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Spatial Spread of Organisms: Modeling ecological and epidemiological processes
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Biology . Linköping University, The Institute of Technology.ORCID iD: 0000-0001-7856-2925
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis focuses on the spread of organisms in both ecological and epidemiological contexts. In most of the studies presented, displacement is modeled with a spatial kernel function, which is characterized by scale and shape. These are measured by the net squared displacement (or kernel variance) and kurtosis, respectively. If organisms disperse by the assumptions of a random walk or correlated random walk, a Gaussian shaped kernel is expected. Empirical studies often report deviations from this, and commonly leptokurtic distributions are found, often as a result of heterogeneity in the dispersal process.

In the studies presented in two of the included papers, the importance of the kernel shape is tested, by using a family of kernels where the shape and scale can be separated effectively. Both studies utilize spectral density approaches for modeling the spatial environment. It is concluded that the shape is not important when studying the population distribution in a habitat/matrix context. The shape is however important when looking at the invasion of organisms in a patchy environment, when the arrangement of patches deviates from randomly distributed. The introduced method for generating patch distribution is also compared to empirical distributions of patches (farms and old trees). Here it is concluded that the assumptions used for modeling of the spatial environment are consistent with the observed patterns. These assumptions include fractal properties such that the same aggregational patterns are found at different scales.

In a series of papers, movements of animals are considered as vectors for between-herd disease spread. The studies are based on data found in databases held by the Swedish Board of Agricultural (SJV), consisting of reported movements, as well as farm location and characteristics. The first study focuses on the distance related probability of contacts between herds. In the following papers, the analysis is expanded to include production type and herd size. Movement data of pigs (and cattle in Paper I) are analyzed with Bayesian models, implemented with Markov Chain Monte Carlo (MCMC). This is a flexible approach that allows for parameter estimations of complex models, and at the same time includes parameter uncertainty.

In Paper IV, the effects of the included factors are investigated. It is shown that all three factors (herd size, production type structure and distance related probability of contacts) are expected to influence disease spread dynamics, however the production type structure is found to be the most important factor. This emphasizes the value of keeping such information in central databases. The models presented can be used as support for risk analysis and disease tracing. However, data reliability is always a problem, and implementation may be improved with better quality data.

The thesis also shows that utilizing spatial kernels for description of the spatial spread of organisms is an appropriate approach. However, these kernels must be flexible and flawed assumptions about the shape may lead to erroneous conclusions. Hence, the joint distribution of kernel shape and scale should be estimated. The flexibility of Bayesian analysis, implemented with MCMC techniques, is a good approach for this, and further allows for implementation of more complex models where other factors may be included.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2010. , 54 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1311
Keyword [en]
Spatial kernel, Spatially explicit modeling, Disease transmission, Animal movements
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:liu:diva-54839ISBN: 978-91-7393-401-5 (print)OAI: oai:DiVA.org:liu-54839DiVA: diva2:310649
Public defence
2010-05-07, Planck, Hus F, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2010-04-15 Created: 2010-04-15 Last updated: 2016-08-31Bibliographically approved
List of papers
1. Estimation of distance related probability of animal movements between holdings and implications for disease spread modeling
Open this publication in new window or tab >>Estimation of distance related probability of animal movements between holdings and implications for disease spread modeling
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2009 (English)In: Preventive Veterinary Medicine, ISSN 0167-5877, E-ISSN 1873-1716, Vol. 91, no 2-4, 85-94 p.Article in journal (Refereed) Published
Abstract [en]

Between holding contacts are more common over short distances and this may have implications for the dynamics of disease spread through these contacts. A reliable estimation of how contacts depend on distance is therefore important when modeling livestock diseases. In this study, we have developed a method for analyzing distant dependent contacts and applied it to animal movement data from Sweden. The data were analyzed with two competing models. The first model assumes that contacts arise from a purely distance dependent process. The second is a mixture model and assumes that, in addition, some contacts arise independent of distance. Parameters were estimated with a Bayesian Markov Chain Monte Carlo (MCMC) approach and the model probabilities were compared. We also investigated possible between model differences in predicted contact structures, using a collection of network measures. We found that the mixture model was a much better model for the data analyzed. Also, the network measures showed that the models differed considerably in predictions of contact structures, which is expected to be important for disease spread dynamics. We conclude that a model with contacts being both dependent on, and independent of, distance was preferred for modeling the example animal movement contact data.

