(a) Spatial and temporal distribution and intensity

The distribution and intensity of infection in reservoir hosts vary among individuals and among populations in space and time. This variation is driven by many within- and between-host factors, including host demography and movement, transmission rates, infectious periods and herd immunity. Below we describe the factors that influence spatial and temporal variation. In most instances, there is little a priori information to decipher the drivers of variation, and these knowledge gaps must be addressed with sampling (table 1).

When a pathogen first invades a population of hosts, transmission dynamics may be synchronized through the invasion process [9]. Such invasion dynamics may characterize West Nile virus and avian influenza H5N1 invasion in wild birds in the USA, or Zika virus invasion in marmosets (Callithrix species) in Brazil [10–12]. During this phase, the basic reproduction number, R₀, the average number of secondary infections generated over an individual's infectious period when infection is rare [13], is a powerful distillation of the efficiency of pathogen spread. Beyond the initial stage of pathogen invasion, however, R₀ does not capture all fundamental elements of pathogen dynamics that affect the distribution of infection in space and time. For example, a pathogen that produces an acute (short-lived) immunizing infection with high transmission and mortality rates might spread quickly through local host populations and then fade out, to be reintroduced after the pool of susceptible hosts is replenished. Such short-lived epidemics of Yersinia pestis in rats, for example, may explain the sporadic outbreaks of bubonic plague in humans in both fourteenth to sixteenth century Europe [14] and modern urban Madagascar [15]. By contrast, another pathogen with a comparable R₀, but a long infectious period and low transmission rate, may persist in the same population for long periods, eventually producing a spatially and temporally stable infection intensity as exemplified by Mycobacterium bovis in white-tailed deer (Odocoileus virginianus) in Michigan, USA [16].

Once a pathogen has established in the reservoir host populations, within-host factors (e.g. duration of infection within hosts) interact with the population dynamics, density and movement of reservoir hosts to determine the distribution of infection among hosts [17–19]. The intensity of infection within individuals is governed by immune responses and pathogen life history. Because individuals acquire immunity, they typically have higher pathogen loads during their first infection than during subsequent infections. For example, juvenile Rousettus aegyptiacus bats that excreted high levels of Marburg virus during their first infections were linked to spillover of the virus to humans in Uganda [20]. Similarly, pathogen burden and shedding rates can vary over the course of infection as a function of changes in the immune response, microbiome and pathogen distribution within the host tissues. Bank voles (Clethrionomys glareolus) infected with Puumala virus shed high titres of virus during the acute phase of infection and low titres during the chronic phase of infection [21]. Pathogen levels also can rise if host individuals are infected with multiple pathogens or are immunocompromised by physiological or environmental stress. Laboratory mice infected with both worms and bacteria, for example, shed more of both for longer than those infected with either pathogen in isolation [22], and bats (Pteropus alecto) are hypothesized to excrete zoonotic viruses during winter, when environmental stress drives reactivation of latent viruses [23–25], but not during summer, when food is abundant [26].

(a) Basic sampling principles

Designing a sampling strategy that identifies how pathogens are distributed in space and time is challenging. In particular, trade-offs between the spatial extent of sampling and intensity of sampling are ubiquitous. Sampling intensity should be informed by temporal and spatial variability in prevalence (the proportion of infected individuals in a population) and by spatial and temporal autocorrelation. In general, more sampling is required in more variable and less autocorrelated systems. The observed autocorrelation depends on resolution of observation and units for sampling and analysis (e.g. individuals, populations or regions; days, months or years), which must reflect the objectives of the study (table 1). For example, canine distemper virus in wolves (Canis lupus) might appear patchily distributed at coarse resolution (e.g. counties within Montana), but synchronous at fine resolution (e.g. Yellowstone National Park [46]). If the resolution of data collection is coarse, one may infer that infection dynamics are spatially independent (figure 2a,b), whereas finer-resolution sampling within a more limited spatial extent may indicate spatial homogeneity (figure 2c,d). Neither choice is erroneous, as long as the inferences are aligned with the scale of investigation. Ultimately, however, trade-offs between spatial versus temporal sampling, and decisions on the resolution and units of analysis, are decided by the prioritization of objectives and resources available for sampling.

