­­­ Figure 1: Limiting factors operate through a hierarchy to constrain the abundance and diversity of plants (a), and the interplay of limiting factors can result in relationships that are context dependent (b).Left panel (a): Effect of limiting factors illustrated using “Liebig’s barrel”, which shows the law of the minimum where an increase in plant abundance or diversity (represented as water in the barrel) will only occur when the primary factor limiting abundance or diversity is elevated (shortest stave of the barrel). The matrix shows hypothesised limiting factors (S: seeds, red; G: growth rate, yellow; R: resources, blue) after a single growing season for: fast and slow invader groups when added as seed to early, mid and late successional communities, and resident plant diversity in early, mid and late successional communities. R, S, and G indicate primary and important­ secondary/tertiary (subscript) limiting factors, e.g. slow invaders are hypothesised as primarily being growth rate-limited but also seed-limited in early succession (GS).Right panel (b): Predicted responses of cover abundance of fast and slow invaders (left y-axis) to seed dose, disturbance and growth season, which reveals seed-, resource- and growth rate-limitation respectively, in early, mid and late successional communities (upper, middle and lower panels respectively). Also shown is resident community diversity (right y-axis) and its predicted response to disturbance, growth season and invader abundance, the latter of which reduces resource availability, increasing resource-limitation. Interactions are shown with solid and dashed lines: S1= growth season 1, S3 = growth season 3, U = undisturbed, D = disturbed, H = high seed dose, L = low seed dose. Seed dose is never 0 in these plots, so invasion is always possible. Interpretation: The extent of response to alleviation of a limiting factor depends on degree of limitation and on constraints from other limiting factors, e.g. if resources are the only limiting factor and resource-limitation is strong, disturbance should facilitate increased abundance, but if resources are not primarily limiting and primary limiting factor is unchanged, then increasing resource availability will have no effect, and if resources are not limiting at all, increasing resource availability would also have no effect). Limiting factors can vary from situation to situation and their relative strengths will determine the effect of a given experimental treatment, environmental gradient or perturbation. The higher the potential number of limiting factors (staves in a barrel), the higher the likelihood of observing context dependence. Example hypotheses: Because fast invaders are seed limited in early succession (S, left panel), their abundance increases with seed dose (i), but they show no response to growth season (ii) or disturbance (iii). Slow invaders are primarily growth rate-limited in early succession but also somewhat seed-limited (GS, left panel), so they should increase with seed dose and growth season (i, ii), with the strength of the responses being conditional on alleviation of the other limiting factor (i.e. interaction effects).