Saddle-Point Approximations,Integrodifference Equations,and Invasions

Invasion, the growth in numbers and spatial spread of a population over time, is a fundamental process in ecology. Governments and businesses expend vast sums to prevent and control invasions of pests and pestilences and to promote invasions of endangered species and biological control agents. Many mathematical models of biological invasions use nonlinear integrodifference equations to describe the growth and dispersal processes and to predict the speed of invasion fronts. Linear models have received less attention, perhaps because they are difficult to simulate for large times. In this paper, we use the saddle-point method, alias the method of steepest descent, to derive asymptotic approximations for the solutions of linear integrodifference equations. We work through five examples, for Gaussian, Laplace, and uniform dispersal kernels in one dimension and for asymmetric Gaussian and radially symmetric Laplace kernels in two dimensions. Our approximations are extremely close to the exact solutions, even for intermediate times. We also employ an empirical saddle-point approximation to predict densities using dispersal data. We use our approximations to examine the effects of censored dispersal data on estimates of invasion speed and population density.     

Predicting the time to colonization of the parasitoid Diadegma semiclausum: The importance of the shape of spatial dispersal kernels for biological control

The time at which natural enemies colonize crop fields is an important determinant of their ability to suppress pest populations. This timing depends on the distance between source and sink habitats in the landscape. Here we estimate the time to colonization of sink habitats from a distant source habitat, using empirical mark-capture data of Diadegma semiclausum in Broccoli. The data originated from experiments conducted at two locations and dispersal was quantified by suction sampling before and after a major disturbance. Three dispersal kernels were fitted to the dispersal data: a normal, a negative exponential, and a square root negative exponential kernel. These kernels are characterized by a thin, intermediate and a fat tail, respectively. The dispersal kernels were included in an integro-difference equation model for parasitoid population redistribution to generate estimates of time to colonization of D. semiclausum in sink habitats at distances between 100 and 2000 m from a source. We show that the three dispersal kernels receive similar support from the data, but can produce a wide range of outcomes. The estimated arrival time of 1% of the D. semiclausum population at a distance 2000 m from the source ranges from 12 days to a length of time greatly exceeding the life span of the parasitoid. The square root negative exponential function, having the thickest tail among the tested functions, gave the fastest spread and colonization in three of the four data sets, but it gave the slowest redistribution in the fourth. In all four data sets, the rate of accumulation at the target increased with the mean dispersal distance of the fitted kernel model, irrespective of the fatness of the tail. This study underscores the importance of selecting a proper dispersal kernel for modelling spread and colonization time of organisms, and of the collection of pertinent data that enable kernel estimation and that can discriminate between different kernel shapes.     

Seed dispersal patterns in a temperate forest during a mast event: performance of alternative dispersal kernels

Seed dispersal patterns were studied in a north-western Spain temperate forest community to assess the performances of alternative dispersal kernels during two years with ecologically contrasting scenarios; a non-mast year, and a mast year of the dominant canopy species, beech Fagus sylvatica. Dispersal kernels were fitted under a Bayesian modeling framework. Both simple and mixture kernels were considered for the five more abundant tree species (Corylus avellana, Crataegus monogyna, F. sylvatica, Ilex aquifolium and Taxus baccata). Mixture kernels provided a better fit for almost all species, and the log-normal performed best for T. baccata. No relationship between dispersal syndromes and the best dispersal kernel function emerged. However, we found temporal changes in the shape of the dispersal kernels that seemed to be related to variation in relative fruit production among species and the resulting changes in the responses of dispersal vectors. This reveals a potential role for disperser-mediated indirect effects in terms of introducing temporal variation in species spread. In this sense, our results highlight the need to consider single species seed dispersal as a community process. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Invasion by extremes: population spread with variation in dispersal and reproduction

