Estimating Abundance from Counts in Large Data Sets of Irregularly-Spaced Plots using Spatial Basis Functions

Monitoring plant and animal populations is an important goal for both academic research and management of natural resources. Successful management of populations often depends on obtaining estimates of their mean or total over a region. The basic problem considered in this paper is the estimation of a total from a sample of plots containing count data, but the plot placements are spatially irregular and non randomized. Our application had counts from thousands of irregularly-spaced aerial photo images. We used change-of-support methods to model counts in images as a realization of an inhomogeneous Poisson process that used spatial basis functions to model the spatial intensity surface. The method was very fast and took only a few seconds for thousands of images. The fitted intensity surface was integrated to provide an estimate from all unsampled areas, which is added to the observed counts. The proposed method also provides a finite area correction factor to variance estimation. The intensity surface from an inhomogeneous Poisson process tends to be too smooth for locally clustered points, typical of animal distributions, so we introduce several new overdispersion estimators due to poor performance of the classic one. We used simulated data to examine estimation bias and to investigate several variance estimators with overdispersion. A real example is given of harbor seal counts from aerial surveys in an Alaskan glacial fjord.Comment: 37 pages, 7 figures, 4 tables, keywords: sampling, change-of-support, spatial point processes, intensity function, random effects, Poisson process, overdispersio

Space–time zero-inflated count models of Harbor seals

Environmental data are spatial, temporal, and often come with many zeros. In this paper, we included space–time random effects in zero-inflated Poisson (ZIP) and ‘hurdle’ models to investigate haulout patterns of harbor seals on glacial ice. The data consisted of counts, for 18 dates on a lattice grid of samples, of harbor seals hauled out on glacial ice in Disenchantment Bay, near Yakutat, Alaska. A hurdle model is similar to a ZIP model except it does not mix zeros from the binary and count processes. Both models can be used for zero-inflated data, and we compared space–time ZIP and hurdle models in a Bayesian hierarchical model. Space–time ZIP and hurdle models were constructed by using spatial conditional autoregressive (CAR) models and temporal first-order autoregressive (AR(1)) models as random effects in ZIP and hurdle regression models. We created maps of smoothed predictions for harbor seal counts based on ice density, other covariates, and spatio-temporal random effects. For both models predictions around the edges appeared to be positively biased. The linex loss function is an asymmetric loss function that penalizes overprediction more than underprediction, and we used it to correct for prediction bias to get the best map for space–time ZIP and hurdle models

A mixed-model moving-average approach to geostatistical modeling in stream networks

Spatial autocorrelation is an intrinsic characteristic in freshwater stream environments where nested watersheds and flow connectivity may produce patterns that are not captured by Euclidean distance. Yet, many common autocovariance functions used in geostatistical models are statistically invalid when Euclidean distance is replaced with hydrologic distance. We use simple worked examples to illustrate a recently developed moving-average approach used to construct two types of valid autocovariance models that are based on hydrologic distances. These models were designed to represent the spatial configuration, longitudinal connectivity, discharge, and flow direction in a stream network. They also exhibit a different covariance structure than Euclidean models and represent a true difference in the way that spatial relationships are represented. Nevertheless, the multi-scale complexities of stream environments may not be fully captured using a model based on one covariance structure. We advocate using a variance component approach, which allows a mixture of autocovariance models (Euclidean and stream models) to be incorporated into a single geostatistical model. As an example, we fit and compare ‘‘mixed models,’’ based on multiple covariance structures, for a biological indicator. The mixed model proves to be a flexible approach because many sources of information can be incorporated into a single model

Evaluation of the spatial linear model, random forest and gradient nearest-neighbour methods for imputing potential productivity and biomass of the Pacific Northwest forests

