The alternate role of direct and environmental transmission in fungal infectious disease in wildlife: threats for biodiversity conservation

Emerging fungal pathogens have substantial consequences for infected hosts, as revealed by the global decline of amphibian species from the chytrid fungus. According to the “curse of the Pharaoh” hypothesis, free-living infectious stages typical of fungal pathogens lengthen the timespan of transmission. Free-living infectious stages whose lifespan exceeds the infection time of their hosts are not constrained by virulence, enabling them to persist at high levels and continue transmitting to further sensitive hosts. Using the only Mesomycetozoea fungal species that can be cultured, Sphaerothecum destruens, we obtained tractable data on infectivity and pathogen life cycle for the first time. Here, based on the outcomes of a set of infectious trials and combined with an epidemiological model, we show a high level of dependence on direct transmission in crowded, confined environments and establish that incubation rate and length of infection dictate the epidemic dynamics of fungal disease. The spread of Mesomycetozoea in the wild raise ecological concerns for a range of susceptible species including birds, amphibians and mammals. Our results shed light on the risks associated with farming conditions and highlight the additional risk posed by invasive species that are highly abundant and can act as infectious reservoir hosts.

are associated with significant modifications to trophic structure and ecosystem function 15,16 . These modifications include species dependent on depleted populations that struggle to survive, or tolerant hosts thriving in the new community as they can transmit the infectious agent without any clinical signs of disease or mortality.
Typically, emerging fungal pathogens are generalists, especially in humid and aquatic habitats [16][17][18][19] . They have recently been responsible for infectious outbreaks worldwide that have led to high biodiversity and economic costs 6,16,20,21 . A newly emerged group, the Mesomycetozoea, on the animal-fungal boundary includes species that can infect and cause mortality in mammals, fish, birds and amphibians, and has led to noticeable infectious threats to wildlife 22,23 . Due to the aquatic nature of their hosts, mesomycetozoea are very difficult to monitor in the wild 24 which makes it extremely difficult to obtain reliable data on patterns of transmission and virulence. They are also difficult to culture in the laboratory with only one exception, Sphaerothecum destruens 25,26 which has allowed tractable data on infectivity and life cycle to be obtained for the first time 27,28 .
Here, combining a unique set of infectivity trials and a custom epidemiological model, we aim to characterise the most influential epidemiological parameters in a fungal pathogen's outbreak using S. destruens as a model system. Specifically, we examine the role of alternate transmission methods (direct and environmental) in disease outbreaks and the effect of infection and incubation duration. These parameters are central to the epidemiological understanding of disease dynamics and control.

Materials and Methods
Ethics statement. All animal procedures followed strict guidelines set forward by the Home Office, UK and were performed in accordance with UK Home Office Regulations. The project was approved by the Bournemouth University ethics committee and was performed under the Home Office project licence number PPL80/1979.

