A flow network model for animal movement on a landscape with application to invasion

Animal movement, whether for foraging, mate-seeking, predator avoidance, dispersal, or migration, is a fundamental aspect of ecology that shapes spatial abundance distributions, genetic compositions, and dynamics of populations. A variety of movement models have been used for predicting the effects of natural or human-caused landscape changes, invading species, or other disturbances on local ecology. Here we introduce the flow network—a general modeling framework for population dynamics and movement in a metapopulation representing a network of habitat sites (nodes). Based on the principles of physical transport phenomena such as fluid flow through pipes (Pouiselle’s Law) and analogously, the flow of electric current across a circuit (Ohm’s Law), the flow network provides a novel way of modeling movement, where flow rates are functions of relative node pressures and the resistance to movement between them. Flow networks offer the flexibility of incorporating abiotic and biotic conditions that affect either pressures, resistance, or both. To illustrate an application of the flow network, we present a theoretical invasion scenario. We consider the effects of spatial structure on the speed of invasion by varying the spatial regularity of node arrangement. In the context of invasion, we model management actions targeting nodes or edges, and consider the effects on speed of invasion, node occupation, and total abundance. The flow network approach offers the flexibility to incorporate spatial heterogeneity in both rates of flow and site pressures and offers an intuitive approach to connecting population dynamics and landscape features to model movement.     

Unexplained variability among spatial replicates in transient elasticity: implications for evolutionary ecology and management of invasive species

Understanding actual and potential selection on traits of invasive species requires an assessment of the sources of variation in demographic rates. While some of this variation is assignable to environmental, biotic or historical factors, unexplained demographic variation also may play an important role. Even when sites and populations are chosen as replicates, the residual variation in demographic rates can lead to unexplained divergence of asymptotic and transient population dynamics. This kind of divergence could be important for understanding long- and short- term differences among populations of invasive species, but little is known about it. We investigated the demography of a small invasive tree Psidium cattleianum Sabine in the rainforest of Hawaiʻi at four sites chosen for their ecological similarity. Specifically, we parameterized and analyzed integral projection models (IPM) to investigate projected variability among replicate populations in: (1) total population size and annual per capita population growth rate during the transient and asymptotic periods; (2) population structure initially and asymptotically; (3) three key parameters that characterize transient dynamics (the weighted distance of the structure at each time step from the asymptotic structure, the strength of the sub-dominant relative to the dominant dynamics, and inherent cyclicity in the subdominant); and (4) proportional sensitivity (elasticity) of population growth rates (both asymptotic and transient) to perturbations of various components of the life cycle. We found substantial variability among replicate populations in all these aspects of the dynamics. We discuss potential consequences of variability across ecologically similar sites for management and evolutionary ecology in the exotic range of invasive species.     

Range Expansion and Population Dynamics of an Invasive Species: The Eurasian Collared-Dove (Streptopelia decaocto)

Invasive species offer ecologists the opportunity to study the factors governing species distributions and population growth. The Eurasian Collared-Dove (Streptopelia decaocto) serves as a model organism for invasive spread because of the wealth of abundance records and the recent development of the invasion. We tested whether a set of environmental variables were related to the carrying capacities and growth rates of individual populations by modeling the growth trajectories of individual populations of the Collared-Dove using Breeding Bird Survey (BBS) and Christmas Bird Count (CBC) data. Depending on the fit of our growth models, carrying capacity and growth rate parameters were extracted and modeled using historical, geographical, land cover and climatic predictors. Model averaging and individual variable importance weights were used to assess the strength of these predictors. The specific variables with the greatest support in our models differed between data sets, which may be the result of temporal and spatial differences between the BBS and CBC. However, our results indicate that both carrying capacity and population growth rates are related to developed land cover and temperature, while growth rates may also be influenced by dispersal patterns along the invasion front. Model averaged multivariate models explained 35–48% and 41–46% of the variation in carrying capacities and population growth rates, respectively. Our results suggest that widespread species invasions can be evaluated within a predictable population ecology framework. Land cover and climate both have important effects on population growth rates and carrying capacities of Collared-Dove populations. Efforts to model aspects of population growth of this invasive species were more successful than attempts to model static abundance patterns, pointing to a potentially fruitful avenue for the development of improved invasive distribution models.     

