Spillover dynamics and asynchronous temporal fluctuations in host density and competence drive fungal parasite persistence in multi‐host, seasonal communities

Abstract

1. Parasites routinely persist in seasonal systems while infecting multiple host species. An important question for parasite control is whether parasite persistence is driven by particular host species, specific times of year or their interaction. We have few empirically tractable models to answer this question.

2. We develop a data‐driven model that partitions species‐specific and temporal drivers of parasite persistence from commonly collected surveillance data. Leveraging standard epidemiological theory, our approach demonstrates a novel way to link time‐varying fluctuations in species‐level contributions to parasite persistence directly to time‐integrated parasite persistence in the community as a whole, while using real‐world field data that is tractable to obtain.

3. We applied our approach to 3 years of parasite surveillance data in seasonal amphibian communities persisting with the fungal pathogen Batrachochytrium dendrobatidis (Bd). We asked three questions: (i) Do amphibians trade‐off in their contributions to Bd persistence across the year? (ii) What host characteristics, such as seasonally fluctuating host density or host competence, drive these trade‐offs? and (iii) what are the relative contributions of species compared to periods of high transmission for enzootic Bd persistence?

4. We found that the identity of the amphibian species driving Bd persistence was highly variable through time. Specifically, temporal variability in host density and less so variability in host competence drove the temporal variation in species' contributions to persistence. Moreover, our model identified two distinct mechanisms of Bd persistence: (i) spillover dynamics from a dominant maintenance species and (ii) temporally asynchronous, but equal, contributions of host species to persistence. In both cases, species‐targeted interventions were as effective or more effective than temporal control for reducing the capacity of Bd to persist.

5. Broadly, our results demonstrate that species contributions to parasite persistence can have strong, asynchronous temporal variability, potentially limiting the effectiveness of targeted seasonal parasite control. Our model is designed to link closely with standard parasite surveillance data and is broadly applicable to other host–parasite systems where it can partition who, when and what drive parasite persistence in multi‐host seasonal communities.

In this study, the authors develop a new model to show that species contributions to parasite persistence can have strong, asynchronous temporal variability, often limiting the effectiveness of targeted seasonal parasite control. The model is broadly applicable for partitioning who, when, and what drive parasite persistence in multi‐host seasonal communities.

1. INTRODUCTION

Parasites routinely persist in highly seasonal systems while infecting multiple host species. Despite extensive focus on the persistence of single‐host parasites in seasonal systems (Altizer et al., 2006; Hridoy, 2025; Martinez, 2018) and parasite persistence in multi‐host systems (Streicker et al., 2013; Toorians et al., 2025), the mechanisms driving persistence in multi‐host, seasonal systems remain underexplored (Bielby et al., 2021; Brown et al., 2013). Recent theoretical work has highlighted two key challenges. First, traits underlying host competence—the ability of hosts to acquire and transmit a parasite (Martin et al., 2019)—can be highly plastic in response to changing biotic and abiotic conditions (Gervasi et al., 2015). As the environment changes over time or as community composition shifts, the role of different host species for parasite persistence may also change. Second, how a species contributes to parasite persistence may rarely be a property of that species, but rather be highly contingent upon the ecosystem in which that species is embedded (Roberts & Heesterbeek, 2020). For example, the degree of resource‐mediated competition between red and grey squirrels can fundamentally change the role each species plays in maintaining squirrel pox virus within a community (Roberts & Heesterbeek, 2021). Thus, depending on when and where a community is measured, who and what are driving parasite persistence can shift drastically. This prediction has received little empirical testing as it requires (i) multi‐host, seasonal parasite systems that are sampled consistently over time and (ii) a theoretical framework to quantify the time‐varying drivers of parasite persistence from empirical data. Addressing this knowledge gap has the potential to inform targeted management strategies and more closely link ecosystem conditions to the drivers of parasite persistence.

Parasites often exhibit seasonal patterns in their incidence rates, prevalence and infection intensity (Altizer et al., 2006; Martinez, 2018). Host phenological behaviours, such as breeding and migration, drive these seasonal infection dynamics in some host–parasite systems (e.g. Hosseini et al., 2004). In other systems, seasonal changes in abiotic variables such as temperature and precipitation directly or indirectly affect disease dynamics (Altizer et al., 2006). For instance, many vector‐borne pathogens, such as malaria or Zika virus, have higher incidence and prevalence during warmer and wetter times of the year (Monaghan et al., 2016; Yamba et al., 2023). In seasonal enzootic systems, a parasite must be able to persist despite these significant cyclical fluctuations in host, parasite and environmental characteristics (Grassly & Fraser, 2006).

Host community structure also drives enzootic disease dynamics. Multi‐host enzootic systems can have one or more species capable of maintaining parasite transmission either alone or in concert. In some communities, a single host may be capable of maintaining the parasite, but infection spills over into other host species (Fenton et al., 2015). Alternatively, multiple host species may contribute to parasite persistence, and removing one species might not result in parasite loss (Fenton et al., 2015; Webster et al., 2017). Quantifying each species' maintenance potential—the ability of species to sustain and transmit a parasite in the absence of other species—offers key insights into the mechanisms of persistence within a system (Streicker et al., 2013; Viana et al., 2014). In addition, maintenance potential provides useful information for interventions and disease management strategies (Barlow, 1996; MacInnes et al., 2001) and can even yield insight into the evolution of specialist versus generalist parasite life‐history strategies (Park et al., 2025).

Despite the recognized importance of seasonal dynamics and host community structure in disease ecology, how these factors jointly contribute to parasite persistence remains poorly understood. For example, the role of ‘maintenance host’ may shift temporally, and parasite persistence may rely on the ideal temporal sequence of species' characteristics conducive for acquiring and spreading infection (Wilber, DeMarchi, et al., 2022). In other words, a species may experience high seasonal prevalence that contributes to their ability to solely maintain a parasite for part of the year, but as prevalence decreases in this species—perhaps due to seasonal changes in susceptibility—this host species may lose the capacity to promote parasite persistence, enhancing the risk of parasite fade‐out. However, if the competence or density of another species increases as the other species' contributions decrease, a parasite can persist by effectively temporally ‘bridging’ across hosts (Caron et al., 2015). Incorporating seasonal dynamics into our theory of multi‐host communities is important for understanding when certain host species are disproportionately contributing to parasite persistence and how the timing of these contributions affects targeted control strategies (Ng et al., 2023).

Previous work has developed metrics to quantify species' contributions to parasite persistence (Fenton et al., 2015; Streicker et al., 2013; Toorians et al., 2025). The basic reproductive number ($R_0$)—the number of secondary infections produced by an infected individual in a fully susceptible population—is a measure of a host's ability to spread and, in many instances, maintain a parasite (but see Roberts, 2007; Wilber, Ohmer, et al., 2022). In a multi‐host community, a parasite has a community $R_0$ that is a combination of host species‐level $R_0$ values (Fenton et al., 2015). Analogously, in a multi‐host, seasonal context, a parasite has an overall $R_0$ that is a combination of time‐varying, species‐level $R_0$ values (Wilber, DeMarchi, et al., 2022).