Model species.
Sphaerothecum destruens is a fungal pathogen that multiplies within host cells, resulting in a slow-growing infection in various organs and leading to chronic mortalities in the wild. The spores are transmitted to other organs and into the water through bile, urine, and intestinal epithelium, where in freshwater they undergo zoosporulation and can be transmitted to other individuals ( Fig. 1) 29 . S. destruens is also carried by the highly invasive fish species Pseudorasbora parva which shows a high tolerance to the parasite and acts as a disease reservoir 30 . See Supplementary Materials (Table S1) for known S. destruens hosts.
Infectivity trials. Three fish hosts of socio-economic importance, common bream Abramis brama, roach Rutilus rutilus and common carp Cyprinus carpio, were challenged with S. destruens infections 31 .
One-year old juveniles of each fish species were housed separately in three replicate tanks of 20 individuals each. All fish were exposed to infectious S. destruens spores at three separate occasions by bath immersion. Fish were placed in special exposure aquariums where they were exposed to a spore concentration of 8.6 × 10 4 spores ml −1 for 4 hours. At the end of the exposure all fish were returned to spore-free aquaria. Infection could have occurred at the time of exposure or subsequently due to direct and indirect transmission. Mortalities were recorded daily for11 months post exposure with the resulting mortalities Spores spread within the host and are released into the water through urine, bile, or gut epithelium; c) In freshwater, each spore can divide into up to 5 uniflagellate zoospores and survive for several days depending on the water temperature. Infection occurs directly or indirectly by ingesting the spores, attachment to the gills or skin, or gut penetration. Photo R. E. Gozlan in the exposed groups : 53% in A. brama, 37% in R. rutilus, and 8% in C. carpio. Infection by S. destruens was confirmed using PCR detection methods in fish tissue samples and histological examination of the fish tissues.
In a separate experiment another susceptible cyprinid, sunbleak Leucaspius delineatus was exposed to S. destruens via intraperitoneal injection as well as bath immersion in two separate exposure trials for 84 days 26 . We used these combined datasets to calibrate and define the parameters and initial conditions of the model, with the aim of creating a model that can be used across all exposure scenarios. Susceptible-exposed-infectious-recovered model (SEIR). We modelled the pathogen-host systems using an adaptation of the SIR framework 32 (Fig. 2). To calibrate the model more accurately to the observed data, we assumed a closed system which disregards natural birth and death rates of the population. Mortality that occurred in the control tanks, where hosts were sham exposed to the pathogen was classified as natural mortality, and factored out of the experimental mortalities before analysis. A series of differential equations determined the rate of change of the population between compartments corresponding to stages of infection. Susceptible individuals (S) become infected (Eq.1) through direct transmission such as contact (β ) with infectious individuals (I) as well as through environmental transmission from the water column (ε ) through spores or zoospores (Z): The role of spores and zoospores in this host-parasite system is unquestionably important, as infection occurs through contact with and ingestion of these spores. The constant k e is the number of spores required for a 50% probability of infection, as has been done for other pathogens such as Vibrio cholera 33 or avian influenza viruses 34 . For these systems, epidemiological parameters such as recovery rate are not dose dependent, as hosts have a fixed contact rate with the environment. However, in our study system hosts are constantly exposed to the environmental free-living stages of the pathogen (spores and zoospores) which can potentially alter some important processes of the epidemiological system. A higher level of spores in the water may accelerate the progress of infection, as spores accumulate in the host more rapidly. Thus, this can accelerate the incubation, mortality and recovery rates. Moreover, this assumption makes sense considering that this group of pathogens has shown a dose dependent disease progression 35 , and the necessity of this assumption was tested for each host species.
Epidemiological models on such systems are very rare. Thus, we fitted our epidemiological model to experimental data by considering both the presence and absence of dose dependent disease progression for each epidemiological parameter following infection. For datasets that use bath immersion as an infection method, elevated spore levels lead to the saturation functions behaving as linear functions. Thus, the addition of the saturation function does not help or harm the model fit. However, for a host infected via intraperitoneal injection with low initial free-living spore concentration, the saturation functions improved the model fit over models that did not include the saturation functions ( Table 1). For that reason, we include saturation functions for all the parameters, to allow a good fit across all species and all experimental datasets. Our results demonstrate that dose dependent disease progression is important for fitting our model to the experimental data (see Supplementary materials for additional details).
Thus becoming infectious, recovered or dead is correlated to the concentration of spores and zoospores in the environment, as a dose-dependent progression of infection is assumed. The threshold Figure 2. A visual representation of the SEIR model categories. Susceptible individuals (S) are exposed to infection at rate β (direct transmission) + ε (environmental transmission). In the exposed state (E), individuals become infectious (I) at rate σ . Infectious individuals either die as a result of disease at rate α , or recover (R) at rate °. Infected individuals release spores (Z) at rate f, including zoosporulation, which have a collective mortality rate of μ .
Scientific RepoRts | 5:10368 | DOi: 10.1038/srep10368 values k s , k g , and k a were introduced for σ , °, and α respectively to reflect this dose-dependent response and better represent the slow growing and chronic nature of the infection in the wild 36 . Exposed (E) individuals (Eq.2) are infected but not yet infectious (they are not releasing spores) and became infectious (I) after an incubation period of 1/σ *(Z/Z + k s ) days: Infectious individuals either experienced mortality as a result of disease at rate α *(Z/Z + k a ), or can recover (R) at rate °*(Z/Z + k g ), corresponding to the length of infection (Eq. 3 and 4): We assumed that recovered individuals are not re-infected. As a result of the experimental design, we assumed that all individuals came into contact with the pathogen. We also assume that individuals that did not die either overcame the infection without noticeable signs of deterioration or were naturally immune. After the experiments were complete, hosts were dissected and tissue samples tested for S. destruens presence. However, it must be noted that it is impossible to differentiate between recovered hosts and naturally immune hosts at the end of the experiment.
Spores released into the water from infected individuals can divide into up to 5 zoospores (additively, they constitute Z) at a rate of ɸ per day and survive for 1/µ days (Eq.5). Zoospore release rates and spore survival were determined experimentally under sterile conditions 28 . These values were comparable to ones reported from close relatives to S. destruens 9 . We have yet to develop a method by which to determine spore or zoospore numbers in non-sterile water, so these empirically determined values were used.
The most appropriate model parameters were determined by establishing a biologically realistic range for parameter values and systematically testing the model output against the observed data for the best fit, using mean squared error as an indicator of model accuracy. To remove any bias from selecting initial values, a 25% random variation was introduced for all parameters for each model iteration. Direct and environmental transmission (β and ε , respectively), and mortality rate due to infection (α ) were optimised in R (Version 0.97.551 © 2009-2012) also incorporating random variation for 100,000 iterations, using the optim() function in the lattice package 37 . Following the randomised iterations, the model parameters that resulted in the lowest mean squared error were selected. A sensitivity analysis was performed by independently varying each parameter until it resulted in a significant change in mean squared error, thus establishing a range of possible values for each parameter.
To examine the role of direct transmission in crowded environments β was set to 0 to observe how the epidemic would progress.

