Seasonal and Diurnal Patterns of Spore Release Can Significantly Affect the Proportion of Spores Expected to Undergo Long-Distance Dispersal

Many of the fungal pathogens that threaten agricultural and natural systems undergo wind-assisted dispersal. During turbulent wind conditions, long-distance dispersal can occur, and airborne spores are carried over distances greater than the mean. The occurrence of long-distance dispersal is an important ecological process, as it can drastically increase the extent to which pathogen epidemics spread across a landscape, result in rapid transmission of disease to previously uninfected areas, and influence the spatial structure of pathogen populations in fragmented landscapes. Since the timing of spore release determines the wind conditions that prevail over a dispersal event, this timing is likely to affect the probability of long-distance dispersal occurring. Using a Lagrangian stochastic model, we test the effect of seasonal and diurnal variation in the release of spores on wind-assisted dispersal. Spores released during the hottest part of the day are shown to be more likely to undergo long-distance dispersal than those released at other times. Furthermore, interactions are shown to occur between seasonal and diurnal patterns of release. These results have important consequences for further modelling of wind-assisted dispersal and the use of models to predict the spread of fungal pathogens and resulting population and epidemic dynamics.     

Effects of dispersal mechanisms on spatio-temporal development of epidemics

The nature of pathogen transport mechanisms strongly determines the spatial pattern of disease and, through this, the dynamics and persistence of epidemics in plant populations. Up to recently, the range of possible mechanisms or interactions assumed by epidemic models has been limited: either independent of the location of individuals (mean-field models) or restricted to local contacts (between nearest neighbours or decaying exponentially with distance). Real dispersal processes are likely to lie between these two extremes, and many are well described by long-tailed contact kernels such as power laws. We investigate the effect of different spatial dispersal mechanisms on the spatio-temporal spread of disease epidemics by simulating a stochastic Susceptible-infective model motivated by previous data analyses. Both long-term stationary behaviour (in the presence of a control or recovery process) and transient behaviour (which varies widely within and between epidemics) are examined. We demonstrate the relationship between epidemic size and disease pattern (characterized by spatial autocorrelation), and its dependence on dispersal and infectivity parameters. Special attention is given to boundary effects, which can decrease disease levels significantly relative to standard, periodic geometries in cases of long-distance dispersal. We propose and test a definition of transient duration which captures the dependence of transients on dispersal mechanisms. We outline an analytical approach that represents the behaviour of the spatially-explicit model, and use it to prove that the epidemic size is predicted exactly by the mean-field model (in the limit of an infinite system) when dispersal is sufficiently long ranged (i.e. when the power-law exponent a相似文献   

Spatial and temporal invasion dynamics of the 2014–2017 Zika and chikungunya epidemics in Colombia

Zika virus (ZIKV) and chikungunya virus (CHIKV) were recently introduced into the Americas resulting in significant disease burdens. Understanding their spatial and temporal dynamics at the subnational level is key to informing surveillance and preparedness for future epidemics. We analyzed anonymized line list data on approximately 105,000 Zika virus disease and 412,000 chikungunya fever suspected and laboratory-confirmed cases during the 2014–2017 epidemics. We first determined the week of invasion in each city. Out of 1,122, 288 cities met criteria for epidemic invasion by ZIKV and 338 cities by CHIKV. We analyzed risk factors for invasion using linear and logistic regression models. We also estimated that the geographic origin of both epidemics was located in Barranquilla, north Colombia. We assessed the spatial and temporal invasion dynamics of both viruses to analyze transmission between cities using a suite of (i) gravity models, (ii) Stouffer’s rank models, and (iii) radiation models with two types of distance metrics, geographic distance and travel time between cities. Invasion risk was best captured by a gravity model when accounting for geographic distance and intermediate levels of density dependence; Stouffer’s rank model with geographic distance performed similarly well. Although a few long-distance invasion events occurred at the beginning of the epidemics, an estimated distance power of 1.7 (95% CrI: 1.5–2.0) from the gravity models suggests that spatial spread was primarily driven by short-distance transmission. Similarities between the epidemics were highlighted by jointly fitted models, which were preferred over individual models when the transmission intensity was allowed to vary across arboviruses. However, ZIKV spread considerably faster than CHIKV.     