Here, we develop and apply theory using $R_0$ to ask three questions relevant across multi‐host, seasonal systems: (i) Are host contributions to parasite persistence seasonal, with different species driving parasite persistence over the course of a year? (ii) What host characteristics, such as seasonally fluctuating host density or competence, contribute most to the seasonal variability in species' contributions to parasite persistence? and (iii) what is the relative importance of who (i.e. what species?) compared to when (i.e. what time of the year?) for controlling parasites in multi‐host, seasonal communities? To answer these questions, we focused on the fungal parasite Batrachochytrium dendrobatidis (Bd), which infects amphibians and causes the disease chytridiomycosis. Bd has caused severe declines in hundreds of amphibian species around the world (Scheele et al., 2019). However, in much of eastern North America, Bd persists enzootically without significant negative effects on amphibian species (Rollins et al., 2013). Bd infects a variety of amphibian species and, while some non‐amphibian hosts have also been identified (e.g. McMahon et al., 2013), no long‐term non‐amphibian reservoir has been found. Moreover, amphibian species can show drastic seasonal variation in abundance related to breeding activity, and Bd infections are highly sensitive to environmental factors such as temperature (Niemiller & Reynolds, 2011; Sheets et al., 2021). These attributes make enzootic amphibian‐Bd systems ideal for studying the drivers of multi‐host, seasonal dynamics.

We sampled >1500 individual amphibians across 10 species, four communities, and 3 years in eastern Tennessee, USA, to parameterize a novel epidemiological model to answer our three questions. We hypothesized that species‐level contributions to Bd persistence would be highly temporally variable, with temporal variability in host density in and around aquatic habitats being a primary driver of temporal fluctuations in species contributions to Bd persistence. Moreover, we expected that overall Bd persistence would be largely driven by a single species or a single temporal period within the year, suggesting that targeted control of certain species or during certain periods of the year could be disproportionately effective for eliminating the parasite (Hossack et al., 2023). The model developed and applied in this paper is broadly suited to ask theoretical and applied questions regarding parasite persistence in multi‐host, seasonal parasite systems.

2. MATERIALS AND METHODS

2.1. Model development

We modelled a seasonal, multispecies community of hosts where Susceptible hosts transition to Infectious hosts through contact with free‐living parasite in the environment, Z (Figure 1). We will refer to these free‐living parasites as zoospores, which are the infectious life stage of Bd. Consistent with Bd transmission dynamics in aquatic systems, we assumed that the majority of transmission occurs in the aquatic environment (Daversa et al., 2018). Moreover, we assumed that the decay of zoospores in the environment happens at a substantially faster rate than zoospores are removed via infection. Given that zoospores are only viable between 1 and 4 days in the environment in laboratory conditions (Woodhams et al., 2008) and between 9 and 14 h in field conditions (Rumschlag et al., 2022), zoospore removal through non‐transmission processes (decay, water filtering by aquatic organisms that removes zoospores without causing infection, Searle et al., 2013) will likely dwarf the removal of zoospores via transmission processes (i.e. the act of a host contacting a zoospore and removing it from the water) in most conditions.

FIGURE 1.

Conceptual diagram of our approach to decompose the drivers of parasite dynamics in multi‐host, seasonal systems. Our approach is centred around parameterizing a multi‐host seasonal model given by the model diagram in the figure. The model consists of two habitat types—aquatic and terrestrial—with transmission occurring exclusively in the aquatic habitat. The model diagram depicts two species moving between these habitats, though we focused our analyses on six species. The relative rates of moving between habitats, $l_{s,\text{in}}$ or $l_{s,\text{out}}$ determine the probability of being found in the aquatic habitat, ${\theta }_s$. We are only concerned with ${\theta }_s$ and not $l_{s,\text{in}}$ or $l_{s,\text{out}}$. Arrows relating to the rates ${\alpha }_s$ and $d_s$ are not shown for visual clarity. The model is parameterized from seasonal surveys of multi‐host communities. The ‘Data collection’ column describes the types of data collected during these surveys and the ‘Seasonal functions’ column indicates how these data streams inform seasonal functions within the model. The parameterized model can be used to decompose the drivers of observed parasite persistence and explore the implications of hypothetical species or seasonal control strategies on parasite persistence. In this study, we use the parameterized model to answer three broad questions (Q1, Q2, and Q3) given in the figure.

To capture phenology and seasonally varying infection dynamics for host species $s$, the transmission parameter ${\beta }_s$, host death rate $d_s$, recovery rate ${\nu }_s$, disease‐induced mortality rate ${\alpha }_s$, parasite shedding rate ${\lambda }_s$ and zoospore decay rate in the environment $\gamma$ vary seasonally. The variable $\tau$ is a particular time point within the year (e.g. varying from 0 to $\tau =365$ if our units are days) and $t$ is the absolute time in days (e.g. from 0 to some arbitrarily large number of days). Hosts can be in the aquatic environment with some time‐varying probability ${\theta }_s\left(\tau \right)$, capturing differences in space use between amphibian species (Niemiller & Reynolds, 2011). We assumed that infection and parasite shedding into the zoospore pool only happen when hosts are in the aquatic environment. Finally, we only modelled the non‐larvae life stage of amphibians (e.g. juveniles and adults). Importantly, given our model, the relative contributions of species to parasite persistence (i.e. how much one species contributes to persistence relative to another) is robust to the exclusion of species or life stages (Appendices S1.1 and S1.2).

The multi‐species seasonal model can be written as (Figure 1)

$$\begin{array}{c}\frac{\partial S_s\left(t,\tau \right)}{\partial t}=f\left(N_s\left(t,\tau \right)\right)-d_s\left(\tau \right)S_s\left(t,\tau \right)-{\beta }_s\left(\tau \right){\theta }_s\left(\tau \right)S_s\left(t,\tau \right)Z\left(t,\tau \right)+{\nu }_s\left(\tau \right)I_s\left(t,\tau \right)-\frac{\partial S_s\left(t,\tau \right)}{\partial \tau }\\ \frac{\partial I_s\left(t,\tau \right)}{\partial t}={\beta }_s\left(\tau \right){\theta }_s\left(\tau \right)S_s\left(t,\tau \right)Z\left(t,\tau \right)-\left({\nu }_s\left(\tau \right)+d_s\left(\tau \right)+{\alpha }_s\left(\tau \right)\right)I_s\left(t,\tau \right)-\frac{\partial I_s\left(t,\tau \right)}{\partial \tau }\\ \frac{\partial Z\left(t,\tau \right)}{\partial t}=\sum _{i\in \text{Species}}{\lambda }_i\left(\tau \right){\theta }_i\left(\tau \right)I_i\left(t,\tau \right)-\gamma \left(\tau \right)Z\left(t,\tau \right)-\frac{\partial Z\left(t,\tau \right)}{\partial \tau }\end{array}$$ (1)

where the parameters described above are written as continuous functions of time‐in‐the‐season $\tau$. The term $f\left(N_s\left(t,\tau \right)\right)$ gives the time‐varying recruitment of susceptible individuals of species $s$ into the population. The exact functional form is irrelevant for our subsequent analyses. In Appendix S1, we describe a more general version of this model that includes a parameter ${\omega }_{\mathit{si}}$ describing the ratio between interspecific and intraspecific transmission for species $s$ and $i$. Conceptually, this parameter can be thought of as the relative spatial overlap between species in the aquatic environment. When ${\omega }_{\mathit{si}}=1$ for all $s$ and $i$, there is complete habitat overlap and we get back Equation (1). When ${\omega }_{\mathit{si}}<1$, species are partially spatially segregated in the aquatic environment and intraspecific transmission is higher relative to interspecific transmission. We included this parameter because recent work has shown the potential for incomplete mixing of zoospores among amphibian species (Byrne et al., 2022). Below, we describe how we vary ${\omega }_{\mathit{si}}$.

