CalCWD: Simulating chronic wasting disease spread in California after the initial detection

Supporting Information: Simulating chronic wasting disease spread in 1 California after the initial detection 2 Cesar Herraiz1,2, Carlos González-Crespo2*, Brandon Munk3, Alexander Heeren3, Pelayo Acevedo1, Beatriz 3 Martínez-López2 4 1 Health and Biotechnology Research Group (SaBio), Institute for Game and Wildlife Research (IREC), CSIC-5 JCCM-UCLM, 13071 Ciudad Real, Spain 6 2 Center for Animal Disease Modeling and Surveillance (CADMS), Department of Medicine & Epidemiology, 7 School of Veterinary Medicine, University of California, Davis 95618 CA, USA 8 3 California Department of Fish and Wildlife (CDFW), Wildlife Health Laboratory (WHL), Rancho Cordova, 9 CA 95670, USA 10 *Corresponding author: 11 Carlos González-Crespo 12 [email protected] 13 Index 14 Appendix 1: ODD Protocol .................................................................................................................................................... 3 15 1.1 Purpose ................................................................................................................................................................ 3 16 1.2 Entities, state variables, and scales ..................................................................................................................... 3 17 1.3 Process overview and scheduling ....................................................................................................................... 4 18 1.4 Design concepts .................................................................................................................................................. 6 19 1.4.1 Basic principles .............................................................................................................................................. 6 20 1.4.2 Emergence ...................................................................................................................................................... 7 21 1.4.3 Adaptation ...................................................................................................................................................... 7 22 1.4.4 Sensing ........................................................................................................................................................... 7 23 1.4.5 Interaction ....................................................................................................................................................... 8 24 1.4.6 Stochasticity ................................................................................................................................................... 8 25 1.4.7 Collectives ...................................................................................................................................................... 8 26 1.5 Initialization ........................................................................................................................................................ 8 27 1.6 Input data ........................................................................................................................................................... 13 28 1.7 Submodels ......................................................................................................................................................... 13 29 1.7.1 Aging ............................................................................................................................................................ 13 30 1.7.2 Natural mortality .......................................................................................................................................... 14 31 1.7.3 Hunting mortality ......................................................................................................................................... 14 32 1.7.4 CWD mortality ............................................................................................................................................. 14 33 1.7.5 Carcass removal ........................................................................................................................................... 15 34 1.7.6 Fawning ........................................................................................................................................................ 15 35 1.7.7 Group dynamics ........................................................................................................................................... 15 36 1.7.8 Dispersal ....................................................................................................................................................... 16 37 1.7.9 Migration ...................................................................................................................................................... 16 38 1.7.10 Carrying capacity dispersal ..................................................................................................................... 