected to long-distance dispersal, as determined by systematic comparison of field data and modelling results, had an over-proportional effect on the spread of this species. The effect of land-use changes on the simulated course of invasion depends on the actual level of habitat saturation; it is larger for populations covering a high proportion of available habitat area than for those in the initial phase of invasion. Our results indicate how empirical field data and model outputs can be linked more closely with each other to improve the understanding of invasion dynamics. The multi-level, but nevertheless simple structure of our model suggests that it can be used for studying the spread of similar species invading in comparable landscapes.     

Transient sensitivities of non-indigenous shrub species indicate complicated invasion dynamics

As biological invasions increasingly affect natural systems, the need for methods that can quantify the processes responsible for invasion success has increased. Further, methods should be geared to the formulation of management strategies. Demographic analyses are designed to explore the causes and properties of population change. Matrix population models, a commonly used technique for demographic analysis, have been applied to the analysis of stage-structured populations. However, most commonly, analyses have focused on long-term outcomes dynamics (ergodic dynamics). The methods available for analysis of matrix population models have recently been extended to facilitate analysis of the transient dynamics most important to invasion analysis. In this paper we analyze the transient population dynamics of three invasive shrubs and compare them to ergodic dynamics. Cytisus scoparius, Clidemia hirta, and Ardisia elliptica come from different parts of the world and are all now found in the United States of America. They also have published transition matrices that measure the probabilities that any one life-history stage will transition to another over an annual time step. These matrices have been estimated from multi-year data collected from plots in various environments. Our comparative study of transient and ergodic dynamics of invasive shrubs shows that, for all the considered shrub species, there was a clear difference between the sensitivities drawn from these two approaches. The transient sensitivities of earlier life-history transitions showed magnified importance relative to ergodic sensitivities. This was especially true of A. elliptica for which the stable population structure was most different from the starting structure analyzed in detail here. For other species, as stable population structures were heavily weighted towards early stages, the differences in the importance of early transitions transiently and ergodically were less dramatic. Late life transitions showed magnified importance in areas towards the center of the invasion or in older invasion areas. Finally, populations with shorter estimated generation times show greater transient sensitivity to early life-history stages; but the pattern was complex and varied according to species, and was also observed across other life-history transitions. Overall, the ambiguity and complexity of the results highlight the power of considering transient population dynamics for invading species, as well as the importance of specific biological and ecological knowledge of the invading species. Although there may be commonalities across invasions, important decisions on control or inference on population dynamics should treat invasions as individual, unique events.     

Dynamics of a plant-herbivore-predator system with plant-toxicity

A system of ordinary differential equations is considered that models the interactions of two plant species populations, an herbivore population, and a predator population. We use a toxin-determined functional response to describe the interactions between plant species and herbivores and use a Holling Type II functional response to model the interactions between herbivores and predators. In order to study how the predators impact the succession of vegetation, we derive invasion conditions under which a plant species can invade into an environment in which another plant species is co-existing with a herbivore population with or without a predator population. These conditions provide threshold quantities for several parameters that may play a key role in the dynamics of the system. Numerical simulations are conducted to reinforce the analytical results. This model can be applied to a boreal ecosystem trophic chain to examine the possible cascading effects of predator-control actions when plant species differ in their levels of toxic defense.     

A dynamic global vegetation model for use with climate models: concepts and description of simulated vegetation dynamics

Changes in vegetation structure and biogeography due to climate change feedback to alter climate by changing fluxes of energy, moisture, and momentum between land and atmosphere. While the current class of land process models used with climate models parameterizes these fluxes in detail, these models prescribe surface vegetation and leaf area from data sets. In this paper, we describe an approach in which ecological concepts from a global vegetation dynamics model are added to the land component of a climate model to grow plants interactively. The vegetation dynamics model is the Lund–Potsdam–Jena (LPJ) dynamic global vegetation model. The land model is the National Center for Atmospheric Research (NCAR) Land Surface Model (LSM). Vegetation is defined in terms of plant functional types. Each plant functional type is represented by an individual plant with the average biomass, crown area, height, and stem diameter (trees only) of its population, by the number of individuals in the population, and by the fractional cover in the grid cell. Three time‐scales (minutes, days, and years) govern the processes. Energy fluxes, the hydrologic cycle, and carbon assimilation, core processes in LSM, occur at a 20 min time step. Instantaneous net assimilated carbon is accumulated annually to update vegetation once a year. This is carried out with the addition of establishment, resource competition, growth, mortality, and fire parameterizations from LPJ. The leaf area index is updated daily based on prevailing environmental conditions, but the maximum value depends on the annual vegetation dynamics. The coupling approach is successful. The model simulates global biogeography, net primary production, and dynamics of tundra, boreal forest, northern hardwood forest, tropical rainforest, and savanna ecosystems, which are consistent with observations. This suggests that the model can be used with a climate model to study biogeophysical feedbacks in the climate system related to vegetation dynamics.     