Between‐lake variation in the trophic ecology of an invasive crayfish

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Empirical and virtual investigation of the population dynamics of an alien plant under the constraints of local carrying capacity: Heracleum mantegazzianum in the Czech Republic

During the last decades, invasive alien species have become a global concern because of their ecological and economic impact. Heracleum mantegazzianum (Apiaceae), is a tall monocarpic perennial native to Caucasus and invasive in Europe since the 1950s. Within an interdisciplinary EU project aimed at assessing suitable management strategy, we analysed the demography and ecology of this species in its invasive range. The monitoring of population dynamics in the Czech Republic led to the result that in the observed sites the species showed decreasing populations. To find an explanation for this unexpected result, two types of models were parameterized, based on the empirical data: (1) a stage-based transition matrix model, which projected a continuous negative development, and (2) a spatially explicit individual-based model (IBM), including individual variation. This second model was able to create a population with steady individual numbers. Analyses of the simulation showed that in more than 54% of the simulated years (n=5000) the growth rate was smaller than one. Still, population increase in the remaining years was sufficient to sustain a population. Nevertheless long-term observations document an invasive behaviour of the observed populations. Hence, we could assume temporal changes in the course of an invasion and thus wanted to evaluate the probability of sampling negative growth in dependence of time since first invasion. By using a method from ‘Virtual Ecology’, we approached the question: first we create an invasive population, based on the empirical data of H. mantegazzianum and second empirical sampling techniques were mimicked using the Virtual Ecologist approach. The results demonstrate how the probability of sampling negative growth increases with time since first invasion. Hence, we assume that the studied populations have already reached a maximum of their local invasive potential and thus stagnate in their size.     

Assessing the importance of disturbance, site conditions, and the biotic barrier for dandelion invasion in an Alpine habitat

Several factors have been identified as relevant in determining the abundance of non-native invasive species. Nevertheless, the relative importance of these factors will vary depending on the invaded habitat and the characteristics of the invasive species. Due to their harsh environmental conditions and remoteness, high-alpine habitats are often considered to be at low risk of plant invasion. However, an increasing number of reports have shown the presence and spread of non-native plant species in alpine habitats; thus, it is important to study which factors control the invasion process in these harsh habitats. In this study, we assessed the role of disturbance, soil characteristics, biotic resistance and seed rain in the establishment and abundance of the non-native invasive species Taraxacum officinale (dandelion) in the Andes of central Chile. By focusing on human-disturbed patches, naturally disturbed patches, and undisturbed patches, we did not find that disturbance per se, or its origin, affected the establishment and abundance of T. officinale. The abundance of this non-native invasive species was not negatively related to the diversity of native species at local scales, indicating no biotic resistance to invasion; instead, some positive relationships were found. Our results indicate that propagule pressure (assessed by the seed rain) and the abiotic soil characteristics are the main factors related to the abundance of this non-native invasive species. Hence, in contrast to what has been found for more benign habitats, disturbance and biotic resistance have little influence on the invasibility of T. officinale in this high-alpine habitat.     