16 39 1.7.11 CWD Force of infection .......................................................................................................................... 17 40 1.7.12 CWD Diffusion ....................................................................................................................................... 19 41 1.7.13 Droughts .................................................................................................................................................. 20 42 1.7.14 Wildfires .................................................................................................................................................. 20 43 Appendix 2: Model evaluation ............................................................................................................................................. 21 44 Appendix 3: Parameter optimization .................................................................................................................................... 24 45 3.1. Hunting pressure (khunt, θhunt) ............................................................................................................................. 24 46 3.2. Probability of visiting a carcass (ρ) ................................................................................................................... 25 47 3.3. Carcass duration in the environment (τ) ............................................................................................................ 25 48 3.4. Wildfire and big fire probability (firep and bigfirep) ....................................................................................... 28 49 Appendix 4: Supplementary Figures .................................................................................................................................... 30 50 References ............................................................................................................................................................................ 31 51 52 Appendix 1: ODD Protocol 53 1.1 Purpose 54 The purpose of the model is to simulate the spatiotemporal dynamics of CWD in mule deer in the state 55 of California. To achieve this, the model comprises two main modules: 56 1. The ecological module, which pertains to the host, and whose purpose is to simulate the mule deer 57 population in California over time and space, considering its response to both natural phenomena, 58 such as fires or droughts, and anthropogenic factors, such as hunting. This module is comprised of 59 two submodules. The first submodule pertains to the environment and encompasses data and 60 processes such as habitat suitability, scavenging pressure, fires and droughts. The second submodule 61 pertains to the host and includes demographic, social, and behavioral information about mule deer, 62 such as natality and mortality, migrations and grouping patterns. 63 2. The epidemiological module, which is related to the pathogen, and whose purpose is to examine the 64 spread of CWD over time in the mule deer population. This module interacts with the ecological 65 one. The evolution of the deer population affects the pathogen spread, which in turn affects the 66 population by causing mortality. 67 1.2 Entities, state variables, and scales 68 The model comprises three agents as entities: deer, carcass, and grid cells. The discretization of the 69 space into grid cell agents allows some processes to be programmed at the cell level, thereby reducing the 70 computational cost and increasing the ability to apply a complex model to large scales. 71 Each deer is defined by 14 state variables related to location, age, sex, fawning, grouping, migratory 72 behavior, and CWD infection status. When an infected deer dies, it becomes a carcass agent, with the location 73 and the days of persistence in the environment as state variables. Grid cells have 9 state variables related to 74 habitat suitability, carrying capacity (K), deer range (year-round, winter, summer, or out of the range), deer 75 abundance (N), infectious deer carcass abundance, CWD prevalence, scavenging pressure, hunting pressure and 76 whether the cell has been damaged by fire. The entities included in the model and their state variables are shown 77 in Table S1. 78 The spatial extent of the grid encompasses the California state, being each grid cell a 10 km x 10 km 79 size square (100 km2). The model has a daily time step, starting in the middle of the summer (day = 213; August 80 1st). 81 Table S1. Entities and their states variables included in the simulation. 