Table 1. A description of the Netherlands bird avoidance model workflow (Fig. 1) presented for a single species, the common buzzard (Buteo buteo). GAM stands for general additive regression model, and BAM for bird avoidance model.

Step 1
GAM
The relationship between the counts on samples sites and environmental variables is described using a GAM. A separate GAM is developed for each survey and applied at a resolution of 1 km², covering the entire Netherlands. For the buzzard, counts are available from five surveys: one breeding bird survey and four point counts of nonbreeding birds throughout the year (Fig. 2A), resulting in five different GAMs and five different maps.

Step 2
Kriging
To account for spatial correlation in the residuals, the residuals for each GAM are spatially interpolated using universal kriging.

Step 3
Regression-kriging
The spatially interpolated residuals are added to the respective GAMs creating regression-kriging distribution maps (Fig. 2B). In this step, a breeding factor is used to convert counts of breeding pairs to numbers of individuals.

Step 4
Combined maps
This step combines the different regression-kriging models to estimate the spatial distribution of each species twice a month. For different groups of birds, different count data are available. For example, for some species, only the breeding bird counts and the nonbreeding bird counts are available; for other species, monthly waterbird counts are available as well. Each regression-kriging map is assigned a weight (data set weight) based on proximity of the survey period to the BAM period (weight diminishes with time). Subsequently, linear interpolation is applied to produce predictive maps for those BAM periods for which no surveys are assigned.

Step 5
Normalized maps
To prevent abrupt changes from one BAM period to another because of differences between the various data sets, the combined maps were smoothed with known seasonal trends. The smoothing procedure was as follows. Total abundance over the Netherlands, on the basis of the combined maps for each species and each BAM period, was normalized to range between 0 and 1; we call this the “model_trend.” We used the known seasonal trends (the expert_trend) to correct the model trend via the following equation:
NMi,t = CMi,t * ( model_trend + ( model_trend - expert_trend )* expert_weight )
where CMi,t stands for Combined Map for bird i in BAM period t, NMi,t stands for Normalized Map for bird species i in BAM period t, and expert_weight is the degree to which expert_trend can correct model_trend (for most birds, expert_weight is set to 0.5).

Step 6
Inflated maps
For each bird species, the altitude distributions and activity patterns were derived for the four periods of day (morning, afternoon, dusk, dawn). Maps of the number of birds in the air are created for each combination of BAM period, time of day, and altitude, producing 480 predictive maps/species (24 periods a year x 4 times a day x 5 flight altitude layers).

Step 7 Classified maps: Each map was classified into eight equal interval classes of birds/km². Composite maps: Maps of all species were combined to create maps of total number of birds/km² and total mass/km². Summary table: The sum of birds was calculated for three regions/time of year, time of day, and altitude layer, for the top 10 most abundant species.