Evidence for non-uniform dispersal in the biological invasions of two naturalized North American bird species

Most previous attempts to model the geographical range expansion of an invading species assume random dispersal of organisms through a homogeneous environment. These models result in a series of uniformly increasing circles radiating out from the centre of origin over time. Although these models often give reasonable fits to available data, they do not typically include mechanisms of dispersal. Alternatively, models that include assumptions of non‐random dispersal and a heterogeneous environment inevitably result in an anisotropic or jagged invasion front. This front will include propagules of pioneer individuals for the expanding species. Existing data from biological invasions reveal that the spatial structure of an invading species usually exhibits these propagules. Using population data gathered from the past century, we investigated the propagules of two North American invading bird species: the European starling (Sturnus vulgaris Linnaeus), and the house finch (Carpodacus mexicanus Müller), and found a correlation between propagule location and habitat quality. These results suggest that dispersing individuals seek out favourable habitat and remain there, thus introducing a possible mechanism for explaining non‐uniform dispersal during invasions. When combined with results from other studies, our results suggest that propagules provide starting points for future population expansion of an invading species.     

Invasion theory and biological control

Recent advances in the mathematical theory of invasion dynamics have much to offer to biological control. Here we synthesize several results concerning the spatiotemporal dynamics that occur when a biocontrol agent spreads into a population of an invading pest species. We outline conditions under which specialist and generalist predators can influence the density and rate of spatial spread of the pest, including the rather stringent conditions under which a specialist predator can successfully reverse a pest invasion. We next discuss the connections between long distance dispersal and invasive spread, emphasizing the different consequences of fast spreading pests and predators. Recent theory has considered the effects of population stage-structure on invasion dynamics, and we discuss how population demography affects the biological control of invading pests. Because low population densities generally characterize early stages of an invasion, we discuss the lessons invasion theory teaches concerning the detectability of invasions. Stochasticity and density-dependent dynamics are common features of many real invasions, influencing both the spatial character (e.g. patchiness) of pest invasions and the success of biocontrol agents. We conclude by outlining theoretical results delineating how stochastic effects and complex dynamics generated by density dependence can facilitate or impede biological pest control.     

Accounting for imperfect observation and estimating true species distributions in modelling biological invasions

The documentation of biological invasions is often incomplete with records lagging behind the species’ actual spread to a spatio‐temporally heterogeneous extent. Such imperfect observation bears the risk of underestimating the already realised distribution of the invading species, misguiding management efforts and misjudging potential future impacts. In this paper, we develop a hierarchical modelling framework which disentangles the determinants of the invasion and observation processes, models spatio‐temporal heterogeneity in detection patterns, and infers the actual, yet partly undocumented distribution of the species at any particular time. We illustrate the model with a case study application to the invasion of common ragweed Ambrosia artemisiifolia in Austria. The invasion part of the model reconstructs the historical spread of this species across a grid of ～ 6 × 6 km² cells as driven by spatio‐temporal variation in physical site conditions, propagule production, dispersal, and ‘background’ introductions from unknown sources. The observation part models the detection of the species’ occurrences based on heterogeneous sampling efforts, human population density, and estimated local invasion level. We fitted the hierarchical model using a Bayesian inference approach with parameters estimated by Markov chain Monte Carlo (MCMC). The actual spread of A. artemisiifolia concentrated on the climatically well‐suited lowlands and was mainly driven by spatio‐temporal propagule pressure from source cells with long‐distance dispersal occurring rather frequently. Annual detection probabilities were estimated to vary between about 1 and up to 28%, depending mainly on sampling intensity. The model suggested that by 2005 about half of the actual distribution of the species was not yet documented. Our hierarchical model offers a flexible means to account for imperfect observation and spatio‐temporal variability in detection efficiency. Inferences can be used to disentangle aspects of the invasion dynamics itself from patterns of data collection, develop improved future surveying schemes, and design more efficient invasion management strategies.     