82 Entity State variable Description Deer cell id of the grid cell in which deer is located residence id of the grid cell where deer resides sex 1 for male and 0 for female age Age in days class 1 if fawn, 2 if yearling, 3 if adult, 4 if old fawning 1 if pregnant female, 0 otherwise mother id of the mother group id of the group to which it belongs solitary 1 if solitary, 0 otherwise migratory 1 if it belongs to a migratory population, 0 otherwise susceptible 1 if uninfected, 0 otherwise exposed 1 if infected but not infectious, 0 otherwise infected 1 if infected and infectious, 0 otherwise clinical 1 if infected with clinical signs, 0 otherwise Carcass loc id of the grid cell in which the deer infectious carcass is located removal Number of days the carcass remains in the environment Grid cell N Mule deer abundance migra Mule deer range: 1 if summer range, 2 winter range, 3 if year-round, -1 otherwise K Number of mule deer that the grid cell can shelter weight Cell resistance huntpressure Proportion of the population annually harvested prevalence CWD prevalence in the cell ncarcass Number of deer infectious carcasses in the cell scavengers 1 to 5 depending on the number of present scavengers’ species daysburnt Days elapsed since the cell was burnt 1.3 Process overview and scheduling 83 Processes referred to the deer agent in the model are related to: 1) mule deer population dynamics; and 84 2) CWD disease dynamics in the mule deer population. Population dynamics processes include aging, natural 85 mortality, hunting mortality, fawning, seasonal group dynamics, yearling dispersal, and seasonal migrations. 86 The CWD disease dynamics processes include pathogen transmission or exposition and CWD-induced 87 mortality. 88 Processes related with the mule deer population dynamics are scheduled as follows (Ahlborn & White 89 2006; Mejia-Salazar et al. 2017; Monteith et al. 2011): On December 16th (day = 350) early gestation (EG) 90 starts, and large mixed groups are formed. On April 1st (day = 91) late gestation (LG) period starts, during which 91 males separate from females and young individuals. Departure from winter range areas to summer range (spring 92 migration) begin in middle April (day = 105). Fawning (F) starts on May 16th (day = 136), resulting in the 93 formation of the smallest groups of the year. Females go apart for giving birth, while fawns from the previous 94 year separate from their mothers’ group and disperse. On August 1st (day = 213) pre-rut (PR) period begins, and 95 males start joining females with fawns. Females without fawns remain in small groups. Hunting mortality occurs 96 between August 14th (day = 226) and November 7th (day = 311). Fall migration commences in mid-October (day 97 = 288). Rut (R) period begins on November 1st (day = 305). Aging and natural mortality occur every step. The 98 day starts from 0 (1st January) after it reaches 365 (31st December). 99 With regard to the CWD processes scheduling, prion shedding commences 6 to 9 months (180 to 270 100 days) after infection (Plummer et al. 2017; Tamguney et al. 2009), thereby enabling direct transmission and 101 environmental deposition. Clinical signs manifest approximately 490 days after infection (Johnson et al. 2011; 102 Williams 2005). Death by disease takes place 14 to 120 days after the onset of clinical signs (Williams 2005). 103 Following death, infected deer become a carcass agent, which remains infectious (Miller et al. 2004). The only 104 process considered for the carcasses is their disappearance. The time carcasses remain in the environment 105 depends on the season and scavenging pressure (Jennelle et al. 2009). 106 The processes referred to the grid cells are droughts, wildfires, and the diffusion of CWD across 107 neighboring cells. Drought has a given probability of occurring at the start of the simulation and can last for a 108 number of days derived from a uniform distribution between 365 and 1460 days (1 to 4 years; Miller et al. 2022). 109 During the summer months, wildfires may occur in cells with a certain probability, affecting carrying capacity 110 (Bristow et al. 2020; Sparks et al. 2018). 111 1.4 Design concepts 112 1.4.1 Basic principles 113 Density dependence in mule deer was assumed to be related with the carrying capacity in the winter 114 range, which entails an effect on fawn survival in winter but not on adult survival (Bergman et al. 2015). The 115 buck:doe ratio was considered not to affect the birth rates since no severe decline in productivity was found as 116 a response to the sex ratio (White et al. 2001). Predation, primarily by coyote (Canis latrans) and mountain lion 117 (Puma concolor), could influence mortality rates in the overall population, particularly in fawns. However, 118 several studies have shown changes in predator communities entailing compensatory effects, leading to the 119 absence of changes in population trends (for further information, see Forrester & Wittmer 2013). Therefore, no 120 changes in mule deer demography based on predator community composition were assumed in the model. 121 This model assumes that CWD can be transmitted through direct animal contact or through the 122 environmental presence of the prion, either in the soil or in an infectious carcass (Miller, Hobbs & Tavener 123 2006). Furthermore, it assumes a CWD diffusion process from where the outbreak originates (Jennelle et al. 124 2014). Vertical transmission was omitted in the model since it is unusual (Miller & Williams 2003) and seems 125 no to have an effect on the disease dynamics (Potapov et al. 2013). In addition to mortality due to CWD, the 126 model assumes an increase in mortality of infected deer due to greater susceptibility to predation, vehicle kill, 127 dehydration, or hypothermia during winter months (Miller et al. 2008; Otero et al. 2021). 