Climate change and other human-caused environmental disturbance may lead to declines in biodiversity. Recently, a number of studies have collated large data sets of monitoring time series for selected ecosystem or organism groups and used these data sets to estimate trends in biodiversity, with many studies identifying large declines in biodiversity across a number of organisms or ecosystems. These results are not without controversy however; data selection and quality issues, as well as questions over statistical methodology have lead to vigorous debate at meetings and in scientific journals. Typically, trends in biodiversity are estimated using linear effects, via generalized linear mixed (or hierarchical) models to account for site-to-site heterogeneity in temporal trends. Additionally, year-to-year variation may enhance or mask estimated losses or gains in biodiversity over time if the first observation year in a given series is unusually rich or depauperate. Using year random effects has been suggested as a mechanism to account for this potential bias. An alternative ��� but related ��� way to model trends in biodiversity time series is using penalized splines for the trends, leading to hierarchical generalized additive models (HGAMs; also called structural additive models). In this talk I'll introduce HGAMs and penalized splines and their use for modelling biodiversity trends, and illustrate the approach using an arthropod time series data set.