To draw valid statistical inferences from field data, theory generally prescribes sampling randomly in space and time [47]. However, for logistical reasons, probabilistic sampling (random selection of samples in which all units have equal probability of being selected) is rare in animal epidemiology. For example, social hosts, such as bats that roost in a common location, are not randomly distributed, and it is also challenging to randomly sample bats within these roosts [48]. Stratified random sampling or other generalized random stratified designs may be more feasible while achieving a spatially well-balanced random sample and valid inferences [49–52]. The stratification can be informed by knowledge of seasonal peaks in prevalence and concentrations of infection to focus efforts in high-risk places and times. Sampling also continues at times and in locations where risk of infection is thought to be low. Designs with unequal probability selection based on an auxiliary variable also can be considered in such cases.

Stratified random sampling is less feasible for pathogens for which prevalence responds to ephemeral environmental drivers, or to transient dynamics in the reservoir host. In these circumstances, one may wish to implement adaptive sampling, in which probabilistic sampling is complemented by more-intensive spatial and temporal sampling during an outbreak or spillover. Opportunistic sampling often is deployed following spillover in an effort to isolate pathogens or identify reservoir hosts [53]. However, if opportunistic sampling is accompanied by some probabilistic sampling, it typically provides more insight into the spatial and temporal dynamics of infection [54–58].

Although adaptive sampling designs are valuable for maximizing data collection around mortality events or spillover, or for sampling when there is little a priori information, simulations suggest that statistical power to detect temporal trends in infection dynamics is greater when populations are sampled repeatedly and consistently over a long period of time (e.g. monthly over a few years) than when a given population is sampled for a short period of time, albeit repeatedly [59] (box 1; e.g. daily or weekly over a few months). Alternative sampling designs [59,73,74] are robust to infrequent sampling, distant sites and large spatial extents. These include: rotating panels, which sample each site repeatedly but during temporal windows that do not fully overlap; augmented, serially alternating panels, which complement rotating panels with consistent sampling of one location; and partially augmented, serially alternating panels, in which infrequent sampling of a given location periodically is complemented with frequent sampling of the location (box 1 and table 2).

Box 1.

Sampling to characterize pathogen prevalence in reservoir hosts.

To illustrate how sampling methods affect interpretation of pathogen dynamics, we used R [60] to simulate infection in a reservoir host as a random realization of a binomial point process [61] (figure 3); see the electronic supplementary material for more information and R code. The kernel-smoothed intensity of this process illustrates spatial and temporal concentrations of infection. We simulated sampling of this hypothetical host over space and time with different designs. Points and thick lines in figure 3 indicate the prevalence estimated by each sampling design. Although this simulation is a clear oversimplification of reality (e.g. no population structure, no underlying mechanistic model of infection dynamics), this serves as a heuristic tool to illustrate the variation in inference about prevalence estimates from different spatio-temporal sampling designs.

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Figure 3.

Allocation of sampling effort over time (months) and space (e.g. along a latitudinal gradient) and consequences for inference of pathogen prevalence. Grey shading in panel (a) denotes the underlying spatial and temporal pattern in infection prevalence (the kernel-smoothed intensity of a random realization of a binomial point process). Open circles represent sampling locations. Colours indicate sampling location. Panel (b) illustrates the observed and true temporal trends in infection prevalence across sampling sites. Thin lines indicate the known infection prevalence over the annual cycle, whereas filled circles are estimated prevalence values given each design and ignoring error in estimation of the prevalence. Thick lines indicate the observed time-series of infection prevalence and only connect points from a single location; locations that are only sampled once within a design have no corresponding thick line. Heuristic sampling designs are as follows: opportunistic (A), single longitudinal (B), replicated longitudinal (C), randomized (D), random stratified (E), adaptive (F), rotating (G), augmented, serially alternating (H) and partially augmented, serially alternating (I). Sampling effort is held relatively constant across A to F and G to I (for which designs can require higher sampling effort). Methods for the simulations are given in electronic supplementary material, Methods.