Rates of spread of marine pathogens

Epidemics of marine pathogens can spread at extremely rapid rates. For example, herpes virus spread through pilchard populations in Australia at a rate in excess of 10 000 km year^?1, and morbillivirus infections in seals and dolphins have spread at more than 3000 km year^?1. In terrestrial environments, only the epidemics of myxomatosis and calicivirus in Australian rabbits and West Nile Virus in birds in North America have rates of spread in excess of 1000 km year^?1. The rapid rates of spread of these epidemics has been attributed to flying insect vectors, but flying vectors have not been proposed for any marine pathogen. The most likely explanation for the relatively rapid spread of marine pathogens is the lack of barriers to dispersal in some parts of the ocean, and the potential for long‐term survival of pathogens outside the host. These findings caution that pathogens may pose a particularly severe problem in the ocean. There is a need to develop epidemic models capable of generating these high rates of spread and obtain more estimates of disease spread rate.     

Comparable ecological dynamics underlie early cancer invasion and species dispersal, involving self-organizing processes

Occupancy of new habitats through dispersion is a central process in nature. In particular, long-distance dispersal is involved in the spread of species and epidemics, although it has not been previously related with cancer invasion, a process that involves cell spreading to tissues far away from the primary tumour.Using simulations and real data we show that the early spread of cancer cells is similar to the species individuals spread and we suggest that both processes are represented by a common spatio-temporal signature of long-distance dispersal and subsequent local proliferation. This signature is characterized by a particular fractal geometry of the boundaries of patches generated, and a power-law scaled, disrupted patch size distribution. In contrast, invasions involving only dispersal but not subsequent proliferation (“physiological invasions”) like trophoblast cells invasion during normal human placentation did not show the patch size power-law pattern. Our results are consistent under different temporal and spatial scales, and under different resolution levels of analysis.We conclude that the scaling properties are a hallmark and a direct result of long-distance dispersal and proliferation, and that they could reflect homologous ecological processes of population self-organization during cancer and species spread. Our results are significant for the detection of processes involving long-range dispersal and proliferation like cancer local invasion and metastasis, biological invasions and epidemics, and for the formulation of new cancer therapeutical approaches.     

Long distance dispersal and landscape occupancy in a metapopulation of the cranberry fritillary butterfly

Movements between habitat patches in a patchy population of the butterfly Boloria aquilonaris were monitored using capture-mark-recapture methods during three successive generations. For each data set, the inverse cumulative proportion of individuals moving 100 m distance classes was fitted to the negative exponential function and the inverse power function. In each case, the negative exponential function provided a better fit than the inverse power function. Two dispersal kernels were generated using both negative exponential and inverse power functions. These dispersal kernels were used to predict movements between 14 suitable sites in a landscape of 220 km². The negative exponential function generated a dispersal kernel predicting extremely low probabilities for movements exceeding 1 km. The inverse power function generated probabilities predicting that between site movements were possible, according to metapopulation size. CMR studies in the landscape revealed that long distance movements occurred at each generation, corresponding to predictions of the inverse power function dispersal kernel. A total of 26 movements between sites (up to 13 km) were detected, together with recolonisation of empty sites. The spatial scale of the metapopulation dynamics is larger than ever reported on butterflies and long distance movements clearly matter to the persistence of this species in a highly fragmented landscape.     

