Conceptual figure summarizing our main hypotheses for how different drivers could influence fine-grain β-diversity via changing mean occupancy of species, based on the findings of Dembicz et al. (2021) and ecological theory. Fine-grain β-diversity (and likewise for larger grain sizes) is mathematically linked to mean occupancy, which can be decomposed into (i) total cover; (ii) mean size of individuals; and (iii) similarity of species composition between adjacent subplots. These three aspects of mean occupancy are affected by the environmental drivers, productivity, stress, disturbances and heterogeneity (green), as well as the mean traits of the analysed species group, namely dispersal distance and niche size (yellow). Note that disturbance can have contrasting effects depending on its type and intensity. To the very left we exemplify how two aggregated environmental parameters, land use intensity and elevation (orange), could influence fine-grain β-diversity via multiple pathways. What we mean with the three aspects that make up mean occupancy is illustrated with a pair of figures showing to the left a situation with low and to the right with high values of the respective aspect. The four different symbols represent individuals of four species distributed in a vegetation plot of a total extent of Aγ = 9 and assessed also at a grain size of Aα = 1. Below each community, we provide the corresponding S̶̄α-, Sγ-, z-values as well as the mean occupancies (ρ̄ i). Since z = log (Sγ /S̄α) / log (Aγ /Aα) and ρ̄ i = S̄α /Sγ, it is obvious that higher ρ̄ i means lower z and vice versa. Influences of one parameter are indicated by the arrows with their + and – symbols; grey arrows correspond to ecological hypotheses and black arrows to strict mathematical relationships. We did not aim to display all possible relationships in this figure, but concentrated on those that we consider most important. The expected effect of a certain driver or aggregated environmental parameter on fine-grain β-diversity can be estimated by multiplying the +/- symbols along the path. If several paths connect to fine-grain β-diversity, their products should be summed (modified from Dembicz et al. 2021).