For populations having dispersal described by fat-tailed kernels (kernels with tails that are not exponentially bounded), asymptotic population spread rates cannot be estimated by traditional models because these models predict continually accelerating (asymptotically infinite) invasion. The impossible predictions come from the fact that the fat-tailed kernels fitted to dispersal data have a quality (nondiscrete individuals and, thus, no moment-generating function) that never applies to data. Real organisms produce finite (and random) numbers of offspring; thus, an empirical moment-generating function can always be determined. Using an alternative method to estimate spread rates in terms of extreme dispersal events, we show that finite estimates can be derived for fat-tailed kernels, and we demonstrate how variable reproduction modifies these rates. Whereas the traditional models define spread rate as the speed of an advancing front describing the expected density of individuals, our alternative definition for spread rate is the expected velocity for the location of the furthest-forward individual in the population. The asymptotic wave speed for a constant net reproductive rate R0 is approximated as (1/T)(piuR)/2)(1/2) m yr(-1), where T is generation time, and u is a distance parameter (m2) of Clark et al.'s 2Dt model having shape parameter p = 1. From fitted dispersal kernels with fat tails and infinite variance, we derive finite rates of spread and a simple method for numerical estimation. Fitted kernels, with infinite variance, yield distributions of rates of spread that are asymptotically normal and, thus, have finite moments. Variable reproduction can profoundly affect rates of spread. By incorporating the variance in reproduction that results from variable life span, we estimate much lower rates than predicted by the standard approach, which assumes a constant net reproductive rate. Using basic life-history data for trees, we show these estimated rates to be lower than expected from previous analytical models and as interpreted from paleorecords of forest spread at the end of the Pleistocene. Our results suggest reexamination of past rates of spread and the potential for future response to climate change.     

Reid's paradox revisited: the evolution of dispersal kernels during range expansion

Current approaches to modeling range advance assume that the distribution describing dispersal distances in the population (the "dispersal kernel") is a static entity. We argue here that dispersal kernels are in fact highly dynamic during periods of range advance because density effects and spatial assortment by dispersal ability ("spatial selection") drive the evolution of increased dispersal on the expanding front. Using a spatially explicit individual-based model, we demonstrate this effect under a wide variety of population growth rates and dispersal costs. We then test the possibility of an evolved shift in dispersal kernels by measuring dispersal rates in individual cane toads (Bufo marinus) from invasive populations in Australia (historically, toads advanced their range at 10 km/year, but now they achieve >55 km/year in the northern part of their range). Under a common-garden design, we found a steady increase in dispersal tendency with distance from the invasion origin. Dispersal kernels on the invading front were less kurtotic and less skewed than those from origin populations. Thus, toads have increased their rate of range expansion partly through increased dispersal on the expanding front. For accurate long-range forecasts of range advance, we need to take into account the potential for dispersal kernels to be evolutionarily dynamic.     

Transmission of Leptosphaeria maculans from a cropping season to the following one

Current modelling of inoculum transmission from a cropping season to the following one relies on the extrapolation of kernels estimated on data at short distances from punctual sources, because data collected at larger distances are scarce. We estimated the dispersal kernel of Leptosphaeria maculans ascospores from stubble left after harvest in the summer previous to newly sown oilseed rape fields, using phoma stem canker autumn disease severity. We built a dispersal model to analyse the data. Source strengths are described in the spatial domain covered by source fields by a log‐Gaussian spatial process. Infection potentials in the following season are described in the space consisting of the target fields, by a convolution of sources and a power‐exponential dispersal kernel. Data were collected on farmers' fields considered as sources in 2009 and 2011 (72 and 39 observation points) and as targets in 2010 and 2012 (172 and 200 points). We applied the Bayesian approach for model selection and parameter estimation. We obtained fat tail kernels for both data sets. This estimation is the first from data acquired over distances of 0 to 1000 m, using several non‐punctual inoculum sources. It opens the prospect of refining the existing simulators, or developing disease risk maps.     

Consequences of Dispersal Heterogeneity for Population Spread and Persistence

Dispersal heterogeneity is increasingly being observed in ecological populations and has long been suspected as an explanation for observations of non-Gaussian dispersal. Recent empirical and theoretical studies have begun to confirm this. Using an integro-difference model, we allow an individual’s diffusivity to be drawn from a trait distribution and derive a general relationship between the dispersal kernel’s moments and those of the underlying heterogeneous trait distribution. We show that dispersal heterogeneity causes dispersal kernels to appear leptokurtic, increases the population’s spread rate, and lowers the critical reproductive rate required for persistence in the face of advection. Wavespeed has been shown previously to be determined largely by the form of the dispersal kernel tail. We qualify this by showing that when reproduction is low, the precise shape of the tail is less important than the first few dispersal moments such as variance and kurtosis. If the reproductive rate is large, a dispersal kernel’s asymptotic tail has a greater influence over wavespeed, implying that estimating the prevalence of traits which correlate with long-range dispersal is critical. The presence of multiple dispersal behaviors has previously been characterized in terms of long-range versus short-range dispersal, and it has been found that rare long-range dispersal essentially determines wavespeed. We discuss this finding and place it within a general context of dispersal heterogeneity showing that the dispersal behavior with the highest average dispersal distance does not always determine wavespeed.     