In opportunistic or haphazard designs, nearby populations are sampled following a spillover event (A). For example, the emergence of severe acute respiratory syndrome in 2002 in Guangdong Province, China was followed rapidly by surveys of mammals in wet markets [62]. Similarly, the emergence of Hendra virus in Brisbane, Australia in 1994 was followed by surveys of wild and domestic animals through Queensland [63]. Although important for isolating virus and identifying reservoir hosts, opportunistic or haphazard sampling may overestimate prevalence, may not capture both spatial and temporal variation in infection dynamics, and may limit the validity of inferences about the population [47]. Repeated (i.e. longitudinal) sampling of single or a few populations (B, C) is common in disease ecology [64–67]. However, longitudinal sampling across a broad number of spatially replicated populations is rare during epidemiological surveillance of wildlife [68]. Opportunistic sampling of multiple populations may be complemented with repeated sampling of one population (e.g. [69]). Longitudinal sampling often is conducted at regular intervals (e.g. every four months), and such designs can capture or consistently fail to detect temporal peaks in viral shedding from reservoirs.

Because pathogen transmission processes are temporally dynamic, even coarse-resolution spatial sampling must be temporally explicit. Estimates of prevalence from one population at one point in time may be misleading if disease dynamics are sufficiently rapid that prevalence changes substantially over the study period. For example, a cross-sectional sample of a travelling wave epidemic could bias estimates of spatial variance if different populations are at troughs and peaks of prevalence. Nevertheless, estimates of prevalence that are based on pooling of samples in space or time frequently are reported in the literature [70].

Random sampling can reduce bias that results from sampling at regular intervals (D). Although sampling with random designs may reduce bias in estimates of spatial and temporal infection dynamics, it may not capture temporal trends within a given location. Furthermore, random samples may be clustered in time and space. Additionally, random selection of sampling locations may have less statistical power than intentional selection of sampling locations [71]. Moreover, truly random sampling may not make sense for certain taxa, such as central-place foragers (e.g. many bats), which are most easily sampled at locations that are not randomly distributed (e.g. roosts) [48]. Stratified random sampling in space and time [72] may be more effective. For example, in E, two samples are drawn from each region. Another alternative to random sampling is adaptive sampling (F), in which random sampling is augmented by more-intensive sampling in the spillover region. This design reduces bias associated with longitudinal surveys while capitalizing on opportunistic sampling following spillover (e.g. virus isolation).

Panels F through I illustrate designs from the sampling literature [59,73,74]. Rotating panels (G) sample each site a finite number of times; as sampling of each site ceases, sampling of another site begins. Although rotating panels can help infer fine-resolution temporal dynamics efficiently over space, they also can restrict broader longitudinal analyses and may change the state of the epidemiological system if sampling of a given site occurs too frequently [73]. Serially alternating sampling is similar to rotating sampling but increases the interval between samples of each site. Both the rotating and the serially alternating designs can be augmented with longitudinal sampling of single or multiple sites (e.g. H). The partially augmented, serially alternating design replaces longitudinal sampling of one site with sampling of multiple sites at consecutive intervals (I). Prior simulations suggested that the power of augmented, serially alternating and partially augmented, serially alternating sampling to detect temporal trends is greater than that of rotating sampling [59]. However, given that these designs include replicated sampling over time per multiple sites, their implementation can require ample sampling effort and therefore resources in terms of personnel, time and funding.

Another framework that recently has emerged from the disease ecology literature is model-guided fieldwork [75], where mathematical models of pathogen dynamics are developed a priori to guide field data collection. Modellers and biologists work together to incorporate multiple hypotheses and uncertainty about the structure of dynamics and then iterate between models and measurement. Such approaches can facilitate transdisciplinary research and lead to more robust inferences.