Variance Propagation for Density Surface Models

Aerial abundance estimates for two sympatric dolphin species at a regional scale using distance sampling and density surface modeling

Monitoring wildlife populations over scales relevant to management is critical to supporting conservation decision-making in the face of data deficiency, particularly for rare species occurring across large geographic ranges. The Pilbara region of Western Australia is home to two sympatric and morphologically similar species of coastal dolphins—the Indo-pacific bottlenose dolphin (Tursiops aduncus) and Australian humpback dolphin (Sousa sahulensis)—both of which are believed to be declining in numbers and facing increasing pressures from the combined impacts of environmental change and extensive industrial activities. The aim of this study was to develop spatially explicit models of bottlenose and humpback dolphin abundance in Pilbara waters that could inform decisions about coastal development at a regional scale. Aerial line transect surveys were flown from a fixed-wing aircraft in the austral winters of 2015, 2016, and 2017 across a total area of 33,420 km2. Spatio-temporal patterns in dolphin density were quantified using a density surface modeling (DSM) approach, accounting for imperfect detection as well as both perception and availability bias. We estimated the abundance of bottlenose dolphins at 3,713 (95% CI = 2,679–5,146; average density of 0.189 ± 0.046 SD individuals per km2) in 2015, 2,638 (95% CI = 1,670–4,168; 0.159 ± 0.135 individuals per km2) in 2016 and 1,635 (95% CI = 1,031–2,593; 0.101 ± 0.103 individuals per km2) in 2017. Too few humpback dolphins were detected in 2015 to model abundance, but their estimated abundance was 1,546 (95% CI = 942–2,537; 0.097 ± 0.03 individuals per km2) and 2,690 (95% CI = 1,792–4,038; 0.169 ± 0.064 individuals per km2) in 2016 and 2017, respectively. Dolphin densities were greatest in nearshore waters, with hotspots in Exmouth Gulf, the Dampier Archipelago, and Great Sandy Islands. Our results provide a benchmark on which future risk assessments can be based to better understand the overlap between pressures and important dolphin habitats in tropical northwestern Australia.

A model-based estimate of winter distribution and abundance of white-tailed deer in the Adirondack Park

In the Adirondack Park region of northern New York, USA, white-tailed deer (Odocoileus virginianus) and moose (Alces alces) co-occur along a temperate-boreal forest ecotone. In this region, moose exist as a small and vulnerable low-density population and over-browsing by white-tailed deer is known to reduce regeneration, sustainability, and health of forests. Here, we assess the distribution and abundance of white-tailed deer at a broad spatial scale relevant for deer and moose management in northern New York. We used density surface modeling (DSM) under a conventional distance sampling framework, tied to a winter aerial survey, to create a spatially explicit estimate of white-tailed deer abundance and density across a vast, northern forest region. We estimated 16,352 white-tailed deer (95% CI 11,762–22,734) throughout the Adirondack Park with local density ranging between 0.00–5.73 deer/km². Most of the Adirondack Park (91.2%) supported white-tailed deer densities of ≤2 individuals/km². White-tailed deer density increased with increasing proximity to anthropogenic land cover such as timber cuts, roads, and agriculture and decreased in areas with increasing elevation and days with snow cover. We conclude that climate change will be more favorable for white-tailed deer than for moose because milder winters and increased growing seasons will likely have a pronounced influence on deer abundance and distribution across the Adirondack Park. Therefore, identifying specific environmental conditions facilitating the expansion of white-tailed deer into areas with low-density moose populations can assist managers in anticipating potential changes in ungulate distribution and abundance and to develop appropriate management actions to mitigate negative consequences such as disease spread and increased competition for limiting resources.

Estimating uncertainty in density surface models

Providing uncertainty estimates for predictions derived from species distribution models is essential for management but there is little guidance on potential sources of uncertainty in predictions and how best to combine these. Here we show where uncertainty can arise in density surface models (a multi-stage spatial modelling approach for distance sampling data), focussing on cetacean density modelling. We propose an extensible, modular, hybrid analytical-simulation approach to encapsulate these sources. We provide example analyses of fin whales Balaenoptera physalus in the California Current Ecosystem.

Extending density surface models to include multiple and double-observer survey data

Spatial models of density and abundance are widely used in both ecological research (e.g., to study habitat use) and wildlife management (e.g., for population monitoring and environmental impact assessment). Increasingly, modellers are tasked with integrating data from multiple sources, collected via different observation processes. Distance sampling is an efficient and widely used survey and analysis technique. Within this framework, observation processes are modelled via detection functions. We seek to take multiple data sources and fit them in a single spatial model. Density surface models (DSMs) are a two-stage approach: first accounting for detectability via distance sampling methods, then modelling distribution via a generalized additive model. However, current software and theory does not address the issue of multiple data sources. We extend the DSM approach to accommodate data from multiple surveys, collected via conventional distance sampling, double-observer distance sampling (used to account for incomplete detection at zero distance) and strip transects. Variance propagation ensures that uncertainty is correctly accounted for in final estimates of abundance. Methods described here are implemented in the dsm R package. We briefly analyse two datasets to illustrate these new developments. Our new methodology enables data from multiple distance sampling surveys of different types to be treated in a single spatial model, enabling more robust abundance estimation, potentially over wider geographical or temporal domains.