Ideally, in the European breeding bird monitoring scheme, all countries start in the same year. Therefore, it would be relatively easy to assess the changes in the yearly all-countries totals of breeding pairs. However, in reality the monitoring schemes start in different years. Therefore, we have to calculate the missing values in first years of monitoring.
The procedure to reach same start of time series is as follows. First, the national yearly all-sites’ totals are converted into national yearly total population sizes in the country. To do so, information on total population sizes collected by BirdLife International (2021) is used. A weighting factor is calculated by dividing the population total as assessed by BirdLife International (2021) by the estimated all-sites totals for those years covered by population size estimates (BirdLife International 2021) and a monitoring scheme. Subsequently, this weighting is applied to all years of the monitoring scheme so that the weighted year totals may be considered the yearly population totals in that country. An example may clarify this. Suppose the estimated all-sites total of species X in the UK amounts to 100 in 2009 and 110 in 2010. If the UK’s population total would be 1000 in 2009, the weighting factor equals 1000/100 = 10. For the year 2010, the population total is 10*110 = 1100.
The yearly population totals’ standard error is (weight factor) x (standard error of all-sites total).
Subsequently, each country’s population totals are summed to yield the supranational population totals for each year. The following statistical rule derived the supranational totals’ standard errors: variance of supranational total = variance of country1 total + variance of country2 total + variance of country3 total, etc., where variance = standard error2. This rule applies because the estimates of the yearly totals are independent between countries. Finally, the supranational totals are converted into indices.
However, the national European monitoring schemes started in different years, leading to missing national all-sites totals. Just as explained in the example for sites above, simple comparisons of the yearly sum of country totals will give misleading inferences on trends because lesser countries contribute in earlier years. Again we used an adapted version of TRIM to estimate the missing country totals, equivalent to imputing missing counts for particular sites. Basically, we computed indices for four European regions (West Europe, North Europe, Central & East Europe, and South Europe). As the example shows, we derived missing national totals from changes in countries in the same European region.
| year 1 | year 2 | year 3 | |
| Country 1 population total | 4000 | 3000 | 2000 |
| Country 2 population total | 4000 | 3000 | 2000 |
| Country 3 population total | missing | missing | 8000 |
| etc. | |||
| West Europe population total | 24 | 18 | 12 |
Thereafter, the regional totals are calculated and summed to obtain European indices as described above.
An extra complication is that also regions differ in the years covered. For instance, the first country in South Europe started its monitoring activities only in 1989, whereas monitoring started in 1982 in Central & East Europe and even earlier in West Europe. To combine totals from the different regions, we perform a third step to combine results using TRIM. Altogether we apply a refined hierarchical imputation procedure to combine country population totals.
To produce supranational indices, we use a slightly adapted version of TRIM tailored to combining all-sites totals and their standard errors instead of raw counts per site. Instead of deriving the standard errors in the usual statistical way from count data and model fit, we apply the standard errors (and the year-year covariances) that result from the calculation of the all-sites totals per country.
In summary, PECBMS combines data from national monitoring schemes, which differ in several aspects. These differences are addressed to produce unbiased results with known precision (Van Strien et al., 2001).
Overview of the effects of methodological differences in national monitoring schemes:
| Difference between countries (national schemes) | Influence on national indices | Consequences for supranational indices |
| Field method | Precision | Include standard error |
| Number of sites | Precision | Include standard error |
| Site selection method | Bias | Remove bias at the national level |
| Index method | Bias/precision | Use the proper method (TRIM) |
| Years covered | Missing yearly indices | Estimate missing indices |
| Population size | None | Weight indices by national population size |
When supranational indices and trends are produced, a control for inter-annual consistency is carried out just as was done for national data (see details in chapter 4. Quality control). In case some inconsistencies occurred, they are examined in detail to determine whether the inconsistency is caused by an enlarged or improved data set or computation errors.
For details about imputing countries, see the computation schedule.