Environmental and Ecological Statistics

Long-term environmental monitoring places a set of demands on a sampling strategy not present in a survey designed for a single time period. The inevitability that a sample will become out of date must be a dominant consideration in planning a long-term monitoring programme. The sampling strategy must be able to accommodate periodic frame update and sample restructuring in order to address changes in the composition of the universe and changes in the perception of issues leading to new questions and concerns. The sampling strategy must be capable of adapting to such changes while maintaining its identification as a probability sample and its capacity to detect trends that span the update occasions. These issues are examined with respect to sub-population estimation, post-stratification via conditioning, and sample enlargement and reduction. Design features that involve complex sample structure create potentially serious difficulties, whereas an equal probability design permits greater adaptability and flexibility. Structure should be employed sparingly and in awareness of its undesirable effects.

In this paper, we propose a semiparametric survival model to investigate the pattern of spatial and temporal variation in disease prevalence of chronic wasting disease (CWD) in wild deer in Wisconsin over the years 2002 and 2006. The semiparametric survival model we suggested allows to build a more flexible model than the parametric model with fewer parametric assumptions by modeling the baseline hazard using a Gamma process prior. Based on the proposed model, we investigate the geographical distribution of CWD, and assess the effect of sex on disease prevalence. We use a Bayesian hierarchical framework where latent parameters capture temporal and spatial trends in disease incidence, incorporating sex and spatially correlated random effects. We also propose bivariate baseline hazard which change over age and time simultaneously to adopt different effects of age and time on the baseline hazard. Inference is carried out by using MCMC simulation techniques in a fully Bayesian framework. Our results suggest that disease has been spreaded mainly in the disease eradication zone and male deer show a significantly higher infection probability than female deer.

Plant–herbivore interactions are complex and affect herbivore fitness components and life history traits in many different ways. In this paper, we present results from an experiment studying the effects of leaf quality on pupal survival and duration of pupation (as measured by time-to-emergence) in the winter moth. Because only surviving pupae are at risk of emerging, analysis of time-to-emergence should exclude the dead pupae. However, due to right censoring, the survival status could not be determined for each individual. This failure to determine the group of moths at risk of emerging a priori motivated the development of a joint model of both survival probability and time-to-emergence. We formulate the model in a Bayesian framework and apply Monte Carlo Markov Chain (MCMC) to obtain posterior distributions. Time-to-emergence is modeled by a Cox Proportional Hazards (CPH) model where only the surviving pupae are at risk of emergence. Probability of pupal survival was modeled by a Generalized Linear Mixed Model (GLMM). The censored individuals were included in the analysis as a missing value in the GLMM. The GLMM then generated prior distributions of survival probabilties—and thus of the probability of being at risk of emergence—for these 19 individuals, conditional on the model parameters. The CPH model was formulated as a count process and the binary frailty was incorporated as a zero-inflated Poisson model. Zeros in this model represent the non-survivors. Leaf quality did not appear to influence time-to-emergence. Pupal survival was affected in a complex and unexpected way showing opposite effects in males and females. We also explored the robustness of our model against increased levels of censoring. While the degree of censoring was low in our study (< 1%), we artificially increased it to 67%. Although further study is required to study the generality of these results in a theoretical framework, our explorations suggest that the newly proposed technique may be widely applicable in a variety of situations where the identification of the at risk population cannot be done in a straightforward way.

Modeling mosquito population dynamics has become an important part of understanding the transmission of mosquito-borne arboviruses. Of these models, those including meteorological variables have mainly focused on conditions during or immediately preceding the mosquito breeding season. While these conditions are clearly critical biologically and statistically, it is also biologically plausible that conditions during the off-season may contribute to interannual variation in mosquito population size. To examine the effect of off-season factors, we develop a pair of Poisson regression models for July captures of Aedes sollicitans and Culex salinarius, two East Coast vector species of arboviruses including Eastern equine encephalitis virus and West Nile virus. Model results indicate that average maximum temperature, total heating degree-days, and the total number of days with a minimum temperature below freezing during the winter months was predictive of mosquito populations. In addition, the average maximum relative humidity from the preceding fall and total rainfall and total heating degree-days during the preceding spring were also associated with vector population dynamics. The descriptive and predictive power of these models is discussed.

We develop a spatial modeling framework for count data that is efficient to implement in high-dimensional prediction problems. We consider spectral parameterizations for the spatially varying mean of a Poisson model. The spectral parameterization of the spatial process is very computationally efficient, enabling effective estimation and prediction in large problems using Markov chain Monte Carlo techniques. We apply this model to creating avian relative abundance maps from North American Breeding Bird Survey (BBS) data. Variation in the ability of observers to count birds is modeled as spatially independent noise, resulting in over-dispersion relative to the Poisson assumption. This approach represents an improvement over existing approaches used for spatial modeling of BBS data which are either inefficient for continental scale modeling and prediction or fail to accommodate important distributional features of count data thus leading to inaccurate accounting of prediction uncertainty.