Saturation excess overland flow accelerates the spread of a generalist soil-borne pathogen

Plant pathogens are a major agent of disturbance in ecosystems worldwide. Disturbance by disease can alter the hydrological function of affected ecosystems. However, many plant pathogens are also sensitive to soil moisture and can be propagated by the transport of infectious tissue or reproductive structures in surface flow, so that hydrological processes can drive pathogen infection. These feedforward and feed-back processes set up the possibility of complex ecohydrological dynamics relating plant disease and the water cycle. Here the generalist root pathogen Phytophthora cinnamomi (Pc) is used as a case study to quantify the potential importance of hydrological dynamics on disease spread. A numerical model of Pc growth and dispersal is used to investigate the importance of Pc transport in intermittent surface runoff compared to more continuous rhizosphere Pc spread via diffusion-like hyphal growth. We apply and test this model at two well-studied sites of Pc infection with contrasting hydrology: a Banksia woodland in Western Australia where deep sandy soils inhibit surface runoff, and an Erica heathland in the Spanish Central Plateau where relatively shallow soils on steep slopes generate intermittent overland flow. Predictions of Pc spatial spread at the Spanish site improve when Pc transport in runoff is incorporated into the model, while no such improvements arise at the Australian site. Omitting transport in overland flow from model predictions at the Spanish site results in an average under-prediction of final pathogen patch areas by 350 m for each year of growth between observations,


