key: cord-0828008-vhdzgdnn authors: Buhnerkempe, Michael G.; Prager, Katherine C.; Strelioff, Christopher C.; Greig, Denise J.; Laake, Jeff L.; Melin, Sharon R.; DeLong, Robert L.; Gulland, Frances M.D.; Lloyd‐Smith, James O. title: Detecting signals of chronic shedding to explain pathogen persistence: Leptospira interrogans in California sea lions date: 2017-04-03 journal: J Anim Ecol DOI: 10.1111/1365-2656.12656 sha: cec4532414e43295bce63c118492705f09304ab4 doc_id: 828008 cord_uid: vhdzgdnn 1. Identifying mechanisms driving pathogen persistence is a vital component of wildlife disease ecology and control. Asymptomatic, chronically infected individuals are an oft‐cited potential reservoir of infection, but demonstrations of the importance of chronic shedding to pathogen persistence at the population‐level remain scarce. 2. Studying chronic shedding using commonly collected disease data is hampered by numerous challenges, including short‐term surveillance that focuses on single epidemics and acutely ill individuals, the subtle dynamical influence of chronic shedding relative to more obvious epidemic drivers, and poor ability to differentiate between the effects of population prevalence of chronic shedding vs. intensity and duration of chronic shedding in individuals. 3. We use chronic shedding of Leptospira interrogans serovar Pomona in California sea lions (Zalophus californianus) as a case study to illustrate how these challenges can be addressed. Using leptospirosis‐induced strands as a measure of disease incidence, we fit models with and without chronic shedding, and with different seasonal drivers, to determine the time‐scale over which chronic shedding is detectable and the interactions between chronic shedding and seasonal drivers needed to explain persistence and outbreak patterns. 4. Chronic shedding can enable persistence of L. interrogans within the sea lion population. However, the importance of chronic shedding was only apparent when surveillance data included at least two outbreaks and the intervening inter‐epidemic trough during which fadeout of transmission was most likely. Seasonal transmission, as opposed to seasonal recruitment of susceptibles, was the dominant driver of seasonality in this system, and both seasonal factors had limited impact on long‐term pathogen persistence. 5. We show that the temporal extent of surveillance data can have a dramatic impact on inferences about population processes, where the failure to identify both short‐ and long‐term ecological drivers can have cascading impacts on understanding higher order ecological phenomena, such as pathogen persistence. With the continued burden of infectious diseases around the world, understanding the mechanisms underlying pathogen persistence is essential to inform disease control and wildlife conservation efforts Tompkins et al. 2015; Plowright et al. 2016) . Classically, the potential for pathogen persistence within a host population has been defined by the critical community size, which is the number of susceptible individuals necessary to maintain unbroken chains of transmission within a population more often than not (Bartlett 1960) . However, more recent studies have shown that the relationship between host population size and pathogen persistence may be modified by other processes, such as spatial structure [e.g. phocine distemper virus (Swinton et al. 1998)] and indirect transmission via vectors [e.g. plague (Buhnerkempe et al. 2011b) ] or environmental reservoirs [e.g. avian influenza Rohani et al. 2009)] . Similarly, chronic shedding of the pathogen by a subset of infected hosts may allow for pathogen persistence (Monack, Mueller & Falkow 2004) , but parsing the role of chronic shedding remains a challenge in disease ecology Plowright et al. 2016) . Although some pathogens such as hepatitis B virus (Edmunds et al. 1993) nearly always result in long-term infections, there is greater uncertainty regarding the role of chronic shedding in persistence of pathogens that can cause either acute, clinical illness or chronic, asymptomatic infection [e.g. feline coronavirus in cats (Foley et al. 1997) , Leptospira spp. in domestic animals (Adler & de la Peña Moctezuma 2010) and Salmonella Typhi in humans (Gonzalez-Escobedo, Marshall & Gunn 2011)]. Such pathogens can cause conspicuous short-term outbreaks that are dominated by acute infections and are often followed by refractory periods where observable infection is rare and disease fadeout is more likely; these refractory periods are also known as inter-epidemic troughs (Lloyd-Smith et al. 2005; Grassly & Fraser 2006) . In these scenarios, chronic shedders could act as an endogenous bridging mechanism between outbreaks [i.e. infection persists without being reintroduced (Buhnerkempe et al. 2011b) ]. However, detecting and assessing the role of chronic shedding using population surveillance data are hampered by several challengestime-scale of surveillance, low prevalence and/or intensity of chronic shedding, case underreporting and interacting signals of epidemic drivers (Plowright et al. 2016) . First, surveillance data are often confined to single outbreak events, which deviate from the mechanistic time-scale inherent in signatures of persistence drivers ). Thus, the duration of surveillance is likely to have profound effects on any inference made Lessler et al. 2015) , especially about chronic shedding. Additionally, chronic shedders may have reduced infection loads leading to lower pathogen-shedding intensities (Leonard et al. 1992; Pathak et al. 2010 ), or, for many host-pathogen systems, most hosts experiencing acute illness recover and eliminate the pathogen rather than becoming chronic shedders (Monack, Mueller & Falkow 2004; Pathak et al. 2010) . Either common, low-intensity chronic shedders or rare, high-intensity chronic shedders may have subtle but significant impacts on disease dynamics and management, but distinguishing between these scenarios is problematic. These inference problems are exacerbated by the universal problem of incomplete case reporting. Asymptomatic cases, whether