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Temporal trends in biological invasions are often described by a lag‐phase of little or no increase in species occurrence followed by an increase‐phase in which species occurrence rises rapidly. While several biological and environmental mechanisms may underlie lag‐phases, they may also represent statistical artefacts or temporal changes in sampling effort. To date, distinguishing the facts from these artefacts has not been possible. Here we describe a method for estimating the lag‐phase in cumulative records of species occurrence, using a piecewise regression model that explicitly differentiates the lag and increase phases. We used the von Bertalanffy, logistic, linear and exponential functions to model the increase phase, and identified the best‐fitting function using model selection techniques. We confirmed the accuracy of our method using simulated data and then estimated the length of the lag‐phase (t_lag …