128 Long-range movements may also play an important role in the spread of the pathogen to farer areas 129 (Diefenbach et al. 2008; Garlick et al. 2014). Therefore, dispersal and migration were incorporated into the 130 model. Mule deer populations in California can be resident or migratory (Ahlborn & White 2006). Resident 131 populations were assumed to remain in the same cell throughout the year, while migratory populations were 132 assumed to move entirely from summer to winter range cells in fall migration, returning to the cell where they 133 were born in spring migration (van de Kerk et al. 2021). Dispersion is carried out by yearlings, mainly males 134 but also females (Robinette 1966), Displacements can occur in any direction within the range (Hamlin & Mackie 135 1989). Cells selected for migratory displacements were assumed to depend on habitat suitability, slope, and its 136 traditional use as migratory corridors. Upon reaching the target cell, the probability of the deer remaining in that 137 cell or moving on to another suitable cell is assumed to depend on the N and K values of the cell, leading to 138 dispersion towards another cell when N approaches K. 139 The model assumes that drought leads to an increase in mortality and in the probability of wildfires 140 (Jackson et al. 2021; Littell et al. 2016; Schuyler, Dugger & Jackson 2018). With regard to wildfires, it is 141 assumed that when they occur, the environmental prion load of the cell is eliminated (Lee 2023). Moreover, it 142 is postulated that wildfires have an effect on the cell's K, reducing it to a minimum during the first year after the 143 fire and almost doubling during the second year, then stabilizing over the next three years (Bristow et al. 2020; 144 Sparks et al. 2018). 145 1.4.2 Emergence 146 The CWD spread emerges from the model based on the mule deer population, grouping and movement 147 patterns, and on transmission dynamics. Mule deer mortality is also influenced by population abundance and 148 CWD prevalence rates, so mule deer population dynamics itself also emerges from the model. 149 1.4.3 Adaptation 150 The mule deer adapt their behavior based on N and K. When N approaches K, either due to an increase 151 in population or a sharp reduction in K as a result of a wildfire, the mule deer disperse to other cells that have 152 the capacity to accommodate them. 153 1.4.4 Sensing 154 The mule deer agents sense the state variables of the grid cell agents, which influence the probability of 155 being hunted, the destination and movement cells for migratory and dispersal movements, and the probability 156 of infection through environmental prion load or the presence of infectious carcasses. Conversely, grid cells also 157 sense mule deer agents, as they sense the number of deer they contain and how many of them are infected, thus 158 determining N, the prevalence of CWD, and the prion load. Moreover, they also sense the presence of infectious 159 carcass agents. Finally, there is also sensing among the mule deer agents themselves, which determines group 160 dynamics and transmission within them, and among the grid cell agents themselves, determining the spread of 161 fires or the diffusion of the pathogen between cells. 162 1.4.5 Interaction 163 Deer agents can interact being able to entail pathogen transmission if one of them is infected and the 164 other one is not. Deer agents can interact with infected deer carcasses agents being able to acquire the pathogen 165 if they are not infected. Deer agents also interact with the grid cell agents, as the prion load of each cell is 166 determined by infected deer that are or have been in it. This prion load can, in turn, lead to the infection. 167 Additionally, grid cell agents interact with each other, as the CWD diffusion process considers new infection in 168 a cell based on the prevalence of neighboring cells. 169 1.4.6 Stochasticity 170 Natality (i.e., the number of offspring per female and the occurrence of twins, as well as the sex of the 171 offspring), mortality (both natural and hunting-related mortality), and dispersal, are based on probabilities that 172 affect each individual, and therefore are stochastic processes. Hunting is also a stochastic process since hunting 173 pressure is defined by a Gamma distribution. These demographic processes condition mule deer abundance, 174 having an effect on cell selection during migration and thus making this process also stochastic. Moreover, the 175 day on which each individual migrates is also stochastic, conditioning the abundance on the target cell at the 176 time of its arrival, and therefore influencing cell selection. Group dynamics is also a stochastic process in which 177 size is provided as a range and the members are randomly selected based on the size and sex and age ratios for 178 each season. All transmission processes and durations of each infection status are stochastic as they are based 179 on probabilities and variable time intervals. Drought has a probability of occurring at the beginning of the 180 simulation, and its duration is variable. Each cell has a certain probability of being burnt by a wildfire each 181 summer. 