The discrepancy between global loss and local constant species richness has led to debates over data quality, systematic biases in monitoring programmes and the adequacy of species richness to capture changes in biodiversity. We show that, more fundamentally, null expectations of stable richness can be wrong, despite independent yet equal colonization and extinction. We analysed fish and bird time series and found an overall richness increase. This increase reflects a systematic bias towards an earlier detection of colonizations than extinctions. To understand how much this bias influences richness trends, we simulated time series using a neutral model controlling for equilibrium richness and temporal autocorrelation (that is, no trend expected). These simulated time series showed significant changes in richness, highlighting the effect of temporal autocorrelation on the expected baseline for species richness changes. The finite nature of time series, the long persistence of declining populations and the potential strong dispersal limitation probably lead to richness changes when changing conditions promote compositional turnover. Temporal analyses of richness should incorporate this bias by considering appropriate neutral baselines for richness changes. Absence of richness trends over time, as previously reported, can actually reflect a negative deviation from the positive biodiversity trend expected by default.