Effect of density dependence on coinfection dynamics

In this paper we develop a compartmental model of SIR type (the abbreviation refers to the number of Susceptible, Infected and Recovered people) that models the population dynamics of two diseases that can coinfect. We discuss how the underlying dynamics depends on the carrying capacity K: from a simple dynamics to a more complex. This can also help in understanding the appearance of more complicated dynamics, for example, chaos and periodic oscillations, for large values of K. It is also presented that pathogens can invade in population and their invasion depends on the carrying capacity K which shows that the progression of disease in population depends on carrying capacity. More specifically, we establish all possible scenarios (the so-called transition diagrams) describing an evolution of an (always unique) locally stable equilibrium state (with only non-negative compartments) for fixed fundamental parameters (density independent transmission and vital rates) as a function of the carrying capacity K. An important implication of our results is the following important observation. Note that one can regard the value of K as the natural 'size' (the capacity) of a habitat. From this point of view, an isolation of individuals (the strategy which showed its efficiency for COVID-19 in various countries) into smaller resp. larger groups can be modelled by smaller resp. bigger values of K. Then we conclude that the infection dynamics becomes more complex for larger groups, as it fairly maybe expected for values of the reproduction number R 0 ≈ 1 . We show even more, that for the values R 0 > 1 there are several (in fact four different) distinguished scenarios where the infection complexity (the number of nonzero infected classes) arises with growing K. Our approach is based on a bifurcation analysis which allows to generalize considerably the previous Lotka-Volterra model considered previously in Ghersheen et al. (Math Meth Appl Sci 42(8), 2019).

Realistic assumptions about spatial locations and clustering of premises matter for models of foot-and-mouth disease spread in the United States

Spatially explicit livestock disease models require demographic data for individual farms or premises. In the U.S., demographic data are only available aggregated at county or coarser scales, so disease models must rely on assumptions about how individual premises are distributed within counties. Here, we addressed the importance of realistic assumptions for this purpose. We compared modeling of foot and mouth disease (FMD) outbreaks using simple randomization of locations to premises configurations predicted by the Farm Location and Agricultural Production Simulator (FLAPS), which infers location based on features such as topography, land-cover, climate, and roads. We focused on three premises-level Susceptible-Exposed-Infectious-Removed models available from the literature, all using the same kernel approach but with different parameterizations and functional forms. By computing the basic reproductive number of the infection (R₀) for both FLAPS and randomized configurations, we investigated how spatial locations and clustering of premises affects outbreak predictions. Further, we performed stochastic simulations to evaluate if identified differences were consistent for later stages of an outbreak. Using Ripley’s K to quantify clustering, we found that FLAPS configurations were substantially more clustered at the scales relevant for the implemented models, leading to a higher frequency of nearby premises compared to randomized configurations. As a result, R₀ was typically higher in FLAPS configurations, and the simulation study corroborated the pattern for later stages of outbreaks. Further, both R₀ and simulations exhibited substantial spatial heterogeneity in terms of differences between configurations. Thus, using realistic assumptions when de-aggregating locations based on available data can have a pronounced effect on epidemiological predictions, affecting if, where, and to what extent FMD may invade the population. We conclude that methods such as FLAPS should be preferred over randomization approaches.

When modeling the spread of infectious livestock diseases such as foot-and-mouth disease (FMD), the distance between premises is an important aspect. In the U.S., locations of premises are not available, forcing modelers to make assumptions about their coordinates. Such assumptions can be more or less crude and will impact the conclusions drawn from the model. To investigate the impact of such assumptions, we modeled outbreaks of FMD within the cattle population of the U.S. under two assumptions about premises locations. Their position was either randomly distributed within counties or informed by a state-of-the-art method developed specifically to simulate realistic locations of agricultural operations. We found that the higher degree of spatial clustering of premises associated with more realistic assumptions about locations leads to a substantially higher risk of outbreaks. Our results also show that the amount with which the risk is under-estimated by randomizing locations is unevenly distributed across the landscape. Together, these findings show a clear support for using informed methods to determine the spatial locations of premises and highlight the importance of spatial clustering when modeling FMD-like diseases.

