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Question

What exactly does the multispecies bird indicator tell us about changes in bird diversity? If the indicator goes down, is bird diversity deteriorating? If the indicator goes up, is bird diversity improving?

Answer

If the indicator goes up, this is a signal that the bird community as a whole is doing well, if it goes down, the bird community is suffering a loss. If it remained stable we have no evidence that the group as a whole has changed.
The indicators are not meant to outweigh gains and losses in species abundances against each other and to calculate the net result. They are meant as a procedure to derive a general inference about a species set. In other words, the indicators are a statistical exercise to measure trends of entire groups of species. Because we include as many species as we can, without differentiating beforehand between bird species that seem to do well or not, this indicator is an unbiased metric that enables us to statistically test if the trend in the bird community as a whole deviates from stability.
A stable indicator does not mean that all constituent species have stable population numbers. Some bird species undergo a decline if the indicator is stable, and this may even occur if the indicator increases. Therefore, for inferences on the fate of individual species, one should consider individual species index and trend values.

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