Comparing short and long‐distance dispersal: modelling and field case studies

Dispersal is a factor of great importance in determining a species spatial distribution. Short distance dispersal (SDD) and long distance dispersal (LDD) strategies yield very different spatial distributions. In this paper we compare spatial spread patterns from SDD and LDD simulations, contrast them with patterns from field data, and assess the significance of biological and population traits. Simulated SDD spread using an exponential function generates a single circular patch with a well‐defined invasion front showing a travelling‐wave structure. The invasive spread is relatively slow as it is restricted to reproductive individuals occupying the outer zone of the circular patch. As a consequence of this dispersal dynamics, spread is slower than spread generated by LDD. In contrast, the early and fast invasion of the entire habitat mediated by power law LDD not only involves a significantly greater invasion velocity, but also an entirely different habitat occupation. As newly dispersed individuals soon reach very distant portions of the habitat as well as the vicinity of the original dispersal focus, new growing patches are generated while the main patch increases its own growth absorbing the closest patches. As a consequence of both dispersal and lower density dependence, growth of the occupied area is much faster than with SDD. SDD and LDD also differ regarding pattern generation. With SDD, fractal patterns appear only in the border of the invasion front in SDD when competitive interaction with residents is included. In contrast, LDD patterns show fractality both in the spatial arrangements of patches as well as in patch borders. Moreover, values of border fractal dimension inform on the dispersal process in relation with habitat heterogeneity. The distribution of patch size is also scale‐free, showing two power laws characteristic of small and large patch sizes directly arising from the dispersal and reproductive dynamics. Ecological factors like habitat heterogeneity are relevant for dispersal, although its importance is greater for SDD, lowering the invasion velocity. Among the life history traits considered, adult mortality, the juvenile bank and mean dispersal distance are the most relevant for SDD. For LDD, habitat heterogeneity and changes in life history traits are not so relevant, causing minor changes in the values of the scale‐free parameters. Our work on short and long distance dispersal shows novel theoretical differences between SDD and LDD in invasive systems (mechanisms of pattern formation, fractal and scaling properties, relevance of different life history traits and habitat variables) that correspond closely with field examples and were not analyzed, at least in this degree of detail, by the previously existing models.     

Risk maps for the spread of highly pathogenic avian influenza in poultry

Devastating epidemics of highly contagious animal diseases such as avian influenza, classical swine fever, and foot-and-mouth disease underline the need for improved understanding of the factors promoting the spread of these pathogens. Here the authors present a spatial analysis of the between-farm transmission of a highly pathogenic H7N7 avian influenza virus that caused a large epidemic in The Netherlands in 2003. The authors developed a method to estimate key parameters determining the spread of highly transmissible animal diseases between farms based on outbreak data. The method allows for the identification of high-risk areas for propagating spread in an epidemiologically underpinned manner. A central concept is the transmission kernel, which determines the probability of pathogen transmission from infected to uninfected farms as a function of interfarm distance. The authors show how an estimate of the transmission kernel naturally provides estimates of the critical farm density and local reproduction numbers, which allows one to evaluate the effectiveness of control strategies. For avian influenza, the analyses show that there are two poultry-dense areas in The Netherlands where epidemic spread is possible, and in which local control measures are unlikely to be able to halt an unfolding epidemic. In these regions an epidemic can only be brought to an end by the depletion of susceptible farms by infection or massive culling. The analyses provide an estimate of the spatial range over which highly pathogenic avian influenza viruses spread between farms, and emphasize that control measures aimed at controlling such outbreaks need to take into account the local density of farms.     

Using phylogeographic approaches to analyse the dispersal history,velocity and direction of viral lineages — Application to rabies virus spread in Iran