Families of discrete kernels for modeling dispersal

Integer lattices are important theoretical landscapes for studying the consequences of dispersal and spatial population structure, but convenient dispersal kernels able to represent important features of dispersal in nature have been lacking for lattices. Because leptokurtic (centrally peaked and long-tailed) kernels are common in nature and have important effects in models, of particular interest are families of dispersal kernels in which the degree of leptokurtosis can be varied parametrically. Here we develop families of kernels on integer lattices with several important properties. The degree of leptokurtosis can be varied parametrically from near 0 (the Gaussian value) to infinity. These kernels are all asymptotically radially symmetric. (Exact radial symmetry is impossible on lattices except in one dimension.) They have separate parameters for shape and scale, and their lower order moments and Fourier transforms are given by simple formulae. In most cases, the kernel families that we develop are closed under convolution so that multiple steps of a kernel remain within the same family. Included in these families are kernels with asymptotic power function tails, which have provided good fits to some observations from nature. These kernel families are constructed by randomizing convolutions of stepping-stone kernels and have interpretations in terms of population heterogeneity and heterogeneous physical processes.     

Modelling population redistribution in a leaf beetle: an evaluation of alternative dispersal functions

1. Dispersal is a fundamental ecological process, so spatial models require realistic dispersal kernels. We compare five different forms for the dispersal kernel of the tansy beetle Chrysolina graminis moving between patches of its host-plant (tansy Tanacetum vulgare) in a riparian landscape. 2. Multi-patch mark-recapture data were collected every 2 weeks over 2 years within a large network of patches and from 2226 beetles. Dispersal was common (28.4% of 880 recaptures after a fortnight) and was more likely over longer intervals, out of small patches, for females and during flooding. Interpatch movement rates did not differ between years and exhibited no density dependence. Dispersal distances were similar for males and females, in both years and over all intervals, with a median dispersal distance of just 9.8 m, although a maximum of 856 m was recorded. 3. A model of dispersal, where patches competed for dispersers based on their size and distance from the beetle's source patch (scaled by the dispersal kernel) was fitted to the field data with a maximum likelihood procedure and each of five alternative kernels. The best fitting had relatively extended tails of long-distance dispersal, while Gaussian and negative exponential kernels performed worst. 4. The model suggests that females disperse more commonly than males and that both are strongly attracted to large patches but do not differ between years, which are consistent with the empirical results. Model-predicted emigration and immigration rates and dispersal phenologies match those observed, suggesting that the model captured the major drivers of tansy beetle dispersal. 5. Although negative exponential and Gaussian kernels are widely used for their simplicity, we suggest that these should not be the models of automatic choice, and that fat-tailed kernels with relatively higher proportions of long-distance dispersal may be more realistic.     

Multiscale resistant kernel surfaces derived from inferred gene flow: An application with vernal pool breeding salamanders

The importance of assessing spatial data at multiple scales when modelling species–environment relationships has been highlighted by several empirical studies. However, no landscape genetics studies have optimized landscape resistance surfaces by evaluating relevant spatial predictors at multiple spatial scales. Here, we model multiscale/layer landscape resistance surfaces to estimate resistance to inferred gene flow for two vernal pool breeding salamander species, spotted (Ambystoma maculatum) and marbled (A. opacum) salamanders. Multiscale resistance surface models outperformed spatial layers modelled at their original spatial scale. A resistance surface with forest land cover at a 500‐m Gaussian kernel bandwidth and normalized vegetation index at a 100‐m Gaussian kernel bandwidth was the top optimized resistance surface for A. maculatum, while a resistance surface with traffic rate and topographic curvature, both at a 500‐m Gaussian kernel bandwidth, was the top optimized resistance surface for A. opacum. Species‐specific resistant kernels were fit at all vernal pools in our study area with the optimized multiscale/layer resistance surface controlling kernel spread. Vernal pools were then evaluated and scored based on surrounding upland habitat (local score) and connectivity with other vernal pools on the landscape, with resistant kernels driving vernal pool connectivity scores. As expected, vernal pools that scored highest were in areas within forested habitats and with high vernal pool densities and low species‐specific landscape resistance. Our findings highlight the success of using a novel analytical approach in a multiscale framework with applications beyond vernal pool amphibian conservation.     