The time‐varying, species‐level $R_{0,s}\left(\tau \right)$ can be written as (Appendix S1.1)

$$R_{0,s}\left(\tau \right)=\underset{\text{Part}\mathrm{A}}{\underbrace{\frac{{\beta }_s\left(\tau \right)N_s\left(\tau \right){\lambda }_s\left(\tau \right){\theta }_s{\left(\tau \right)}^2}{\gamma \left(\tau \right)b_s\left(\tau \right)}}}=\underset{\text{Part}\mathrm{B}}{\underbrace{\frac{1+\frac{1}{b_s\left(\tau \right)N_s^{*}\left(\tau \right)P_s^{*}\left(\tau \right)}\frac{d{I}_s^{*}\left(\tau \right)}{\mathit{d\tau }}}{\left[1-P_s^{*}\left(\tau \right)\right]\left(\sum _{i\in \text{Species}}\frac{N_i^{*}\left(\tau \right)}{N_s^{*}\left(\tau \right)}\frac{P_i^{*}\left(\tau \right)}{P_s^{*}\left(\tau \right)}\frac{{\lambda }_i\left(\tau \right)}{{\lambda }_s\left(\tau \right)}\frac{{\theta }_i\left(\tau \right)}{{\theta }_s\left(\tau \right)}-\frac{1}{{\lambda }_s\left(\tau \right){\theta }_s\left(\tau \right)N_s^{*}\left(\tau \right)P_s^{*}\left(\tau \right)}\frac{d{Z}^{*}\left(\tau \right)}{\mathit{d\tau }}\right)}}}$$ (2)

where $b_s\left(\tau \right)=\left({\nu }_s\left(\tau \right)+d_s\left(\tau \right)\right)$. In our specific enzootic system ${\alpha }_s\left(\tau \right)\approx 0$ (DeMarchi et al., 2026).

We can interpret Equation (2) as a counterfactual—if we were to remove all other species and hold the focal species $s$ at the conditions experienced at time $\tau$, it would have $R_0$ given by part A in Equation (2). Part B can be derived by making an assumption that the system is in enzootic equilibrium (hence the ‘*’ superscripts; Appendix S1.1). There are two advantages to part B. First, it allows us to calculate time‐varying, species‐level $R_{0,s}\left(\tau \right)$ from data that we can collect in the field such as relative host density, Bd prevalence, infection intensity, and habitat use. In contrast, while part A in Equation (2) is conceptually useful, parameters such as ${\beta }_s\left(\tau \right)$ (the time‐varying transmission rate) are notoriously difficult to measure. Second, part B provides a means to ‘correct’ for the presence of other species at certain times of the year when calculating the contributions of a particular species to Bd persistence. For example, just observing high prevalence on species A at a particular time of the year $\tau$ does not mean that $R_{0,s}\left(\tau \right)$ is high for species A at $\tau$. The density, Bd prevalence and Bd intensity on other species prior to $\tau$, and the dynamics of parasite decay in the environment could be the primary drivers of the high prevalence in species A.

2.1.1. From time‐varying, species‐level ${\mathit{R}}_{\mathbf{0}\mathbf{,}\mathit{s}}\left(\mathit{\tau }\right)$ to community ${\mathit{R}}_{\mathbf{0}\mathbf{,}\mathit{T}}$

Equation (2) isolates the counterfactual contributions of a species, but does not inform us on the robustness of Bd persistence in the seasonal community. The next‐generation matrix of Equation (1), $\mathbf{R}$, provides this information (Diekmann et al., 2013) and can be parameterized from Equation (2) (Appendix S1.3). The spectral radius of $\mathbf{R}$ yields $R_{0,T}$—our measure of the overall capacity of Bd to persist in a multi‐host, seasonal community (see Toorians et al., 2025, for an equivalent non‐seasonal metric). If $R_{0,T}>1$, then following Bd introduction into a completely susceptible host community, prevalence will on average increase over the course of a 1 year period $T$. For our model, the condition that $R_{0,T}>1$ directly corresponds to long‐term Bd persistence in the system over many periods of length $T$.

We can directly modify $\mathbf{R}$ to examine how controlling infection (i) on particular species across all times or (ii) at particular times of the year across all species, changes $R_{0,T}$ (Appendix S1.3). Moreover, removing all species but species $s$ from $\mathbf{R}$ and computing the spectral radius yields $R_{0,s,T}$—the time‐integrated contribution of species $s$ to parasite persistence in the absence of all other species. It is important to understand the relationship between $R_{0,s}\left(\tau \right)$ and $R_{0,s,T}$ or $R_{0,T}$. $R_{0,s}\left(\tau \right)$ identifies the $R_0$ of species $s$ if conditions were held constant at the conditions experienced at $\tau$ in a fully susceptible population. If $R_{0,s}\left(\tau \right)=0$ for some range of time $\mathrm{\Delta }\tau$, this does not mean that $R_{0,s,T}=0$. For example, individuals of species $s$ may leave the pond for some time period $\left[{\tau }_0,{\tau }_0+\mathrm{\Delta }\tau \right]$ and not produce any new infections such that $R_{0,s}\left(\tau \right)=0$ for all $\tau$ in this range. However, individuals of the species could remain infected during this time and zoospores could potentially remain viable in the environment. When amphibians return to the aquatic habitat, transmission can then resume. In this case, $R_{0,s,T}>0$ despite $R_{0,s}\left(\tau \right)=0$ for some period of time.

2.2. Study system and data collection

To parameterize our model, we conducted seasonal surveys at four sites in eastern Tennessee, USA (additional details in Appendix S2). We conducted 15–16 standardized sampling events over 2 years (2023 and 2024), with additional sampling in 2022 to confirm Bd presence. Six amphibian species were encountered frequently enough to be included in our models: green frogs (Rana clamitans), American bullfrogs (R. catesbeiana), Cope's grey tree frogs (Hyla chrysoscelis), spring peepers (Pseudacris crucifer), upland chorus frogs (P. feriarum) and eastern newts (Notophthalmus viridescens). Previous studies have shown that susceptibility to infection varies among these species, with eastern newts often showing high infection prevalence (DeMarchi et al., 2026; Hobart et al., 2026). However, to our knowledge, chytridiomycosis has rarely been observed and Bd‐induced declines have never been observed in wild amphibians in Tennessee (this study and Le Sage et al., 2021; Wilber, Ohmer, et al., 2022; DeMarchi et al., 2026). The permits necessary for this study were: University of Tennessee's IACUC Protocol #2867‐1021; Tennessee Wildlife and Resource Agency permit #5297; the Tennessee Department of Environment and Conservation permit #2022‐010.