182 1.4.7 Collectives 183 Deer agents are organized in social groups that fluctuate in size and sex and age ratios seasonally. The 184 transmission processes of CWD differ within and outside of these groups. 185 1.5 Initialization 186 The initial sex and age ratios of the mule deer population are shown in Table S2. All deer are initially 187 susceptible to infection. The outbreak initiates with the infection of an adult male, based on observed infection 188 rates (Miller & Conner 2005; Osnas et al. 2009). The location and start date of the outbreak can be selected for 189 each simulation. Mule deer demographic and epidemiological parameters employed for the simulation are 190 described in Tables 3 and 4, respectively. 191 Table S2. Initial proportion of the population by sex and age based on Furnas et al. (2018); Rittenhouse, Mong and Hart 192 (2015); Wood et al. (1989). 193 Initial proportion of the population Fawn male (0 - 1 year) 0.17 Fawn female (0 - 1 year) 0.17 Yearling male (1 - 2 years) 0.11 Yearling female (1 - 2 years) 0.14 Adult male (2 - 9 years) 0.09 Adult female (2 - 11 years) 0.25 Old male (9 - 12 years) 0.02 Old female (11 - 16 years) 0.05 1.7.8 Dispersal 275 When the time comes for dispersal, each yearling deer has disp probability for dispersion. If N ≥ 0.7·K 276 in the grid cell where the deer is located, the probability of dispersal is 1. When a deer disperses, it moves to the 277 nearest grid cell in which N ≤ 0.7·K in a disprange range of cells around its starting grid cell. Cells outside the 278 summer or year-round range are discarded. If there are no cells in disprange that meet the aforementioned 279 conditions, the deer will move to the cell with the least weight in disprange. Movements were assumed to follow 280 the principle of least effort (Zipf 1949), which means that displacements occur through the cells with a lower 281 weight value. The speed of movement is determined by the speed parameter. 282 1.7.9 Migration 283 As the fall migration period begins, all migratory deer move from their cells in the summer range to a 284 randomly selected cell in the winter range that meets N ≤ 0.8·K within a migrrange range of cells around its 285 starting grid cell. Therefore, they do not necessarily migrate to the same area every year (van de Kerk et al. 286 2021). Migrations occur in groups (Shellard & Mayor 2020), with all deer belonging to the same group migrating 287 to the same cell. If there are no cells in a migrrange distance that meet this condition, the deer will move to the 288 cell with the least weight in the winter range in a the migrrange range of cells. In spring migration, all migratory 289 deer moves from its cell in the winter range to the cell where it was located before fall migration. Displacements 290 occur through the cells with the lower weight values at a speed determined by the speed parameter. 291 1.7.10 Carrying capacity dispersal 292 The model assumes that when N > 0.9·K in a cell, a dispersal process begins as a result of intraspecific 293 competition for available resources (Valente et al. 2020). In a cell where this condition is met, the probability 294 of a deer leaving the cell at each step (Pk) is determined as follows: 295 𝑃:=)0.1·(𝑁−0.9·𝐾) 0.9·𝐾 ? (9) This process causes the population to fluctuate slightly around the K of the cell. When a deer leaves the 296 cell, it moves to the nearest grid cell where N ≤ 0.7·K in a disprange range of cells around its starting grid cell. 297 The target cell must belong to the same seasonal range as the starting cell (summer or winter) or be a year-round 298 range cell. If there are no cells in disprange that meet these conditions, it moves to the cell with the least weight 299 in disprange. The deer move through the cells with the lower weight value at a speed determined by the speed 300 parameter. 301 1.7.11 CWD Force of infection 302 CWD transmission may be frequency-dependent (FD) density-dependent (DD), or a combination of 303 both (Grear et al. 2010; Jennelle et al. 2014; Storm et al. 2013; Winter & Escobar 2020). FD within-group 304 transmission is considered to be the main mechanism of CWD transmission (Potapov et al. 2013; 2016; Storm 305 et al. 2013). However, intergroup environmental transmission, which is a DD mechanism, has been shown to 306 play a role in the disease dynamics, especially after a long period of time when the disease becomes endemic 307 (Almberg et al. 2011; Miller, Hobbs & Tavener 2006). Therefore, we considered both within-group transmission 308 and environmental transmission between groups, excluding FD transmission between groups since direct 309 contacts between groups are rare and the likelihood of infection from a single contact is low (Belsare & Stewart 310 2020; Habib et al. 2011; Kjaer 2010). We also considered the possibility of transmission from an infectious 311 carcass (Miller et al. 2004). Thus, the probability of becoming infected at each step for a given individual is 312 determined by the probability of becoming infected by another individual of the same group (λG), the probability 313 of becoming infected by the environment (λE), and the probability of becoming infected by an infectious carcass 314 (λC). 