Latitudinal diversity of biting midge species within the Obsoletus group across three habitats in Europe

Culicoides species from the Obsoletus group are important vectors of bluetongue and Schmallenberg virus. This group consists of several species that cannot easily be identified using morphological characteristics. Therefore, limited information is available about their distribution and habitat preferences. In this study, we aimed to elucidate the species composition of the Obsoletus group in three habitat types at climatically different latitudes across Europe. Traps were placed in three habitat types in three countries at different latitudes. After DNA extraction, biting midges were identified using PCR and gel electrophoresis. Extraction of DNA using Chelex proved to be a cost and time efficient method for species identification. A latitudinal effect on the relative abundance of species from the Obsoletus group was found. Species composition was unique for most country-habitat combinations. The majority of biting midges were either C. obsoletus s.s. or C. scoticus, and both species were found at all latitudes and habitats. Their wide distribution and their high abundance at livestock farms make these species likely candidates for rapid farm-to-farm transmission of pathogens throughout Europe. Our results emphasize the need to differentiate Obsoletus group species to better understand their ecology and contribution to pathogen transmission.

Enhancing nutrient recycling from excreta to meet crop nutrient needs in Sweden - a spatial analysis

Increased recycling of nutrient-rich organic waste to meet crop nutrient needs is an essential component of a more sustainable food system. However, agricultural specialization continues to pose a significant challenge to balancing crop nutrient needs and the nutrient supply from animal manure and human excreta locally. For Sweden, this study found that recycling all excreta (in 2007) could meet up to 75% of crop nitrogen and 81% of phosphorus needs, but that this would exceed crop potassium needs by 67%. Recycling excreta within municipalities could meet 63% of crop P nutrient needs, but large regional differences and imbalances need to be corrected to avoid over or under fertilizing. Over 50% of the total nitrogen and phosphorus in excreta is contained in just 40% of municipalities, and those have a surplus of excreta nutrients compared to crop needs. Reallocation of surpluses (nationally optimized for phosphorus) towards deficit municipalities, would cost 192 million USD (for 24 079 km of truck travel). This is 3.7 times more than the total NPK fertilizer value being transported. These results indicate that Sweden could reduce its dependence on synthetic fertilizers through investments in excreta recycling, but this would likely require valuing also other recycling benefits.

Need for speed: An optimized gridding approach for spatially explicit disease simulations

Numerical models for simulating outbreaks of infectious diseases are powerful tools for informing surveillance and control strategy decisions. However, large-scale spatially explicit models can be limited by the amount of computational resources they require, which poses a problem when multiple scenarios need to be explored to provide policy recommendations. We introduce an easily implemented method that can reduce computation time in a standard Susceptible-Exposed-Infectious-Removed (SEIR) model without introducing any further approximations or truncations. It is based on a hierarchical infection process that operates on entire groups of spatially related nodes (cells in a grid) in order to efficiently filter out large volumes of susceptible nodes that would otherwise have required expensive calculations. After the filtering of the cells, only a subset of the nodes that were originally at risk are then evaluated for actual infection. The increase in efficiency is sensitive to the exact configuration of the grid, and we describe a simple method to find an estimate of the optimal configuration of a given landscape as well as a method to partition the landscape into a grid configuration. To investigate its efficiency, we compare the introduced methods to other algorithms and evaluate computation time, focusing on simulated outbreaks of foot-and-mouth disease (FMD) on the farm population of the USA, the UK and Sweden, as well as on three randomly generated populations with varying degree of clustering. The introduced method provided up to 500 times faster calculations than pairwise computation, and consistently performed as well or better than other available methods. This enables large scale, spatially explicit simulations such as for the entire continental USA without sacrificing realism or predictive power.

Numerical models for simulating the outbreak of infectious disease are powerful tools that can be used to inform policy decisions by simulating outbreaks and control actions. However, they rely on considerable computational power to explore all outcomes and scenarios of interest. Focusing on model types commonly used for livestock diseases, we here introduce novel algorithms for efficient computation, alongside techniques to optimize them based on simplifying assumptions. Through simulations of FMD outbreak in the US, the UK and Sweden, as well as in computer generated landscapes, we test how these methods perform under realistic conditions. We find that our optimization techniques works well, and when the introduced algorithms are implemented with these optimizations, computation time can be reduced by more than two orders of magnitude compared to pairwise calculations. We propose that the considered algorithms—which are straight forward to implement—will be useful for simulation of a wide range of diseases, and will promote the use of simulation models for policy recommendation.