At each site and sampling event, we collected four data streams used to parameterize Equation (2): host abundance ($N_s\left(\tau \right)$), Bd prevalence ($P_s\left(\tau \right)$), Bd load (related to ${\lambda }_s\left(\tau \right)$), and the probability that an amphibian was found in aquatic habitat (${\theta }_s\left(\tau \right)$). Note we drop the ‘*’ superscripts on abundance $N$ and prevalence $P$ moving forward for notational convenience. We describe how each of these data streams were collected and analysed below.

2.2.1. Host abundance (${\mathit{N}}_{\mathit{s}}\left(\mathit{\tau }\right)$)

We estimated amphibian abundance at sites using repeated count data and N‐mixture models (Royle, 2004). For each sampling event at a site, we conducted three visual encounter surveys within three consecutive days (Appendices S2 and S3). We used Bayesian N‐mixture models to calculate abundance and detectability for amphibian species at each site and sampling event (Appendix S3; Royle, 2004). The N‐mixture models estimated the abundance of species $s$ at sampling time $\tau$, $N_{\mathit{s\tau }}$. To obtain $N_s\left(\tau \right)$ for each site, we smoothed the $N_{\mathit{s\tau }}$ estimates using a Poisson generalized linear model (GLM) and a log‐link function: $\log \left(N\right)=f\left(\tau \right)$, where $f\left(\tau \right)$ is a flexible site‐specific spline function over the time period of a year (both sampling years were pooled to model annual seasonal trends). We used cyclic, cubic B‐splines and chose the optimal number of knots based on minimizing Poisson deviance with fivefold cross‐validation. Eastern newt abundance was estimated using enclosure sampling within ponds (Gray et al., 2013) and modelled using the same smoothing approach described above (Appendix S3).

2.2.2. Prevalence (${\mathit{P}}_{\mathit{s}}\left(\mathit{\tau }\right)$) and parasite load (${\mathit{\lambda }}_{\mathit{s}}\left(\mathit{\tau }\right)$)

We caught up to 20 individuals (adults or post‐metamorphic subadults) of each species present during the sampling events. We used a sterile swab to rub the ventral side of the amphibian 30 times. We extracted DNA from these swabs using Qiagen DNEasy kits and estimated Bd presence and load using real‐time quantitative polymerase chain reaction (qPCR) (Hyatt et al., 2007). All samples were run in duplicate and average CT scores were used. Observed qPCR outputs from field swabs were converted to zoospore equivalents (ZE) using a laboratory‐specific standard curve generated from in‐house Bd cultures of a Tennessee Bd isolate (FMB003, GPL‐1) (DeMarchi et al., 2026).

To calculate the function $P_s\left(\tau \right)$, we modelled infection prevalence using a Binomial GLM. We estimated the time‐varying prevalence of infection throughout the year for each amphibian species at each site. To do this, we allowed the prevalence $P$ to be a flexible, cyclic function of time (day of year pooled across years): $\text{logit}\left(P\right)=f\left(\tau \right)$ where $f\left(\tau \right)$ is a cyclic, B‐spline that captures seasonal variability in infection prevalence. We chose the optimal number of knots by optimizing the F1 score using fivefold cross‐validation. This yielded the function $P_s\left(\tau \right)$.

To calculate the species‐specific, time‐varying shedding function ${\lambda }_s\left(\tau \right)$, we first modelled natural log infection intensity (excluding zeros on the natural scale) $x$ using a GLM with a normal error distribution (Schrock et al., 2025). We modelled species‐ and site‐specific mean log infection intensity as $x=f\left(\tau \right)$, where $f\left(\tau \right)$ is a cyclic, cubic B‐spline. We chose the optimal number of knots by maximizing mean‐squared error using fivefold cross‐validation. This yielded the function $x_s\left(\tau \right)$.

To link infection intensity on the natural scale $\exp \left(x_s\left(\tau \right)\right)$ to shedding ${\lambda }_s\left(\tau \right)$, we used recent results from DeMarchi et al. (2026) that showed three of our focal species shed at similar rates per unit of skin surface area for a given swab load. We applied this finding to all six species in this study and linked observed infection intensity to shedding by scaling each infection intensity estimate by animal surface area, which in turn scales with body mass (Figure S1). Note that we are not accounting for any measurement error in prevalence and infection intensity (DiRenzo et al., 2018). However, prevalence and infection intensity primarily enter Equation (2) as ratios and multiplicative measurement error due to the swabbing process would generally cancel out and not affect our results.

2.2.3. Probability of being in the aquatic environment, ${\mathit{\theta }}_{\mathit{s}}\left(\mathit{\tau }\right)$

We recorded microhabitat characteristics for every captured individual. To calculate the time‐varying probability of an individual of species $s$ being in the aquatic habitat where it could potentially acquire and shed zoospores, we simplified our microhabitat designation to ‘in the water’ (1) or ‘not in the water’ (0). This classification captures broad differences in how species use the aquatic environment. We estimated ${\theta }_s\left(\tau \right)$ for each species and site using the same approach described for $P_s\left(\tau \right)$.

2.2.4. Loss of infection rates, ${\mathit{\nu }}_{\mathit{s}}\left(\mathit{\tau }\right)$

To calculate species‐specific loss of infection rates ${\nu }_s\left(\tau \right)$, we used species‐specific load‐dependent loss of infection rates estimated in DeMarchi et al. (2026) for green frogs, bullfrogs and eastern newts in Tennessee (Figure S2). We assumed that spring peepers, upland chorus frogs, and Cope's grey tree frogs followed the same load‐dependent loss of infection function. Our results were robust to this assumption (Appendix S3.1). Given the loads observed, amphibians tended to hold infection for between 14 and 50 days on average, depending on species and time in the year $\tau$ (Figure S2).

2.3. Question 1: Do amphibians trade‐off in their contributions to Bd persistence across the year?

We paired Equation (2) with $N_s\left(\tau \right)$, $P_s\left(\tau \right)$, ${\lambda }_s\left(\tau \right)$, and ${\theta }_s\left(\tau \right)$ estimated from our field data and calculated $R_{0,s}\left(\tau \right)$ for each species at each site. We allowed zoospores to survive in the environment for on average 4 days (Woodhams et al., 2008), with this almost certainly being an upper bound on survival (Rumschlag et al., 2022). When computing $R_{0,s}\left(\tau \right)$, we varied ${\omega }_{\mathit{si}}$ between 0.25 and 1, where ${\omega }_{\mathit{si}}=1$ represents complete spatial overlap in the aquatic environment (Appendix S3.2).

