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The authors have declared that no competing interest exist.

Current address: Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland

Current address: Department of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland

Spatial analyses of pathogen occurrence in their natural surroundings entail unique opportunities for assessing in vivo drivers of disease epidemiology. Such studies are however confronted by the complexity of the landscape driving epidemic spread and disease persistence. Since relevant information on how the landscape influences epidemiological dynamics is rarely available, simple spatial models of spread are often used. In the current study we demonstrate both how more complex transmission pathways could be incorpoted to epidemiological analyses and how this can offer novel insights into understanding disease spread across the landscape. Our study is focused on

Studying pathogen transmission dynamics within their natural environments can yield important new insights both on the known and unknown determinants of the real-world transmission process. In this study we analyse how a fungal plant pathogen occurs within a landscape, showing that the road network dictates where the pathogen occurs, not only by providing suitable habitat for the host plant, but also by enhancing transmissions along the roads. Mechanistic understanding of how and where the transmission is expected to occur can yield novel insights into the ecology of pathogens, and is essential for design of control strategies.

The process of transmission is a critical component in understanding the ecology of any pathogen. It is driven both by the within-host processes, that influence the transmissability of the pathogen in various ways [

The challenge for epidemiological studies is that information on infectious contacts and transmission success rarely exists. When hosts are mobile and lead complicated lives, even the task of outlining the relevant elements involved could be challenging. Recently a substantial amount of methodological work has been dedicated to reconstructing the transmission pathways from different kinds of epidemiological data, including for example genetic information of the sampled pathogens [

In general, a natural assumption is that the movement of pathogens and hosts and the intensity and amount of contacts between them always plays a role and should be incorporated into epidemiological analyses. For example, studies have shown the significant impact of the social network among giraffes coinciding with the patterns of direct transmission of

In this study we assess the effect of the road network on the transmission of a wild plant pathogen within a natural archipelago system, inside of which the almost 4000 host populations are scattered in a fragmented manner. The landscape is strongly influenced by humans, especially due to agricultural practices, with the road network effectively spanning over the entire populated area. Ecological impacts of roads are diverse: by fragmenting the landscape they influence the movement and dispersal of many other species besides the humans [

Our study demonstrates how information on a complicated transmission network can be incorporated into analyses to better understand disease spread. We anticipate that adopting a similar network perspective could improve our understanding of a broad range of spatially structured biological systems. Regardless of the network type, e.g. a road- or a river network, its properties can induce dispersal routes, as well as unique habitats alongside to them that influence disease transmission. In particular, this approach could be essential for the sustainable management of plant diseases in agriculture [

Our study is focused on a powdery mildew

Dispersal process of a fungal spore involves the following three phases: 1) the take-off, where the spores escape to the atmospheric layer, 2) the transport, where the spores travel in it, and 3) the deposition, where the spores land back to the surface [

As the winds and small-scale gusts are complex and chaotic and thus challenging to model, and the fungal spore size of

The study system, illustrated in

At the beginning of September, each year during the consecutive years 2012-2015, all the host populations within the system were surveyed for the presence of infection. This was done by visual inspection, as towards the late summer the powdery mildew infections are visible to the naked eye (see

The road network shapefiles, and the Åland archipelago map, visualized in

To gain mechanistic understanding on the transmission process, we fitted an explicit transmission model [

The model works in discrete time and we denote with

The second modeling assumption is that the dispersal distance of a pathogen spore is distributed according to a negative exponential distribution both along the road and along the land, where we denote with _{road} and _{euc}, the mean dispersal distances of the pathogen spores by roads and by land, respectively. Then, the rate at which any local host population _{road} and _{euc} are the relative transmission rates along the road and along the land, and

The probabilities of other possible observed transitions in the data are defined as:

Since it is not known if and how the roads influence the transmission dynamics, we consider three alternative model formulations.

Model 1: transmission distances are the same, i.e. we assume _{road} = _{euc}, while _{road} and _{euc} are given independent prior distributions.

Model 2: transmission distances and transmission rates are allowed to be distinct for road- and land-based transmission, i.e. all the parameters _{road}, _{euc}, _{road} and _{euc} are all assumed to have independent prior distributions.

Model 3: transmission rate is assumed to be the same for transmission along the road and along the land, i.e. _{road} = _{euc}, while _{road} and _{euc} are both assumed to be unknown and estimated separately.