Route optimization as an instrument to improve animal welfare and economics in pre-slaughter logistics

Each year, more than three million animals are transported from farms to abattoirs in Sweden. Animal transport is related to economic and environmental costs and a negative impact on animal welfare. Time and the number of pick-up stops between farms and abattoirs are two key parameters for animal welfare. Both are highly dependent on efficient and qualitative transportation planning, which may be difficult if done manually. We have examined the benefits of using route optimization in cattle transportation planning. To simulate the effects of various planning time windows and transportation time regulations and number of pick-up stops along each route, we have used data that represent one year of cattle transport. Our optimization model is a development of a model used in forestry transport that solves a general pick-up and delivery vehicle routing problem. The objective is to minimize transportation costs. We have shown that the length of the planning time window has a significant impact on the animal transport time, the total driving time and the total distance driven; these parameters that will not only affect animal welfare but also affect the economy and environment in the pre-slaughter logistic chain. In addition, we have shown that changes in animal transportation regulations, such as minimizing the number of allowed pick-up stops on each route or minimizing animal transportation time, will have positive effects on animal welfare measured in transportation hours and number of pick-up stops. However, this leads to an increase in working time and driven distances, leading to higher transportation costs for the transport and negative environmental impact.

Community analysis of the abundance and diversity of mosquito species (Diptera: Culicidae) in three European countries at different latitudes

BACKGROUND

Studies on mosquito species diversity in Europe often focus on a specific habitat, region or country. Moreover, different trap types are used for these sampling studies, making it difficult to compare and validate results across Europe. To facilitate comparisons of trapping sites and community analysis, the present study used two trap types for monitoring mosquito species diversity in three habitat types for three different countries in Europe.

METHODS

Mosquitoes were trapped using Biogents Sentinel (BGS), and Mosquito Magnet Liberty Plus (MMLP) traps at a total of 27 locations in Sweden, the Netherlands and Italy, comprising farm, peri-urban and wetland habitats. From July 2014 to June 2015 all locations were sampled monthly, except for the winter months. Indices of species richness, evenness and diversity were calculated, and community analyses were carried out with non-metric multidimensional scaling (NMDS) techniques.

RESULTS

A total of 11,745 female mosquitoes were trapped during 887 collections. More than 90% of the mosquitoes belonged to the genera Culex and Aedes, with Culex pipiens being the most abundant species. The highest mosquito diversity was found in Sweden. Within Sweden, species diversity was highest in wetland habitats, whereas in the Netherlands and Italy this was highest at farms. The NMDS analyses showed clear differences in mosquito communities among countries, but not among habitat types. The MMLP trapped a higher diversity of mosquito species than the BGS traps. Also, MMLP traps trapped higher numbers of mosquitoes, except for the genera Culex and Culiseta in Italy.

CONCLUSIONS

A core mosquito community could be identified for the three countries, with Culex pipiens as the most abundant species. Differences in mosquito species communities were more defined by the three countries included in the study than by the three habitat types. Differences in mosquito community composition across countries may have implications for disease emergence and further spread throughout Europe. Future research should, therefore, focus on how field data of vector communities can be incorporated into models, to better assess the risk of mosquito-borne disease outbreaks.

Biodiversity, extinctions, and evolution of ecosystems with shared resources

We investigate the formation of stable ecological networks where many species share the same resource. We show that such a stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of coexisting species, and we find a relation describing how many species that may become extinct as a result of a sharp environmental change. We introduce a special parameter that is a combination of species traits and resource characteristics used in the model formulation. This parameter describes the pressure on the system to converge, by extinctions. When that stress parameter is large, we obtain that the species traits are concentrated at certain values. This stress parameter is thereby a parameter that determines the level of final biodiversity of the system. Moreover, we show that the dynamics of this limit system can be described by simple differential equations.

Latitudinal Diversity of Culex pipiens Biotypes and Hybrids in Farm, Peri-Urban, and Wetland Habitats in Europe

Despite the presence of Culex (Cx.) pipiens mosquitoes and circulation of West Nile virus (WNV), WNV outbreaks have so far not occurred in northern Europe. The species Cx. pipiens consists of two morphologically identical biotypes, pipiens and molestus, which can form hybrids. Until now, population dynamic studies of Cx. pipiens have not differentiated between biotypes and hybrids at the European scale, nor have they used comparative surveillance approaches. We therefore aimed to elucidate the relative abundance of Cx. pipiens biotypes and hybrids in three habitat types at different latitudes across Europe, using two different surveillance traps. BG-Sentinel and Mosquito-Magnet Liberty Plus traps were placed in three habitat types (farms, peri-urban, wetlands), in three European countries (Sweden, The Netherlands, Italy). Collected Cx. pipiens mosquitoes were identified to biotype with real-time PCR. Both trap types collected equal ratios of the biotypes and their hybrids. From northern to southern latitudes there was a significant decrease of pipiens and an increase of molestus. Habitat types influenced the relative ratios of biotypes and hybrids, but results were not consistent across latitudes. Our results emphasize the need to differentiate Cx. pipiens to the biotype level, especially for proper future WNV risk assessments for Europe.

