# How we estimate bear density

The observations of polar bears will be used to calculate densities of animals within a defined area. We use helicopter to cover the land areas in Svalbard with transect lines and in some areas do total counts (we try to count all animals in some areas), and in addition we have put out transect lines in a defined area in the drifting sea ice north of the archipelago.

This is a large area, we are talking about a rectangle 300 km long and 200 km wide, and we will fly transects 4,5 km apart throughout it. Yet, our study area is only a fraction of the vast Arctic Ocean.

## Distance sampling

The method we use to estimate bear density is called distance sampling. Therefore perhaps not surprising, the key information recorded is the distance from the transect.

We also need the group size, typically either a lone adult, male or female, or a female with cubs. Additionally we also record a qualitative measure of habitat structure, easy, medium or hard to survey, say, as well as the habitat the bear was on, namely ice, land or glacier. Densities might be different depending on habitat, which we can treat as different strata, and we can account for it later if required.

## Bear density estimation

Distances are used to estimate the probability of detecting a bear: by modelling the detection fall off with distance we can infer the proportion of animals missed. Given the random placement of lines with respect to the animal locations, the distribution of all distances should be uniform (i.e. no distance should be favoured).

So the fact that we see more bears close to the line than away from the line tell us about our ability to detect bears as a function of distance. This intuitively allows us to estimate the total number of bears present, and hence bear density, which is our ultimate goal. If one counts 4 bears, and the probability of detection is 1/3, then 12 bears were around: we just divide the number of bears detected by the probability of detecting them.

That is distance sampling in a nut shell. Of course there’s more to it than meets the eye, but the details would be as boring as doing the work itself is exciting.

**Tiago Marces** at the University of St Andrews, Scotland is a biostatistician with the estimation of animal abundance using “Distance Sampling” as main field of expertise.