acute or chronic, will be underreported in conventional data streams that rely on detection using obvious signs of infection (Lessler et al. 2015) . Without observing these individuals directly, signatures of chronic shedding may be detected via their influence on patterns of overtly ill individuals. Short-term epidemic drivers can further complicate inference about the presence of chronic shedders and their role in persistence. Specifically, seasonal transmission and contact patterns have been recognized as important drivers of seasonal outbreaks (Altizer et al. 2006; Grassly & Fraser 2006) . Similarly, seasonal reproduction can drive outbreaks and affect pathogen persistence through pulsed recruitment of new susceptible individuals (Peel et al. 2014) . The focus on short-term outbreak mechanisms, however, largely ignores the mechanisms that operate during inter-epidemic troughs to enable pathogen persistence. Interactions between short-term drivers, such as seasonal transmission and susceptible recruitment, and long-term drivers, such as chronic carriage, will be key to understanding persistence (Lloyd-Smith et al. 2005; Breban et al. 2009; Rohani et al. 2009; Brown et al. 2013) . Discerning the signal of chronic shedders operating in inter-epidemic troughs from epidemic drivers operating through multiple epidemic cycles remains a challenge in wildlife systems [(Lloyd-Smith et al. 2005; Buhnerkempe et al. 2015) , although research has progressed on the related problem of environmental reservoirs Rohani et al. 2009; Brown et al. 2013) ]. As a case study in addressing the above challenges, we use leptospirosis in California sea lions (Zalophus californianus). Leptospirosis, caused by spirochetes of the genus Leptospira that are transmitted primarily via urinary shedding (either directly or indirectly through environmental contamination), is a disease of global concern and affects most mammals including humans (Levett 2001; Bharti et al. 2003) . In 1970, Leptospira interrogans serovar Pomona was identified as the cause of a large stranding event in California sea lions where high numbers of sick or dead sea lions were observed on the coast of California and Oregon (McIlhattan et al. 1971; Vedros et al. 1971) . Surveillance in stranded sea lions has revealed yearly leptospirosis outbreaks occurring between July and December since at least 1984 ( Fig. 1 ; Gulland et al. 1996; Lloyd-Smith et al. 2007 ). These outbreaks follow shortly after the recruitment of susceptible yearlings to the coastal population, which occurs following weaning in the spring, and coincide with altered mixing patterns linked to seasonal migrations in late summer and fall (Fig. S1 , Supporting Information; Gulland et al. 1996; ). Genetic analyses of circulating Leptospira strains have revealed that strains isolated from California sea lions are distinct from other known strains of L. interrogans serovar Pomona, indicating that repeated spillovers from other hosts are unlikely to have driven such patterns and that Leptospira has persisted enzootically in this population for at least 30 years (Zuerner & Alt 2009 ). The mechanisms underlying this enzootic persistence are unclear, but chronic shedding has been hypothesized as important (Gulland et al. 1996; Lloyd-Smith et al. 2007) . Shedding by asymptomatic individuals has been demonstrated, and this shedding can last for 12 weeks and potentially longer (Dierauf et al. 1985; Prager et al. 2013 Prager et al. , 2015 . With asymptomatic shedders, a long history of disease surveillance, and seasonality in both transmission and susceptible recruitment, the sea lion/leptospirosis system provides a unique opportunity to assess chronic shedding as a mechanism of pathogen persistence in wildlife, and to highlight challenges researchers may face conducting similar assessments in other systems. Here, we assess the predicted role of chronic shedding in the transmission dynamics of Leptospira infection in California sea lions. We show that chronic shedding can enable Leptospira persistence within this host population, but the ability to detect signatures of chronic shedding is complicated by the time-scale of surveillance data and trade-offs among duration, prevalence and intensity of chronic shedding. Finally, we show how seasonal susceptible recruitment and seasonal transmission combine with chronic shedding to create observed seasonal patterns in incidence. To do this, we use knowledge of sea lion demography and Leptospira biology to build mechanistic models of pathogen spread. We fit these models to leptospirosis surveillance data from stranded sea lions using recent advances in model fitting for partially observed incidence time series and use simulations to study persistence. We used stranding data collected by The Marine Mammal Center (TMMC, Sausalito, CA, USA) from 1984 to 2012 (collection methods described elsewhere; Gulland et al. 1996; Lloyd-Smith et al. 2007 ). The TMMC stranding range includes the central and northern California coast (Fig. S2 ). This range is determined by jurisdictional boundaries (counties in California) rather than by animal distribution, and it covers the central portion of the migratory range of a genetically distinct population of California sea lions, the Pacific Temperate population, that extends from the US-Mexico border into Canada and Alaska ( Fig. S2 ; Schramm et al. 2009 ). The Pacific Temperate population of California sea lions give birth and breed on the California Channel Islands in June and July. Adult females then nurse a pup for 10-12 months and remain associated with the rookery islands throughout the year (Fig. S1 ). Although some juveniles (i.e. yearlings to 4 years old) remain around rookery islands, most males and non-breeding females this age migrate north to the central California coast in fall and overwinter there. Subadult and adult males migrate north from the rookeries following the breeding season and overwinter in coastal waters from central California to British Columbia, returning south in the spring. Thus, juveniles and non-nursing adult females