Spatial Modelling

'Spatial modelling' (density surface estimation) is an area of ongoing research in RUWPA. Stimulated by the need of wildlife managers to relate animal density and abundance to features of their habitat, and to do so with reasonable precision (even for small sub-areas of the survey region), RUWPA has been at the forefront of developing spatial modelling methods suitable for analysing distance sampling data since the mid-1990s. The methods we have developed have primarily been applied to line transect data on marine mammals and seabirds and use generalized additive (or generalized linear) modelling coupled with computer intensive methods for variance estimation. Examples of projects on which we have worked are given below:

• Harbour Porpoise in the North Sea
• Antarctic Pack Ice Seals
• North Atlantic Humpback Whales
• Harp Seals off Newfoundland
• Waterfowl and Seabirds off Denmark

• Antarctic Baleen Whales and Krill
• Pelagic Seabirds in the Eastern Tropical Pacific
• Mackerel and Horse Makerel
• Sardine and Anchovy
• Methods Development

Above: Density of harbour porpoise schools in the North Sea and surrounding waters, predicted from SCANS 1994 shipboard data, (click on image to enlarge).

'SCANS' Project

In 1994 and 2005 multi-ship and aerial line transect surveys of the North Sea and surrounding waters were conducted, to provide an abundance estimate of harbour porpoise (and other frequently sighted cetaceans). Harbour porpoise are subject to bycatch from gillnet (and other) fisheries operations. Spatial modelling provides density maps showing where porpoises are most likely to occur; these are of critical importance in management objectives to mitigate bycatch.

Above: Harbour porpoise (photo: Department of Fisheries and Oceans, Canada).

'APIS'

The APIS program is an international, multi-disciplinary research initiative aimed at improving understanding of the ecological role of pack-ice seals. A key objective of the APIS program is to obtain accurate estimates of the circumpolar distribution and abundance of the four species: crabeater, weddell, ross and leopard seals. Sightings data are collected from shipboard and helicopter transects conducted within the pack ice region; the targets are those seals hauled out on the ice. These can be difficult to see: the analysis carried out by RUWPA investigated the effect of several environmental covariates (including ice cover, distance from ice edge, distance from shelf break, depth, slope and distance from seamount) on detection probability. Having adjusted for variation in detectability, the aerial and shipboard data were combined and spatial models were fitted to the counts of seals.

Left Above: Crabeater seal (photo: Colin Southwell)

Left Below: Seal density on the Antarctica coastline between 70 degrees and 150 degrees east, (click on image to enlarge).

Above: Harp seal adult female with pup (photo: AmericaZoo.com)

Carried out with the Department of Fisheries and Oceans, Canada (DFO)

The DFO surveys harp seals annually using photographic strip transect survey methods. The resulting data lend themselves particularly well to one of the spatial modelling methods developed by RUWPA (the 'count' method - see Hedley et al., 2004). This method uses a generalized additive model to fit the response (here, the observed number of seals in an aerial photograph) as some nonlinear function of geographic and environmental variables. The photographs are 'standardized' for variations in size using an offset variable equivalent to the area 'searched' in the photograph. In addition to analysing these data to obtain estimates of abundance, RUWPA has also developed customized software for use by DFO managers for analysing future surveys, and has organized a training workshop in the application of these methods. Ongoing research in this area includes a suite of simulation studies to investigate the utility and suitability of different (resampling) estimators of variance, including jackknife, non-parametric bootstrap, parametric bootstrap and block bootstrap methods.

Above: Common Scoter

Above: Offshore wind farm

Carried out in collaboration with the National Environmental Research Institute, Denmark (NERI)

Denmark is the focal point for sea duck migration in Europe and because of the increasing number of offshore wind turbines being proposed and built around Denmark, there is a need to assess their potential impact (in terms of habitat loss) on the marine bird populations. NERI is involved in monitoring these effects and conducts aerial line transect surveys to assess changes in density and abundance throughout the year. RUWPA has written custom-built software for spatial (and potentially, spatio-temporal) modelling of these data. This software is being used to analyse and model the spatial distribution of common scoters in the Ålborg Bugt off the eastern coast of Jutland, and plans are underway to extend its utility.

Above: Example of the predicted distribution (in early Spring) of common scoters from an aerial survey off Denmark. Red dots indicate sightings

This project was carried out with the International Whaling Commission (IWC) and the Commission for the Conservation of Antarctic Marine Living Resources (CCAMLR).

