Fig. 4. Conceptual representation of the intermediate stochasticity hypothesis (ISH) to describe patterns of assembly and structure along a disturbance frequency gradient, for communities in secondary succession (starting at time point t₀).

(1) Initially, stochastic assembly mechanisms (e.g., priority effects, historical contingency and legacy effects) are favored at intermediate disturbance frequencies, promoting re-colonization processes from the low-abundance fraction of the community or seed bank. (2) Subsequently, these are followed by changes in the community structure that manifest as a peak of α-diversity at intermediate levels of disturbance. (3) Over time, three separated clusters of β-diversity ordination may form comprising low, intermediate, and high levels of the disturbance range (in this schematic, n = 3). Furthermore, stochasticity operating at intermediate disturbance levels may lead to variable within-treatment (4a) β-diversity, visualized as partially overlapping cluster similarity (dashed ovals), and (4b) community function, displayed as wider confidence intervals (shaded area between dashed lines). (5) The output of some functions (in this study, nitrogen removal) could be higher at intermediate disturbance frequencies during initial successional stages due to higher stochastic assembly. Additionally, the overall relative contribution of stochasticity decreases with succession time (see top row of subpanels).