2.4. Question 2: What characteristics drive the temporal variability in amphibian contributions to Bd persistence?

We computed the total variance in $R_{0,s}\left(\tau \right)$ across species in a site as ${\mathrm{Var}}_{\text{Total}}=\sum _{s\text{in Species}}{\mathrm{Var}}_{\tau }\left(R_{0,s}\left(\tau \right)\right)$. We then performed a sensitivity analyses where we removed the temporal variability in each of the four data streams $N_s\left(\tau \right)$, $P_s\left(\tau \right)$, ${\lambda }_s\left(\tau \right)$, and ${\theta }_s\left(\tau \right)$ and asked how much ${\mathrm{Var}}_{\text{Total}}$ changed. A larger change in ${\mathrm{Var}}_{\text{Total}}$ when a data stream was held constant indicated a larger contribution of this data stream to observed temporal variability in $R_{0,s}\left(\tau \right)$ for the community. For species such as spring peepers, Cope's grey tree frogs, and upland chorus frogs, data streams $P_s\left(\tau \right)$, ${\lambda }_s\left(\tau \right)$, and ${\theta }_s\left(\tau \right)$ were only observed for short periods of the year when the abundance of these species at our sites was non‐zero (Figure 2). As such, empirical estimates of $P_s\left(\tau \right)$, ${\lambda }_s\left(\tau \right)$, and ${\theta }_s\left(\tau \right)$ had less opportunities to fluctuate seasonally for these species. To remove the potential for bias, we restricted this analysis to green frogs, bullfrogs, and newts that were generally available for sampling for most of the year if they occupied a site.

FIGURE 2.

Mean empirical patterns of Bd prevalence (a–d), infection intensity (e–h), host abundance (i–l) and probability of being in the water (m–p) for all species present at our four focal communities. Lines give mean model predictions from fitted splines and points indicate aggregated empirical data. For (a–d, m–p) large points are proportional to the sample size used to calculate the proportion. Different colours indicate different species. Flat lines either indicate (i) observations were consistently high or low for a particular species (e.g. newts were always found in the water at Complex) or (ii) there was limited data across the season for a particular variable by species combination. For example, upland chorus frogs were only observed for a short period of the year; thus, infection intensity during that part of the year was extrapolated across the year. Note that this does not affect $R_{0,s}\left(\tau \right)$ predictions because abundance—which we could measure across the year—going to zero at time $\tau$ ensures $R_{0,s}\left(\tau \right)$ also goes to zero regardless of extrapolated values. Thick regions of a line indicate the range where observed data were available for that metric, and thin portions indicate where the statistical model was extrapolated from previous time points because no data were available (i.e. amphibians were not present to be caught and swabbed).

2.5. Question 3: What are the relative contributions of species compared to temporal periods for Bd persistence?

We used the next‐generation matrix $\mathbf{R}$ to conduct in silico control experiments. For each site, we first computed the baseline $R_{0,T}$ without any control and then perturbed species and temporal periods. For species controls, we prevented transmission to a single species for the whole year and recalculated $R_{0,T}$. We repeated this for each species in the community. For temporal controls, we prevented transmission from all species over a 90‐day period and recalculated $R_{0,T}$. We did this for 13 equally spaced and overlapping 90‐day periods across the year. We chose 90 days as this was approximately a fourth of a year and, if four species in a community were equally and asynchronously trading off in their contributions to Bd persistence, the effect of a single species control would be equivalent to a 90‐day temporal control. We also explored a 120‐day control, which is the temporal equivalent to a three species community in the way described above. For each control, we calculated the percent reduction in baseline $R_{0,T}$ and then compared the percent reductions between species and temporal controls. We computed these control experiments for ${\omega }_{\mathit{si}}=0.5\text{and}1$, where ${\omega }_{\mathit{si}}=0.5$ was a biologically realistic lower bound (Appendix S3.2).

3. RESULTS

3.1. Summary of field patterns across sites

Figure 2 summarizes the empirical patterns for each species at each site. We will reference these patterns below as we describe how they jointly contribute to $R_{0,s}\left(\tau \right)$.

3.2. Question 1: Do amphibians trade‐off in their contributions to Bd persistence?

We found that one species was never the dominant contributor to Bd dynamics across the entire year (Figure 3). At the three sites where eastern newts were present (Complex, Lotus and Hastie), newts had the highest $R_{0,s}\left(\tau \right)$ (i.e. were the dominant contributor) compared to other species for 47%–80% of the year (Figure 3). Early in the year when newt density and Bd prevalence were high (Figure 2), newt $R_{0,s}\left(\tau \right)$ was predicted to be substantially higher than other amphibian species within the community (Figure 3b–d). However, as the season progressed into late summer and early fall, newt contributions declined as abundance, prevalence, and infection intensity decreased (Figure 2). The model predicted that this decrease was enough such that (i) newts generally lost the capacity to independently maintain Bd ($R_{0,s}\left(\tau \right)<1$) and (ii) another species (green frogs in two sites and bullfrogs in another site), became the dominant driver of Bd dynamics (though not necessarily with $R_{0,s}\left(\tau \right)>1$; Figure 3b–d).

FIGURE 3.

Absolute (a–d) and ranked (e–h) $R_{0,s}\left(\tau \right)$ values for species $s$ across time‐in‐the‐year $\tau$ for each of the four sites. Different coloured lines indicate different species. For (a–d), the black dashed line indicates where $R_{0,s}\left(\tau \right)=1$ and the dotted red line is the sum of $R_{0,s}\left(\tau \right)$ across species at $\tau$ which is representative of instantaneous, total Bd fitness. For (e–h) a high rank indicates species with a higher relative $R_{0,s}\left(\tau \right)$. All $R_{0,s}\left(\tau \right)$ values are derived from Equation (2) and the empirical data in Figure 2 and shedding rates are scaled by amphibian surface area (Figure S1). For this plot, ${\omega }_{\mathit{si}}=1$ for all $s$ and $i$. The relative $R_{0,s}\left(\tau \right)$ values were largely insensitive to ${\omega }_{\mathit{si}}$ between 0.25 and 1.

Across all sites, green frogs were often among the top two contributors to Bd persistence (Figure 3e,f). Their contributions were primarily driven by high abundance and large body size, which contribute to zoospore shedding (Figure 2, Figure S1). Green frogs never had the highest infection intensity or prevalence within a site, but they were always one of the two most numerically abundant amphibian species (Figure 2). Hastie was a notable exception—despite their relatively high abundance, low prevalence and infection intensity reduced green frog contributions relative to bullfrogs and newts.

Bullfrogs were found at three of our four sites, but in relatively low abundance. However, at Hastie, where they were found in the highest abundance relative to other species (Figure 2l), their high infection intensity, large body size and high prevalence made it such that they had the highest contributions to Bd persistence during late summer and early fall (Figure 3d), surpassing both newts and green frogs.

At Woodlot, where newts were absent, dominant contributors shifted notably throughout the year (Figure 3). Early in the year (February and March), the model predicted that upland chorus frogs were briefly the most significant contributors to Bd persistence. This was due to a short period of high abundance during their breeding, paired with significant time spent in the aquatic habitat (e.g. males call for females from the aquatic environment) and high Bd prevalence (Figure 2a,e,i,m). Upland chorus frogs also have high variability in their $R_{0,s}\left(\tau \right)$ rank as they shift from an unimportant driver of Bd dynamics for most of the year, to one of the most important for a brief period of time (Figure 3e). While spring peeper abundance was seasonally very high at Woodlot (Figure 2i), they spent significantly less time in the aquatic environment than upland chorus frogs and had substantially lower Bd prevalence (Figure 2). While the model predicted an increase in $R_{0,s}\left(\tau \right)$ during the spring peeper breeding season, it was only enough for them to briefly become the dominant contributor to Bd dynamics (Figure 3a). As the seasonal pulse of upland chorus frogs and peepers diminished at Woodlot and green frog abundance increased, the model predicted that green frogs took over as dominant contributors, followed by bullfrogs (Figure 3a).