Reconstructing range dynamics and range fragmentation of European bison for the last 8000 years

Aim Understanding what constituted species’ ranges prior to large‐scale human influence, and how past climate and land use change have affected range dynamics, provides conservation planners with important insights into how species may respond to future environmental change. Our aim here was to reconstruct the Holocene range of European bison (Bison bonasus) by combining a time‐calibrated species distribution models (SDM) with a dynamic vegetation model. Location Europe. Method We used European bison occurrences from the Holocene in a maximum entropy model to assess bison range dynamics during the last 8000 years. As predictors, we used bioclimatic variables and vegetation reconstructions from the generalized dynamic vegetation model LPJ‐GUESS. We compared our range maps with maps of farmland and human population expansion to identify the main species range constraints. Results The Holocene distribution of European bison was mainly determined by vegetation patterns, with bison thriving in both broadleaved and coniferous forests, as well as by mean winter temperature. The heartland of European bison was in Central and Eastern Europe, whereas suitable habitat in Western Europe was scarce. While environmentally suitable regions were overall stable, the expansion of settlements and farming severely diminished available habitat. Main conclusions European bison habitat preferences may be wider than previously assumed, and our results suggest that the species had a more eastern and northern distribution than previously reported. Vegetation and climate transformation during the Holocene did not affect the bison’s range substantially. Conversely, human population growth and the spread of farming resulted in drastic bison habitat loss and fragmentation, likely reaching a tipping point during the last 1000 years. Combining SDM and dynamic vegetation models can improve range reconstructions and projections, and thus help to identify resilient conservation strategies for endangered species.     

Statistical models for monitoring and predicting effects of climate change and invasion on the free-living insects and a spider from sub-Antarctic Heard Island

Terrestrial ecosystems of sub-Antarctic islands are particularly sensitive to global and local human impacts, including climate change and species invasion. Invertebrates form a central component of these ecosystems. We conducted a stratified survey of 60 sites on sub-Antarctic Heard Island and used Poisson regression models to describe the spatial distribution and abundance of five of the ten free-living species captured. Acari and Collembola were not considered. Five species were not caught in traps in sufficient numbers to model. The distributions of species were described by altitude, vegetation type and aspect. The resulting distribution models can be used to both monitor and predict the effects of climate change and species invasion on this unique and valuable ecosystem.     

Coevolution in a one predator-two prey system

Background

Our understanding of coevolution in a predator–prey system is based mostly on pair-wise interactions.

Methodology and Principal Findings

Here I analyze a one-predator–two-prey system in which the predator''s attack ability and the defense abilities of the prey all evolve. The coevolutionary consequences can differ dramatically depending on the initial trait value and the timing of the alternative prey''s invasion into the original system. If the invading prey species has relatively low defense ability when it invades, its defense is likely to evolve to a lower level, stabilizing the population dynamics. In contrast, if when it invades its defense ability is close to that of the resident prey, its defense can evolve to a higher level and that of the resident prey may suddenly cease to evolve, destabilizing the population dynamics. Destabilization due to invasion is likely when the invading prey is adaptively superior (evolution of its defense is less constrained and fast), and it can also occur in a broad condition even when the invading prey is adaptively inferior. In addition, invasion into a resident system far from equilibrium characterized by population oscillations is likely to cause further destabilization.

Conclusions and Significance

An invading prey species is thus likely to destabilize a resident community.     

Invasion Waves in Populations with Excitable Dynamics

Whilst the most obvious mechanism for a biological invasion is the occupation of a new territory as a result of direct ingress by individuals of the invading population, a more subtle “invasion” may occur without significant motion of invading individuals if the population dynamics in a predator prey scenario has an “excitable” character. Here, “excitable” means that a local equilibrium state, either of coexistence of predator and prey, or of prey only, may, when disturbed by a small perturbation, switch to a new, essentially invaded state. In an invasion of this type little spatial movement of individuals occurs, but a wave of rapid change of population level nevertheless travels through the invaded territory. In this article we summarise and review recent modelling research which shows that the macroscopic features of these invasion waves depend strongly on the detailed spatial dynamics of the predator–prey relationship; the models assume simple (linear) diffusion and pursuit-evasion, represented by (non-linear) cross-diffusion, as examples. In the context of plankton population dynamics, such waves may be produced by sudden injections of nutrient and consequent rapid increase in plankton populations, brought about, for example, by the upwelling caused by a passing atmospheric low pressure system.     