Introduction
Plant pathogens can affect forest composition, structure, and function, but the dynamics of these disturbances are generally less well understood than compared to those of abiotic disturbances (Flower et al., 2015). Vegetation infection and mortality caused by pathogens can alter forest water balance (Batini et al., 1980;Schofield et al., 1989, e.g.), and there are also potential feed-forward mechanisms by which hydrology can directly impact pathogens. For example, the growth and spread rates of many soil pathogens vary with water potential (Crist et al., 1975;Ferrin et al., 2006;Colhoun, 1973;Malajczuk et al., 1979;Dickenson et al., 1981;Madar et al., 1989;Cook et al., 1972;Boyer, 1995;Schober et al., 1999;Suleman et al., 2001;Desprez-Loustau et al., 2006), meaning that pathogen infection can influence, while also being influenced by, root zone water dynamics. The potential for pathogen propagules and infectious material to be transported by surface flow adds scope for further complex hydrologicalpathogen feedback processes. In previous work, relationships between soil water potential and pathogen dynamics were used to relate regional hydroclimatic variations to pathogen risk (Thompson et al., 2013;Thompson et al., 2014). The influence of hydrological transport processes on more localized pathogen spread, however, remain largely unexplored. Yet better understanding of this feed-forward relationship between hydrology and disease disturbance is necessary for understanding coupled forest -pathogenwater systems and the implications for disturbance and ecosystem function.
In this study, we consider the soil-borne pathogen Phytophthora cinnamomi (Pc) as a case study of hydrological transport mechanisms for disease spread. Pc is one of the world's most destructive plant pathogens (Burgess et al., 2017), posing a global threat to natural and agricultural systems (Lowe et al., 2000) that is expected to worsen as climates warm (Thompson et al., 2014;Chakraborty et al., 2000;Bergot et al., 2004). Pc forms necrotic lesions on roots and stems of infected host plants. Severe infection results in the loss of the majority of the fine root system in susceptible plants, inhibiting water uptake and causing mortality. Pc is a generalist pathogen affecting a huge array of plant species. For example, in south-west Western Australia, some 40% of the more than 5000 endemic plant species are susceptible to Pc (Shearer, CE Crane, et al., 2004). In Europe, Pc is decimating oak woodlands of Quercus ilex and Quercus suber (Brasier, 1996) and the chestnut forests (Vettraino et al., 2005). Pc is persistent in the environment and spreads rapidly through infected soil and water. Within the soil, it can spread via mycelial growth and root-root contact, and through the production of oospores, or motile zoocytes (Hardham et al., 2018). Under unfavorable conditions such as drought, Pc forms resilient chlamydospores that can persist and remain viable for months to years (Jung, Colquhoun, et al., 2013;Hwang et al., 1978). Long-distance spread occurs through the mobilization of infected roots, soil, or fungal propagules by natural and anthropogenic processes (Ristaino et al., 2000).
In natural ecosystems, management strategies to address Pc infection involve prioritizing areas for quarantine, monitoring, and treatment. A component of this prioritization involves making assessments about the likely pathways and rates of Pc establishment and spread in a given landscape (e.g. National Heritage Trust and Environment Australia, 2001; Commonwealth of Australia, 2014). Quantitative modeling provides an avenue to predict the importance of these pathways in a given setting. The growth dynamics of Pc are strongly coupled to environmental conditions (Thompson et al., 2013). Mycelial growth is inhibited under low water potentials (i.e. dry soil), declines with falling temperatures (Malajczuk et al., 1979), and the pathogen is killed by protracted sub-freezing conditions (Marçais et al., 1996). In previous work, we used these environmental dependencies to predict the likelihood of Pc infection across soil type and climate conditions under steady state conditions (Thompson et al., 2013;Thompson et al., 2014). Here, we extend the modeling framework to consider the spatial dynamics of Pc spread and its dependence on transport processes in the environment, with a particular focus on how varying local hydrology impacts these processes.
We address the following research questions: • Can the rate of Pc spread from disease foci within susceptible plant communities be predicted as a function of soil, plant and climate properties?, and • How do different mechanisms of pathogen mobility contribute to observed patterns of Pc infection spread?
We consider multiple potential transport pathways that could contribute to Pc spread around disease foci. Mycelial root pathogens, including Pc, spread locally via growth along the host root system, a process that is well-represented via diffusion in soil pathogen models (Cunniffe et al., 2008;Park et al., 2001). Pc also spreads locally due to zoocyte motility. In practice, the maximum observed scales of zoocyte movement and of mycelial extension are comparable, on the order of millimeters per day (Benjamin et al., 1982;Malajczuk et al., 1979). Since observations of disease patches are typically coarse in space and time (e.g. observed on monthly timescales or longer, and on spatial scales of one to tens of meters) (Dawson et al., 1985;Cardillo et al., 2018;Wilson et al., 2012), it is unlikely that the relative contribution of motile zoocytes versus mycelial expansion to this local growth can be determined, and thus will be considered jointly represented by the "diffusive" spread. However, natural (rather than anthropogenic) transport of Pc may not be limited to the rhizosphere. Observations of Pc spread persistently reveal features -such as faster downslope than upslope spread, or spatial associations between Pc infection and surface flow channels -which are consistent with Pc transport in surface flow (see Table 1 for details). Although repeated recovery of Pc material in surface flow, subsurface flows and drainage waters (Thomson et al., 1974;Kliejunas et al., 1976;Kinal et al., 1993;Reeser et al., 2011) supports the feasibility of this transport mechanism, its importance is not well understood. Pc will not grow in permanently saturated conditions (Malajczuk et al., 1979), but water flow outside such areas tends to be episodic and infrequent -associated with intense storms (Horton, 1933) or transient saturation of soils (Dunne et al., 1970). Although the intermittent nature of surface runoff might suggest it is unimportant for Pc spread, water could readily transport Pc over tens to hundreds of meters, suggesting that its role should be explored.  Thomson et al. (1974) Arizona, USA Various Phytophthora species Found Phytophthora propagules in recycled irrigation water from citrus crops G. Weste, Ruppin, et al. (1976) Victoria, Australia

P. cinnamomi
Disease spread with clearly defined boundaries in direction of drainage from road Kliejunas et al. (1976) Hawaii, USA

P. cinnamomi
Recovery of zoospores in runoff water Shea et al. (1983) Western Australia

P. cinnamomi
Lateral transport of zoospores in subsurface water above lateritic layer Kinal et al. (1993) Western Australia

P. cinnamomi
Recovered pathogen from laterally flowing subsurface water in lateritic soil Hill et al. (1994) Western Australia

P. cinnamomi
Faster spreading disease fronts in low-lying areas than compared to upslope areas Reeser et al. (2011) Oregon and Alaska, USA Various Phytophthora species Recovered Phytophthora from streams in forested areas Jung and Dobler (2002) Dominican Republic