Spatiotemporal Variation in Distance Dependent Animal Movement Contacts: One Size Doesn't Fit All

The structure of contacts that mediate transmission has a pronounced effect on the outbreak dynamics of infectious disease and simulation models are powerful tools to inform policy decisions. Most simulation models of livestock disease spread rely to some degree on predictions of animal movement between holdings. Typically, movements are more common between nearby farms than between those located far away from each other. Here, we assessed spatiotemporal variation in such distance dependence of animal movement contacts from an epidemiological perspective. We evaluated and compared nine statistical models, applied to Swedish movement data from 2008. The models differed in at what level (if at all), they accounted for regional and/or seasonal heterogeneities in the distance dependence of the contacts. Using a kernel approach to describe how probability of contacts between farms changes with distance, we developed a hierarchical Bayesian framework and estimated parameters by using Markov Chain Monte Carlo techniques. We evaluated models by three different approaches of model selection. First, we used Deviance Information Criterion to evaluate their performance relative to each other. Secondly, we estimated the log predictive posterior distribution, this was also used to evaluate their relative performance. Thirdly, we performed posterior predictive checks by simulating movements with each of the parameterized models and evaluated their ability to recapture relevant summary statistics. Independent of selection criteria, we found that accounting for regional heterogeneity improved model accuracy. We also found that accounting for seasonal heterogeneity was beneficial, in terms of model accuracy, according to two of three methods used for model selection. Our results have important implications for livestock disease spread models where movement is an important risk factor for between farm transmission. We argue that modelers should refrain from using methods to simulate animal movements that assume the same pattern across all regions and seasons without explicitly testing for spatiotemporal variation.

Environmental variability uncovers disruptive effects of species' interactions on population dynamics

How species respond to changes in environmental variability has been shown for single species, but the question remains whether these results are transferable to species when incorporated in ecological communities. Here, we address this issue by analysing the same species exposed to a range of environmental variabilities when (i) isolated or (ii) embedded in a food web. We find that all species in food webs exposed to temporally uncorrelated environments (white noise) show the same type of dynamics as isolated species, whereas species in food webs exposed to positively autocorrelated environments (red noise) can respond completely differently compared with isolated species. This is owing to species following their equilibrium densities in a positively autocorrelated environment that in turn enables species-species interactions to come into play. Our results give new insights into species' response to environmental variation. They especially highlight the importance of considering both species' interactions and environmental autocorrelation when studying population dynamics in a fluctuating environment.

Hamiltonian dynamics for complex food webs

We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.

The impact of movements and animal density on continental scale cattle disease outbreaks in the United States

Globalization has increased the potential for the introduction and spread of novel pathogens over large spatial scales necessitating continental-scale disease models to guide emergency preparedness. Livestock disease spread models, such as those for the 2001 foot-and-mouth disease (FMD) epidemic in the United Kingdom, represent some of the best case studies of large-scale disease spread. However, generalization of these models to explore disease outcomes in other systems, such as the United States's cattle industry, has been hampered by differences in system size and complexity and the absence of suitable livestock movement data. Here, a unique database of US cattle shipments allows estimation of synthetic movement networks that inform a near-continental scale disease model of a potential FMD-like (i.e., rapidly spreading) epidemic in US cattle. The largest epidemics may affect over one-third of the US and 120,000 cattle premises, but cattle movement restrictions from infected counties, as opposed to national movement moratoriums, are found to effectively contain outbreaks. Slow detection or weak compliance may necessitate more severe state-level bans for similar control. Such results highlight the role of large-scale disease models in emergency preparedness, particularly for systems lacking comprehensive movement and outbreak data, and the need to rapidly implement multi-scale contingency plans during a potential US outbreak.