315 1.7.11.1 Transmission rates (β and β´) 316 Actual values of transmission rates for mule deer in California are not available, although estimates 317 have been made for other populations and species have been carried out (Almberg et al. 2011; Jennelle et al. 318 2014; Miller, Hobbs & Tavener 2006; Potapov et al. 2016; Wasserberg et al. 2009). CWD prevalence rates in 319 males can be up to twice as high as in females, and lower in yearlings (Edmunds et al. 2016; Heisey et al. 2010; 320 Osnas et al. 2009), leading Jennelle et al. (2014) to suggest a different transmission rate for males and females 321 as the most plausible option in their study of white-tailed deer (Odocoileus virginianus). However, higher 322 prevalence in males and adults is likely associated with consumption and interaction behavior (Potapov et al. 323 2013), which may vary between species. Consequently, we decided to use sex-independent transmission rates 324 of β = 0.85 infections·year -1 (Jennelle et al. 2014; Potapov et al. 2016) for within-group transmission and β´ = 325 2·10-4 infections·year -1·individual-1 (Jennelle et al. 2014) for environmental transmission, and combine them 326 with parameters related to food consumption and interaction rates. 327 1.7.11.2 Probability of group infection (λG) 328 For the within-group transmission, we included a parameter related to interaction rates (δ), with higher 329 values assigned to males than to females and fawns (Mejia Salazar 2017). The probability of an individual being 330 infected by a group member each time step for females (f), males (m) and fawns (fa) is calculated as follows: 331 𝜆5$ )=)𝛽365 ?·𝛿#$ ·)𝐼#3; 𝑁#3; +𝛽365 ?·𝛿$$ ·) 𝐼$3; +𝐼$(3; 𝑁$3; +𝑁$(3; (10) 𝜆5# )=)𝛽365 ?·𝛿## ·)𝐼#3; 𝑁#3; +𝛽365 ?·𝛿$# ·) 𝐼$3; +𝐼$(3; 𝑁$3; +𝑁$(3; (11) 𝜆5$( )=)𝛽365 ?·𝛿#$ ·)𝐼#3; 𝑁#3; +𝛽365 ?·𝛿$$ ·) 𝐼$3; +𝐼$(3; 𝑁$3; +𝑁$(3; (12) 1.7.11.3 Probability of environmental infection (λE) 332 Although CWD prion can be found in the soil and plants for a long time after excretion (Mathiason et 333 al. 2009; Miller et al. 2004; Plummer et al. 2018), Miller et al. (2004) reported a rapid rate of removal of the 334 amount of prions from the environment. Potapov et al. (2013) evaluated the impact of infected deer in the past, 335 concluding that the effect is weak and justifying the assumption of one year of pathogen survival in the 336 environment. Consequently, we calculated the probability of infection from an environmental source of prions 337 for a given deer at each step considering the sum of days that every excreting deer spent in the grid cell during 338 the previous 365 days. A food parameter related to food consumption (φ) was also included: 339 𝜆5$ )=)𝛽′ 365 ?·𝜑$·) Y 𝑑! <!"#$%&& !=> (13) 𝜆5# )=)𝛽′ 365 ?·𝜑$·) Y 𝑑! <!"#$%&& !=> (14) 𝜆5$( )=)𝛽′ 365 ?·𝜑$( ·) Y 𝑑! <'()*$%&&+!"#,*-./ !=> (15) 1.7.11.4 Probability of carcass infection (λC) 340 The transmission from infectious deer carcasses to healthy deer has already been proven (Miller et al. 341 2004). Furthermore, the nutrient supply from the carcass to the soil leads to an increase in vegetation, entailing 342 attraction effect for ungulates (Towne 2000; Walker et al. 2020). However, transmission from carcasses is 343 usually overlooked in CWD epidemiological studies. We used the data collected by Jennelle et al. (2009) to 344 estimate the probability of a given deer in a cell visiting a carcass at each step (ρ), which was then combined 345 with the probability of infection through contact with a carcass (βC) estimated by Miller et al. (2004). 346 Consequently, the probability of infection by a carcass present in the grid cell at each step can be estimated. 347 When combined with the number of carcasses present in the grid cell (Ncarcass), this leads to the probability of 348 infection from carcasses at each step. 349 𝜆?)=)𝛽?·)ρ·𝑁1(;1(00 (16) 1.7.12 CWD Diffusion 350 The discretization of space into a grid signifies that the only way an individual in a cell other than the 351 outbreak cell can become infected is through the arrival of an infected individual, either by dispersal or 352 migration. Since individuals at the edge of a cell could come into contact and form groups with individuals from 353 neighboring cells, thereby spreading the pathogen, a diffusion model is also added to the simulation. The spread 354 rate is typically between 5 and 10 km per year from a focus of all infected individuals (Garlick et al. 2014; Xu, 355 Merrill & Lewis 2022). In our grid, this would imply that from a cell where all individuals are infected, all 8 356 neighboring cells would also be infected within a year. The lower the prevalence, the lower the probability of 357 neighboring cells becoming infected. For the diffusion model, we assume that the relationship between 358 prevalence and the probability of diffusion is linear. Xu, Merrill and Lewis (2022) observed a correlation 359 between the density of deer groups and the speed of spread, since a higher number of groups increases the 360 likelihood of contact between them. Based on their calculations, we assumed that there is a linear relationship 361 between the speed of expansion and the density of deer groups present, from 1.5 km/year (which would take 362 approximately 5 years to spread to neighboring cells) for 1 group per 100 km², to 7.5 km/year (which would 363 take approximately 1 year) for 100 groups per 100 km². Consequently, for each infected cell i (i.e., with at least 364 one infected individual) with Ngr deer groups inside, the probability (βdif) of an individual in a neighboring cell 365 z becoming infected at each step is calculated as follows: 366 𝛽𝑑𝑖𝑓@)=)𝑝𝑟𝑒𝑣𝑎𝑙𝑒𝑛𝑐𝑒!