P. cinnamomi
Disease spread follows downslope path of runoff from diseased trees Oudemans (1999) New Jersey, USA P. cinnamomi Recovered pathogen from streams, irrigation reservoirs, and drainage canals To better understand the drivers of Pc spread at the hillslope scale, we extend the Pc growth model presented in Thompson et al. (2013) and Thompson et al. (2014) to account for spatial spread of Pc. We include diffusion-like local spread and passive transport in surface water. The model is calibrated and tested at two contrasting sites in Western Australia and Spain. The spatial spread of Pc infection at both sites has been intensively monitored, displaying quite different spatial patterns (Figure 1). We calibrate the model twice at each site, including and omitting overland flow as a Pc transport mechanism, and compare the model performance in each case. The degradation in model performance when overland flow is omitted (in the "diffusion optimized setup") provides a metric of whether including overland flow is necessary to describe observed patterns of spread. The fully calibrated models (including the overland flow terms) are then run without overland flow. The resulting predictions of the spatial patterns provide an estimate of the relative importance of "diffusive" dispersal versus transport in surface runoff for disease spread at each site. The model does not include transport in subsurface water flows: subsurface lateral flow is negligible above the water table at the Western Australian site (Xu et al., 2003;Salama et al., 2005), and while the saturated hydraulic conductivity of the soils at the Spanish site is reasonably high (4.47 cm/min (Gómez-Paccard et al., 2015)), the soil moisture content of the soils is generally low (see Section H), greatly reducing soil conductivity and limiting lateral transport in unsaturated soils. In general, however, such subsurface transport is feasible and should be considered in sites where significant lateral subsurface flows occur (Shea et al., 1983;Kinal et al., 1993).

Model
The mean-field spatial dynamics of soil-borne pathogens can be modeled with reaction-diffusion type equations (Park et al., 2001;Cunniffe et al., 2008), specifying the growth rate of pathogen biomass at a point, and its diffusivity (Andow et al., 1990;Okubo et al., 2013). The strong dependence of Pc mycelial growth and survival on soil moisture and temperature means that both growth and diffusion terms in the spread model are functions of local environmental conditions. The soil environmental conditions must therefore also be modeled or prescribed based on climate observations and local soil properties. To add transport via overland flow to this model involves specifying a soil water excess available to produce runoff, a routing model to define the direction of flow, and a representation of mobilization, mixing and deposition of propagules in the surface water flow. The model thus has three components: a soil water balance model (detailed in Section2.1), a runoff routing and propagule transport model (detailed in Section 2.2), and the pathogen growth and spread model (detailed in Section 2.3). The model is implemented on a two-dimensional square grid, where cells take dimensions of ∆x and ∆y. Table 2 summarizes all the variables and parameters of the model components, and a schematic showing the relation between components is shown in Figure 2.

Soil water balance
Soil water is represented with a mass balance model ( Figure 2A) within a homogeneous vertical domain z r [mm], taken here as either the depth of the host plants' root zone or the depth to an impermeable soil layer, whichever is smaller. The mean relative soil water content s [-] in this zone is given by where V water is the volume of water per unit area [mm] and n is the porosity of the soil [-]. The mass balance for the soil moisture is given by: where f () represents the rate of infiltration, g() the rate of evapotranspiration, and L() the rate of leakage at the bottom boundary. This mass balance is implemented independently for each spatial location. Lateral transport of water in the soil is assumed negligible.
The rate of infiltration is defined as a function of the rainfall rate P [mm/day], the soil moisture, and the soil infiltration capacity, which we approximate with its saturated hydraulic conductivity K sat [mm/day], as follows: overland flow (q storm ) as outputs. In the event of overland flow generation, the routing of runoff between source (i) and sink (j) cells along flowpaths ( ) and the resulting advective transport is calculated in the overland transport portion of the model (B). The soil moisture and temperature from the water balance and environmental conditions are used to parameterize the growth rate and diffusion coefficient (C) which, along with any input from overland transport, determine the change in biomass density in each cell. With these changes in biomass density, the Pc biomass density field is output at the end of each time step (D). This is then further binarized to presence or absence of Pc infection, where cells with biomass density at least 0.5B max categorized as infected.
is the exponent of the soil-water retention curve for the corresponding soil type from Clapp et al. (1978). For cases where the bottom boundary of the modeled soil domain is impervious, the leakage term is set to zero.
The water balance connects to the other two model components via the value of the soil moisture s, which is used as input to the pathogen biomass growth model (see Section 2.3 and Figure 2C), and by the production of overland flow q = P − f [mm/day], which is produced when soils are saturated (s = 1) or when precipitation occurs a rate exceeding the infiltration capacity of the soil. The runoff model ( Figure 2B and Figure 3), described in more detail in Section 2.2, operates on the storm-averaged rate of flow production, (q storm , mm day −1 ): where t storm [day] is the length of the storm event and ∆t is the time step resolution of the model [day]. The duration of a storm event is considered to be the cumulative time of consecutive non-zero precipitation records, up to a maximum of 24 hours, after which it is treated as two discrete events.