The target of the inference for the mechanistic transmission model is the joint distribution of the parameters:

We define the likelihood of the parameters as the probability of all the observed within-population transitions: a host population remaining or becoming colonized by the pathogen and the host population becoming or remaining free of infection, as defined in Eqs

As the stationary distribution for the initial states is intractable, we have omitted the term

The prior distributions and their truncation were chosen based on inital model fits.

parameter | prior distribution | truncation |
---|---|---|

_{road} |
normal(1000, 1000) | [1, 10000] |

_{euc} |
normal(1000, 1000) | [1, 10000] |

_{road} |
normal(0, 200) | [0.001, 1000] |

_{euc} |
normal(0, 200) | [0.001, 1000] |

_{i} for |
normal(0, 3000) | [0.001, 10000] |

_{i} for |
beta(1,1) | [0.001, 10000] |

Posterior predictive simulations were used for model comparison and evaluation as well as for studying the properties of predicted epidemics. To compare the predictive performances of the three models, we simulated transmission dynamics under each mechanistic model, sampling

The mechanistic transmission model only considers the shortest distances between the host populations along the road, omitting thus the information that certain host populations could be connected by the road via several alternative routes, and that the amount of traffic along the roads is not uniform across the network. Therefore, as an alternative analysis, we fitted a generalized additive model on the pathogen presence-absence data, modeling both pathogen presence-absence across the years and the colonization process: i.e. the presence-absence of the pathogen within populations that were found empty the previous year, and using covariates that measure the connectedness and centrality of locations within the road network. To account within the model the possible spatiotemporal dependencies between locations and consecutive years, the model also has a spatiotemporal part, denoted with _{t}. It is defined by assuming 1st order autoregressive process for the temporal dependency:
_{t} being a zero-mean Gaussian vector, with spatially structured covariances. We assume _{t} to have Matérn covariance function:

To link each local population to the underlying road network, we calculated for each local population summary statistics based on the location of it relative to road network. For these calculations, the centroid of each local host population was projected and equated with the closest point to it in the road network, and summary statistics and distances to other habitat patches used in the statistical analyses were computed based on these projections. For additional predictors, we used the abundance of infection in the previous year, the local host-coverage and pathogen- and host connectivity, both of which have been previously shown to influence the pathogen dynamics [

The first network centrality measure we considered is the _{ivj} equals the number of paths traversing from node _{ij} is the total number of paths from

In addition, we calculated for each host population the

Previous studies have shown the impact of both host- and pathogen _{j} = 1, if population _{j} = 0 othervise. Similarly, the host connectivity is computed as follows:
_{j} is the size (^{2}) of the host population _{j} and _{j} were set based on the observed covariates of the current year. The concept of connectivity is elaborated for instance in [

To allow for non-linear effects of the covariates in the statistical model, the effect of all covariates with continuous support (all other predictors exluding the abundance categories), was modelled by fitting a function of random walk of order 2 to their support:
_{i−1}, _{i} and _{i+1} correspond to consecutive (discretized) values of the considered covariate, and

For model selection, we utilize the

As seen in

When a different transmission rate was defined for both the land- and road-based transmission, but the dispersal distance distribution was assumed to be the same, the results show that transmission occurs at a much higher rate (posterior mean for _{road} being 151.3 ([121.24, 185.33] 95% CI), and for _{euc} it was estimated to be 19.67 ([5.79, 47.78] 95% CI). The corresponding mean dispersal distance was then estimated to be 404 ([341, 473] 95% CI).

When both the transmission rate and the transmission distance were allowed to differ between roads and land, we acquire similar conclusions, as still the rate of transmission is significantly higher along the roads (posterior mean for _{road} being 148.62 ([112.71, 190.95] 95% CI), and for _{euc} being 30.69 ([7.32, 82.8] 95% CI). The average dispersal distance is inferred to be shorter for road-based transmission than land-based (posterior mean for _{road} being 403, ([323, 494] 95% CI), and for _{euc} being 1989, ([838, 3643] 95% CI).