Results
Model parameterization. Infections in bream were rapid with a minimum length of 10 days of infection from first exposure and an epidemic occurring within 7 days (Fig. 3). Bream have higher transmission rates (β = 0.15-0.99, ε = 0.12-0.7) than the other host species. This is supported by the results of experimental infections, where bream were highly susceptible to S. destruens infection and represented the most sensitive host. During these experimental challenges to the pathogen, all mortalities occurred within 23 days of the last exposure to the pathogen, suggesting both a short incubation rate and high transmission rate between infected hosts. Although the infection rate was lower than for bream, roach are also highly susceptible to infection with S. destruens, with a minimum infection time of 26 days after the first exposure to the first mortality (Fig. 3). Transmission parameters for roach optimised to 0.08-0.1 (β ), while environmental transmission was much lower at 0.003-0.007. In contrast, carp are not as sensitive to infection as the other species, despite being tested at the same life stage (Fig. 3). They experienced a significantly longer timescale of infection, with the first mortality occurring 55 days post first exposure to S. destruens spores. Overall, carp appeared to be more resistant to the pathogen (only 8% of the treatment group experienced mortality and survivors had no S. destruens DNA detected 11 months post exposure), indicating a full recovery or a natural immunity to the pathogen. The parameterization reflected these observations, with direct and indirect transmission values at 0.0155-0.017 and 0.0008-0.0012 respectively. Mortality from infection (α = 0.017-0.025) is significantly lower than that of bream and roach.
In sunbleak, the outcome of the model was sensitive to other parameters, as a result of the different experimental setup. While both incubation (0.23-0.233) and recovery rate (0.14-0.17) were still crucial determining factors of the infection, parameters related to spore release including threshold levels for each stage of infection were also important. This demonstrates why it was necessary to include saturation functions for each parameter (Fig. 4). All parameter ranges are listed in Table 2.