are the age classes primarily found in the TMMC stranding range outside the breeding season, with subadult and adult males passing through the range in the autumn and spring on their north and south migrations. Infection with L. interrogans serovar Pomona in this population exhibits clear, yearly outbreaks in the fall during northward migration, typically peaking from July to December. Evidence of leptospirosis is rarely observed outside this outbreak season, including in animals returning from north of the TMMC stranding range in the spring (Figs S1 and S2; Gulland et al. 1996; Greig, Gulland & Kreuder 2005; Lloyd-Smith et al. 2007) or in pups and females inhabiting the rookery islands year-round south of the stranding range (Figs S1 and S2; R.L. DeLong, unpublished data); available data thus indicate that seasonality in leptospirosis-induced strandings reflects the true seasonality of infection in this system. In addition, leptospirosis outbreaks have exhibited clear 3-5 year cycles that are reflected in data from stranded sea lions (Gulland et al. 1996; Greig, Gulland & Kreuder 2005; Lloyd-Smith et al. 2007) . Changes in climatic and oceanographic conditions, such as El Niño events, impact sea lion demography (Weise, Costa & Kudela 2006; Melin et al. 2010 Melin et al. , 2012 and may also impact the survival of leptospires (Johnson & Harris 1967) . The impacts of changing environmental conditions on both sea lions and Leptospira are expected to alter periodicity in the system (Gulland et al. 1996) . Deviations from the regular cyclic pattern are particularly noteworthy during the late 1990s (around the historically strong El Niño event of 1997-1998) when relatively large outbreaks were observed annually for Fig. 1 . Weekly strands of California sea lions due to leptospirosis. Highlighted regions indicate the four stranding eras over which models were fit (grey boxes; 1984-1987, 1988-1991, 1991-1994 and 2004-2007) . Note that the eras from 1995-1997, 2000-2003 and 2009-2011 , while qualitatively similar to the four eras specified above, are not considered because they are preceded by relatively large outbreaks so the criterion of initial population susceptibility is not satisfied. [Colour figure can be viewed at wileyonlinelibrary.com] several years (Fig. 1) . Because we are focused on intrinsic disease drivers, large environmental perturbations may obscure signals of these drivers and are beyond the scope of this study. Hence, we focused on four 2Á5-year eras in the stranding record that are typical of the regular cyclic patternan isolated large outbreak (i.e. not preceded by another large outbreak) followed by two smaller outbreaks (1984 -1987 , 1988 -1991 , 1991 -1994 -2007 Fig. 1) . Here, the large first outbreak depletes the susceptible pool, increasing the likelihood of post-epidemic fadeout and maximizing the potential to detect signatures of chronic shedders as a persistence mechanism. Weekly data for all stranding eras began on 17 June of the first year specified to fully capture the initial outbreak for each stranding era. Data available from the Dryad Digital Repository: https://doi.org/10.5061/dryad.j15ns (Buhnerkempe et al. 2017). To study chronic shedding in this system, we used a discrete-time, stochastic model with weekly time steps that was based on a continuous-time process model and simulated using the Euler-Maruyama method implemented in the POMP package King, Nguyen & Ionides 2016) in R statistical software version 3.1 (R Development Core Team 2014). Here, a susceptible (S)exposed (E)acutely infected (I)recovered (R) model was modified to incorporate progression from acute to chronic shedding (C; eqns 1-8). To avoid confounding effects between chronic infection and over-dispersed acute infectious periods, we divided the acutely infected period into four stages (I 1 -I 4 ; eqns 3-6) so the acute infectious period was gammadistributed (Conlan et al. 2010) . State variables and parameters are described in Table 1 . We assumed transmission is frequency-dependent (based on the total population N) similar to phocine distemper in harbour seals (Swinton et al. 1999) . Chronic shedders were a fraction, 00Á7 (results not shown), and with the proportion of sea lions that were seronegative for anti-Leptospira antibodies in July of 2004 (0Á77 among those stranding for reasons other than leptospirosis), the only stranding era for which we have randomly sampled serology data (Lloyd-Smith et al. 2007). Results were qualitatively similar for lower initial proportions of susceptible individuals (S(0) = 0Á5; results not shown). We used maximum likelihood to estimate disease parameters that were not fixed based on independent data (Table 1 ). To calculate model likelihoods, the stranding time series was linked to model outputs through an observation process depending on disease severity. Individuals stranding due to clinical leptospirosis are typically severely ill with 60-70% mortality in rehabilitation despite receiving supportive clinical care (Gulland et al. 1996) . We assumed that without clinical care, these severely ill animals would die in the wild. Thus, we linked disease-induced stranding to the modelled flux of sea lions dying due to leptospirosis. We included a parameter for the proportion, p obs , of individuals dying due to leptospirosis that are observed as a strand, and used a partially observed Markov process model to account for this observation process. The model was fit to weekly counts of leptospirosis strands using a multiple iterated filtering algorithm to find the maximum likelihood across parameter space, including 50 random start values for the free parameters ( Initial fraction of the population that was susceptible 0Á8 E(0) Initial fraction of the population that was exposed 0Á0025 I 1 (0), I 2 (0), I 3 (0), I 4 (0) Initial fraction of the population that was in each of the four acute infection stages 0Á001 C(0) Initial fraction of the population that was chronically infected 0Á005 R(0) Initial fraction of the population that was recovered and immune to infection 0Á1885 N Initial fraction