Linking process to pattern: estimating spatiotemporal dynamics of a wildlife epidemic from cross‐sectional data

Abstract

Underlying dynamic event processes unfolding in continuous time give rise to spatiotemporal patterns that are sometimes observable at only a few discrete times. Such event processes may be modulated simultaneously over several spatial (e.g., latitude and longitude) and temporal (e.g., age, calendar time, and cohort) dimensions. The ecological challenge is to understand the dynamic latent processes that were integrated over several dimensions (space and time) to produce the observed pattern: a so-called inverse problem. An example of such a problem is characterizing epidemiological rate processes from spatially referenced age-specific prevalence data for a wildlife disease such as chronic wasting disease (CWD). With age-specific prevalence data, the exact infection times are not observed, which complicates the direct estimation of rates. However, the relationship between the observed data and the unobserved rate variables can be described with likelihood equations. Typically, for problems with multiple timescales, the likelihoods are integral equations without closed forms. The complexity of the likelihoods often makes traditional maximum-likelihood approaches untenable. Here, using seven years of hunter-harvest prevalence data from the CWD epidemic in white-tailed deer (Odocoileus virginianus) in Wisconsin, USA, we develop and explore a Bayesian approach that allows for a detailed examination of factors modulating the infection rates over space, age, and time, and their interactions. Our approach relies on the Bayesian ability to borrow strength from neighbors in both space and time. Synthesizing a number of areas of event time analysis (current-status data, age/period/cohort models, Bayesian spatial shared frailty models), our general framework has very broad ecological applicability beyond disease prevalence data to a number of important ecological event time analyses, including general survival studies with multiple time dimensions for which existing methodology is limited. We observed strong associations of infection rates with age, gender, and location. The infection rate appears to be increasing with time. We could not detect growth hotspots, or location by time interactions, which suggests that spatial variation in infection rates is determined primarily by when the disease arrives locally, rather than how fast it grows. We emphasize assumptions and the potential consequences of their violations.

Multiscale population genetic analysis of mule deer (Odocoileus hemionus hemionus) in western Canada sheds new light on the spread of chronic wasting disease

“…This should result in a pattern of CWD spread that resembles a point source with outward diffusion, as documented for bovine tuberculosis in white-tailed deer (Schmitt et al 1997). However, there has been considerable heterogeneity observed in the pattern of CWD prevalence that has been related to different spread parameters, including history of disease in the area and habitat diversity (Conner and Miller 2004;Miller et al 2004;Wolfe et al 2004;Heisey et al 2010). Migratory behavior may also contribute to CWD spread (Conner and Miller 2004) and the populations we studied are partially migratory, with rates and distances migrated varying across the study area.…”

Deer density and disease prevalence influence transmission of chronic wasting disease in white‐tailed deer

“…The Deviance information criteria is considered a Bayesian analogue to Akaike's information criterion (AIC) (Spiegelhalter et al 2002), and like AIC can favor models with more parameters over simpler models (Link and Barker 2006). We used DIC because of ease of interpretation, widespread familiarity with information-theoretic methods, and the use of DIC in similar investigations (Farnsworth et al 2006, Heisey et al 2010, Walter et al 2011). We assessed whether 95% BCIs overlapped 0.…”

Wildlife disease elimination and density dependence

“…Assuming there is no difference in CWD duration between species, because CWD is mostly evident in adult deer [22], we can interpret b as recruitment of new adults, which accounts for both birth rate and survival of juveniles during their first year. White-tailed deer have high fertility and, on average, adult females bear close to two or more fawns each year.…”