Surface flow routing and propagule transport
This component of the model is new to this study, and therefore explained in detail below. Figure 3 outlines several of the key components of the transport model.  (Tarboton, 1997) is used to determine the flow between a source cell (i) with upslope area A i and a downslope sink cell (j). In the algorithm, flow is assumed to travel in the direction of the steepest downhill descent. When this results in flow being split between two adjacent cells, the relative fraction to each cell (φ) is determined by the angles as shown in (A). For each sink cell, the contributions of each upslope source cell are treated individually, with the final cumulative deposited biomass (M + j ) coming from the superposition of all the upslope sources (B).

Surface flow routing
Storm averaged runoff (q storm ) is routed along the land surface using the D-∞ method (Tarboton, 1997) which specifies the fraction (φ i,j ) of flow in any upslope location (indexed as i) that passes through any specified downslope cell (indexed as j) (see Figure 3A). We approximate the dynamic processes of runoff production, routing and their variation throughout a storm with a single, storm-averaged rate of flow production, and steady conditions assumed for runoff depths (h), bulk velocity (u) and transport properties. With these assumptions, φ i,j and the average rate of runoff production (q storm ) fully specify the runoff routing.

Pathogen transport
We model the transport of Pc in the flow using a simple advection equation following the mean water flow path. The flow path is not necessarily aligned with the topographic grid, and has its own coordinate, [m] ( Figure 2B). For flow along this path, the concentration of pathogen biomass (C, [g m −3 ]) evolves as: where q c is the water flux per unit width of the flowpath [m 2 day −1 ], and Source and Sink denote the rates of concentration increase due to Pc biomass being introduced to the flow from soil beneath the flowpath, and decrease due to its deposition. We assume that deposition follows first order linear kinetics, such that Sink( , t) = βC( , t), where β [day −1 ] is an unknown rate constant.
With these linear kinetics, and recognizing that the flow is independent of the Pc concentration, we can separately track the fate of biomass concentrations C i originating from each upslope source cell i ( Figure 3B). For an individual source cell, the concentration evolves along the downslope flowpath as: Written in this way, the Source terms in Equation 6 are translated into the boundary conditions on This differential equation can be solved to identify the concentration of pathogen biomass in the runoff at location j, located downstream along the flowpath from source location i, that can be attributed to the mobilization of biomass from source i: where C io is the boundary condition for this concentration at cell i and represents the storm-averaged biomass concentration generated by mobilizing Pc into the flow at that site. The Sink term at location j associated with biomass originating from i is given by multiplying Equation 9 by the rate constant β, and can be used to compute the total transport of biomass from source location i to sink location j during the storm: In this expression, A i [m 2 ] is the upslope contributing area which generates runoff that passes through is the storm-averaged runoff velocity at cell j, and ∆ is the travel path length passing through location j (and can be approximated by the grid size ∆x). Equation 10 can be interpreted as the product of the rate of biomass deposition (first term), the average residence time of water in cell j (second term), and the total volume of runoff that is routed from i to j over the course of the storm (third term).

Hydraulic assumptions
To implement Equations 9 and 10, expressions are needed for the distance j − i , as well as the stormaveraged flow velocity and depth terms. We approximate j − i with the Euclidean distance between the points i and j (χ i,j ). We use Manning's Equation to describe the flow behavior at a point as: Where K [m 1 3 day −1 ] is a kinematic resistance factor (Brutsaert et al., 2005), given by ] parameterizes the resistance of the land surface to flow. For the one dimensional flows we consider, flow velocity u = q c /h, and for steady conditions, q c depends on the storm averaged rate of runoff production q storm and the upslope contributing area A: where ∆y is again used to approximate the flowpath width. With Equation 11, this expression for h gives the velocity as: u can then be used in Equation 10. However, with this substitution, Equation 10 contains two unknown parameters: the linear rate constant β, and the land surface roughness ν (forming, with the land surface slope, the kinematic resistance term K).
To facilitate calibration of the model, it is helpful to lump these parameters together in a single term within Equation 10, which we express as α: Where α = ν averaged to give υ i,j , an approximation to its spatial mean along the flow path between the cells.
When Equation 14 is summed over all upslope source cells, it gives the total deposition at a cell j with n upslope source cells as a result of an overland runoff event:

