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Figure S1 Results from a more general model: <![CDATA[P_i\,=\,n_i E_i C_i/[\sum\nolimits_j {n_j E_j C_j]}]]> where Ei is the probability that a seed or seedling survives the pre-competition stage and Ci is its subsequent competitive ability.

Figure S2 Model runs with nine species all with seed mass equivalent to the largest species in the annual plant guild for comparison with Fig. S1.

Figure S3 Typical trajectories of nine sand-dune annual species in the growth model when all seeds are dispersed globally (a,c,e) or when only 40% of seeds are dispersed globally and 60% of seeds are retained within patches (b,d,f).

Appendix S1 Local dispersal and disturbance.

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