The role of long‐distance seed dispersal in the local population dynamics of an invasive plant species

Aim Long‐distance dispersal is important for plant population dynamics at larger spatial scales, but our understanding of this phenomenon is mostly based on computer modelling rather than field data. This paper, by combining field data and a simulation model, quantifies the fraction of the seed of the alien species Heracleum mantegazzianum that needs to disperse over a long distance for successful invasion. Location Central Europe, Czech Republic. Methods To assess the role of random dispersal in long‐term population dynamics of the studied species, we combined longitudinal data covering 50 years of the invasion of this plant from its very start, inferred from a series of aerial photographs of 60‐ha plots, with data on population dynamics at a fine scale of 10‐m² plots. Results A simulation model based on field data indicates that the fraction of seed that is dispersed from source plants not described by the short‐distance dispersal kernel ranges from 0.1 to 7.5% of the total seed set. The fraction of long‐distance dispersed seed that provides the best prediction of the observed spread was significantly negatively correlated with the percentage of habitats suitable for invasion. Main conclusions Our results indicate that the fraction of seeds that needed to be dispersed over long distances to account for the observed invasion dynamics decreased with increasing proportion of invasible habitats, indicating that the spatial pattern of propagule pressure differs in landscapes prone to invasion. Long‐distance dispersal is an important component of the population dynamics of an invasive species even at relatively small scales.     

Spreading speed, traveling waves, and minimal domain size in impulsive reaction-diffusion models

How growth, mortality, and dispersal in a species affect the species' spread and persistence constitutes a central problem in spatial ecology. We propose impulsive reaction-diffusion equation models for species with distinct reproductive and dispersal stages. These models can describe a seasonal birth pulse plus nonlinear mortality and dispersal throughout the year. Alternatively, they can describe seasonal harvesting, plus nonlinear birth and mortality as well as dispersal throughout the year. The population dynamics in the seasonal pulse is described by a discrete map that gives the density of the population at the end of a pulse as a possibly nonmonotone function of the density of the population at the beginning of the pulse. The dynamics in the dispersal stage is governed by a nonlinear reaction-diffusion equation in a bounded or unbounded domain. We develop a spatially explicit theoretical framework that links species vital rates (mortality or fecundity) and dispersal characteristics with species' spreading speeds, traveling wave speeds, as well as minimal domain size for species persistence. We provide an explicit formula for the spreading speed in terms of model parameters, and show that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions. We also give an explicit formula for the minimal domain size using model parameters. Our results show how the diffusion coefficient, and the combination of discrete- and continuous-time growth and mortality determine the spread and persistence dynamics of the population in a wide variety of ecological scenarios. Numerical simulations are presented to demonstrate the theoretical results.     

Synchronization in ecological systems by weak dispersal coupling with time delay

One of the most salient spatiotemporal patterns in population ecology is the synchronization of fluctuating local populations across vast spatial extent. Synchronization of abundance has been widely observed across a range of spatial scales in relation to the rate of dispersal among discrete populations. However, the dependence of synchrony on patterns of among-patch movement across heterogeneous landscapes has been largely ignored. Here, we consider the duration of movement between two predator–prey communities connected by weak dispersal and its effect on population synchrony. More specifically, we introduce time-delayed dispersal to incorporate the finite transmission time between discrete populations across a continuous landscape. Reducing the system to a phase model using weakly connected network theory, it is found that the time delay is an important factor determining the nature and stability of phase-locked states. Our analysis predicts enhanced convergence to stable synchronous fluctuations in general and a decreased ability of systems to produce in-phase synchronization dynamics in the presence of delayed dispersal. These results introduce delayed dispersal as a tool for understanding the importance of dispersal time across a landscape matrix in affecting metacommunity dynamics. They further highlight the importance of landscape and dispersal patterns for predicting the onset of synchrony between weakly coupled populations.     

Do species population parameters and landscape characteristics affect the relationship between local population abundance and surrounding habitat amount?