Concentration boundary condition due to Pc mobilization at a cell
The only remaining unknown in the transport model is the boundary condition at each source cell i, C io .
Source cells are those where Pc biomass areal density B i [g m −2 ] is sufficiently high to cause the host to appear 'infected' (see Section 2.4). At these cells, we assume that each runoff generating event will mobilize all Pc biomass within an "effective depth of interaction" (δ, mm) (Ahuja et al., 1981), measured downward from the soil surface. This means that there is a specified total biomass M − i [g], that will be transported out from each source cell: Mass balance requires that M − i = n j=1 M + i,j -that is, all biomass originating from i that is deposited to n downslope cells must sum to the mobilized biomass from i. By equating this sum (taken from where here the use of both labels j and i emphasizes the potentially dual role any site can have as both a source and sink of Pc.

Pathogen growth and diffusive spread
Pathogen biomass density (on a per-area basis, B, [g/m 2 ]) grows following a logistic-type growth equation.
The growth rate r varies with soil moisture s and temperature (T soil ), such that r = r max (T soil ) × m (s).
Here, r max (T soil ) represents the growth rate of the mycelia under ambient temperature and optimal soil moisture conditions. r max varies linearly with temperature as r max (T soil ) = r 0 + ∆rT soil (Shearer, Shea, et al., 1987), where r 0 is the growth rate in optimal soil moisture conditions at T = 0 • C and ∆r [ is a fitted parameter describing the temperature dependence of pathogen growth. The function m(s) represents the effect of changing soil moisture on pathogen growth rates, which are impaired at very high and very low soil water potentials (Malajczuk et al., 1979). From the soil water potentials, we find the relative water content s using the Brooks-Corey water retention curve (Brooks et al., 1964), and follow Thompson et al. (2013) in approximating m(s) with a linear piecewise function, shown in Appendix B.
We account for a constant (time and environmentally independent) mortality rate for mycelia d [days −1 ]. The pathogen growth model at a point is given by: where B max represents the maximum biomass density that can be sustained at a point, assumed to be constant. Note that the model omits Pc mortality due to freezing (Marçais et al., 1996) as a simplifying measure given the warm temperatures experienced at the case study sites explored here.

Pathogen spread
Pc spread due to the spatial growth of mycelium and dispersal of propagules within the soil is modeled continuously in time and approximated with a diffusive process. The diffusion coefficient is isotropic and is scaled down from its maximum (D max , m 2 day −1 ) by the soil moisture function m(s) to ensure that soil moisture conditions that inhibit Pc growth also inhibit Pc spread. Pathogen transport in overland flow appears as the addition of biomass B runof f (Equation 17), which is non-zero only at the end of a runoff-producing storm event. The biomass model is then given by: Note that the dynamics of the model are independent of the numerical value of B max . We define the threshold for host 'infection' as 0.5B max (also independently of B max ), and arbitrarily set B max to 1 g Maximum evapotranspiration rate L T −1 mm day −1 P Precipitation rate L T −1 mm day −1 q storm Average rate of flow production for storm event L T −1 mm day −1 L Rate of leakage at bottom boundary L T −1 mm day −1 b Soil-water retention curve exponent --Runoff routing and propagule transport φ i,j Storm-averaged runoff velocity at j L T −1 m day −1 Pathogen growth and diffusive spread r max Maximum fractional growth rate at ambient temperature -- Pathogen growth soil moisture dependence factor -r o Pathogen fractional growth rate at T = 0 • C --∆r Pathogen growth rate temperature dependence Steady state pathogen biomass density M L −2 g m −2 D max Maximum pathogen diffusion coefficient L 2 T −1 m 2 day −1 Daily maximum and minimum temperatures were used to compute potential evaporation via Hargreaves' equation (Hargreaves et al., 1985). Climate gap filling used average temperature data (for the given day of year in all other years), and a satellite weather product (CHIRPS, version 2.0 final) for daily rainfall (Funk et al., 2015). A 5×5 m, LiDAR-derived DEM for the site (Geoscience Australia, 2015) was interpolated onto a 1 m grid.

