Population estimates

As part of the atlas project, we produced an estimate of the size of the current breeding population for every species. In each case, we calculated a lower and upper confidence limit for the estimate. The approach differed depending on the species, and in many cases, there were several possible options. Thus, most of the specified lower and upper limits are based on the results of various methods, introduced in the following sections.

Complete count

For several rare and colonial species, population size could be determined based on the records from www.ornitho.ch or special monitoring projects (e.g. Great Cormorant, Common Tern, Black-headed Gull, Rook). For species that mainly occur in wetlands, the results from the wetland monitoring scheme were supplemented with the records collected in other areas to arrive at an estimate of the total population.

Complete counts were conducted for 64 species; for a further 22 species, the results from well-monitored areas were supplemented with estimates from areas with poorer coverage. In the case of very rare species as well as those monitored on a yearly basis, the upper and lower limits specified in the atlas correspond to the highest and lowest annual count within the 2013–2016 period. In all other cases, they reflect the uncertainty of the estimate.

Extrapolation of results from the territory mapping surveys

Based on the territory mapping data, we used four different methods of extrapolation that vary in complexity. While more complex methods account for a range of influences, they also require a large quantity of data in order to estimate all the parameters included in the model. Simpler methods require fewer data, but they also integrate fewer factors. The extrapolation methods described below were used for about 100 species. Rather than choosing a single method, we often took advantage of the results produced by different analyses to establish a reasonable lower and upper estimate.

1. The simplest method of extrapolation involved dividing the sum of all territories recorded during the surveys by the proportion of the surface area of Switzerland covered by the surveys and extrapolating to 100 % of the surface area. We restricted the surface area to the altitude belt occupied by the species concerned, i.e. we only took into account the area between the lowest and highest altitude at which the species was recorded during the surveys.
2. We analysed the results of the territory mapping surveys using a Poisson regression model and extrapolated the population for the whole of Switzerland, without accounting for detection probability but accounting for the environmental variables (details on p. 68) and spatial auto-correlation.
   While the surveyed areas were selected to be representative of the atlas square in terms of habitats and altitude, certain habitats and their characteristic species may be over- or underrepresented in the sample, which could produce a systematic error in a simple extrapolation. However, the various environmental variables at least partly correct for this possible bias.
3. A further available option is to add up the estimates per kilometre square represented on the density maps across the entire area of Switzerland. These estimates are based on a binomial mixture model. In addition to the factors considered in a normal Poisson regression (environmental variables and spatial autocorrelation), this model also accounts for detection probability, an approach that generally leads to significantly higher population estimates.
4. In a collaboration with the Patuxent Wildlife Research Institute in the United States, Andy Royle also processed the territory mapping data using a spatial capture-recapture model. In addition to the factors accounted for by the binomial mixture model, this approach also estimates and accounts for territory size. The spatial capture-recapture model corrects for the fact that species with small territories or low detection probability are often not found if their territories lie within the kilometre square but far from the survey route. The model also corrects for the fact that species with large territories may be observed within the square even though the centre of their territory lies outside of it. Not taking this circumstance into account can lead to overestimates.

Extrapolation of occurrence-probability estimates

For just under 50 species, we produced a distribution map using a site-occupancy model based on data from the territory mapping surveys as well as the complete species lists and individual observations supplied by the Swiss Ornithological Institute's volunteer collaborators (registered members of the Ornithological Information Service). This resulted in an estimate of occurrence probability for each kilometre square. Adding up the occurrence probability for all of Switzerland produces an estimate of the number of occupied kilometre squares. This value can be used as a basis for the following extrapolations:

1. For species with large territories, we multiplied the estimated number of occupied kilometre squares with large-scale density estimates taken from the literature. This was the approach taken for Eurasian Sparrowhawk and European Honey-buzzard, for example.
2. Species with large territories may be recorded in a kilometre square although the centre of their territory lies outside of the surveyed area. Theoretically, this extends the area covered during the survey of a kilometre square by the species' average territory radius and can result in an overestimation of the total population. We tried to correct for this by dividing the estimated number of occupied kilometre squares by 1 + radius² * π + 4 * radius, which corresponds to the extended area of the kilometre square. We used information offered in the literature to determine a territory's average radius. This approach served to estimate the populations of Grey-faced Woodpecker and Lesser Spotted Woodpecker, for example.
3. In the case of species with small territories, a single kilometre square may hold several territories. With the help of the survey results, we calculated the relationship between the estimated occurrence probability and the number of recorded territories and were thus able to convert the estimated occurrence probability into a density estimate for every kilometre square. We then added up these density estimates across the whole of Switzerland. Population estimates for Rock Partridge and Meadow Pipit, for example, were produced using this approach.

Extrapolation of regional population estimates

Fairly accurate population estimates exist in some areas of Switzerland with a precisely defined perimeter as well as in Liechtenstein for certain species, species groups, or even all breeding birds that occur in that area. These estimates were established in special monitoring schemes or in regional atlas projects. We used them to calculate a population estimate for all of Switzerland applying the rule of three with the help of the following formula:

N_CH = N_reg / occ_reg * occ_CH.

N_reg corresponds to the regional population estimate, and occreg to the sum of the occurrence probabilities estimated within the project perimeter using a site-occupancy model. Occ_CH is the sum of the occurrence probabilities for all of Switzerland. N_CH corresponds to the resulting population estimate for all of Switzerland. For certain species, we replaced the estimated occurrence probability with the estimated density, calculated using a binomial mixture model.

In general, we chose this approach when none of the other methods yielded satisfactory results. Northern Goshawk and Northern Long-eared Owl are examples of two species whose population estimates were produced using this approach.