Coexpression patterns indicate that GPI-anchored non-specific lipid transfer proteins are involved in accumulation of cuticular wax, suberin and sporopollenin

The non-specific lipid transfer proteins (nsLTP) are unique to land plants. The nsLTPs are characterized by a compact structure with a central hydrophobic cavity and can be classified to different types based on sequence similarity, intron position or spacing between the cysteine residues. The type G nsLTPs (LTPGs) have a GPI-anchor in the C-terminal region which attaches the protein to the exterior side of the plasma membrane. The function of these proteins, which are encoded by large gene families, has not been systematically investigated so far. In this study we have explored microarray data to investigate the expression pattern of the LTPGs in Arabidopsis and rice. We identified that the LTPG genes in each plant can be arranged in three expression modules with significant coexpression within the modules. According to expression patterns and module sizes, the Arabidopsis module AtI is functionally equivalent to the rice module OsI, AtII corresponds to OsII and AtIII is functionally comparable to OsIII. Starting from modules AtI, AtII and AtIII we generated extended networks with Arabidopsis genes coexpressed with the modules. Gene ontology analyses of the obtained networks suggest roles for LTPGs in the synthesis or deposition of cuticular waxes, suberin and sporopollenin. The AtI-module is primarily involved with cuticular wax, the AtII-module with suberin and the AtIII-module with sporopollenin. Further transcript analysis revealed that several transcript forms exist for several of the LTPG genes in both Arabidopsis and rice. The data suggests that the GPI-anchor attachment and localization of LTPGs may be controlled to some extent by alternative splicing.

A bayesian approach for modeling cattle movements in the United States: scaling up a partially observed network

Networks are rarely completely observed and prediction of unobserved edges is an important problem, especially in disease spread modeling where networks are used to represent the pattern of contacts. We focus on a partially observed cattle movement network in the U.S. and present a method for scaling up to a full network based on Bayesian inference, with the aim of informing epidemic disease spread models in the United States. The observed network is a 10% state stratified sample of Interstate Certificates of Veterinary Inspection that are required for interstate movement; describing approximately 20,000 movements from 47 of the contiguous states, with origins and destinations aggregated at the county level. We address how to scale up the 10% sample and predict unobserved intrastate movements based on observed movement distances. Edge prediction based on a distance kernel is not straightforward because the probability of movement does not always decline monotonically with distance due to underlying industry infrastructure. Hence, we propose a spatially explicit model where the probability of movement depends on distance, number of premises per county and historical imports of animals. Our model performs well in recapturing overall metrics of the observed network at the node level (U.S. counties), including degree centrality and betweenness; and performs better compared to randomized networks. Kernel generated movement networks also recapture observed global network metrics, including network size, transitivity, reciprocity, and assortativity better than randomized networks. In addition, predicted movements are similar to observed when aggregated at the state level (a broader geographic level relevant for policy) and are concentrated around states where key infrastructures, such as feedlots, are common. We conclude that the method generally performs well in predicting both coarse geographical patterns and network structure and is a promising method to generate full networks that incorporate the uncertainty of sampled and unobserved contacts.

Influence on disease spread dynamics of herd characteristics in a structured livestock industry

Studies of between-herd contacts may provide important insight to disease transmission dynamics. By comparing the result from models with different levels of detail in the description of animal movement, we studied how factors influence the final epidemic size as well as the dynamic behaviour of an outbreak. We investigated the effect of contact heterogeneity of pig herds in Sweden due to herd size, between-herd distance and production type. Our comparative study suggests that the production-type structure is the most influential factor. Hence, our results imply that production type is the most important factor to obtain valid data for and include when modelling and analysing this system. The study also revealed that all included factors reduce the final epidemic size and also have yet more diverse effects on initial rate of disease spread. This implies that a large set of factors ought to be included to assess relevant predictions when modelling disease spread between herds. Furthermore, our results show that a more detailed model changes predictions regarding the variability in the outbreak dynamics and conclude that this is an important factor to consider in risk assessment.