Recent years have seen the extensive use of phylogeographic approaches to unveil the dispersal history of virus epidemics. Spatially explicit reconstructions of viral spread represent valuable sources of lineage movement data that can be exploited to investigate the impact of underlying environmental layers on the dispersal of pathogens. Here, we performed phylogeographic inference and applied different post hoc approaches to analyse a new and comprehensive data set of viral genomes to elucidate the dispersal history and dynamics of rabies virus (RABV) in Iran, which have remained largely unknown. We first analysed the association between environmental factors and variations in dispersal velocity among lineages. Second, we present, test and apply a new approach to study the link between environmental conditions and the dispersal direction of lineages. The statistical performance (power of detection, false‐positive rate) of this new method was assessed using simulations. We performed phylogeographic analyses of RABV genomes, allowing us to describe the large diversity of RABV in Iran and to confirm the cocirculation of several clades in the country. Overall, we estimate a relatively high lineage dispersal velocity, similar to previous estimates for dog rabies virus spread in northern Africa. Finally, we highlight a tendency for RABV lineages to spread in accessible areas associated with high human population density. Our analytical workflow illustrates how phylogeographic approaches can be used to investigate the impact of environmental factors on several aspects of viral dispersal dynamics.     

Landscape epidemiology and control of pathogens with cryptic and long-distance dispersal: sudden oak death in northern Californian forests

Exotic pathogens and pests threaten ecosystem service, biodiversity, and crop security globally. If an invasive agent can disperse asymptomatically over long distances, multiple spatial and temporal scales interplay, making identification of effective strategies to regulate, monitor, and control disease extremely difficult. The management of outbreaks is also challenged by limited data on the actual area infested and the dynamics of spatial spread, due to financial, technological, or social constraints. We examine principles of landscape epidemiology important in designing policy to prevent or slow invasion by such organisms, and use Phytophthora ramorum, the cause of sudden oak death, to illustrate how shortfalls in their understanding can render management applications inappropriate. This pathogen has invaded forests in coastal California, USA, and an isolated but fast-growing epidemic focus in northern California (Humboldt County) has the potential for extensive spread. The risk of spread is enhanced by the pathogen's generalist nature and survival. Additionally, the extent of cryptic infection is unknown due to limited surveying resources and access to private land. Here, we use an epidemiological model for transmission in heterogeneous landscapes and Bayesian Markov-chain-Monte-Carlo inference to estimate dispersal and life-cycle parameters of P. ramorum and forecast the distribution of infection and speed of the epidemic front in Humboldt County. We assess the viability of management options for containing the pathogen's northern spread and local impacts. Implementing a stand-alone host-free "barrier" had limited efficacy due to long-distance dispersal, but combining curative with preventive treatments ahead of the front reduced local damage and contained spread. While the large size of this focus makes effective control expensive, early synchronous treatment in newly-identified disease foci should be more cost-effective. We show how the successful management of forest ecosystems depends on estimating the spatial scales of invasion and treatment of pathogens and pests with cryptic long-distance dispersal.     

A model of spatially evolving herpesvirus epidemics causing mass mortality in Australian pilchard Sardinops sagax

In 1995 mass mortality of pilchards Sardinops sagax occurred along >5000 km of Australian coast; similar events occurred in 1998/99. This mortality was closely associated with a herpesvirus. The pilchard is an important food source for larger animals and supports commercial fisheries. Both epidemics originated in South Australian waters and spread as waves with velocities of 10 to 40 km d(-1). Velocity was constant for a single wave, but varied between the epidemics and between the east- and west-bound waves in each epidemic. The pattern of mortality evolved from recurrent episodes to a single peak with distance from the origin. A 1-dimensional model of these epidemics has been developed. The host population is divided into susceptible, infected and latent, infected and infectious, and removed (recovered and dead) phases; the latent and infectious periods are of fixed duration. This model produces the mortality patterns observed locally and during the spread and evolution of the epidemic. It is consistent with evidence from pathology. The wave velocity is sensitive to diffusion coefficients, viral transmission rates and latent period. These parameters are constrained using the local and large-scale patterns of epidemic spread. The relative roles of these parameters in explaining differences between epidemics and between east- and west-bound waves within epidemics are discussed. The model predicts very high levels of infection, indicating that many surviving pilchards recovered following infection. Control appears impracticable once epidemics are initiated, but impact can be minimised by protecting juvenile stocks.     