In landscape ecology, correlational approaches are typically used to analyse links between local population abundance, and the surrounding habitat amount to estimate biologically-relevant landscape size (extent) for managing endangered or pest populations. The direction, strength, and spatial extent of the correlations are then sometimes interpreted in terms of species population parameters. Here we simulated the population dynamics of generalized species across spatially explicit landscapes that included two distinct habitat types. We investigated how characteristics of a landscape (structure), including the variation in habitat quality and spatial aggregation of the habitat, and the precise population-dynamic properties of the simulated species (dispersal and growth rates) affect the correlation between population abundance and amount of surrounding favourable habitat in the landscape. To evaluate these spatial extents of correlation, proportions of favourable habitat were calculated within several circles of increasing diameter centred on sampling patches of favourable habitat where population abundance was recorded.We found that the value of the correlation coefficients between population abundance and amount of surrounding favourable habitat depended on both population dynamic parameters and landscape characteristics. Coefficients of correlation increased with the variation in habitat quality and the aggregation of favourable habitat in the landscape, but decreased with the dispersal distance. The distance at which the correlation was maximized was sensitive to an interaction between the level of aggregation of the habitat and the dispersal distance; whereas the greatest distance at which a significant correlation occurred was more sensitive to the variation in habitat quality. Our results corroborate the view that correlational analyses do provide information on the local population dynamics of a species in a given habitat type and on its dispersal rate parameters. However, even in simplified, model frameworks, direct relationships are often difficult to disentangle and global landscape characteristics should be reported in any studies intended to derive population-dynamic parameters from correlations. Where possible, replicated landscapes should be examined in order to control for the interaction between population dynamics and landscape structure. Finally, we recommend using species-specific, population-dynamic modelling in order to interpret correctly the observed patterns of correlation in the landscape.     

Gridlock and beltways: the genetic context of urban invasions

The rapid expansion of urban land across the globe presents new and numerous opportunities for invasive species to spread and flourish. Ecologists historically rejected urban ecosystems as important environments for ecology and evolution research but are beginning to recognize the importance of these systems in shaping the biology of invasion. Urbanization can aid the introduction, establishment, and spread of invaders, and these processes have substantial consequences on native species and ecosystems. Therefore, it is valuable to understand how urban areas influence populations at all stages in the invasion process. Population genetic tools are essential to explore the driving forces of invasive species dispersal, connectivity, and adaptation within cities. In this review, we synthesize current research about the influence of urban landscapes on invasion genetics dynamics. We conclude that urban areas are not only points of entry for many invasive species, they also facilitate population establishment, are pools for genetic diversity, and provide corridors for further spread both within and out of cities. We recommend the continued use of genetic studies to inform invasive species management and to understand the underlying ecological and evolutionary processes governing successful invasion.     

The implicit assumption of symmetry and the species abundance distribution

Species abundance distributions (SADs) have played a historical role in the development of community ecology. They summarize information about the number and the relative abundance of the species encountered in a sample from a given community. For years ecologists have developed theory to characterize species abundance patterns, and the study of these patterns has received special attention in recent years. In particular, ecologists have developed statistical sampling theories to predict the SAD expected in a sample taken from a region. Here, we emphasize an important limitation of all current sampling theories: they ignore species identity. We present an alternative formulation of statistical sampling theory that incorporates species asymmetries in sampling and dynamics, and relate, in a general way, the community-level SAD to the distribution of population abundances of the species integrating the community. We illustrate the theory on a stochastic community model that can accommodate species asymmetry. Finally, we discuss the potentially important role of species asymmetries in shaping recently observed multi-humped SADs and in comparisons of the relative success of niche and neutral theories at predicting SADs.     

A general modeling framework for describing spatially structured population dynamics