Increasingly, forest management and conservation plans require spatially explicit information within a management or conservation unit. Forest biomass and potential productivity are critical variables for forest planning and assessment in the Pacific Northwest. Their values are often estimated from ground-measured sample data. For unsampled locations, forest analysts and planners lack forest productivity and biomass values, so values must be predicted. Using simulated data and forest inventory and analysis data collected in Oregon and Washington, we examined the performance of the spatial linear model (SLM), random forest (RF) and gradient nearest neighbour (GNN) for mapping and estimating biomass and potential productivity of Pacific Northwest forests. Simulations of artificial populations and subsamplings of forest biomass and productivity data showed that the SLM had smaller empirical root-mean-squared prediction errors (RMSPE) for a wide variety of data types, with generally less bias and better interval coverage than RFand GNN. These patterns held for both point predictions and for population averages, with the SLM reducing RMSPE by 30.0 and 52.6 per cent over two GNN methods in predicting point estimates for forest biomass and potential productivity

Modeling growth of mandibles in the Western Arctic caribou herd

We compared growth curves for ramus length and diastema length from two autumn collections of mandibles of male Western Arctic Herd caribou in Alaska. We were primarily interested in determining if growth curves of caribou mandibles differed between caribou born during 1959-1967, after the herd had been high for several years and was probably declining in size, and those born during 1976-1988, when the herd was increasing in size. To compare these growth curves, we used a nonlinear model and used maximum likelihood estimates and likelihood ratio tests. We found that growth rates were similar between periods, but intercepts and variances of growth curves differed. From this we infer that calves were smaller in autumn during the 1960s and that significant compensatory growth did not occur later in life

A Comparison of the Spatial Linear Model to Nearest Neighbor (k-NN) Methods for Forestry Applications

Forest surveys provide critical information for many diverse interests. Data are often collected from samples, and from these samples, maps of resources and estimates of aerial totals or averages are required. In this paper, two approaches for mapping and estimating totals; the spatial linear model (SLM) and k-NN (k-Nearest Neighbor) are compared, theoretically, through simulations, and as applied to real forestry data. While both methods have desirable properties, a review shows that the SLM has prediction optimality properties, and can be quite robust. Simulations of artificial populations and resamplings of real forestry data show that the SLM has smaller empirical root-mean-squared prediction errors (RMSPE) for a wide variety of data types, with generally less bias and better interval coverage than k-NN. These patterns held for both point predictions and for population totals or averages, with the SLM reducing RMSPE from 9% to 67% over some popular k-NN methods, with SLM also more robust to spatially imbalanced sampling. Estimating prediction standard errors remains a problem for k-NN predictors, despite recent attempts using model-based methods. Our conclusions are that the SLM should generally be used rather than k-NN if the goal is accurate mapping or estimation of population totals or averages

Body size of female calves and natality rates of known-aged females in two adjacent Alaskan caribou herds, and implications for management

We studied body mass of female calves and natality rate of adult females in two adjacent Interior Alaskan caribou (Rangifer tarandus granti) herds during 1991-2001. Mass of newborn calves was similar in both herds, but Delta calves gained significantly more mass over summer than Nelchina calves. In contrast, Nelchina calves consistently maintained their mass during winter while Delta calves lost mass. Metatarsus length was similar in both herds in 4-month-old and 10-month-old calves, and it increased over winter in both herds. Natality rates of females >3 years old were consistently higher in the Delta Herd than in the Nelchina Herd, primarily because natality in 3- to 5-year-old Nelchina females was low. Although body mass of Delta Herd calves consistently declined over winter, we concluded that nutrition was not significantly limiting herd growth. Managers are more likely to maximize harvest by maintaining the Delta Herd near its present size (i.e., 3500), or allowing it to increase only slightly. The only real option for increasing harvestable surpluses of caribou in the Delta Herd is reducing predation during calving and summer. In contrast, we conclude that summer nutrition significantly limits potential population growth and body mass in the Nelchina Herd, and managers are more likely to maximize harvest by maintaining herd size at or below 30 000 than by allowing the herd to grow to near historical highs (i.e., 60 000-70 000)