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Appendix S3: Relaxation of Global dispersal assumption
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In the main text, to facilitate analytical tractability, we assumed that a runner species
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could potentially place a ramet in any plot from any plot with equal probability (1-pr).
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Here we relax this assumption and assume that plots exist in a 1-dimensional or 2-
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dimensional array with reflecting boundaries and that dispersal of ramets occurs only
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among adjacent plots. For these simulations and plots, all parameters not specifically
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mentioned were set to be identical to those described in the main text. The goal of the
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simulations was to confirm the finding that the invasion criterion for the runner’s is a
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saturating function of the competitive ability of the clumper species and does not depend
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on the simplifying dispersal assumption. Figure 6 shows that indeed, even in the most
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limited spatially explicit context with only nearest-neighbor ramet dispersal in one spatial
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dimension, the invasion criterion for the runner’s is a saturating function of the
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competitive ability. In addition, it shows that a more-locally dispersed (clumper) species
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can exclude a more widely-dispersed species that is a better resource competitor at low
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productivity. Figures 7 &8 show this for simulations in two dimensions with dispersal to
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the nearest 4 neighbors, and with intermediate strategies.
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Fig. 6 Invasibility plots as a function of competitive ability in a uniform environment for
a runner (i.e. pc  0, Rc* ) and clumper (i.e. pn  1, Rn* ) species in (a) low and (b) higher
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productivity environment. Runner species with trait Rc* can invade a monoculture of the
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clumper with values of Rn* that lie below the solid black curve. Clumper species with trait
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Rn* can invade runner species with values of Rc* that lie above the straight black line. The
dotted line shows equal competitive ability. Plots were made with log-normally
distributed equilibrium resource concentrations with m =-0.7, s =0.7 in a) and to m =0, s
=0.7 in b). Curves were derived by simulation in a 1-dimensional system of 100 patches
with nearest-neighbor dispersal.
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Fig. 7 Invasibility plots as a function of competitive ability in a uniform environment for
a runner (i.e. pc  0, Rc* ) and clumper (i.e. pn  1, Rn* ) species in (a) low and (b)
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highproductivity environment. Runner species with trait Rc* can invade a monoculture of
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the clumper with values of Rn* that lie below the solid black curve. Clumper species with
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trait Rn* can invade runner species with values of Rc* that lie above the straight black line.
The dotted line shows equal competitive ability. Plots were made with log-normally
distributed equilibrium resource concentrations with m =-0.7, s =0.7 in a) and to m =0, s
=0.7 in b). Curves were derived by simulation in a 2-dimensional system of 100 patches
with dispersal to nearest 4-neighbors.
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Fig. 8 Invasibility plots as a function of competitive ability in a uniform environment for
a runner (i.e. pc  .1, Rc* ) and clumper (i.e. pn  .9, Rn* ) species in (a) low and (b) high
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productivity environment. Runner species with trait Rc* can invade a monoculture of the
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clumper with values of Rn* that lie below the solid black curve. Clumper species with trait
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Rn* can invade runner species with values of Rc* that lie above the straight black line. The
dotted line shows equal competitive ability. Plots were made with log-normally
distributed equilibrium resource concentrations with m =-0.7, s =0.7 in a) and to m =0, s
=0.7 in b). Curves were derived by simulation in a 2-dimensional system of 100 patches
with dispersal to nearest 4-neighbors.
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