of the population that was exposed 0Á0035 I 1 (0), I 2 (0), I 3 (0), I 4 (0) Initial fraction of the population that was in each of the four acute infection stages 0Á002 C(0) Initial fraction of the population that was chronically infected 0 q Proportion of acutely infected individuals that become chronically infected 0 CRchronic shedding and seasonal susceptible recruitment Tables S1-S4. (R Development Core Team 2014). For full details of settings (e.g. cooling schedules, number of particles, random walk standard deviation) used in the filtering algorithm, see Appendix S1. To provide the most complete analysis of the role of chronic shedding in this system, we began by fitting the CSR and SR models to the full 2Á5 years of surveillance data from the four stranding eras. challenges in detecting signatures of chronic carriage We expect that inference on the importance of chronic shedding for pathogen persistence will depend critically on the duration of disease surveillance. We thus fit CSR and SR to all four stranding eras over three surveillance durations: 2Á5, 1Á5 and 0Á5 years, which capture three, two and one outbreaks respectively. Within each stranding era/surveillance duration combination, we compared models using the Akaike information criterion (AIC), which rewards model fit while penalizing model complexity (Burnham & Anderson 2003) . We compared the probability of Leptospira persistence predicted by each best-fit model. Persistence was assessed using the proportion of 100 stochastic simulations where the disease was maintained after 30 years (the minimum observed persistence time in this population). It is also desirable to characterize the prevalence, intensity and duration of chronic shedding, but distinguishing among these properties is challenging. To explore this issue, we jointly varied the probability of becoming chronically infected, q, the rate at which chronic shedders recover, d, and the relative transmission intensity of chronic shedders, e, over the possible ranges of values for these parameters, while leaving all other parameters at their maximum likelihood estimates, using model CSR fit to the full 2Á5 years of data from 1984 to 1987. We calculated the likelihood of these parameter sets to determine the likelihood surface for the parameters related to chronic infection. Interactions between chronic shedding and seasonal epidemic drivers, such as seasonal transmission and seasonal susceptible recruitment, may be important for persistence across interepidemic troughs, but the primary drivers of seasonality in our system are poorly understood. To probe these relationships, we formulated two additional models -'CR', which removed seasonal transmission by assuming constant transmission throughout the year, and 'CS', which removed seasonal susceptible recruitment by assuming that recruitment occurs at a constant level throughout the year while requiring annual susceptible recruitment to be equivalent to the seasonal model (Table 1) . Predictions from the full model with chronic shedders, seasonal transmission and seasonal susceptible recruitment (CSR) closely mirrored the pattern of leptospirosis strandings observed in California sea lions (Figs 2a and 5) . The force of infection during outbreak seasons was dominated by transmission from acute infections (Fig. 2a, b) . During inter-epidemic troughs, transmission from acute infections decreased markedly (Fig. 2b) , and chronic shedders became much more important (Fig. 2c) . Even though total transmission from chronic shedders was low throughout the year (Fig. 2b) , the presence of sustained transmission during inter-epidemic troughs has potential to impact long-term dynamics by creating a stable reservoir of chronic shedders. Although not predictive of actual strandings, simulations (using parameters fit to the 1984-1987 era) showed that this mechanism could enable persistent pathogen circulation over a 30-year time span (Fig. 2d) . Furthermore, in all stranding eras (1984-1987, 1988-1991, 1991-1994 and 2004-2007) , CSR was clearly preferred over the model without chronic shedding (SR); the preferred model, CSR, predicted persistence in all simulations when the models were fit to data spanning multiple outbreak cycles (i.e. 2Á5 years of data; Fig. 3 ; Tables S1-S4). Inference on the importance of chronic shedding depended strongly on the surveillance duration used (Fig. 3) either 2Á5 years (multiple outbreaks and interepidemic troughs), 1Á5 years (two outbreaks with a single inter-epidemic trough) or 0Á5 years (one outbreak and no inter-epidemic trough). The CSR model was preferred by AIC with 2Á5 and 1Á5 years of surveillance data across all stranding eras (Fig. 3b , Tables S1-S4). However, with only 0Á5 years of surveillance, model SR was preferred across all stranding eras (Fig. 3b , Tables S1-S4). The effect of surveillance duration on predicted persistence was even more striking (Fig. 3c , Tables S1-S4). With 2Á5 or 1Á5 years of data, simulations of CSR with parameters fit to any stranding era generated persistence of Leptospira in greater than 98% of simulations (Fig. 3c , Tables S1-S4). However, when parameterized to 0Á5 years of surveillance data (i.e. no inter-epidemic trough), simulations of this same model failed to generate persistence when fit to two of the four stranding eras (1988 ( -1991 ( and 1991 ( -1994 . In these instances, the inferred parameter values governing chronic shedding rendered this mechanism negligible (Tables S2-S3) , and the persistence behaviour of CSR more closely resembled that of SR, which failed to generate meaningful persistence at any surveillance duration (Fig. 3c , Tables S1-S4). The estimated probability of becoming a chronic shedder (q), and the estimated intensity (e) and duration of chronic shedding (d) were variable across model fits (Tables S1-S4), pointing to challenges with identifiability in these quantities. The likelihood space for these parameters revealed several patterns (Fig. 4) . First, if chronically infected individuals are assumed to be common (Fig. 4a) , chronic shedding intensity must