Place, publisher, year, edition, pages
Elsevier, 2009
Keyword
Markov Chain Monte Carlo, Mixture models, Model selection, Animal movements, Disease transmission, Network analysis
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-20742 (URN)10.1016/j.prevetmed.2009.05.022 (DOI)
Available from: 2009-09-18 Created: 2009-09-18 Last updated: 2017-12-13
2. Estimating animal movement contacts between holdings of different production types
Open this publication in new window or tab >>Estimating animal movement contacts between holdings of different production types
2010 (English)In: Preventive Veterinary Medicine, ISSN 0167-5877, E-ISSN 1873-1716, Vol. 95, no 1-2, 23-31 p.Article in journal (Refereed) Published
Abstract [en]

Animal movement poses a great risk for disease transmission between holdings. Heterogeneous contact patterns are known to influence the dynamics of disease transmission and should be included in modeling. Using pig movement data from Sweden as an example, we present a method for quantification of between holding contact probabilities based on different production types. The data contained seven production types: Sow pool center, Sow pool satellite, Farrow-to-finish, Nucleus herd, Piglet producer, Multiplying herd and Fattening herd. The method also estimates how much different production types will determine the contact pattern of holdings that have more than one type. The method is based on Bayesian analysis and uses data from central databases of animal movement. Holdings with different production types are estimated to vary in the frequency of contacts as well as in what type of holding they have contact with, and the direction of the contacts. Movements from Multiplying herds to Sow pool centers, Nucleus herds to other Nucleus herds, Sow pool centers to Sow pool satellites, Sow pool satellites to Sow pool centers and Nucleus herds to Multiplying herds were estimated to be most common relative to the abundance of the production types. We show with a simulation study that these contact patterns may also be expected to result in substantial differences in disease transmission via animal movements, depending on the index holding. Simulating transmission for a 1 year period showed that the median number of infected holdings was 1 (i.e. only the index holding infected) if the infection started at a Fattening herd and 2161 if the infection started on a Nucleus herd. We conclude that it is valuable to include production types in models of disease transmission and the method presented in this paper may be used for such models when appropriate data is available. We also argue that keeping records of production types is of great value since it may be helpful in risk assessments.

Place, publisher, year, edition, pages
Elsevier, 2010
Keyword
Markov Chain Monte Carlo; Animal databases; Animal movements; Production types
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-54834 (URN)10.1016/j.prevetmed.2010.03.002 (DOI)000278281600004 ()20356640 (PubMedID)
Available from: 2010-04-15 Created: 2010-04-15 Last updated: 2017-12-12
3. Bayesian analysis of animal movements related to factors at herdand between herd levels: Implications for disease spread modeling
Open this publication in new window or tab >>Bayesian analysis of animal movements related to factors at herdand between herd levels: Implications for disease spread modeling
2011 (English)In: Preventive Veterinary Medicine, ISSN 0167-5877, E-ISSN 1873-1716, Vol. 98, no 4, 230-242 p.Article in journal (Other academic) Published
Abstract [en]

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 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 farms. 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.

Place, publisher, year, edition, pages
Elsevier, 2011
Keyword
Markov Chain Monte Carlo; Hierarchical Bayesian; Mixture models; Indicator variable; Animal databases; Animal movements; Contact structure
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-54835 (URN)10.1016/j.prevetmed.2010.11.005 (DOI)000287904900002 ()
Available from: 2010-04-15 Created: 2010-04-15 Last updated: 2017-12-12
4. Expected effect of herd size, production type and between herd distances on the dynamic of between herd disease spread
Open this publication in new window or tab >>Expected effect of herd size, production type and between herd distances on the dynamic of between herd disease spread
2010 (English)Manuscript (preprint) (Other academic)
Abstract [en]

Studies of between herd contacts may provide important insight to disease transmission dynamics. By comparing the result from models with different level of details in the description of animal movement we studied how factors influence the final epidemic size as well as the stochastic behavior 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 modeling and analyzing 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 modeling disease spread between herds. Furthermore our results show that a more detailed model predicts more stochasticity in the outbreak dynamics and conclude that this is an important factor to consider in risk assessment.

Keyword
Disease spread modeling, Heterogeneous contact structure
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-54837 (URN)20356640 (PubMedID)
Available from: 2010-04-15 Created: 2010-04-15 Last updated: 2016-08-31
5. Splitting the tail of the displacement kernel shows the unimportance of kurtosis
Open this publication in new window or tab >>Splitting the tail of the displacement kernel shows the unimportance of kurtosis
2008 (English)In: Ecology, ISSN 0012-9658, E-ISSN 1939-9170, Vol. 89, no 7, 1784-1790 p.Article in journal (Refereed) Published
Abstract [en]

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.