Variation in movement across time and space fundamentally shapes the abundance and distribution of populations. Although a variety of approaches model structured population dynamics, they are limited to specific types of spatially structured populations and lack a unifying framework. Here, we propose a unified network‐based framework sufficiently novel in its flexibility to capture a wide variety of spatiotemporal processes including metapopulations and a range of migratory patterns. It can accommodate different kinds of age structures, forms of population growth, dispersal, nomadism and migration, and alternative life‐history strategies. Our objective was to link three general elements common to all spatially structured populations (space, time and movement) under a single mathematical framework. To do this, we adopt a network modeling approach. The spatial structure of a population is represented by a weighted and directed network. Each node and each edge has a set of attributes which vary through time. The dynamics of our network‐based population is modeled with discrete time steps. Using both theoretical and real‐world examples, we show how common elements recur across species with disparate movement strategies and how they can be combined under a unified mathematical framework. We illustrate how metapopulations, various migratory patterns, and nomadism can be represented with this modeling approach. We also apply our network‐based framework to four organisms spanning a wide range of life histories, movement patterns, and carrying capacities. General computer code to implement our framework is provided, which can be applied to almost any spatially structured population. This framework contributes to our theoretical understanding of population dynamics and has practical management applications, including understanding the impact of perturbations on population size, distribution, and movement patterns. By working within a common framework, there is less chance that comparative analyses are colored by model details rather than general principles.     

Dispersal patterns, dispersal mechanisms, and invasion wave speeds for invasive thistles

Understanding and predicting population spread rates is an important problem in basic and applied ecology. In this article, we link estimates of invasion wave speeds to species traits and environmental conditions. We present detailed field studies of wind dispersal and compare nonparametric (i.e., data-based) and mechanistic (fluid dynamics model-based) dispersal kernel and spread rate estimates for two important invasive weeds, Carduus nutans and Carduus acanthoides. A high-effort trapping design revealed highly leptokurtic dispersal distributions, with seeds caught up to 96 m from the source, far further than mean dispersal distances (approx. 2 m). Nonparametric wave speed estimates are highly sensitive to sampling effort. Mechanistic estimates are insensitive to sampling because they are obtained from independent data and more useful because they are based on the dispersal mechanism. Over a wide range of realistic conditions, mechanistic spread rate estimates were most sensitive to high winds and low seed settling velocities. The combination of integrodifference equations and mechanistic dispersal models is a powerful tool for estimating invasion spread rates and for linking these estimates to characteristics of the species and the environment.     

Effects of landscape structure on the invasive spread of black cherry Prunus serotina in an agricultural landscape in Flanders, Belgium

Analysing invasive spread from a landscape ecological perspective forms an important challenge in plant invasion ecology. The present study examines the effects of landscape structure on the spatial and temporal dynamics of an expanding black cherry Prunus serotina population within a rural landscape in Flanders, Belgium, carrying a dense network of interconnected hedgerows. The study area, 251 ha in size, harboured a total of 2962 P. serotina individuals. The population was characterised by a negative exponential age distribution, a high growth rate and an early and continuous reproduction throughout the species' life cycle. The historical rate of spread of the species through the hedgerow network progressively increased with time, especially during the last decade. Spatial point pattern analysis revealed that the individuals had a significantly clustered distribution pattern and were spatially aggregated around seed sources, hedgerow intersections and roosting trees. Logistic regression analysis confirmed the effect of landscape structure on P. serotina occurrence, suggesting directional long distance dispersal by avian dispersal vectors, resulting in a differential seed pressure throughout the hedgerow network due to the preference of dispersing birds for roosting in structurally rich hedgerow with large trees near hedgerow intersections. Hence, the distribution of P. serotina in agricultural landscapes was strongly mediated by dispersal processes. Furthermore, decreasing spatial aggregation along the species life cycle, with especially seedlings and saplings being significantly aggregated while adult individuals were mostly distributed at random, and a relative outward shift of seedling recruitment curves with time indicate density dependent mortality, probably caused by intraspecific competition.     

