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).