Mismatch of Persistence and Occupancy Patterns in Natural Conditions
We found support for our prediction that persistence and occupancy were mismatched across a productivity gradient, both when species were considered individually and together as a community. Each species tended to occupy a greater proportion of sites as productivity increased (Fig. 1, bottom row); these increases were strongest for Bromus , a species that was largely absent from sites of low to intermediate productivity (𝛽1= 1.04 ± 0.30; Table S2), and weakest forPlantago (𝛽1= 0.26 ± 0.26; Table S2, bottom row of Fig. 1). By contrast, we observed strong mismatches between persistence (i.e.,λ \(\geq\)1) and occupancy. Under conditions with neighbors, two species (Micropus , Festuca ) were significantly more likely to persist in more productive environments (Table S3), mirroring occupancy, whereas for the two others (Plantago , Bromus ), less productive sites were more conducive to persistence (Table S3; Fig. 1 red lines). Note that Micropus was not predicted to persist in any location (λ << 1). Surprisingly, for all species, occupancy patterns more closely reflect persistence in the abiotic treatment (Fig. 1, blue) compared to the biotic treatment (red).
When scaling from species to the community, persistence significantly decreased with productivity (slope = -0.25 [-0.40, -0.096], brackets denote 95% CIs), whereas occurrence responded oppositely, increasing with productivity (slope = 0.57 [0.42, 0.72]; i.e., significant interaction between productivity and data type (i.e., persistence data vs. occupancy data); χ2 = 84.94, df = 2, P< 0.001; Fig. 2). As a result, in unproductive environments, fewer species occurred than could persist. In contrast, in productive environments, most species could occur but relatively few could persist at their current population size (i.e. λ <1).