Evolution of local adaptations in dispersal strategies

The optimal probability and distance of dispersal largely depend on the risk to end up in unsuitable habitat. This risk is highest close to the habitat's edge and consequently, optimal dispersal probability and distance should decline towards the habitat's border. This selection should lead to the emergence of spatial gradients in dispersal strategies. However, gene flow caused by dispersal itself is counteracting local adaptation. Using an individual based model we investigate the evolution of local adaptations of dispersal probability and distance within a single, circular, habitat patch. We compare evolved dispersal probabilities and distances for six different dispersal kernels (two negative exponential kernels, two skewed kernels, nearest neighbour dispersal and global dispersal) in patches of different size. For all kernels a positive correlation between patch size and dispersal probability emerges. However, a minimum patch size is necessary to allow for local adaptation of dispersal strategies within patches. Beyond this minimum patch area the difference in mean dispersal distance between center and edge increases linearly with patch radius, but the intensity of local adaptation depends on the dispersal kernel. Except for global and nearest neighbour dispersal, the evolved spatial pattern are qualitatively similar for both, mean dispersal probability and distance. We conclude, that inspite of the gene-flow originating from dispersal local adaptation of dispersal strategies is possible if a habitat is of sufficient size. This presumably holds for any realistic type of dispersal kernel.     

Why trees migrate so fast: confronting theory with dispersal biology and the paleorecord

Reid's paradox describes the fact that classical models cannot account for the rapid (10(2)-10(3) m yr-1) spread of trees at the end of the Pleistocene. I use field estimates of seed dispersal with an integrodifference equation and simulation models of population growth to show that dispersal data are compatible with rapid spread. Dispersal estimates lay to rest the possibility that rapid spread occurred by diffusion. The integrodifference model predicts that, if the seed shadow has a long 'fat' tail, then rapid spread is possible, despite short average dispersal distances. It further predicts that velocity is more sensitive to life history than is classical diffusion. Application of such models is frustrated because the tail of the seed shadow cannot be fitted to data. However, the data can be used to test a 'long-distance' hypothesis against alternative ('local') models of dispersal using Akaike's Information Criterion and likelihood ratio tests. Tests show that data are consistent with >10% of seed dispersed as a long (10(2) m) fat-tailed kernel. Models based on such kernels predict spread as rapid as that inferred from the pollen record. If fat-tailed dispersal explains these rapid rates, then it is surprising not to see large differences in velocities among taxa with contrasting life histories. The inference of rapid spread, together with lack of obvious life-history effects, suggests velocities may have not reached their potentials, being stalled by rates of climate change, geography, or both.     

Self‐recruitment in a Caribbean reef fish: a method for approximating dispersal kernels accounting for seascape

Characterizing patterns of larval dispersal is essential to understanding the ecological and evolutionary dynamics of marine metapopulations. Recent research has measured local dispersal within populations, but the development of marine dispersal kernels from empirical data remains a challenge. We propose a framework to move beyond point estimates of dispersal towards the approximation of a simple dispersal kernel, based on the hypothesis that the structure of the seascape is a primary predictor of realized dispersal patterns. Using the coral reef fish Elacatinus lori as a study organism, we use genetic parentage analysis to estimate self‐recruitment at a small spatial scale (<1 km). Next, we determine which simple kernel explains the observed self‐recruitment, given the influx of larvae from reef habitat patches in the seascape at a large spatial scale (up to 35 km). Finally, we complete parentage analyses at six additional sites to test for export from the focal site and compare these observed dispersal data within the metapopulation to the predicted dispersal kernel. We find 4.6% self‐recruitment (CI_95%: ±3.0%) in the focal population, which is explained by the exponential kernel y = 0.915^x (CI_95%: y = 0.865^x, y = 0.965^x), given the seascape. Additional parentage analyses showed low levels of export to nearby sites, and the best‐fit line through the observed dispersal proportions also revealed a declining function y = 0.77^x. This study lends direct support to the hypothesis that the probability of larval dispersal declines rapidly with distance in Atlantic gobies in continuously distributed habitat, just as it does in the Indo‐Pacific damselfishes in patchily distributed habitat.     

