The consequences of using different measures of mean abundance to characterize the abundance–occupancy relationship

Aim  To investigate the influence of choice of the measure of mean abundance on the abundance–occupancy relationship, and to examine the implications for identifying causal mechanisms. Innovation  Simulations were performed to generate stochastic abundance–occupancy data sets covering a wide range of scenarios representative of empirical abundance–occupancy data. Two common measures of mean abundance were used: local mean abundance (mean abundance calculated using only data from occupied sites) and global mean abundance (mean abundance calculated using all sites or samples). I found that the choice of mean abundance measure had a strong effect on the correlation between abundance and occupancy. Local mean abundance was associated with a high proportion of negative correlations (mean percentage of negative correlations across 24 simulations = 44.39), while global mean abundance was strongly associated with positive correlations (mean percentage of negative correlations across 24 simulations = 0.02). Main conclusions  The choice of abundance measure influences the correlation between abundance and occupancy. Negative correlations between local mean abundance and occupancy are an inherent and unavoidable consequence of using this measure of abundance. Efforts to identify causal mechanisms that give rise to the abundance–occupancy relationship have attempted to explain occasional negative correlations when the expectation was for positive correlations. This study shows that negative correlations arise from the choice of mean abundance measure and that this artefact confounds efforts to identify ecological causal mechanisms.