Sensitivity analysis.
The outcome of the model was most sensitive to the rate of recovery (γ ) (alternatively duration of infection 1/γ ). The incubation rate of the pathogen (σ ) also greatly affected the duration of an epidemic (Fig. 5). The rate of mortality from infection (α ) was important in the progression of an epidemic in bream and roach, the two most susceptible species. When direct transmission was set to 0, environmental transmission increased. However, there is no collinearity between direct and environmental transmission (Fig. 6), and this increase is largely due to the confines of the data and model structure. Direct and environmental transmission operate at different timescales so are independent of one another; while direct transmission requires contact between infected individuals, environmental transmission occurs on a longer timescale that is dependent on the lifetime of infectious propagules. Transmission is more dependent on population density, although to different degrees for direct and environmental transmission. Thus, the optimised levels of environmental transmission are not sufficient to cause the observed outbreaks in every species, and direct transmission is necessary. It was expected that direct transmission plays an important role in these conditions, and this result supports that.
Other parameters only substantially affected the model output when they were altered by magnitudes of 10-1000. For parameters that did not affect the model output except when altered by a magnitude of ≥ 100, we set a range of values that were biologically relevant for this particular pathogen, based on our existing empirical knowledge.

Discussion
Direct transmission through contact between infectious and susceptible individuals (such as in farming conditions or breeding aggregations) was predicted to play a stronger role in the development of the epidemic. Our results have also identified that the incubation rate (σ ) and length of infection (γ ) are the two key parameters influencing the severity of S. destruens outbreaks. Altering these parameters greatly affected transmission and thus the progression of the epidemic 38 with the incubation rate largely impacting the pace of the epidemic. At the community level, species with a long infection time that are  also tolerant to the parasite could act as reservoirs by shedding low levels of infectious spores over a longer time period, potentially leading to a sustained disease outbreak. This has a direct implication in the management of future fungal outbreaks. Fungal spores can survive in the environment outside their hosts for several days, increasing the probability of contact with sensitive hosts 28 . For example, the saprobic free-living stages of the chytrid  fungus have been shown to be a main driver of epidemics of this pathogen 9 . The documented variation in the number and longevity of S. destruens' spores and zoospores may have played a minimal role in driving the epidemic in these closed systems, as the experimental numbers used were well above infection threshold levels. This variation however could play a more significant role for environmental transmission in natural systems where host densities and water flow vary. The high levels of transmission and susceptibility observed here confirm the risk posed by S. destruens of spreading to new aquatic areas. This is further reinforced by the existence of a reservoir host that has a broad thermal tolerance and can disperse rapidly 28,30 . Currently, bream is both the most sensitive to and the highest transmitter of the disease, which may affect communities to varying degrees based on their structure 3,39 . As a generalist parasite, S. destruens shows a range of infectivity of hosts and an increased species richness can in effect lower the prevalence of the disease in that environment 3 . Determining which community composition can best constrain pathogen emergence and prevent a widespread outbreak has important implications for controlling disease risk and ultimately for species conservation. Ecosystems are rapidly changing and will continue to do so as a result of global changes such as significant alterations in land-use, species introductions and habitat destruction 8,40 . These all directly or indirectly affect the environmental transmission and contact frequencies between potential hosts, with a knock-on effect on the evolutionary bi-stability of the pathogen's transmission patterns 11,41,42 . Although creating this evidence-based model has established an important baseline for understanding disease dynamics in fungal parasites, a more comprehensive community level network model should be developed in order to really understand the dynamics and potential impacts of such pathogens on host populations and biodiversity. The role of host community structure in disease dynamics, in particular spore and zoospore production, will alter the incubation rate and length of infection modulating the severities of observed infections and needs to be further explored.