Exploring the interaction of avian frugivory and plant spatial heterogeneity and its effect on seed dispersal kernels using a simulation model

Seed dispersal by avian frugivores is one of the key processes influencing plant spatial patterns, but may fail if there is disruption of plant–frugivore mutualisms, such as decline in abundance of dispersers, fragmentation of habitat, or isolation of individual trees. We used simulation model experiments to examine the interaction between frugivore density and behaviour and the spatial arrangement of fruiting plants and its effect on seed dispersal kernels. We focussed on two New Zealand canopy tree species that produce large fruits and are dispersed predominantly by one avian frugivore (Hemiphaga novaeseelandiae). Although the mean seed dispersal distance decreased when trees became more aggregated, there were more frugivore flights between tree clusters, consequently stretching the tails of the dispersal kernels. Conversely, when trees were less aggregated in the landscape, mean dispersal distances increased because seeds were deposited over larger areas, but the kernels had shorter tails. While there were no statistically meaningful changes in kernel parameters when frugivore density changed, decreases in density did cause a proportional reduction in the total number of dispersed seeds. However, birds were forced to move further when fruit availability and fruit ripening were low. Sensitivity analysis showed that dispersal kernels were primarily influenced by the model parameters relating to disperser behaviour, especially those determining attractiveness based on distance to candidate fruiting trees. Our results suggest that the spatial arrangement of plants plays an important role in seed dispersal processes – although tree aggregation curbed the mean seed dispersal distance, it was accompanied by occasional long distance events, and tree dispersion caused an increase in mean dispersal distance, both potentially increasing the probability of seeds finding suitable habitats for germination and growth. Even though low frugivore densities did not cause dispersal failure, there were negative effects on the quantity of seed dispersal because fewer seeds were dispersed.     

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.     

Human-Mediated Dispersal of Seeds by the Airflow of Vehicles

Human-mediated dispersal is known as an important driver of long-distance dispersal for plants but underlying mechanisms have rarely been assessed. Road corridors function as routes of secondary dispersal for many plant species but the extent to which vehicles support this process remains unclear. In this paper we quantify dispersal distances and seed deposition of plant species moved over the ground by the slipstream of passing cars. We exposed marked seeds of four species on a section of road and drove a car along the road at a speed of 48 km/h. By tracking seeds we quantified movement parallel as well as lateral to the road, resulting dispersal kernels, and the effect of repeated vehicle passes. Median distances travelled by seeds along the road were about eight meters for species with wind dispersal morphologies and one meter for species without such adaptations. Airflow created by the car lifted seeds and resulted in longitudinal dispersal. Single seeds reached our maximum measuring distance of 45 m and for some species exceeded distances under primary dispersal. Mathematical models were fit to dispersal kernels. The incremental effect of passing vehicles on longitudinal dispersal decreased with increasing number of passes as seeds accumulated at road verges. We conclude that dispersal by vehicle airflow facilitates seed movement along roads and accumulation of seeds in roadside habitats. Dispersal by vehicle airflow can aid the spread of plant species and thus has wide implications for roadside ecology, invasion biology and nature conservation.     

Evolution of dispersal in explicitly spatial metacommunities

We apply an evolutionary game theoretic approach to the evolution of dispersal in explicitly spatial metacommunities, using a flexible parametric class of dispersal kernels, namely 2Dt kernels, and study the resulting evolutionary dynamics and outcomes. We observe strong selective pressure on mean dispersal distance (i.e., the first moment), and weaker, but significant, one on the shape of dispersal kernel (i.e., higher moments). We investigate the effects of landscape topology and spatial heterogeneity on the resulting ‘optimal’ dispersal kernels. The shape—importantly the tail structure—and stability of evolutionarily optimal dispersal strategies are strongly affected by landscape topology or connectivity. Specifically, the results suggest that the optimal dispersal kernels in the river network topology have heavier tails and are stable, while those in the direct topology, where organisms are allowed to travel directly from one location to another, have relatively thin tails and may be unstable. We also find that habitat spatial heterogeneity enables coexistence and controls spatial distribution of distinct groups of dispersal strategies and that alteration in topology alone may not be sufficient to change such coexistence. This work provides a tool to translate environmental changes such as global climate change and human intervention into changes in dispersal behavior, which in turn may lead to important alterations of biodiversity and biological invasion patterns.     

Long‐distance dispersal and genetic structure of natural populations: an assessment of the inverse isolation hypothesis in peat mosses

