*Ecological Archives*
E084-078-A2

**Sean R. Connolly and Soyoka
Muko. 2003. Space pre emption,
size-dependent competition, and the coexistence of clonal growth forms. ***Ecology*
84:2979–2988.

Appendix B. Transition from
coexistence to priority effect: the role of understory turnover rate.
Define the critical understory longevity
of species *i*, , as
the understory longevity at which species *i*'s invasibility criterion
is just met. Then the isoclines in Fig. 1 plot the critical understory longevities
of the understory species (
,) and the canopy former (
) as functions of understory colonization ability. The transition from coexistence
to priority effect occurs where the invasibility thresholds cross; i.e., where
. A priority effect occurs
when two conditions are met: (1)
(i.e., the canopy former's invasibility threshold lies below the understory
species' in Fig. 1); and (2)
(the understory species can persist in the absence of the canopy former).
If we combine these conditions, and rearrange, we obtain the following
expression for the existence of a priority effect:

(B.1)

for standoff competition and

(B.2)

for reversal competition. *K*_{C}
and *K*_{J} represent the single-species equilibrium cover of adult
and juvenile canopy formers, respectively. The point where these inequalities
are just satisfied are the points where invasibility isoclines cross in Fig.
1D,E. It is clear from inequality B.1 that, under standoff competition,
the transition from coexistence to priority effect is increasingly favored as
understory life history shifts towards low spatial turnover (as
and decline, a broader range
of canopy former parameters can satisfy the inequality). This is apparent in
the shift from coexistence to priority effect as one moves towards lower understory
space colonization ability and greater longevity (leftwards and upwards in Fig.
1D,E). Since appears in
the right-hand side of inequality B.2, a similar proof cannot be offered for
the reversal case. However, extensive numerical investigations indicate
that the transition from coexistence to priority effect occurs with decreasing
understory spatial turnover in this model as well.

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