3.3. Question 2: What characteristics drive the temporal variability in amphibian contributions to Bd persistence?

The temporal variance in $R_{0,s}\left(\tau \right)$ was primarily driven by seasonal changes in host abundance $N_s\left(\tau \right)$ at three of our four sites—removing temporal variability in $N_s\left(\tau \right)$ consistently reduced variability more than removing temporal variability in intensity, prevalence or space use (Figure 4). At one site, Lotus, the abundance of newts and green frogs was relatively stable, and seasonal changes in prevalence drove the observed temporal variation in $R_{0,s}\left(\tau \right)$ (Figure 4).

FIGURE 4.

Change in the total variance in $R_{0,s}\left(\tau \right)$ (${\mathrm{Var}}_{\text{Total}}$) after removing temporal variability in either density $N_s\left(\tau \right)$, intensity ${\lambda }_s\left(\tau \right)$, prevalence $P_s\left(\tau \right)$ or space use ${\theta }_s\left(\tau \right)$ for all species at a site. The change in the total variance in $R_{0,s}\left(\tau \right)$ is calculated as (new variance ‐ baseline variance)/baseline variance. The total variance is only calculated across green frogs, bullfrogs, and newts for each of these sites to avoid any biases introduced by species that are only present at our sites for short temporal periods (spring peepers, Cope's grey tree frogs, and upload chorus frogs).

3.4. Question 3: What are the relative contributions of species compared to temporal periods for Bd persistence?

We first calculated the time‐integrated, species‐specific contributions to Bd persistence $R_{0,s,T}$—that is the $R_0$ value for a species alone in a community over the entire year. When ${\omega }_{\mathit{si}}=1$ $\forall$ $s,i$ (a shared zoospore pool assumption), our four communities had different predicted mechanisms of Bd persistence. Two communities (Woodlot and Lotus) were predicted to be the so‐called obligate communities (Fenton et al., 2015)—no particular species could maintain Bd on its own (i.e. $R_{0,s,T}<1$ for all species) but their joint contributions were such that $R_{0,T}>1$ (Figure 5a,b). In two other communities (Complex and Hastie), we saw spillover dynamics—the $R_{0,s,T}$ of newts was greater than 1 while it was less than one for all other species (Figure 5c,d). As ${\omega }_{\mathit{si}}$ decreased (interspecific transmission became less important relative to intraspecific transmission), all communities eventually transitioned to facultative communities, where multiple hosts could independently maintain Bd. However, for all sites this transition happened when ${\omega }_{\mathit{si}}<0.5$, at or below our empirically estimated lower bound for ${\omega }_{\mathit{si}}$ (Appendix S3.2).

FIGURE 5.

Time‐integrated, species‐level $R_{0,s,T}$ values for each community and species and how they vary with the interspecific to intraspecific transmission ratio ${\omega }_{\mathit{si}}$ (a–d). The quantity $R_{0,s,T}$ quantifies Bd's ability to persist on each species independently given the observed seasonality of period $T$ at each site. $R_{0,s,T}>1$ (above the black dashed line) indicates that a species can act as a maintenance species and independently maintain Bd in the seasonal system. ${\omega }_{\mathit{si}}=1$ indicates a completely shared zoospore pool. The coloured circles show the integrated $R_{0,s,T}$ values for ${\omega }_{\mathit{si}}=1$, which was the value used in Figure 3. The red line shows how the total community time‐integrated $R_{0,T}$ changes with ${\omega }_{\mathit{si}}$. The grey box shows the empirical range of ${\omega }_{\mathit{si}}$ (0.44–1) for our sites if spatial overlap is a reasonable proxy for ${\omega }_{\mathit{si}}$ (Appendix S3.2). Finally, the coloured blue bar indicates when communities transition from (O)bligate communities where no species have $R_{0,s,T}>1$, to (S)pillover communities where one species as $R_{0,s,T}>1$, to (f)acultative communities where multiple species have $R_{0,s,T}>1$ (following terminiology in Fenton et al., 2015).

Eliminating Bd transmission from newts always led to the largest reduction in $R_{0,T}$. When ${\omega }_{\mathit{si}}=1$, removing newts reduced $R_{0,T}$ by 72% on average and resulted in community‐level $R_{0,T}<1$ for all communities with newts (Figure 6a). In comparison, removing transmission from green frogs and bullfrogs led to an average 31% and 21% reduction in $R_{0,T}$, respectively (Figure 6a). When ${\omega }_{\mathit{si}}=0.5$, Bd persistence was more robust to species control (Figure 6c). The percent reductions in $R_{0,T}$ were smaller and removing newts was the only perturbation that led to $R_{0,T}<1$ (Figure 6c).

FIGURE 6.

(a, c) The percent reduction in $R_{0,T}$ given control of a particular species. Bars indicate the mean across all sites where a species was present and different shapes show the site‐level changes for particular species. Large, hatched shapes indicate that the control was sufficient to reduce $R_{0,T}<1$ and small shapes indicate that $R_{0,T}>1$ following control. Panel (a) shows results for ${\omega }_{\mathit{si}}=1$ and (c) shows results for ${\omega }_{\mathit{si}}=0.5$. The statistics show the Kruskal‐Wallis (KW) test results comparing whether there was a significant difference in rank reductions in $R_{0,T}$ among species. (b, d) The percent reduction in $R_{0,T}$ given a 90‐day control where transmission is prevented from every species in the 90‐day time interval. The time point on the x‐axis gives the mid‐point of the 90‐day control. Different colours show different sites. Thick lines show where temporal control reduced $R_{0,T}<1$ and thin lines indicate where $R_{0,T}>1$ after control. Inset plots in (b, d) show the maximum reduction in $R_{0,T}$ with species control compared to the maximum reduction in $R_{0,T}$ with temporal control. A value greater than 1 indicates that species control was more effective than temporal control. A 90‐day temporal control would have equivalent effects on $R_{0,T}$ to a species‐level control if four species in the community had the same $R_{0,s,T}$ and were completely asynchronous in their species‐level $R_{0,s}\left(\tau \right)$ values.

When newts were present, removing newts led to a larger reduction in $R_{0,T}$ (64%–85%) than preventing transmission in any 90‐ to 120‐day temporal period (90‐day: 8%–49%; 120‐day: 14% ‐ 57%) (Figure 6a,b). In contrast, when newts were absent (Woodlot), the most effective species control (removing green frogs, 48% or bullfrogs, 47%) was approximately equivalent to the most effective temporal control (90‐day: 43%; 120‐day: 55%, Figure 6b, Figure S3b). When ${\omega }_{\mathit{si}}=0.5$, a realistic lower bound for our system, temporal controls became more impactful on $R_{0,T}$, but species‐level control was still as effective or more effective than temporal control for all sites but Woodlot (Figure 6d). Both 90‐ and 120‐day controls were largely ineffective for reducing $R_{0,T}<1$ for most time periods across all sites (Figure 6; Figure S3).