be very low (0Á3-1% of acute shedding intensity) with a mean chronic shedding duration longer than 30 weeks to achieve high model likelihoods. If chronic shedding is less common (Fig. 4b) , chronic shedding intensity has to increase to compensate (10-30% of acute shedding intensity), and the mean duration of chronic infections has to span a year or more for high model likelihoods. If chronic infections are extremely rare (Fig. 4c) , chronic shedding intensity still has to be 10-30% of acute shedding intensity but now mean durations must be considerably longer (2 years or more) to achieve high model likelihoods. Identifying important seasonal drivers was critical to fully understanding the role of chronic shedding in the system (e.g. does chronic shedding link periods of elevated susceptible supply or does it just bridge over seasons of low transmission?). In all four stranding eras, models with seasonal transmission were preferred by AIC, whether or not they had seasonal susceptible recruitment (Fig. 5 , Tables S1-S4). The model lacking seasonal transmission (CR) was generally not able to capture the second and third seasonal stranding peaks (Fig. 5a,b,d) , and fit reasonably only in 1992-1993 when these peaks were much less pronounced (Fig. 5c) . This inability to fit the data arose from the less pronounced cycles in acute infections in the model including only seasonal susceptible recruitment (CR; Figs S5b-S8b). In contrast, the model lacking seasonal susceptible recruitment (CS) was either preferred outright or indistinguishable from CSR using data from 1984 -1987 , 1988 -1991 -2007 and generated large, persistent, seasonal fluctuations in acute infections (Figs S5c-S8c ). In addition, although the probability of long-term persistence was largely unchanged with the removal of either seasonal driver (Tables S1-S4), preferred models (either CSR, CS or both) generated a large, persistent reservoir of chronically infected individuals in the long term (Figs S5-S8 ). This reservoir contrasted with the declining influence of chronic shedding in non-preferred models (CR) over a 30-year period (Figs S5-S8 ). Chronic shedding by asymptomatic individuals remains an oft-cited but relatively understudied mechanism driving pathogen persistence in wildlife disease systems. Although chronic shedding is readily observed in longitudinal studies of individuals, identifying it in cross-sectional disease surveillance data is difficult. We have shown that the role of chronic shedding can be characterized if: (i) observation occurs over at least two outbreak seasons including the intervening inter-epidemic trough; (ii) specific inference about the prevalence, intensity or duration of chronic shedding is not required; and (iii) the analysis DAIC in panel b) . In all panels, colours denote the stranding era: 1984-1987 (green), 1988-1991 (blue), 1991-1994 (orange) and 2004-2007 (red) . Fig. 4 . Likelihood space for chronic shedding parameters. Using the estimated parameter values for the CSR model fit to the 1984-1987 stranding era with 2Á5 years of surveillance data, the average duration of chronic infection (1/d) and the transmission efficiency of chronic shedding relative to acute shedding (e) were varied, and the log-likelihood of the parameters was recalculated. This was done for three values of the probability of becoming a chronic shedder (q), (a) 1, (b) 0Á01 and (c) 0Á0001. Log-likelihood ranges from high (white) to low (dark grey). The contour line gives the 99% confidence region for a likelihood ratio test when all parameters except for the three chronic shedding parameters are fixed. We note that this is not a true profile confidence region due to computational constraints and is meant to be only illustrative. accounts for interactions with short-term epidemic drivers. For leptospirosis in California sea lions, we have demonstrated that chronic shedding has the potential both to describe the observed patterns in strands and to drive long-term persistence of Leptospira in this population (Figs 2 and 3) . The apparent importance of chronic shedding to Leptospira persistence depended on the time-scale of observation. When fitting data from only a single outbreak, simpler models without chronic shedding were preferred (Fig. 3) . However, after observing just a single inter-epidemic trough, models with chronic shedding were strongly preferred, and these models predicted markedly higher probability of pathogen persistence (Fig. 3) . The recognition that inference about population dynamics depends on the time-scale of observation has gained traction in conservation biology and ecology more generally (Hastings 2010; Buhnerkempe et al. 2011a) but is not yet widely appreciated in disease ecology. We postulate that this is largely due to a historical focus on the basic reproduction number, R 0 (the expected number of secondary infections caused by a single infectious individual in a wholly susceptible population), which is typically estimated during initial invasion of a population or at a long-term steady state. R 0 alone is ill-suited to address the non-equilibrium dynamics occurring in inter-epidemic troughs that operate on intermediate time-scales and ultimately govern pathogen persistence (Grassly & Fraser 2006) . As we have demonstrated, observations and models must reflect the time-scales relevant to the ecological drivers being studied (Hastings 2010) . Clear identifiability issues between the properties of chronic shedding rendered it difficult to distinguish between signals of common low-intensity shedding and rare high-intensity shedding (Fig. 4) . Wild captures of apparently healthy California sea lions during a leptospirosis outbreak revealed that 39% of individuals were asymptomatic shedders, suggesting the possibility of relatively common chronic shedding (Prager et al. 2013) . However, surveys to detect changes in the proportions of symptomatic and asymptomatic shedders across seasons are needed to understand how fluctuations in the prevalence of chronic shedding impact persistence. Additionally, the best model fits indicated