When transmission rate is assumed equal regardless of the transmission route, then we infer that the average dispersal distance is shorter for road-based transmission and longer for land-based transmission, posterior mean for _{road} being 306 ([240, 383] 95% CI), and for _{euc} being 2013 ([772, 3962] 95% CI). The transmission rate parameter

The posterior distributions for the fitted parameters of the different mechanistic transmission models are visualized in

Panels A, B and C correspond to mechanistic model 1, panels D, E and F correspond to mechanistic model 2 and panels G, H and I correspond to mechanistic model 3. As an example, panel A depicts the estimated mean dispersal distances by land (_{E}) and by road (_{R}), while panels B and C depict the estimated colonization rates from patches with different abundance of infection (_{1} being the smallest abundance class), and the estimated pathogen population extinction rates for the pathogen populations with different abundances of infection. The axis limits are different in each plot.

All considered models were structured to allow the observed infection abundances to influence the dispersal- and extinction rates of the different pathogen populations. It is worth noting that the transmission rate parameters in Model 3 have a different interpretation, due to different model structure, and therefore are on a different scale. The results on these parameters across the models suggest that the infection outbound rate is higher when the infection abundance class is higher, while the opposite holds for the pathogen population extinction probability. In particular, the infection outbound rate can be 1/3 larger for abundance class 2 and 1/2 larger for abundance class 3, compared to class 1. For the extinction rates it seems that pathogen populations go extinct with probabilities approximately 0.5, 0.25, and 0.1, when the pathogen abundance previous year was 1, 2 or 3, respectively. Both conclusions match our expectations.

The results for statistical models with the best predictive accuracy measured by WAIC, are shown in

The covariates were scaled prior to analysis and the effects are shown in the scaled axis as well. Panel A depicts the effect of pathogen abundance classes (ab1-ab2) previous year on the infection presence the next year. The results for the models with best WAICs among the considered models are shown.

Model | Nominal variance | Range (meters) | |
---|---|---|---|

Presence Absence | 0.36, [0.12, 0.56] | 0.97, [0.68, 1.38] | 6034.9, [4016.8, 9056.9] |

New Pathogen population | 0.29, [0, 0.54] | 0.94, [0.68, 1.31] | 6017.7 [4077.9, 8879] |

In addition to model comparison, posterior predictive simulations allowed us to assess how in practice the epidemics would occur under different modelling assumptions. Based on these simulations, we conclude that the posterior medians for proportion of transmissions that occur along the road are 0.84, 0.77 and 0.43, for Models 1, 2 and 3 respectively. Hence, if different transmission rates are assumed for land- and road transmission, then a considerably larger fraction of transmissions is expected to occur along the roads. If equal rates are assumed, this conclusion does not hold. The boxplots for the simulated proportions are shown in panel A of

Panel A shows for each model what proportion of transmissions on average occur via a road-based transmission pathway, and what proportion traverses by land for each three mechanistic transmission models. In panels B-D, we show how the initial location of the epidemic influences its potential to spread (for model 2). In B we have initiated epidemics in locations with high, average and low betweenness, and the colors illustrate in how many simulations (from a total of 5000) the different locations were infected during 10-year’s time. Panel C illustrates for the same epidemic initializations the probability distribution for the epidemic time-span, and D illustrates for the locations that got infected in at least one simulation, in how many simulations in total they were infected. The maps in panel B were created using data produced by National Land Survey of Finland.

For further illustration, we simulated epidemics under Model 2 (that had the best predictive success) with three different kinds of starting locations, and considered high-, average and low betweenness for the initial epidemic locations. In panel B of

In this study we have presented two arguments for showing the significant role of road network and -traffic in the transmission dynamics of the powdery mildew epidemics within the Åland islands archipelago. We further combine these arguments when simulating the transmissions, thereby demonstrating how the road network topology influences the dynamics in the system. This is in agreement with theoretical arguments [

Previous studies on the same pathosystem have mostly focused on estimating the mean dispersal distance along a landscape that was considered homogenenous [

In conclusion, we highlight the strong influence of the human handprint, here the road traffic, on disease dynamics within a semi-natural landscape. We expect that similar considerations would be needed to correctly understand the transmission in other agricultural- and wild disease systems, or any ecological system with complex dispersal processes. Apart from traffic networks, we believe that a network-based analysis may be necessary, when studying for instance ecological systems within river networks [

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E.N. wishes especially to thank Elise Vaumourin for the field work we did together in Åland islands, which inspired this work. We also thank Torsti Schulz for help with GIS and STAN, Timo Vesala for introducing the physics of micrometeorology, Hanna Susi for plant pathosystem consultancy, Jarno Vanhatalo for support and finally Krista Raveala and numerous field assistants for collecting the field data.