Genetic discontinuities and disequilibria in recently established populations of the plant pathogenic fungus Mycosphaerella fijiensis

Dispersal processes of fungal plant pathogens can be inferred from analysis of spatial genetic structures resulting from recent range expansion. The relative importance of long‐distance dispersal (LDD) events vs. gradual dispersal in shaping population structures depends on the geographical scale considered. The fungus Mycosphaerella fijiensis, pathogenic on banana, is an example of a recent worldwide epidemic. Founder effects in this species were detected at both global and continental scale, suggesting stochastic spread of the disease through LDD events. In this study, we analysed the structure of M. fijiensis populations in two recently (∼1979–1980) colonized areas in Costa Rica and Cameroon. Isolates collected in 10–15 sites distributed along a ∼250‐ to 300‐ km‐long transect in each country were analysed using 19 microsatellite markers. We detected low‐to‐moderate genetic differentiation among populations in both countries and isolation by distance in Cameroon. Combined with historical data, these observations suggest continuous range expansion at the scale of banana‐production area through gradual dispersal of spores. However, both countries displayed specific additional signatures of colonization: a sharp discontinuity in gene frequencies was observed along the Cameroon transect, while the Costa Rican populations seemed not yet to have reached genetic equilibrium. These differences in the genetic characteristics of M. fijiensis populations in two recently colonized areas are discussed in the light of historical data on disease spread and ecological data on landscape features.     

Long-distance dispersal of the gypsy moth (Lepidoptera: Lymantriidae) facilitated its initial invasion of Wisconsin

Gypsy moth (Lymantria dispar L.) spread is dominated by stratified dispersal, and, although spread rates are variable in space and time, the gypsy moth has invaded Wisconsin at a consistently higher rate than in other regions. Allee effects, which act on low-density populations ahead of the moving population that contribute to gypsy moth spread, have also been observed to be consistently weaker in Wisconsin. Because a major cause of an Allee effect in the gypsy moth is mate-finding failure at low densities, supplementing low-density populations with immigrants that arrive through dispersal may facilitate establishment and consequent spread. We used local indicator of spatial autocorrelation methods to examine space-time gypsy moth monitoring data from 1996 to 2006 and identify isolated, low-density colonies that arrived through dispersal. We measured the distance of these colonies from the moving population front to show that long-distance dispersal was markedly present in earlier years when Wisconsin was still mainly uninfested. Recently, however, immigrants arriving through long-distance dispersal may no longer be detected because instead of invading uninfested areas, they are now supplementing high-density colonies. In contrast, we observed no temporal pattern in the distance between low-density colonies and the population front in West Virginia and Virginia. We submit that long-distance dispersal, perhaps facilitated through meteorological mechanisms, played an important role in the spread dynamics of the initial Wisconsin gypsy moth invasion, but it currently plays a lesser role because the portion of Wisconsin most susceptible to long-distance immigrants from alternate sources is now heavily infested.     

Virulence evolution at the front line of spreading epidemics

Understanding and predicting the spatial spread of emerging pathogens is a major challenge for the public health management of infectious diseases. Theoretical epidemiology shows that the speed of an epidemic is governed by the life‐history characteristics of the pathogen and its ability to disperse. Rapid evolution of these traits during the invasion may thus affect the speed of epidemics. Here we study the influence of virulence evolution on the spatial spread of an epidemic. At the edge of the invasion front, we show that more virulent and transmissible genotypes are expected to win the competition with other pathogens. Behind the front line, however, more prudent exploitation strategies outcompete virulent pathogens. Crucially, even when the presence of the virulent mutant is limited to the edge of the front, the invasion speed can be dramatically altered by pathogen evolution. We support our analysis with individual‐based simulations and we discuss the additional effects of demographic stochasticity taking place at the front line on virulence evolution. We confirm that an increase of virulence can occur at the front, but only if the carrying capacity of the invading pathogen is large enough. These results are discussed in the light of recent empirical studies examining virulence evolution at the edge of spreading epidemics.     