Linking a spatially-explicit model of acacias to GIS and remotely-sensed data

Spatially-explicit and landscape-related simulation models are increasingly used in ecology, but are often criticized because their parameterization has high data requirements. A frequently suggested approach to overcome this difficulty is the linkage of spatially-explicit or landscape-related models with GIS (geographic information system) and remote-sensing technology. GIS can provide data on relevant landscape features, such as topography, and satellite images can be used to identify spatial vegetation distribution. In this paper, we use these techniques for simple, cost-inexpensive (in both time and money) parameterization based on readily-available GIS and remotely-sensed data. We use a previously developed, spatially-explicit model of the population dynamics of anAcacia species in the Negev desert of Israel (SAM, spatialAcacia model) to investigate if model initialization (measurement of current tree distribution) can be obtained from readily-available satellite images using a radiometric vegetation index (NDVI, normalized difference vegetation index). Furthermore, we investigate the applicability and the advantages of using an explicit consideration of landscape features in the model based on topographic data from a GIS. Using a DEM (digital elevation model), we compare the wadi topography to the current tree distribution observed in the field.     

Wildfire–vegetation dynamics affect predictions of climate change impact on bird communities

Community‐level climate change indicators have been proposed to appraise the impact of global warming on community composition. However, non‐climate factors may also critically influence species distribution and biological community assembly. The aim of this paper was to study how fire–vegetation dynamics can modify our ability to predict the impact of climate change on bird communities, as described through a widely‐used climate change indicator: the community thermal index (CTI). Potential changes in bird species assemblage were predicted using the spatially‐explicit species assemblage modelling framework – SESAM – that applies successive filters to constrained predictions of richness and composition obtained by stacking species distribution models that hierarchically integrate climate change and wildfire–vegetation dynamics. We forecasted future values of CTI between current conditions and 2050, across a wide range of fire–vegetation and climate change scenarios. Fire–vegetation dynamics were simulated for Catalonia (Mediterranean basin) using a process‐based model that reproduces the spatial interaction between wildfire, vegetation dynamics and wildfire management under two IPCC climate scenarios. Net increases in CTI caused by the concomitant impact of climate warming and an increasingly severe wildfire regime were predicted. However, the overall increase in the CTI could be partially counterbalanced by forest expansion via land abandonment and efficient wildfire suppression policies. CTI is thus strongly dependent on complex interactions between climate change and fire–vegetation dynamics. The potential impacts on bird communities may be underestimated if an overestimation of richness is predicted but not constrained. Our findings highlight the need to explicitly incorporate these interactions when using indicators to interpret and forecast climate change impact in dynamic ecosystems. In fire‐prone systems, wildfire management and land‐use policies can potentially offset or heighten the effects of climate change on biological communities, offering an opportunity to address the impact of global climate change proactively.     

Forecasting species ranges by statistical estimation of ecological niches and spatial population dynamics

Aim The study and prediction of species–environment relationships is currently mainly based on species distribution models. These purely correlative models neglect spatial population dynamics and assume that species distributions are in equilibrium with their environment. This causes biased estimates of species niches and handicaps forecasts of range dynamics under environmental change. Here we aim to develop an approach that statistically estimates process‐based models of range dynamics from data on species distributions and permits a more comprehensive quantification of forecast uncertainties. Innovation We present an approach for the statistical estimation of process‐based dynamic range models (DRMs) that integrate Hutchinson's niche concept with spatial population dynamics. In a hierarchical Bayesian framework the environmental response of demographic rates, local population dynamics and dispersal are estimated conditional upon each other while accounting for various sources of uncertainty. The method thus: (1) jointly infers species niches and spatiotemporal population dynamics from occurrence and abundance data, and (2) provides fully probabilistic forecasts of future range dynamics under environmental change. In a simulation study, we investigate the performance of DRMs for a variety of scenarios that differ in both ecological dynamics and the data used for model estimation. Main conclusions Our results demonstrate the importance of considering dynamic aspects in the collection and analysis of biodiversity data. In combination with informative data, the presented framework has the potential to markedly improve the quantification of ecological niches, the process‐based understanding of range dynamics and the forecasting of species responses to environmental change. It thereby strengthens links between biogeography, population biology and theoretical and applied ecology.     

Analysis of phenotypic change in relation to climatic drivers in a population of Soay sheep Ovis aries