that mean chronic durations of a year or more were needed to promote persistence (Fig. 4) . This relatively long-lived infection is consistent with existing data, where sea lions were observed shedding leptospires for at least 12 weeks (Prager et al. 2015) or 22 weeks (Dierauf et al. 1985) ; however, the intensity and intermittency of chronic shedding are unknown for sea lions and most other species (Ellis 2015) . In this study, the reduced transmission coefficient for chronic shedders can represent either low-intensity, constant shedding or intermittent shedding following acute infection, but studies employing quantitative PCR approaches are needed to differentiate these scenarios in sea lions. As a point of comparison, Norway rats (Rattus norvegicus) in Brazil exhibit 84-88% prevalence of chronic shedding of L. interrogans serovar Copenhageni, shedding consistently and at relatively high levels, almost exclusively without symptoms (Costa et al. 2015) . These traits align Norway rats with the classical 'maintenance host' paradigm for Leptospira. Our findings suggest that California sea lions, by exhibiting dramatic outbreaks, high morbidity and mortality, and probably lower prevalence of chronic shedding, represent a different class of 'maintenance hosts' that still can enable population persistence of Leptospira. 1984-1987, 1988-1991, 1991-1994 and 2004-2007 stranding eras respectively. Models CSR (solid black line), CS (dotted red line) and CR (dashed blue line) were compared. Because of the importance of chronic infection over longer surveillance durations (Fig. 3) , all models were fit with 2Á5 years of stranding data. Preferred models for each dataset, as determined by Akaike information criterion (AIC) (Tables S1-S4), are shown above each panel. Simulations began on 17 June, and axis ticks marking the years occur on this date. Inference about chronic shedding depended on epidemic drivers such as seasonal transmission and seasonal susceptible recruitment. Models without seasonal susceptible recruitment generally could not be differentiated from the full model, indicating that pulsed susceptible introduction plays a smaller role in outbreak dynamics ( Fig. 5 ; Tables S1-S4). The relatively tight window for susceptible recruitment in our system is expected to increase the amplitude of oscillations in prevalence, and increase disease fadeout as a result (Peel et al. 2014) . However, the long life span of sea lions (c. 17 years for males and 20 for females) may combine with the potential for extended duration of chronic shedding to mute the impact of the susceptible pulse on the expected oscillatory behaviour (Peel et al. 2014) . We also assumed susceptible recruitment was associated with springtime weaning when pups join the coastal population. Individual variation in weaning time (Melin et al. 2000) or when pups first become at risk of leptospirosis could impact assessment of the role of seasonal susceptible recruitment. In contrast, models without seasonal transmission were strongly selected against, indicating that seasonal transmission strongly shapes outbreak patterns ( Fig. 5 ; Tables S1-S4). The probability of persistence was similar in the full model and models lacking either of the shortterm drivers, further implicating chronic shedding as the principal driver of persistence (Tables S1-S4) . Overall, our findings show that seasonal transmission is the predominant driver of seasonality in outbreaks of leptospirosis in California sea lions, while chronic shedding provides the bridge over periods when transmission was generally low (Fig. 2) . We modelled seasonal transmission phenomenologically without a specific mechanistic underpinning, but seasonal transmission is likely to be governed by migration patterns, geographic differences in haul-out substrates, and animal density and mixing patterns at haul-outs (Riedman 1990; ), all acting in concert with environmental changes. However, characterizing seasonality in this system is potentially limited by stranding data that only covers a portion of the migratory range of this population (Fig. S2) . Despite this potential limitation, we believe that the stranding data reflect true seasonality in the system given that the major age classes affected by leptospirosis [juveniles and subadults (Greig, Gulland & Kreuder 2005; Lloyd-Smith et al. 2007 )] remain within the TMMC stranding range following the outbreak season. Additionally, there is no evidence of different seasonal signatures outside the TMMC stranding range, including (i) extremely rare signs of current or recent infection amongst older age classes during their southward migration from north of the stranding range and (ii) extremely rare evidence of infection in pups in the US population (R.L. DeLong, unpublished data) that inhabit the rookery islands south of the stranding range year-round. These observations support the assumption that persistence via continuous chains of transmission between acutely infected individuals to the north or south of the TMMC stranding range is unlikely. However, because migration patterns and leptospirosis prevalence differ between age and sex classes (Dierauf et al. 1985; Gulland et al. 1996; Greig, Gulland & Kreuder 2005; Lloyd-Smith et al. 2007) , future field and modelling studies that account for sea lion demographic structure could elucidate the mechanisms underlying seasonal transmission. Our model also allows for a link between observed infections in the stranding record and total incidence in the population. In our system, the disease mortality rate, a, and the probability of observing a dying sea lion as a strand, p obs , together determine the probability that a new infection will be observed. Identifiability concerns between disease mortality and the observation probability make it difficult to tease apart the specific determinants of case observation (Fig. S9 ), but the combination of these two parameters yields a consistent probability of an infection resulting in an observed stranding event (3Á3 to 6Á3 of every 1000 infections stranding and being observed; Fig. S9 ). Because of the simplicity of our model, precise estimates of this probability are unlikely to be accurate, but qualitatively, we find that total incidence may be at least two orders of magnitude greater than the observed strandings. We did not explore potential seasonal variation in the probability of observing a strand, which could arise from seasonality in human visits to coastal sites or from sea lion migratory patterns that cause seasonal variation in the proportion of the population found within the TMMC range. However, seroprevalence data suggest that, at least during major outbreak years, Leptospira infection is likely widespread in the California sea lion population off the coast of the US, representing a significant reservoir of this zoonotic pathogen in the California coastal ecosystem (Lloyd-Smith et al. 2007) . The observed role of chronic shedding in Leptospira persistence is strikingly similar to that of environmental transmission in recurrent epidemics of avian influenza Rohani et al. 2009; Brown et al. 2013) . Environmental transmission also has a relatively small influence during outbreaks but even low levels of environmental contamination can serve to generate secondary outbreaks Rohani et al. 2009; Brown et al. 2013) . Environmental contamination can also play a role in the transmission of Leptospira (Levett 2001; Adler & de la Peña Moctezuma 2010) , and Leptospira DNA has been detected in urine-contaminated sand around stranded pinnipeds (Cameron et al. 2008 ). We did not account for this mode of transmission in the current model, but the long-term viability of leptospires detected at haul-out sites remains an open question (Cameron et al. 2008 ). In addition, persistence in wildlife disease systems can be achieved by spillover from alternate host reservoirs (Haydon et al. 2002) . Pathogenic Leptospira is known to infect many mammal species (Levett 2001 ; Adler & de la Peña Moctezuma 2010). This potential persistence mechanism was not incorporated in our model, because genetic typing of L. interrogans serovar Pomona has shown that all strains isolated from California sea lions are distinct from strains previously isolated from terrestrial species (Zuerner & Alt 2009 ). Our group and others are actively seeking to characterize Leptospira strains in the California coastal ecosystem, which will strengthen (or overturn) the evidence for no external reservoir, but existing evidence indicates that spillover from alternative hosts does not play an important role in disease dynamics in this sea lion population. Finally, transmission from spatially distinct subpopulations can support pathogen persistence. Sea lions in the California coastal ecosystem are thought to be a genetically distinct population that migrates through the TMMC stranding range during the year (Schramm et al. 2009 ). Evidence of Leptospira infection has been reported in another population of California sea lions further south on the Pacific coast of the Baja peninsula (Schramm et al. 2009 ), which may encounter our study population during its migration (particularly older males, which are likely to migrate northward following the breeding season). Currently available data on Leptospira diagnostics in the Baja population show different serologic response profiles (potentially indicating a different infecting strain) and demographic infection patterns (including evidence of infection in pups) that do not resemble patterns seen in our study population (Avalos-T ellez et al. 2016) . Further research is needed to identify the infecting strain in the Mexican population and to investigate possible connectivity or epidemiological interactions between these populations, to determine whether spatial coupling may contribute to pathogen persistence in this system. Although our work has shown that chronic shedding can provide a bridge over periods of low transmission, the processes that cause inter-annual variability in outbreak sizes remain unclear. Here, by assuming a large proportion of the population is initially susceptible entering each stranding era, we have chosen implicitly to focus on the build-up of susceptible individuals through reproduction as the primary driver of the observed large outbreaks (Gulland et al. 1996) . However, changes in transmissibility of Leptospira may also underlie variability in outbreak size with climatic and oceanographic conditions, such as El Niño events, potentially impacting sea lion condition or contact patterns (Weise, Costa & Kudela 2006) or survival of leptospires in the environment (Johnson & Harris 1967) . Accounting for these mechanisms explicitly in future work will allow for a fuller understanding of transmission dynamics in this system, but such work is unlikely to undermine the fundamental importance of chronic shedding for long-term persistence. Chronic shedding can be an important mechanism for pathogen persistence, but signals of chronic shedders in disease surveillance data can be cryptic. These signals are most easily detected from long-term surveillance datasets, which enable identification of short-term epidemic drivers alongside characterization of interactions between these short-term drivers and long-term drivers operating in inter-epidemic troughs. Longitudinal data from experimental infection or clinical studies have tremendous value for confirming the existence of chronic infections, and potentially to differentiate common low-intensity from rare high-intensity chronic shedding; this also provides unique opportunities to merge within-host models of disease progression with population models of disease transmission (Gog et al. 2015) . Continued development of approaches to study chronic shedding, from individual-and population-scale data, will provide insights on the persistence of specific pathogens and on the broader problem of the role of inapparent infections in disease dynamics. Details of electronic Supporting Information are provided below. Appendix S1. Details of POMP model fitting. Table S1 . Model selection results and parameter estimates for models fit to the 1984-1987 