4. DISCUSSION

We developed and applied theory to understand the dynamics of parasite persistence in multi‐host, seasonal systems. We found consistent evidence that temporal fluctuations in host density and, to a lesser extent, competence, drove strong seasonal fluctuations in species‐specific, seasonal $R_{0,s}\left(\tau \right)$, producing highly dynamic species contributions to parasite persistence. Moreover, we observed that species could trade‐off in who was contributing the most to parasite persistence at any particular time—that is one species was never a dominant maintenance species for the entire year. However, despite these dynamic, species‐level fluctuations at all sites, our analyses indicated that Bd persistence was still largely driven by the presence of a single dominant maintenance species (i.e. eastern newts) and spillover dynamics. In the absence of a dominant maintenance species, parasite persistence was driven by temporal asynchrony in species contributions that consistently allowed Bd fitness to remain high throughout the year.

High temporal variability in species maintenance potential has important implications for parasite persistence in multi‐host, seasonal systems. If Bd primarily infected a single host species, the observed temporal heterogeneity in species‐level maintenance potential (i.e. $R_{0,s}\left(\tau \right)$) could severely hinder long‐term Bd persistence, even if a species had high maintenance potential at certain times (Mangel, 2006; Wilber, Ohmer, et al., 2022). In contrast, generalist parasites can mitigate the negative effects of temporally variable resources (i.e. hosts) by exploiting multiple temporally fluctuating resources that, on aggregate, reduce fluctuation in parasite fitness (a so‐called ‘portfolio effect’, Schindler et al., 2015). By exploiting multiple hosts with temporally fluctuating competence and density, it is likely that Bd can reduce the negative impacts of temporal fluctuations in one species' maintenance potential on its overall fitness.

While the above argument suggests a clear advantage for generalist parasites in temporally heterogeneous environments, there may also be substantial costs to generalism (Leggett et al., 2013). The ability to infect multiple host species can require trade‐offs that reduce a parasite's ability to hyper‐efficiently infect and transmit from any one species (Leggett et al., 2013). Thus, host species infected with specialist parasites are typically more infected (higher prevalence and higher infection intensity) than the most infected host for a generalist parasite (Park et al., 2025, but see Hellgren et al., 2009). Interestingly, we did not clearly observe this pattern in our system. Bd obtained its highest fitness at different times of the year on five different, distantly related amphibian species (e.g. caudates and anurans), suggesting weak phylogenetic constraints. Overall, this suggests that the benefits Bd gains through generalism by mitigating the negative effects of temporal fluctuations on its overall fitness offsets the negative effects of less than optimally exploiting a particular species. An exciting future direction is to rigorously examine the conditions under which temporal heterogeneity in host abundance and competence in multi‐host communities can favour the evolution of generalist life‐history strategies for parasites.

We also saw notable spatial heterogeneity among our four communities in terms of (i) the temporal dynamics of host abundance, host competence and Bd fitness and (ii) the overall strength of Bd persistence. The goal of this study was not to describe why we saw temporal and spatial heterogeneity in prevalence, intensity and abundance, but rather to understand the dynamical consequences of this variability for Bd persistence. That being said, there were some notable differences in the abiotic (e.g. pH and dissolved oxygen) and biotic conditions (community composition) among sites that were likely contributing to site‐level differences in the capacity for Bd persistence, $R_{0,T}$ (Figures S4–S6; Chew et al., 2024). Linking the modelling approach developed here with temporally fluctuating abiotic variables such as temperature could provide more mechanistic insight into site‐level differences in parasite persistence capacity, $R_{0,T}$.

Despite among sites differences in $R_{0,T}$, the relative contributions of species to Bd dynamics within sites were largely consistent across sites. Most notably, when eastern newts were present they tended to have the highest integrated contributions across the year and were predicted to be the dominant maintenance species, followed by green frogs and bullfrogs. These results parallel recent lab results from DeMarchi et al. (2026). Using exposure experiments, DeMarchi et al. found that eastern newts and bullfrogs were the most competent species (but through different mechanisms), while green frogs were less competent. While our study consistently showed that eastern newts had the highest contributions to Bd fitness in multi‐host communities, the model also predicted that green frogs had higher contributions to Bd persistence than predicted by competence alone. This discrepancy between the field and laboratory results was because of host density—the high abundance of green frogs (particularly relative to bullfrogs) made them notable contributors to Bd persistence relative to other species in the community (e.g. similar to Streicker et al., 2013). In amphibian‐Bd systems in particular, where Bd prevalence and intensity are relatively easy to measure, less effort is often put into rigorously estimating host density (e.g. Grear et al., 2025; Wilber, Ohmer, et al., 2022). Host density is essential for understanding parasite persistence in temporally variable and stable systems, and should be a standard quantity collected in amphibian‐Bd surveillance.

A major impetus for quantifying the seasonal contributions of species to parasite persistence is to identify targeted seasonal or species‐level control strategies. Control of particular species (MacInnes et al., 2001) or transmission in particular seasons (Grassly & Fraser, 2006) can be highly effective for disease control. The relative efficacy of species control compared to temporal control can be largely predicted by three simple criteria. First, if there is strong inequality in how species are contributing to parasite persistence, where one species dominates, species control will be more effective than temporal control. Second, if there is relative equality in how at least a few species are contributing to parasite persistence and contributions are temporally variable and asynchronous, then the most efficient temporal control will be approximately equivalent to species control. Third, if there is relative equality in how a few species are contributing to parasite persistence and contributions are temporally variable and synchronous, then the most efficient temporal control will be more effective than species control. These criteria are intuitive but, prior to the development of this model, were difficult to tractably assess in seasonal, multi‐host systems.

Our model provides two key advances that allow us to assess these criteria and rigorously evaluate parasite control strategies. First, our model quantifies the magnitude of temporal variability and (a)synchrony in species' maintenance potential through time. Critically, simply observing seasonal variability in density, intensity, prevalence or space use in isolation is not sufficient to make statements about seasonal variability in a species' maintenance potential (i.e. $R_{0,s}\left(\tau \right)$). Rather, our model shows that it is the integration of these data streams among multiple species and the accounting of key time‐lags within and among species that allows us to extract estimates of $R_{0,s}\left(\tau \right)$. Second, by providing a recipe to directly calculate $R_{0,T}$ and $R_{0,s,T}$ from trajectories of $R_{0,s}\left(\tau \right)$, we can quantify the degree of parity in species contributions to parasite persistence, integrated across each species' temporal variability. Applying this approach to our study, we found both inequality (e.g. newts in Hastie) and equality but asynchrony (e.g. bullfrogs and green frogs in Woodlot) in species contributions, such the species control was generally more effective or as effective compared to temporal control. We note that our simulated control focused on transmission reduction—which in practice might look like setting up drift fences or seining ponds for periods of the year to temporarily remove amphibians from the aquatic habitat—but other forms of control could also be explored. For example, simulated control focussed on reducing infection intensity—which in practice could be achieved through anti‐fungal treatments in amphibian‐Bd systems (Knapp et al., 2022)—would not only reduce transmission by reducing shedding, but would also increase loss of infection rates, further impacting species' time‐varying contributions to Bd persistence. Our model provides a theoretically grounded and empirically tractable approach to explore these different temporal control strategies and their effects on parasite persistence.