Covariation between the physiological and behavioral components of pathogen transmission: host heterogeneity determines epidemic outcomes

Although heterogeneity in contact rate, physiology, and behavioral response to infection have all been empirically demonstrated in host–pathogen systems, little is known about how interactions between individual variation in behavior and physiology scale‐up to affect pathogen transmission at a population level. The objective of this study is to evaluate how covariation between the behavioral and physiological components of transmission might affect epidemic outcomes in host populations. We tested the consequences of contact rate covarying with susceptibility, infectiousness, and infection status using an individual‐based, dynamic network model where individuals initiate and terminate contacts with conspecifics based on their behavioral predispositions and their infection status. Our results suggest that both heterogeneity in physiology and subsequent covariation of physiology with contact rate could powerfully influence epidemic dynamics. Overall, we found that 1) individual variability in susceptibility and infectiousness can reduce the expected maximum prevalence and increase epidemic variability; 2) when contact rate and susceptibility or infectiousness negatively covary, it takes substantially longer for epidemics to spread throughout the population, and rates of epidemic spread remained suppressed even for highly transmissible pathogens; and 3) reductions in contact rate resulting from infection‐induced behavioral changes can prevent the pathogen from reaching most of the population. These effects were strongest for theoretical pathogens with lower transmissibility and for populations where the observed variation in contact rate was higher, suggesting that such heterogeneity may be most important for less infectious, more chronic diseases in wildlife. Understanding when and how variability in pathogen transmission should be modelled is a crucial next step for disease ecology.     

Drivers of plant species’ potential to spread: the importance of demography versus seed dispersal

Understanding the ability of plants to spread is important for assessing conservation strategies, landscape dynamics, invasiveness and ability to cope with climate change. While long‐distance seed dispersal is often viewed as a key process in population spread, the importance of inter‐specific variation in demography is less explored. Indeed, the relative importance of demography vs seed dispersal in determining population spread is still little understood. We modelled species’ potential for population spread in terms of annual migration rates for a set of species inhabiting dry grasslands of central Europe. Simultaneously, we estimated the importance of demographic (population growth rate) versus long‐distance dispersal (99th percentile dispersal distance) characteristics for among‐species differences in modelled population spread. In addition, we assessed how well simple proxy measures related to demography (the number and survival of seedlings, the survival of flowering individuals) and dispersal (plant height, terminal velocity and wind speed during dispersal) predicted modelled spread rates. We found that species’ demographic rates were the more powerful predictors of species’ modelled potential to spread than dispersal. Furthermore, our simple proxies were correlated with modelled species spread rates and together their predictive power was high. Our findings highlight that for understanding variation among species in their potential for population spread, detailed information on local demography and dispersal might not always be necessary. Simple proxies or assumptions that are based primarily on species demography could be sufficient.     

Long distance seed dispersal by wind: measuring and modelling the tail of the curve

The size and shape of the tail of the seed dispersal curve is important in determining the spatial dynamics of plants, but is difficult to quantify. We devised an experimental protocol to measure long-distance dispersal which involved measuring dispersal by wind from isolated individuals at a range of distances from the source, but maintaining a large and constant sampling intensity at each distance. Seeds were trapped up to 80 m from the plants, the furthest a dispersal curve for an individual plant has been measured for a non-tree species. Standard empirical negative exponential and inverse power models were fitted using likelihood methods. The latter always had a better fit than the former, but in most cases neither described the data well, and strongly under-estimated the tail of the dispersal curve. An alternative model formulation with two kernel components had a much better fit in most cases and described the tail data more accurately. Mechanistic models provide an alternative to direct measurement of dispersal. However, while a previous mechanistic model accurately predicted the modal dispersal distance, it always under-predicted the measured tail. Long-distance dispersal may be caused by rare extremes in horizontal wind speed or turbulence. Therefore, under-estimation of the tail by standard empirical models and mechanistic models may indicate a lack of flexibility to take account of such extremes. Future studies should examine carefully whether the widely used exponential and power models are, in fact, valid, and investigate alternative models. Received: 7 March 1999 / Accepted: 2 April 2000     