Spanish site
The

Selection of disease patches to model
We identified isolated disease patches that did not initially intersect roads, bare patches or other barriers to Pc dispersal. Where patch growth caused the patch to intersect channels or other unvegetated areas, we treated those features as boundaries, forcing Pc biomass to remain zero on the other side of the boundaries. The locations of these features was identified using the D-∞ algorithm to map upslope contributing area, and corroborated against aerial imagery. With these constraints, eight patches (

Numerical implementation
Within each observed disease patch the model was initialized with B = B max . Soil moisture was initialized using a one year spin-up starting at the end of the dry season, when it was assumed s = s wp .
The model was implemented on a two-dimensional spatial grid (1m x 1m) that aligned with the DEM grid, using a 1 day time step (we confirmed that results were stable to changes in the time and space grids). A centered difference scheme was used for the second-order spatial terms from the diffusion equation. An explicit (forward) scheme was used for time stepping. Open flux boundary conditions were assumed, with one-sided difference schemes used at the spatial boundaries. The D-∞ algorithm was implemented using tools developed by Eddins (2018). Model output, consisting of the Pc biomass density (B(x, y, t)) was binarized at a threshold of B = 0.5B max , to allow comparison to mapped infection boundaries ( Figure   2D).

Parameterization
In Western Australia, we modeled the 1.5 m deep root zone containing most Banksia roots (Hill et al., 1994), with a freely-draining bottom boundary (accounting for the, on average, 8 m of unsaturated sand overlying the water table at this site). For the Spanish sites, we modeled the 0.7 m deep soil with an impermeable bottom boundary representing a low permeability B horizon (Espejo, 1987). Hydraulic parameters for the soils were taken from Laio et al. (2001) using the "sand" for Western Australia and "sandy loam" for Spain. These soils types were used to determine the effective depth of interaction (δ) following Ahuja et al. (1981).
Given the relatively shallow soil depths, we approximated T soil with T air at all times for both sites. The moisture dependence of the growth (m(s)) was estimated as a piecewise function based on experimental data from Malajczuk et al. (1979) (Appendix B.1).

Calibration
Four model parameters needed to be calibrated to run the model: the mortality rate (d), diffusion coefficient (D max ), temperature dependence of growth (∆r), and the overland transport parameter (α).
We estimated plausible ranges for the pathogen mortality rate (d) from Hwang et al. (1978), of growth temperature dependence ∆r from Thompson et al. (2014) and Malajczuk et al. (1979), of maximum diffusion coefficient D max from patch growth rates in the upslope direction (assumed to be due to purely diffusive transport). The combined pathogen sink rate constant and land surface roughness parameter α is poorly constrained a priori, so several orders of magnitude of α values were screened to find a plausible range for calibration.

Calibration metrics
Model calibration aimed to maximize agreement between mapped observations of the spatial extent of Pc infection and predictions for each patch, focusing on four features: the orientation of the disease patch, its eccentricity, the length of its major axis, and an areal growth increment. Differences between these features and observations were computed, and standardized to lie between 0 (complete disagreement) and 1 (perfect agreement). Fitting, differencing and standardization of the features are described in the Appendix C. The four standardized scores were averaged to give a composite score for each modeled patch.

Calibration and Model Experiments
We calibrated the growth and diffusion related parameters ∆r, D max , and d together for each site (i.e. these parameters were common to every patch at the site).
We did this for two cases: one in which overland flow transport of Pc was omitted (the "diffusion optimized" case), and one in which overland flow transport of Pc was included. In the diffusion optimized case, we ran the calibration in two stages -firstly sampling parameter values from a coarse factorial grid spanning the range of plausible values, and secondly sampling over a finer range of values identified after the first step. No constraints were placed upon the parameter values, and the refinement process was continued until an optimum value of each parameter was found, such that changing the value of any parameter while holding the others constant resulted in a decrease in the mean composite score.
Combinations of site-wide parameters were tested and the scores averaged for a range of α values. Once the values of these site-wide parameters were determined, we then further calibrated α individually for each patch to account for differences in surface cover across the landscape.
We used the two versions of the calibrated model to firstly identify whether, and at which sites, including overland transport resulted in an improved description of patch growth geometry relative to a model with only diffusive spread included. For those sites where overland transport did improve the model performance, we re-ran the calibrated (overland flow) models, but 'turned off' overland transport.
The differences in predictions provide a measure of the importance of within-soil versus overland flow driven spread of Pc.