Climatic change has frequently been identified as a key driver of change in biological communities. These changes can take the form of alterations to population dynamics, phenotypic characters, genetics and the life history of organisms and can have impacts on entire ecosystems. This study presents a novel investigation of how changes in a large scale climatic index, the North Atlantic Oscillation (NAO) can influence population dynamics and phenotypic characters in a population of ungulates. We use an integral projection model combined with actual climate change predictions to project future body size distributions for a population of Soay sheep Ovis aries. The climate change predictions used to direct our model projections were taken from published results of climate models, covering a range of different emissions scenarios. Our model results showed that for positive changes in the mean NAO large population declines occurred simultaneously with increases in mean body weight. The exact direction and magnitude of changes to population dynamics and character distributions were dependent on the greenhouse gas emissions scenario and model used to predict the NAO. This study has demonstrated how integral projection models can use outputs of climate models to direct projections of population dynamics and phenotypic character distributions. This approach allows the results of this study to be placed within current climate change research. The nature of integral projection models means that this methodology can be easily applied to other populations. The model can also be easily updated when new climate change predictions become available, making it a useful tool for understanding potential population level responses to climatic change. Synthesis Understanding how changes in climate affect biological communities is a key component in predicting the future form of populations. Utilising a novel approach that incorporates climatic drivers (in this instance the winter North Atlantic Oscillation) into an integral projection model framework, we predict future Soay sheep dynamics under specific climate change scenarios. Tracking quantitative trait distributions and life history metrics, our results predict declining population size and increasing body weight for an increasingly positive winter North Atlantic Oscillation index, as predicted by climate models. This has important implications for future wildlife management strategies and linking demographic responses to climate change.     

Allee effects, invasion pinning, and species' borders

All species' ranges are the result of successful past invasions. Thus, models of species' invasions and their failure can provide insight into the formation of a species' geographic range. Here, we study the properties of invasion models when a species cannot persist below a critical population density known as an "Allee threshold." In both spatially continuous reaction-diffusion models and spatially discrete coupled ordinary-differential-equation models, the Allee effect can cause an invasion to fail. In patchy landscapes (with dynamics described by the spatially discrete model), range limits caused by propagation failure (pinning) are stable over a wide range of parameters, whereas, in an uninterrupted habitat (with dynamics described by a spatially continuous model), the zero velocity solution is structurally unstable and thus unlikely to persist in nature. We derive conditions under which invasion waves are pinned in the discrete space model and discuss their implications for spatially complex dynamics, including critical phenomena, in ecological landscapes. Our results suggest caution when interpreting abrupt range limits as stemming either from competition between species or a hard environmental limit that cannot be crossed: under a wide range of plausible ecological conditions, species' ranges may be limited by an Allee effect. Several example systems appear to fit our general model.     

Relative nonlinearity and permanence

We modify the commonly used invasibility concept for coexistence of species to the stronger concept of uniform invasibility. For two-species discrete-time competition and predator-prey models, we use this concept to find broad easily checked sufficient conditions for the rigorous concept of permanent coexistence. With these results, permanent coexistence becomes a tractable concept for many discrete-time population models. To understand how these conditions apply to nonpoint attractors, we generalize the concept of relative nonlinearity and use it to show how population fluctuations affect the long-term low-density growth rate (“the invasion rate”) of a species when it is invading the system consisting of the other species (“the resident”) at a single-species attractor. The concept of relative nonlinearity defines circumstances when this invasion rate is increased or decreased by resident population fluctuations arising from a nonpoint attractor. The presence and sign of relative nonlinearity is easily checked in models of interacting species. When relative nonlinearity is zero or positive, fluctuations cannot decrease the invasion rate. It follows that permanence is then determined by invasibility of the resident’s fixed points. However, when relative nonlinearity is negative, invasibility, and hence permanent coexistence, can be undermined by resident population fluctuations. These results are illustrated with specific two-species competition and predator-prey models of generic forms.     

Feasibility constraints on the elastic expansion of ecosystem models

Stable n-species ecosystem models may be expanded into larger (n + 1)-species stable models when an invading species is introduced. Such invasions are referred to as being successful due to the elasticity of the original community. Elasticity is dependent upon the interaction terms of both the original community members and the invading species. Feasibility constraints for elasticity and inelasticity are presented here for these terms in the context of a generalized ecosystem model where invasion causes only minor displacements in equilibrium population densities.     

Modeling the presence probability of invasive plant species with nonlocal dispersal

Mathematical models for the spread of invading plant organisms typically utilize population growth and dispersal dynamics to predict the time-evolution of a population distribution. In this paper, we revisit a particular class of deterministic contact models obtained from a stochastic birth process for invasive organisms. These models were introduced by Mollison (J R Stat Soc 39(3):283, 1977). We derive the deterministic integro-differential equation of a more general contact model and show that the quantity of interest may be interpreted not as population size, but rather as the probability of species occurrence. We proceed to show how landscape heterogeneity can be included in the model by utilizing the concept of statistical habitat suitability models which condense diverse ecological data into a single statistic. As ecologists often deal with species presence data rather than population size, we argue that a model for probability of occurrence allows for a realistic determination of initial conditions from data. Finally, we present numerical results of our deterministic model and compare them to simulations of the underlying stochastic process.