·(0.2+0.008·𝑁𝑔𝑟!)365 ⁄ (17) 1.7.13 Droughts 367 Every year there is a probability droughtp that an interannual drought will begin, lasting between 365 368 and 1460 days (1 to 4 years; Miller et al. 2022). The drought covers the entire State of California resulting in an 369 increase in mortality rates by 15% (Jackson et al. 2021; Schuyler, Dugger & Jackson 2018) and in the probability 370 of wildfires by 40% (Littell et al. 2016; Madadgar et al. 2020). Furthermore, a 25% reduction in K is also 371 considered. 372 1.7.14 Wildfires 373 Each cell has a probability firep of undergoing a wildfire during the summer. Similarly, each wildfire 374 has a probability bigfirep of spreading the wildfire to the neighboring cells. When a cell burns out, it is assumed 375 that the environmental prion load is removed by high temperatures (Lee 2023), signifying that ∑𝑑! <!"#$%&& !=> =0 376 (see Equations 13-15). 377 Furthermore, an effect on K of the cell is considered (Bristow et al. 2020; Sparks et al. 2018). This effect 378 is observed to decrease to a minimum during the first year after the fire (5%), increase over the second year due 379 to the growth of low vegetation (190%), and stabilize from the third and fourth years (90%) before returning to 380 its original value from the fifth year after the wildfire. The substantial reduction in K due to a fire initiates a 381 dispersion process (see Equation 9), in which a large difference between N and K would result in the vast 382 majority of deer in the cell fleeing ahead in a very short time (van Mantgem, Keeley & Witter 2015). 383 384 Appendix 2: Model evaluation 385 The ecological module of the model was evaluated through long-term population trends. In California, 386 mule deer populations have been slightly declining for several decades (Loft & Bleich 2014; Webb 2013). To 387 ensure that this pattern was reflected in the model, 20 iterations were conducted over a simulation of 50 years 388 (18,250 steps) with a population of 10,000 deer in an area of 41,000 km2 covering all mule deer ranges (summer, 389 winter and year-round). These simulations were performed without initiating CWD outbreaks, in order to assess 390 the population dynamics in the absence of the pathogen. The simulations showed a slight decline in the mule 391 deer population over a 50-year period, with an average abundance of 8,370 individuals across the 20 iterations 392 (ranging from 6,326 to 11,166) at the end of the simulation (see Figure S2). This outcome aligns with the 393 observed population pattern of mule deer in California over the past few decades (Loft & Bleich 2014; Webb 394 2013). 395 396 Figure S2. Evolution of the total number of mule deer over a 50-year simulation. The initial population was 10,000 deer 397 in an area of 41,000 km². The black line represents the average value across 20 iterations, while the gray shading 398 represents the maximum and minimum values. 399 The epidemiological module is more challenging to evaluate due to the lack of empirical data on the 400 prevalence and distribution of the disease in California. Observed patterns in CWD dynamics indicate a higher 401 prevalence in bucks (adult and old males) than in does (adult and old females) and yearlings (Edmunds et al. 402 2016; Grear et al. 2006; Miller & Conner 2005; Osnas et al. 2009) and a spread velocity between 3.7 and 11 403 km/year (Garlick et al. 2014; Xu, Merrill & Lewis 2022). Consequently, the model's results were evaluated 404 through these patterns. To this end, 5 iterations of simulations lasting 7 years and 9 months (2,828 steps) were 405 conducted, with an initial modeled population of 46,160 mule deer, assumption based on publicly reported 406 statewide population estimates of 500,000–1,000,000 deer (WAFWA, 2025) and distributed across a 41,000 407 km2 of simulation landscape according to the proportional distribution. The outbreaks were initiated on May 1st, 408 as this is the month when the first cases have been detected (Munk & Benedet 2024). This is 9 months after the 409 start of the simulation on August 1st, signifying 7 years of pathogen spread simulation. The outbreaks were 410 initiated in a non-migratory population to avoid the potential impact of migratory movements on the spatial 411 dynamics of the pathogen, since such movements could influence the spread rate or prevalence rates. 412 Table S6. Accumulated exposed mule deer and CWD prevalences by sex and age class over 7 years of pathogen presence 413 in an initial population of 46,160 mule deer in an area of 41,000 km², with the outbreak initiating in a non-migratory 414 population. The values at the end of the simulation are shown for the 5 iterations. 