Results
The results of the experiments are summarized in Figure 4 Figure 4F). With overland flow included, the model performance was comparable to that in Western Australia, with an average composite score of 0.864 ( Figure 4E). For two patches (blue dots - Figures 4E and 4F) little to no improvement resulted from adding overland transport. These patches also had the lowest composite scores in the overland transport model ( Figure 4E). The patches where overland transport improved predictions (red dots - Figures 4E and 4F) the mean composite score of was higher (0.876 for the overland transport model) and resulted from more improvement (0.204) over the diffusion optimized calibration.
Turning overland flow off in the calibrated model for the Spanish patches lead to a notable degradation in model performance ( Figure 4F), with the exception of the two patches (blue dots) which were insensitive to overland flow during calibration. In the other patches, excluding overland transport lowered the composite score by an average of 0.220. Additionally, the model omitted other transport pathways, notably spread via vectors (relevant considering the Spanish site is used as goat pasture), and transport within the soil. Considering that the model generally underestimated Pc spread in the patches where its performance was poor, additional transport mechanisms could be responsible.
Overall, the modeling results demonstrate the feasibility of describing the spatiotemporal dynamics of Pc spread provided information about the rhizosphere and transport mechanisms is available. Further, it showed how hydrological processes can act as a driver of disturbance caused by plant pathogens, with the overland runoff generation at the Spanish site introducing a relatively rapid and long-distance transport mechanism for Pc. Models of pathogen growth and spread such as the one presented here could be readily incorporated into scenario planning around water and drainage management -for example by coupling this model to distributed hydrological models already in use. Alternatively, some of the key dynamics revealed in this study can be used to suggest ways to augment Pc risk assessments to account for potential transport via overland flow in addition to the simple annual climate, soil and slope metrics that are currently used to describe disease risk. For example, Porporato et al. (2004) showed that the probability of soils saturating is controlled by two dimensionless ratios: the soil water holding capacity to the average storm depth, and the ratio of the mean rate of water input (e.g. average storm depth multiplied by average time between storms) to the rate of water loss by evaporation. These ratios can be readily calculated (on a seasonal basis) to identify the likelihood of saturation, and therefore overland flow events. Where saturation is more topographically than edaphically controlled, metrics such as the topographic wetness index (TWI) (Beven et al., 1979) To account for possible transport outside the domain, the fraction of biomass accounted for within the domain that originated at i, γ i , is found: where n is the number of down-gradient cells within the modeled domain. For the theoretical limit of ∞ down-gradient cells, the sum is computed using ∆x as the increment in distance between the cells (χ i,j ) and the velocities, υ j and υ i,j , are approximated using the respective averages of those values within the modeled domain. This sum is computed until the incremental change in the sum with each additional term falls below a prescribed threshold value (set to 0.00001 in this case). This value can then be used in the calculation of C io as derived in the main text: B Moisture Dependence of Growth

C Patch Image Analysis
Using the image analysis tools in Matlab, an ellipse is fit to the infected cells (B ≥ 0.5B max ) such that the ellipse has the same normalized second moment of mass as the disease patch. With this fitted ellipse, the major axis, orientation, and eccentricity are then calculated. , an ellipse (red) is fitted. The major and minor axes of the ellipse (blue) are then found and further used to calculate the eccentricity. The orientation is determined as the angle between the major axis and the horizontal plane (dotted yellow).

D Calculation of Composite Score
A composite score that quantifies how each patch prediction compares to the observed patch is calculated as the average of the following four components. The first three component scores use metrics from the ellipse fitting as described in C. For each of the individual components, as well as the overall score, the values range from 0 (poor match to observations) to 1 (perfect match to observations).
Orientation score: The orientation (degrees) of the major axis of the fitted ellipses is measured in degrees in the x-y plane.
The differences between orientation for model and observations is computed, normalized by the half circle and differenced from one (to ensure that a score that is closer to one represents better model-observation Eccentricity score: The eccentricity (-) of the fitted ellipse is calculated as the distance from the center of the ellipse to the focus divided by one-half the major axis length. It will be equal to 0 for a perfect circle and 1 for a line and in terms of the major and minor axis lengths this is: Eccentricity = (0.5 × major axis) 2 + (0.5 × minor axis) 2 0.5 × major axis (D. 3) The eccentricities are compared between model and observations, to form a standardized score:

H Soil moisture dynamics
Histograms of the modeled soil moisture values for both sites are shown below. At the site in Western Australia, saturated conditions never occurred whereas at the Spanish site there were incidences of saturation (s = 1) and therefore generation of overland flow, although these events were infrequent.