Flexible dispersal strategies in native and non‐native ranges: environmental quality and the ‘good–stay,bad–disperse’ rule

Dispersal strategies are one of the most important determinants of range dynamics and a surrogate for invasiveness. We tested three inter‐related hypotheses derived from demographic and ecological models: (H₁) short‐distance dispersal strategies arise at native range margins due to their demographic advantage; (H₂) in non‐native areas a high diffusion rate is favoured at the advancing range front for niche filling; (H₃) environmental deterioration can increase dispersal and lead to a ‘good–stay, bad–disperse’ strategy. Spatially and temporally explicit rates of spread and dispersal kernels of the European starling Sturnus vulgaris were generated for its native range (Britain) using ringing records from 1909 to 2008, and for a non‐native area (South Africa) using ringing data and distributional records since its introduction in 1897. There was a marked spatial and temporal variation in the rate of spread within both native and non‐native ranges. In the native range the rate of spread declined with increasing distance from the species’ European distribution (contradicting H₁). In the non‐native range the rate of spread increased with distance from the introduction locality (supporting H₂). The annual rate of spread in the native range also increased significantly when environmental conditions were deteriorating as indicated by marked population declines and relatively low abundance (H₃), providing clear evidence for flexible dispersal strategies based on a ‘good–stay, bad–disperse’ rule. Starlings’ dispersal kernel followed an inverse power law and showed strong anisotropy and significant divergence between native and invasive populations, suggesting a flexible strategy comprising a dynamic response to spatial and temporal environmental variation with implications for predicting dispersal and range dynamics arising from environmental change.     

Pattern formation triggered by rare events: lessons from the spread of rabies.

Understanding of large-scale spatial pattern formation is a key to successful management in ecology and epidemiology. Neighbourhood interactions between local units are known to contribute to large-scale patterns, but how much do they contribute and what is the role of regional interactions caused by long-distance processes? How much long-distance dispersal do we need to explain the patterns that we observe in nature? There seems to be no way to answer these questions empirically. Therefore, we present a modelling approach that is a combination of a grid-based model describing local interactions and an individual-based model describing dispersal. Applying our approach to the spread of rabies, we show that in addition to local rabies dynamics, one long-distance infection per 14000 km2 per year is sufficient to reproduce the wave-like spread of this disease. We conclude that even rare ecological events that couple local dynamics on a regional scale may have profound impacts on large-scale patterns and, in turn, dynamics. Furthermore, the following results emerge: (i) Both neighbourhood infection and long-distance infection are needed to generate the wave-like dispersal pattern of rabies; (ii) randomly walking rabid foxes are not sufficient to generate the wave pattern; and (iii) on a scale of less than 100 km x 100 km, temporal oscillations emerge that are independent from long-distance dispersal.     

Modelling effects of habitat fragmentation on the ability of trees to respond to climatic warming

The ability of trees to migrate in response to climatic warming was simulated under various conditions of habitat availability. The model uses Holocene tree migration rates to approximate maximum migration rates in a forested landscape. Habitat availability and local population size was varied systematically under two dispersal and colonization models. These dispersal models varied in the likelihood of long-distance dispersal events. The first model used a negative exponential function that severely limited the probability of long-distance dispersal. The results of this model indicate that migration rate could decline an order of magnitude where the habitat availability is reduced from 80 to 20% of the matrix. The second model, using an inverse power function, carried a higher probability of long-distance dispersal events. The results from this model predict relatively small declines in migration rates when habitat availability is reduced to 50% of the simulation matrix. Below 50% habitat availability, mean migration rate was similar to the negative exponential model. These results predict a failure of many trees to respond to future climatic change through range expansion.