415 Iteration Accumulated exposed mule deer Prevalence rates (whole simulation area) Bucks Does Yearlings Fawns 1 2,884 4.48 % 4.81 % 3.78 % 4.78 % 2 2,890 8.71 % 8.52 % 7.87 % 9.76 % 3 2,143 7.88 % 6.29 % 5.71 % 7.23 % 4 2,171 3.54 % 3.20 % 2.77 % 3.91 % 5 2,289 5.75 % 4.99 % 4.62 % 5.98 % As a result, CWD exhibited an average spread of 50 km across the 10 iterations (ranging from 48 to 53 416 km) over the 7 years, resulting in an average spread rate of 7.1 km/year (ranging from 6.9 to 7.6 km/year). This 417 value is consistent with the expected rates observed in previous studies (3.7 to 11 km/year in Garlick et al. 2014; 418 7.3 km/year in Xu, Merrill & Lewis 2022). The prevalence of CWD was found to be higher in bucks than in 419 does and yearlings in all iterations, with a the exception of one iteration where the prevalence in does was slightly 420 higher (4.81% compared to 4.48%, see Table S6), as expected by previously reported values (Edmunds et al. 421 2016; Grear et al. 2006; Miller & Conner 2005). The prevalence of CWD in fawns was indeed higher than 422 expected based on previously reported values (Heisey et al. 2010; Osnas et al. 2009). However, the few data 423 regarding prevalence rates in fawns pertain to populations of a different species (white-tailed deer) in areas 424 where CWD is endemic, and the disease dynamics may differ. 425 Therefore, the demographic patterns of mule deer populations and the epidemiological patterns of CWD 426 are shown to be within the expected range based on previous observational studies. Thus, the model's 427 parameterization is shown to be reliable, lending credibility to the potential emergence of spatiotemporal 428 patterns derived from the model. 429 430 Appendix 3: Parameter optimization 431 Some of the parameters included in the modeling were estimated based on information derived from 432 previous scientific research and reports published by the California Department of Fish and Wildlife (CDFW) 433 and the California Department of Forestry and Fire Protection (CALFIRE). This appendix provides an account 434 of the processes employed to obtain these parameters. 435 3.1. Hunting pressure (khunt, θhunt) 436 Hunting pressure was estimated based on mule deer population estimates and hunting statistics reports 437 from CDFW. These reports are publicly available at 438 https://wildlife.ca.gov/Conservation/Mammals/Deer/Population and https://wildlife.ca.gov/Hunting/Deer, 439 respectively. In order to ascertain the distribution of hunting pressure by age and sex classes, the percentage of 440 hunted mule deer corresponding to male yearlings, adult/old females (does), and adult/old males (bucks) was 441 calculated based on the data included in the hunting statistics reports which included the information categorized 442 by sex and age class, spanning from 2013 to 2017 (see Table S7). 443 Table S7. Hunting statistics for the entire state of California by sex and age class between the years 2013 and 2017. 444 Year % Yearling males % Does % Males 2013 0.1 2.2 97.6 2014 0.1 2.0 97.9 2015 0.1 1.7 98.2 2016 0.1 1.6 98.3 2017 0.1 1.8 98.1 Average 0.1 1.9 98.0 The proportion of the mule deer population in each hunting area was derived from statewide abundance 445 estimates of 500,000–1,000,000 deer (WAFWA, 2025) and the proportional distribution provided by CDFW 446 (unpublished data). Sexand age-class abundances (male yearlings, does, and adult bucks) were estimated using 447 the proportions in Table S8 of the ODD protocol. Hunting pressure within each area was then calculated by 448 multiplying the total number of individuals harvested by the proportional distribution and dividing this value by 449 the abundance of the corresponding sex and age class (see Table S8). A Gamma distribution Γ (k, θ) was 450 employed to fit the hunting pressure for each sex and age class (see Figure S1). The hunting pressure in each 451 cell is calculated annually by sampling from each of these Gamma distributions, thereby introducing spatial and 452 temporal stochasticity to the hunting pressure. The increases in mortality of old and adult male deer resulting 453 from the calculated hunting pressure are consistent with data derived from studies conducted in other areas 454 (Bishop et al. 2005; Forrester & Wittmer 2013). 455 456 Figure S1. Gamma fitting to the mule deer hunting pressure values from the different game management areas of California. 457 3.2. Probability of visiting a carcass (ρ) 458 Jennelle et al. (2009) observed an average of 0.24 visits per day by white-tailed deer (Odocoileus 459 virginianus) to carcasses of the same species. The study was conducted in an area of 544 km², with a mean deer 460 density of 14.5 individuals per km². This would signify an approximate abundance of 7,888 deer throughout 461 their study area. Given the aforementioned visit frequency, the probability of each deer visiting a single carcass 462 in 544 km2 would be 0.24/7888 = 3.10-5. If the carcass were located in the more restricted space of 100 km2 by 463 a cell of the grid utilized in the model, the probability would be ρ = 3·10-5 · 544/100 = 1.6·10-4. 464 3.3. Carcass duration in the environment (τ) 465 In the same study, Jennelle et al. 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