Bayesian analysis of animal movements related to factors at herd and between herd levels: Implications for disease spread modeling

A method to assess the influence of between herd distances, production types and herd sizes on patterns of between herd contacts is presented. It was applied on pig movement data from a central database of the Swedish Board of Agriculture. To determine the influence of these factors on the contact between holdings we used a Bayesian model and Markov chain Monte Carlo (MCMC) methods to estimate the posterior distribution of model parameters. The analysis showed that the contact pattern via animal movements is highly heterogeneous and influenced by all three factors, production type, herd size, and distance between holdings. Most production types showed a positive relationship between maximum capacity and the probability of both incoming and outgoing movements. In agreement with previous studies, holdings also differed in both the number of contacts as well as with what holding types contact occurred with. Also, the scale and shape of distance dependence in contact probability was shown to differ depending on the production types of holdings.To demonstrate how the methodology may be used for risk assessment, disease transmissions via animal movements were simulated with the model used for analysis of contacts, and parameterized by the analyzed posterior distribution. A Generalized Linear Model showed that herds with production types Sow pool center, Multiplying herd and Nucleus herd have higher risk of generating a large number of new infections. Multiplying herds are also expected to generate many long distance transmissions, while transmissions generated by Sow pool centers are confined to more local areas. We argue that the methodology presented may be a useful tool for improvement of risk assessment based on data found in central databases.

The shape of the spatial kernel and its implications for biological invasions in patchy environments

Ecological and epidemiological invasions occur in a spatial context. We investigated how these processes correlate to the distance dependence of spread or dispersal between spatial entities such as habitat patches or epidemiological units. Distance dependence is described by a spatial kernel, characterized by its shape (kurtosis) and width (variance). We also developed a novel method to analyse and generate point-pattern landscapes based on spectral representation. This involves two measures: continuity, which is related to autocorrelation and contrast, which refers to variation in patch density. We also analysed some empirical data where our results are expected to have implications, namely distributions of trees (Quercus and Ulmus) and farms in Sweden. Through a simulation study, we found that kernel shape was not important for predicting the invasion speed in randomly distributed patches. However, the shape may be essential when the distribution of patches deviates from randomness, particularly when the contrast is high. We conclude that the speed of invasions depends on the spatial context and the effect of the spatial kernel is intertwined with the spatial structure. This implies substantial demands on the empirical data, because it requires knowledge of shape and width of the spatial kernel, and spatial structure.

Spatial and temporal investigations of reported movements, births and deaths of cattle and pigs in Sweden

Background

Livestock movements can affect the spread and control of contagious diseases and new data recording systems enable analysis of these movements. The results can be used for contingency planning, modelling of disease spread and design of disease control programs.

Methods

Data on the Swedish cattle and pig populations during the period July 2005 until June 2006 were obtained from databases held by the Swedish Board of Agriculture. Movements of cattle and pigs were investigated from geographical and temporal perspectives, births and deaths of cattle were investigated from a temporal perspective and the geographical distribution of holdings was also investigated.

Results

Most movements of cattle and pigs were to holdings within 100 km, but movements up to 1200 km occurred. Consequently, the majority of movements occurred within the same county or to adjacent counties. Approximately 54% of the cattle holdings and 45% of the pig holdings did not purchase any live animals. Seasonal variations in births and deaths of cattle were identified, with peaks in spring. Cattle movements peaked in spring and autumn. The maximum number of holdings within a 3 km radius of one holding was 45 for cattle and 23 for pigs, with large variations among counties. Missing data and reporting bias (digit preference) were detected in the data.

Conclusion

The databases are valuable tools in contact tracing. However since movements can be reported up to a week after the event and some data are missing they cannot replace other methods in the acute phase of an outbreak. We identified long distance transports of cattle and pigs, and these findings support an implementation of a total standstill in the country in the case of an outbreak of foot-and-mouth disease. The databases contain valuable information and improvements in data quality would make them even more useful.

Splitting the tail of the displacement kernel shows the unimportance of kurtosis

Animals disperse in space through different movement behaviors, resulting in different displacement distances. This is often described with a displacement kernel where the long-distance dispersers are within the tail of the kernel. A displacement with a large proportion of long-distance dispersers may have impact on different aspects of spatial ecology such as invasion speed, population persistence, and distribution. It is, however, unclear whether the kurtosis of the kernel plays a major role since a fatter tail also influences the variance of the kernel. We modeled displacement in landscapes with different amounts and configurations of habitats and handled kurtosis and variance separately to study how these affected population distribution and transition time. We conclude that kurtosis is not important for any of these aspects of spatial ecology. The variance of the kernel, on the other hand, was of great importance to both population distribution and transition time. We argue that separating variance and kurtosis can cast new light on the way in which long-distance dispersers are important in ecological processes. Consequences for empirical studies are discussed.