Decomposing trends in Swedish bird populations using generalized additive mixed models

Estimating trends of populations distributed across wide areas is important for conservation and management of animals. Surveys in the form of annually repeated counts across a number of sites are used in many monitoring programmes, and from these, nonlinear trends may be estimated using generalized additive models (GAM). I use generalized additive mixed models (GAMM) to decompose population change into a long‐term, smooth, trend component and a component for short‐term fluctuations. The long‐term population trend is modelled as a smooth function of time and short‐term fluctuations as temporal random effects. The methods are applied to analyse trends in goldcrest and greenfinch populations in Sweden using data from the Swedish Breeding Bird Survey. I use simulations to investigate statistical properties of the model. The model separates short‐term fluctuations from longer term population change. Depending on the amount of noise in the population fluctuations, estimated long‐term trends can differ markedly from estimates based on standard GAMs. For the goldcrest with wide among‐year fluctuations, trends estimated with GAMs suggest that the population has in recent years recovered from a decline. When filtering out, short‐term fluctuations analyses suggest that the population has been in steady decline since the beginning of the survey. Simulations suggest that trend estimation using the GAMM model reduces spurious detection of long‐term population change found with estimates from a GAM model, but gives similar mean square errors. The simulations therefore suggest that the GAMM model, which decomposes population change, estimates uncertainty of long‐term trends more accurately at little cost in detecting them. Policy implications. Filtering out short‐term fluctuations in the estimation of long‐term smooth trends using temporal random effects in a generalized additive mixed model provides more robust inference about the long‐term trends compared to when such random effects are not used. This can have profound effects on management decisions, as illustrated in an example for goldcrest in the Swedish breeding bird survey. In the example, if temporal random effects were not used, red listing would be highly influenced by the specific year in which it was done. When temporal random effects are used, red listing is stable over time. The methods are available in an R‐package, poptrend.