stranding era. Table S2 . Model selection results and parameter estimates for models fit to the 1988-1991 stranding era. Table S3 . Model selection results and parameter estimates for models fit to the 1991-1994 stranding era. Leptospira and leptospirosis Seasonality and the dynamics of infectious diseases Pathogenic Leptospira serovars in free-living sea lions in the Gulf of California and along the Baja California coast of Mexico The critical community size for measles in the United States Leptospirosis: a zoonotic disease of global importance The role of environmental transmission in recurrent avian influenza epidemics Dissecting a wildlife disease hotspot: the impact of multiple host species, environmental transmission and seasonality in migration, breeding and mortality The utility of transient sensitivity for wildlife management and conservation: bison as a case study Transmission shifts underlie variability in population responses to Yersinia pestis infection Eight challenges in modelling disease ecology in multi-host, multi-agent systems Data from: Detecting signals of chronic shedding to explain pathogen persistence: Leptospira interrogans in California sea lions Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach Detection of pathogenic Leptospira bacteria in pinniped populations via PCR and identification of a source of transmission for zoonotic leptospirosis in the marine environment Resolving the impact of waiting time distributions on the persistence of measles Patterns in Leptospira shedding in Norway rats (Rattus norvegicus) from Brazilian slum communities at high risk of disease transmission An epizootic of leptospirosis in California sea lions The influence of age on the development of the hepatitis B carrier state Animal Leptospirosis. Current Topics in Microbiology and Immunology: Leptospira and Leptospirosis Leptospira as an emerging pathogen: a review of its biology, pathogenesis and host immune responses Patterns of feline coronavirus infection and fecal shedding from cats in multiple-cat environments Seven challenges in modeling pathogen dynamics within-host and across scales Chronic and acute infection of the gall bladder by Salmonella Typhi: understanding the carrier state Seasonal infectious disease epidemiology A decade of live California sea lion (Zalophus californianus) strandings along the Central California Coast: causes and trends Leptospirosis in California sea lions (Zalophus californianus) stranded along the central California coast Timescales, dynamics, and ecological understanding Identifying reservoirs of infection: a conceptual and practical challenge Inference for dynamic and latent variable models via iterated, perturbed Bayes maps Differentiation of pathogenic and saprophytic leptospires I. Growth at low temperatures pomp: Statistical Inference for Partially Observed Markov Processes. Available at Statistical inference for partially observed Markov processes via the R package pomp Duration of urinary excretion of leptospires by cattle naturally or experimentally infected with Leptospira interrogans serovar hardjo Seven challenges for model-driven data collection in experimental and observational studies Should we expect population thresholds for wildlife disease? Cyclical changes in seroprevalence of leptospirosis in California sea lions: endemic and epidemic disease in one host species? Recent abundance of California sea lions in western Baja California, Mexico and the United States Isolation of Leptospira pomona from a naturally infected California sea lion Attendance patterns of California sea lion (Zalophus californianus) females and pups during the non-breeding season at San Miguel Island Unprecedented mortality of California sea lion pups associated with anomalous oceanographic conditions along the central California coast in 2009 Age-specific recruitment and natality of California sea lions at San Miguel Island, California Persistent bacterial infections: the interface of the pathogen and the host immune system Immune regulation of a chronic bacteria infection and consequences for pathogen transmission The effect of seasonal birth pulses on pathogen persistence in wild mammal populations Transmission or within-host dynamics driving pulses of zoonotic viruses in reservoir-host populations Asymptomatic and chronic carriage of Leptospira interrogans serovar Pomona in California sea lions (Zalophus californianus) Antibiotic efficacy in eliminating leptospiruria in California sea lions (Zalophus californianus) stranding with leptospirosis R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing The Pinnipeds: Seals, Sea Lions, and Walruses Environmental transmission of low pathogenicity avian influenza viruses and its implications for pathogen invasion Phylogeography of California and Gal apagos sea lions and population structure within the California sea lion Persistence thresholds for phocine distemper virus infection in harbour seal Phoca vitulina metapopulations Scaling of phocine distemper virus transmission with harbour seal community size. Ecologie Emerging infectious diseases of wildlife: a critical perspective Leptospirosis epizootic among California sea lions Movement and diving behavior of male California sea lion (Zalophus californianus) during anomalous oceanographic conditions of Variable nucleotide tandem-repeat analysis revealing a unique group of Leptospira interrogans serovar Pomona isolates associated with California sea lions Geographical dissemination of Leptospira interrogans serovar Pomona during seasonal migration of California sea lions We thank the volunteers and staff from The Marine Mammal Center who helped in sample collection from stranded sea lions, and the National Marine Mammal Laboratory for sharing demographic data. We also thank Aaron King and the Lloyd-Smith lab for useful discussions about this manuscript. This work was supported by the National Science Foundation ( Weekly numbers of leptospirosis strands for all four stranding eras can be found on the Dryad Data Repository: https://doi.org/10.5061/dryad.j15ns (Buhnerkempe et al. 2017) .