Changing climate is already impacting the spatial distribution of many taxa, including bees, plants, birds, butterflies and fishes. A common goal is to detect range shifts in response to climate change, including changes in the centre of the population's distribution (the centre of gravity, COG), population boundaries and area occupied. Conventional estimators, such as the abundance-weighted average (AWA) estimator for COG, confound range shifts with changes in the spatial distribution of available survey data and may be biased when the distribution of survey data shifts over time. AWA also does not estimate the standard error of COG in individual years and cannot incorporate data from multiple survey designs. To explicitly account for changes in the spatial distribution of survey effort, we propose an alternative species distribution function (SDF) estimator. The SDF approach involves calculating distribution metrics, including COG, population boundary and area occupied, directly from the predicted species distribution or density function. We illustrate the SDF approach using a spatiotemporal model that is available as an r package. Using simulated data, we confirm that the SDF substantially decreases bias in COG estimates relative to the AWA estimator. We then illustrate the method by analysing data from two data sets spanning 1977–2013 for 18 marine fishes along the U.S. West Coast. In our case study, the SDF estimator shows significant northward shifts for six of 18 species (with southward shifts for only 2), where two species (darkblotched and greenstriped rockfishes) have both a northward shift and a decreased area occupied. Pelagic species (e.g. Pacific hake and spiny dogfish) have more variable distribution than bottom-associated species. We also find substantial differences between AWA and SDF estimates of COG that are likely caused by shifts in sampling distribution (which affect the AWA but not the SDF estimator). We caution that common estimators for range shift can yield inappropriate inference whenever sampling designs have shifted over time. We conclude by suggesting further improvements in model-based approaches to analysing climate impacts, including methods addressing the impact of local and regional temperature changes on species distribution.