An important unknown in our model was the interspecific to intraspecific transmission ratio ${\omega }_{\mathit{si}}$. An assumption in many previous multi‐host amphibian‐Bd models was that host species share a zoospore pool (Wilber et al., 2020). However, a shared zoospore pool assumption may not always be appropriate (Byrne et al., 2022). If ${\omega }_{\mathit{si}}$ was largely determined by host spatial overlap—which would be exactly true given perfect mass action transmission dynamics, equal infectivity of zoospores from species $i$ to species $j$, and limited zoospore movement—we found that our conclusions about who was driving Bd persistence were largely robust to ${\omega }_{\mathit{si}}$ between our empirically estimated values of 0.44 to 1. However, when ${\omega }_{\mathit{si}}<0.3$ our communities transitioned to facultative multi‐host communities (Fenton et al., 2015), with temporal control becoming increasingly effective relative to species‐level control. That being said, for the three primary species contributing to Bd dynamics in our system—newts, green frogs and bullfrogs—there are three reasons we think that interspecific transmission is significant. First, spatial overlap of these species was substantial, with median ${\omega }_{\mathit{si}}=0.92$. Second, our observations in the field showed that individuals of these species could sometimes be literally on top of each other (Figure S7). Finally, we know from experiments that these three species can all be infected with the same strain of Bd (DeMarchi et al., 2026). Taken together, these lines of evidence support the potential for high interspecific transmission and the presence of spillover and obligate multi‐host enzootic dynamics that we predict from our model.

Our model is broadly applicable to multi‐host, seasonal systems but has limitations and possible extensions not considered here. First, rarely can all species or life stages contributing to parasite persistence be sampled. In this study, we did not sample larval amphibians. For some species, high tadpole densities could significantly affect the species contributions to community‐level Bd dynamics (Hollanders et al., 2024, but see Wilber, Ohmer, et al., 2022 and Blaustein et al., 2020). While we are currently exploring the importance of tadpoles in our study system, the relative quantities of $R_{0,s}\left(\tau \right)$ produced by our model are robust to the exclusion of missing species or life stages as ${\omega }_{\mathit{si}}$ approaches one (Appendix S1.2). However, users of this model should use discretion when interpreting absolute $R_0$ values from incompletely sampled communities. Second, parameterization requires seasonal data streams on at least abundance, prevalence and intensity. Repeated samples of multi‐host communities can be challenging, thus parameterizing our model in other host–parasite systems may sometimes be difficult. Redistributing effort typically put into spatial replication (many multi‐host communities are sampled only once per year, e.g. Stutz et al., 2018) into temporal replication (fewer communities sampled more intensively through time) could be fruitful for answering novel questions regarding parasite persistence and evolution in seasonal, multi‐host systems. Finally, while not considered here, our model can be extended to ask questions such as, how much is observed prevalence on a species at time $\tau$ driven by within‐species transmission compared to between‐species transmission? These extensions can provide direct links to management goals as well as testable predictions in the field, allowing for a data‐driven, model‐informed, and field‐tested understanding of pathogen persistence in seasonal multi‐host communities.

AUTHOR CONTRIBUTIONS

Sarah Schrock led the data collection, with contributions from Mark Wilber and Joseph DeMarchi. Sarah Schrock and Mark Wilber led the analyses and writing of the manuscript. All authors contributed substantially to the conceptualization of the project and revisions.

CONFLICT OF INTEREST STATEMENT

None.

Supporting information

Table S1. Site area and mean pond area by location.

Figure S1. Mean surface areas for species at different sites (± SE). The numbers below each bar give the number of individuals for each species that we weighed in the field and whose mass we then converted to surface area. The scaling relationships we used were surface area cm² = 13.1826 × mass (g)^0.6091 for anurans and surface area cm² = 8.42 × mass (g)^0.694 for caudates (Klein et al., 2016; DeMarchi et al., 2026). We converted the observed average body mass of each species at each of our sites to surface area and then scaled shedding rate as λ _s (τ) ∝ exp(x _s (τ)) × Average surface area _s . Only relative values of λ _s (τ) are needed for Equation 2 in the main text.

Figure S2. Site‐ and species‐varying load‐dependent loss of infection rates ν _s (τ). Loss of infection rates were estimated by applying Equation S7 to observed seasonal trajectories of Bd infection intensities x _s (τ) and then converting to a daily rate.

Figure S3. (a, c) The percent reduction in R _0,T given control of a particular species. Bars indicate the mean across all sites where a species was present and different shapes show the site‐level changes for particular species. Large shapes indicate that the control was sufficient to reduce R _0,T  < 1 and small shapes indicate that R _0,T  > 1 following control. Panel (a) shows results for ω _si  = 1 and (c) shows results for ω _si  = 0.5. The statistics show the Kruskal‐Wallis (KW) test results comparing whether there was a significant difference in rank reductions in R _0,T among species. (b, d) The percent reduction in R _0,T given a 120‐day control where transmission is prevented from every species in the 120‐day time interval. The time point on the x‐axis gives the mid‐point of the 120‐day control. Different colours show different sites. Thick lines show where a temporal control reduced R _0,T  < 1 and thin lines indicate where R _0,T  > 1 after control. Inset plots in (b, d) show the maximum reduction in R _0,T with species control compared to the maximum reduction in R _0,T with temporal control. A value greater than 1 indicates that species control is more effective than temporal control. A 120‐day temporal control would have equivalent effects on R _0,T to a species‐level control if three species in the community had the same R _0,s,T and were completely asynchronous in their species‐level R _0,s (τ) values.

Figure S4. Pond pH throughout the year (a) Woodlot (b) Lotus, (c) Complex, and (d) Hastie.

Figure S5. Pond percent dissolved oxygen throughout the year (a) Woodlot (b) Lotus, (c) Complex, and (d).

Figure S6. Pond temperature (C) throughout the year at (a) Woodlot, (b) Lotus, (c) Complex, and (d) Hastie.

Figure S7. Picture of a male green frog (Rana clamitans) attempting to amplex a female bullfrog (Rana catesbeiana) at our Hastie site. Beyond this extreme behaviour, bullfrogs and green frogs were regularly found in close proximity at our sites.

Figure S8. Plot of the temporal sampling at each of our four focal sites used in this study. Primary sampling was done in 2023 and 2024, starting in February and ending in October or November. Temporal clusters of points represent both VES surveys and amphibian captures which together defined a sampling event. There were 7–9 sampling events per site per year in 2023–2024 (note the 7–9 clusters of points per year in 2023 and 2024). Additional sampling was done in 2022 to establish the viability of sites for the study. A total of 18 unique sites were surveyed in eastern Tennessee (not shown here) from which our four focal sites were selected based on the criteria specified in Appendix S2.

Schrock, S. A. R. , DeMarchi, J. A. , Gardner, B. J. , Gray, M. J. , Ohmer, M. E. B. , & Wilber, M. Q. (2026). Spillover dynamics and asynchronous temporal fluctuations in host density and competence drive fungal parasite persistence in multi‐host, seasonal communities. Journal of Animal Ecology, 95, 2104–2118. 10.1111/1365-2656.70333

DATA AVAILABILITY STATEMENT

Data and code available from Zenodo https://doi.org/10.5281/zenodo.21224592 (Schrock et al., 2026).