It can be very expensive to conduct line transect surveys, particularly in remote marine environments such as the Southern Ocean. Although the IWC has been conducting cetacean sighting surveys in the Antarctic since the late 1970s, in the late 1990s it was beginning to be recognized that abundance estimates alone were not sufficient to assess with any confidence the potential impact of climate change on cetacean populations, and a more integrated approach to the study of the Antarctic ecosystem was required. In the austral summer of 2000, the first collaborative IWC-CCAMLR survey in the part of the Southern Ocean off the Antarctic Peninsula was conducted. RUWPA coordinated the cetacean sightings data collection on three CCAMLR vessels, whose primary research concerned the collection of oceanographic and active acoustic data for estimating krill abundance. Because of the multidisciplinary nature of the survey, it was not possible to design transects suitable for conventional line transect analyses, and so these 'Platform of Opportunity' data had to be analysed using model-based estimation. Spatial models were used to estimate the distribution and abundance of the three most frequently sighted baleen whale species on the survey: fin, humpback and minke whales. (Hedley et al., 2000)

Right Above: Estimated density of fin whale schools from the 2000 IWC-CCAMLR survey (shown on the logarithmic scale). Pink dots are sightings of fin whales, (click on image to enlarge).

Right Below: Fin whale (photo courtesy of animals.timduru.org)

Above: This figure shows the western seaboard of the United States (in pink) and, in the centre of the plot, the Southeast Farallon Islands, one of the main breeding sites of the western gull. From the GAM model of the 1990 at-sea survey data it can be seen that the majority of the gulls are concentrated around the island but that they also disperse along the adjacent coastline.

A collaborative project with Larry Spear of H.T. Harvey and Associates, California, USA. In this project, generalized additive models were used to estimate the population size of three species of seabirds (western gull, guillemot and waved albatross), based on at-sea survey data. The models yielded accurate and precise population estimates that not only complemented the more traditional estimates of population size based on breeding colonies, but also could be used where colony estimates were not available. In addition, the analysis enabled changes in the foraging behaviour of the western gull to be quantified by comparing colony and at-sea population estimates. Further details of the results can be found in Clarke et al. (2003).

Above: Western gull, (courtesy of Mike Yip)

Above: Atlantic mackerel (photo: T.G. McInnes)

Also EU funded, this project extended GAM-based Daily Egg Production Method (DEPM) developed by RUWPA to deal with data containing multiple observed stages. This involved development of innovative GAM methods (now implemented in the R library mgcv) and methods for simultaneous estimation of an egg mortality spatial model as well as new methods for analysis of incubation experiment data.

The project produced updated series of estimates of spawning stock biomass and egg production, and their distribution in space and with respect to environmental variables, together with estimates of the relationships between environmental variables and egg production. See the project report for details.

Left above: Sardines

Left below: Anchovy Shoal

The example projects above highlight a few applications to which RUWPA has applied spatial or spatio-temporal models. Some of these projects have required concurrent methodological development in order for the models to be successfully applied, whilst others are more standard examples of the work undertaken. Nevertheless, spatial modelling of wildlife is a relatively new topic and there are a number of research challenges still remaining. In this section we briefly describe our current work in this area, and why it is needed.

The basic framework for our work to date has been based on generalized additive modelling. This allows flexible functional forms to be fitted to the response variable (often the number, or estimated number, of animals in some relatively small effort segment, but alternatively the distance between successive sightings). We have taken advantage of the free software R and Simon Wood's mgcv package in particular to fit these models. However, wildlife populations often occur in highly clustered aggregations which cannot easily be modelled using a GAM; residual correlation between successive observations of the response remains even after fitting a relatively complex model. Allied to this is the problem of selecting a 'correct' model - if the model assumptions are invalid, the model selection procedure is unlikely to be reliable. Despite these drawbacks, we have found that the spatial models generally perform well in fitting broad-scale trends in distribution and in estimating point estimates of abundance, but have performed less well in estimating precision, despite the use of resampling techniques which require fewer assumptions than analytical estimators of variance.

Resampling techniques essentially sample independent units from the original data, in order to generate a 'new' sample from which to estimate abundance. By repeating this many times, a distribution of resampled estimates is generated and from this distribution, inferences about the precision ofthe point estimate can be made. However, with some survey designs, it is not always apparant what the independent sampling unit should be or how it should be chosen in order to preserve the correlation between observations and generate a large number of independent units from which to sample. The DFO have funded a project which investigated different resampling techniques and choices of sampling unit. These techniques were tested on both simulated and real survey data.

As part of a project funded by the U.S. Office of Naval Research, RUWPA is collaborating with Mark Bravington of CMIS, CSIRO, Hobart and Simon Wood to improve density surface estimation methodology. Spatial autocorrelation is being addressed using a random field approximation to the log-likelihoods and model selection automated via modifications to the spline algorithms in the mgcv package. In addition, some attention is being given to the question of 'smoother taming', so that predicted densities are restricted to remain within reasonable values given the data, and to how to fit smooth functions around irregular topographical features such as complex coastlines and in archipelagic regions of sea. If successful, these developments will enhance the usefulness and validity of the spatial modelling techniques at our disposal, and as part of the ONR project, RUWPA will be incorporating the new methods in a future version of the distance sampling software, Distance.