It is well accepted that the shape of the dispersal kernel, especially its tail, has a substantial effect on the genetic structure of species. Theory predicts that dispersal by fat‐tailed kernels reshuffles genetic material, and thus, preserves genetic diversity during colonization. Moreover, if efficient long‐distance dispersal is coupled with random colonization, an inverse isolation effect is predicted to develop in which increasing genetic diversity per colonizer is expected with increasing distance from a genetically variable source. By contrast, increasing isolation leads to decreasing genetic diversity when dispersal is via thin‐tailed kernels. Here, we use a well‐established model group for dispersal biology (peat mosses: genus Sphagnum) with a fat‐tailed dispersal kernel, and the natural laboratory of the Stockholm archipelago to study the validity of the inverse isolation hypothesis in spore‐dispersed plants in island colonization. Population genetic structure of three species (Sphagnum fallax, Sphagnum fimbriatum and Sphagnum palustre) with contrasting life histories and ploidy levels were investigated on a set of islands using microsatellites. Our data show (, amova , IBD) that dispersal of the two most abundant species can be well approximated by a random colonization model. We find that genetic diversity per colonizer on islands increases with distance from the mainland for S. fallax and S. fimbriatum. By contrast, S. palustre deviates from this pattern, owing to its restricted distribution in the region, affecting its source pool strength. Therefore, the inverse isolation effect appears to hold in natural populations of peat mosses and, likely, in other organisms with small diaspores.     

Dispersal of Monochamus galloprovincialis (Col.: Cerambycidae) as recorded by mark–release–recapture using pheromone traps

The spread of the pine wood nematode (PWN), Bursaphelenchus xylophylus (Nematoda; Aphelenchoididae), the causal agent of the pine wilt disease, is greatly constrained to the dispersal of its vectors, long‐horned beetles of the Monochamus genus. Disease spread at global and regional scales has been mainly caused by human‐mediated transport, yet at a local scale, the short‐ and long‐distance dispersal behaviour of the beetles determine colonization dynamics. Three mark–release–recapture experiments using commercial traps and lures allowed the parameterization of the dispersal kernel under two landscape fragmentation scenarios for the only known European PWN vector, Monochamus galloprovincialis. The respective release of 171 and 353 laboratory‐reared beetles in continuous pine stands in 2009 and 2010 resulted in 36% and 28% recapture rates, yet, at a fragmented landscape in 2011, only 2% of the released 473 individuals could be recaptured. Recaptures occurred as soon as 7–14 days after their release, in agreement with the requirement of sexual maturation to respond to the pheromone–kairomone attractants. Data from the first two experiments were fitted to one mechanical and two empirical dispersal models, from which the distance dispersal kernels could be computed. Derived estimated radii enclosing 50% and 99% of dispersing M. galloprovincialis under continuous pine stands ranged between 250–532 m and 2344–3495 m depending on the replicate and choice of model. Forecasted recaptures in 2011 resulted in a moderate underestimation of long‐distance dispersal, probably influenced by the high degree of habitat fragmentation. In addition, trapping parameters such as the effective sampling area (0.57–0.76 ha) or the seasonal sampling range (426–645 m) could be derived. Observed results, derived dispersal kernels and trapping parameters provide valuable information for the integrated pest management of PWD. Furthermore, estimated dispersal distances indicate that ongoing clear‐cut measures for eradication in the European Union are likely ineffective in stopping the vectors dispersal.     

Simultaneous evolution of multiple dispersal components and kernel

Global climate is changing rapidly and is accompanied by large‐scale fragmentation and destruction of habitats. Since dispersal is the first line of defense for mobile organisms to cope with such adversities in their environment, it is important to understand the causes and consequences of evolution of dispersal. Although dispersal is a complex phenomenon involving multiple dispersal‐components like propensity (tendency to leave the natal patch) and ability (to travel long distances), the relationship between these traits is not always straight‐forward, it is not clear whether these traits can evolve simultaneously or not, and how their interactions affect the overall dispersal profile. To investigate these issues, we subjected four large (n ～ 2400) outbred populations of Drosophila melanogaster to artificial selection for increased dispersal, in a setup that mimicked increasing habitat fragmentation over 33 generations. The propensity and ability of the selected populations were significantly greater than the non‐selected controls and the difference persisted even in the absence of proximate drivers for dispersal. The dispersal kernel evolved to have significantly greater standard deviation and reduced values of skew and kurtosis, which ultimately translated into the evolution of a greater frequency of long‐distance dispersers (LDDs). We also found that although sex‐biased dispersal exists in D. melanogaster, its expression can vary depending on which dispersal component is being measured and the environmental condition under which dispersal takes place. Interestingly though, there was no difference between the two sexes in terms of dispersal evolution. We discuss possible reasons for why some of our results do not agree with previous laboratory and field studies. The rapid evolution of multiple components of dispersal and the kernel, expressed even in the absence of stress, indicates that dispersal evolution cannot be ignored while investigating eco‐evolutionary phenomena like speed of range expansion, disease spread, evolution of invasive species and destabilization of metapopulation dynamics.