Keyword
Displacement; kurtosis; long-distance dispersers; population distribution
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-43068 (URN)10.1890/07-1363.1 (DOI)71401 (Local ID)71401 (Archive number)71401 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13
6. The shape of the spatial kernel and its implications for biological invasions in patchy environments
Open this publication in new window or tab >>The shape of the spatial kernel and its implications for biological invasions in patchy environments
2011 (English)In: Proceedings of the Royal Society of London. Biological Sciences, ISSN 0962-8452, E-ISSN 1471-2954, Vol. 278, no 1711, 1564-1571 p.Article in journal (Refereed) Published
Abstract [en]

Ecological and epidemiological invasions occur in a spatial context. In the study presented we tested how these processes relate to the distance dependence of spread or dispersal between spatial entities such as habitat patches or infective units. The distance dependence was described by a spatial kernel which can be characterized by its shape, quantified by kurtosis, and width, quantified by the kernel variance. We also introduced a method to analyze or generate non randomly distributed infective units or patches as point pattern landscapes. The method is based on Fourier transform and consists of two measures in the spectral representation; Continuity that relates to autocorrelation and Contrast that refers to difference in density of patches, or infective units, in different areas of the landscape. The method was also used to analyze some relevant empirical data where our results are expected to have implications for ecological or epidemiological studies. We analyzed distributions of large old trees (Quercus and Ulmus) as well as the distributions of farms (both cattle and pig) in Sweden. We tested the invasion speed in generated landscapes with different amount of Continuity and Contrast. The results showed that kurtosis, i.e. the kernel shape, was not important for predicting the invasion speed in randomly distributed patches or infective units. However, depending on the assumptions of dispersal, it may be highly important when the distribution of patches or infective units deviates from randomness, in particular when the Contrast is high. We conclude that speed of invasions and spread of diseases depends on its spatial context through the spatial kernel intertwined to the spatial structure. This implies high demands on the empirical data; it requires knowledge of both shape and width of the spatial kernel as well as spatial structure of patches or infective units.

Place, publisher, year, edition, pages
Royal Society, 2011
Keyword
Kurtosis, Spread of disease, Point patterns, Spectral density, Dispersal, Invasion
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-54838 (URN)10.1098/rspb.2010.1902 (DOI)000289719100016 ()20356640 (PubMedID)
Available from: 2010-04-15 Created: 2010-04-15 Last updated: 2017-12-12
7. The effect on dispersal from complex correlations in small-scale movement
Open this publication in new window or tab >>The effect on dispersal from complex correlations in small-scale movement
2008 (English)In: Ecological Modelling, ISSN 0304-3800, E-ISSN 1872-7026, Vol. 213, no 2, 263-272 p.Article in journal (Refereed) Published
Abstract [en]

Calculations of large-scale displacement distances were made to evaluate the combined effect of small-scale movement pattern of a Collembola, Protaphorura armata. The effect of presence of food and conspecific density on turning angle, step length and activity/motility was investigated. Calculations of net square displacement were made both by assuming correlated random walk (CRW) and by resampling data to account for correlation structures in movement patterns that violate the assumptions of CRW. In presence of food, individuals spent less time moving (decreased activity), but when they moved they showed larger turning angles than individuals moving in areas without food. Increased conspecific density did not affect time spent moving by individuals, but when step length decreased and turning angle increased. P. armata showed negative density-dependent dispersal and exhibited area-restricted search as a response to both food and increased conspecific density. The CRW was relatively robust to some violations of its underlying assumptions. However, the expected displacement increased substantially, as much as 50%, when accounting for observed auto-correlation in step length and correlation between step length and turning angle. Hence, an explanation for increased displacement and dispersal of a species can also be the result of a more complex correlation of its behaviour rather than solely altering specific movement parameters, for example increasing step length or decreasing turning angle. The results emphasise the importance of careful analysis of small-scale movement before using them as predictors of population distribution and invasion speed in heterogeneous landscapes. © 2007 Elsevier B.V. All rights reserved.

National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-44411 (URN)10.1016/j.ecolmodel.2007.12.011 (DOI)76579 (Local ID)76579 (Archive number)76579 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13

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