Population decline but increased distribution of an invasive ant genotype on a Pacific atoll

Populations of invasive species are often studied when their effects are perceived as a problem. Yet observing the dynamics of populations over longer time periods can highlight changes in effects on invaded communities, and assist with management decisions. In this study we revisit an invasion of the yellow crazy ant (Anoplolepis gracilipes) in the Tokelau archipelago to determine if the distribution and abundance of the ant has changed ~7 years after surveys completed in 2004. We were particularly interested in whether populations of a previously identified invasive haplotype (D) had increased in distribution and abundance, as this haplotype was implicated in negative effects on resident ant communities. Indeed, haplotype D populations have become more widespread since the initial survey, more likely owing to new introductions or movement by humans, rather than intrinsic characteristics of the haplotype. We also found that despite no significant change in the abundance of A. gracilipes overall, haplotype D populations have declined in abundance. Residents of the Tokelau atolls no longer consider the ant to be a pest as they did 7 years ago, when populations of this ant interfered with their food production and many other aspects of daily life. We observed no significant differences between A. gracilipes invaded and uninvaded communities, which suggests that the ant is at a level of abundance below which significant negative ecological effects may occur. Population declines of invasive species are not infrequent, and understanding these population dynamics, particularly the underlying mechanisms promoting population declines or stabilisation, should be a high priority for invasion ecology.     

Body Size and Geographic Range Do Not Explain Long Term Variation in Fish Populations: A Bayesian Phylogenetic Approach to Testing Assembly Processes in Stream Fish Assemblages

We combine evolutionary biology and community ecology to test whether two species traits, body size and geographic range, explain long term variation in local scale freshwater stream fish assemblages. Body size and geographic range are expected to influence several aspects of fish ecology, via relationships with niche breadth, dispersal, and abundance. These traits are expected to scale inversely with niche breadth or current abundance, and to scale directly with dispersal potential. However, their utility to explain long term temporal patterns in local scale abundance is not known. Comparative methods employing an existing molecular phylogeny were used to incorporate evolutionary relatedness in a test for covariation of body size and geographic range with long term (1983 – 2010) local scale population variation of fishes in West Fork White River (Indiana, USA). The Bayesian model incorporating phylogenetic uncertainty and correlated predictors indicated that neither body size nor geographic range explained significant variation in population fluctuations over a 28 year period. Phylogenetic signal data indicated that body size and geographic range were less similar among taxa than expected if trait evolution followed a purely random walk. We interpret this as evidence that local scale population variation may be influenced less by species-level traits such as body size or geographic range, and instead may be influenced more strongly by a taxon’s local scale habitat and biotic assemblages.     

Understanding species distribution in dynamic populations: a new approach using spatio‐temporal point process models

Understanding and predicting a species’ distribution across a landscape is of central importance in ecology, biogeography and conservation biology. However, it presents daunting challenges when populations are highly dynamic (i.e. increasing or decreasing their ranges), particularly for small populations where information about ecology and life history traits is lacking. Currently, many modelling approaches fail to distinguish whether a site is unoccupied because the available habitat is unsuitable or because a species expanding its range has not arrived at the site yet. As a result, habitat that is indeed suitable may appear unsuitable. To overcome some of these limitations, we use a statistical modelling approach based on spatio‐temporal log‐Gaussian Cox processes. These model the spatial distribution of the species across available habitat and how this distribution changes over time, relative to covariates. In addition, the model explicitly accounts for spatio‐temporal dynamics that are unaccounted for by covariates through a spatio‐temporal stochastic process. We illustrate the approach by predicting the distribution of a recently established population of Eurasian cranes Grus grus in England, UK, and estimate the effect of a reintroduction in the range expansion of the population. Our models show that wetland extent and perimeter‐to‐area ratio have a positive and negative effect, respectively, in crane colonisation probability. Moreover, we find that cranes are more likely to colonise areas near already occupied wetlands and that the colonisation process is progressing at a low rate. Finally, the reintroduction of cranes in SW England can be considered a human‐assisted long‐distance dispersal event that has increased the dispersal potential of the species along a longitudinal axis in S England. Spatio‐temporal log‐Gaussian Cox process models offer an excellent opportunity for the study of species where information on life history traits is lacking, since these are represented through the spatio‐temporal dynamics reflected in the model.     

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.