Global stability of an age-structured population model on several temporally variable patches.

We consider an age-structured density-dependent population model on several temporally variable patches. There are two key assumptions on which we base model setup and analysis. First, intraspecific competition is limited to competition between individuals of the same age (pure intra-cohort competition) and it affects density-dependent mortality. Second, dispersal between patches ensures that each patch can be reached from every other patch, directly or through several intermediary patches, within individual reproductive age. Using strong monotonicity we prove existence and uniqueness of solution and analyze its large-time behavior in cases of constant, periodically variable and irregularly variable environment. In analogy to the next generation operator, we introduce the net reproductive operator and the basic reproduction number [Formula: see text] for time-independent and periodical models and establish the permanence dichotomy: if [Formula: see text], extinction on all patches is imminent, and if [Formula: see text], permanence on all patches is guaranteed. We show that a solution for the general time-dependent problem can be bounded by above and below by solutions to the associated periodic problems. Using two-side estimates, we establish uniform boundedness and uniform persistence of a solution for the general time-dependent problem and describe its asymptotic behaviour.

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).

Biting midge dynamics and bluetongue transmission: a multiscale model linking catch data with climate and disease outbreaks.

Bluetongue virus (BTV) serotype 8 has been circulating in Europe since a major outbreak occurred in 2006, causing economic losses to livestock farms. The unpredictability of the biting activity of midges that transmit BTV implies difficulty in computing accurate transmission models. This study uniquely integrates field collections of midges at a range of European latitudes (in Sweden, The Netherlands, and Italy), with a multi-scale modelling approach. We inferred the environmental factors that influence the dynamics of midge catching, and then directly linked predicted midge catches to BTV transmission dynamics. Catch predictions were linked to the observed prevalence amongst sentinel cattle during the 2007 BTV outbreak in The Netherlands using a dynamic transmission model. We were able to directly infer a scaling parameter between daily midge catch predictions and the true biting rate per cow per day. Compared to biting rate per cow per day the scaling parameter was around 50% of 24 h midge catches with traps. Extending the estimated biting rate across Europe, for different seasons and years, indicated that whilst intensity of transmission is expected to vary widely from herd to herd, around 95% of naïve herds in western Europe have been at risk of sustained transmission over the last 15 years.

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.

Author Correction: Enhancing nutrient recycling from excreta to meet crop nutrient needs in Sweden - a spatial analysis.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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 51%. 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.

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 biting midge species (Diptera: Ceratopogonidae) in three European countries at different latitudes.

BACKGROUND: The outbreaks of bluetongue and Schmallenberg disease in Europe have increased efforts to understand the ecology of Culicoides biting midges and their role in pathogen transmission. However, most studies have focused on a specific habitat, region, or country. To facilitate wider comparisons, and to obtain a better understanding of the spread of disease through Europe, the present study focused on monitoring biting midge species diversity in three different habitat types and three countries across Europe. METHODS: Biting midges were trapped using Onderstepoort Veterinary Institute light 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 during the winter months. Trapped midges were counted and identified morphologically. Indices on species richness, evenness and diversity were calculated. Community compositions were analysed using non-metric multidimensional scaling (NMDS) techniques. RESULTS: A total of 50,085 female midges were trapped during 442 collection nights. More than 88% of these belonged to the Obsoletus group. The highest midge diversity was found in Sweden, while species richness was highest in the Netherlands, and most specimens were trapped in Italy. For habitats within countries, diversity of the trapped midges was lowest for farms in all countries. Differences in biting midge species communities were more distinct across the three countries than the three habitat types. CONCLUSIONS: A core midge community could be identified, in which the Obsoletus group was the most abundant. Variations in vector communities across countries imply different patterns of disease spread throughout Europe. How specific species and their associated communities affect disease risk is still unclear. Our results emphasize the importance of midge diversity data at community level, how this differs across large geographic range within Europe, and its implications on assessing risks of midge-borne disease outbreaks.

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.

Stability of Ecosystems Under Invasions.

This paper considers a model of foodwebs taking into account species extinction and invasion. We show that system stability depends not only on usual parameters (mortality rates, self-limitation coefficients, and resource abundances), but also on an additional parameter ("biodiversity potential"). The main result is as follows. For foodwebs with random parameters, we obtain an estimate of probability that the foodweb exposed to invasion survives. This estimate involves different system parameters, size and its topological properties.

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.

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.

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.

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.

SpecNet: a spatial network algorithm that generates a wide range of specific structures.

Network measures are used to predict the behavior of different systems. To be able to investigate how various structures behave and interact we need a wide range of theoretical networks to explore. Both spatial and non-spatial methods exist for generating networks but they are limited in the ability of producing wide range of network structures. We extend an earlier version of a spatial spectral network algorithm to generate a large variety of networks across almost all the theoretical spectra of the following network measures: average clustering coefficient, degree assortativity, fragmentation index, and mean degree. We compare this extended spatial spectral network-generating algorithm with a non-spatial algorithm regarding their ability to create networks with different structures and network measures. The spatial spectral network-generating algorithm can generate networks over a much broader scale than the non-spatial and other known network algorithms. To exemplify the ability to regenerate real networks, we regenerate networks with structures similar to two real Swedish swine transport networks. Results show that the spatial algorithm is an appropriate model with correlation coefficients at 0.99. This novel algorithm can even create negative assortativity and managed to achieve assortativity values that spans over almost the entire theoretical range.