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Supporting Information: Appendix S1
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Here we provide the analytical justification of the results presented in the main text. Also, we
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show numerical simulations explaining the shapes of the graphs shows in the conceptual Fig. 3
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of the manuscript.
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As noted in the main text, previous research suggests that novel, invasive genotypes may have
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undergone an evolutionary shift in expressed carbon:nutrient ratios in leaf tissue (Eppinga et al.
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2011). This trait will affect the consumption vector of the invasive population, which is
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expressed as (Eppinga et al. 2011):
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(S1)
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In which qR,I indicates the nutrient content of the invader’s tissue, and thus inversely related to
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the invader’s carbon:nutrient ratio. From equation S1 it follows that a higher carbon:nutrient
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ratio (i.e. a decreasing value of qR,I) decreases the slope of the invader’s consumption vector,
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whereas a lower carbon:nutrient ratio (i.e. an increasing value of qR,I) increases the slope of the
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invader’s consumption vector.
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Using the same model framework as presented in the main text, Eppinga et al. (2011) derived the
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conditions under which an increase in an invader’s leaf tissue carbon:nutrient ratio may alter the
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outcome of competition with a native population. More specifically, we focused on a case where
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the system shifted from a state where the invasive population would be excluded into a situation
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where alternative stable states are possible (as shown in Fig. 3 of the main text). From a
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quantitative perspective, such a shift would require the slope of the invader’s nutrient-light
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consumption ratio to become smaller than the nutrient-light supply ratio in the system. Eppinga
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et al. (2011) showed that this occurs when:
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(S4)
In which:
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(S5)
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The following parameter values were assigned in Fig. 3 of the main text (following Eppinga et
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al. 2011):
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gL,N= 0.25 day-1, gL,I=0.25 day-1, kL,N= 50 mol.m-2.day-1, kL,I= 35 mol.m-2.day-1, gR,N= 0.25 day-
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1
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day-1, qR,N= 15 mg.g-1, qR,I= 15 mg.g-1, ρ= 530 g.m-3, lRoot= 1 m, QR,N= 15 mg.g-1, QR,I= 15 mg.g-
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1
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γL,I= 0.04 m2.g-1, αR,N= 0.01 m2.g-1, αR,I= 0.013 m2.g-1, S=8 mg.kg-1. The same parameterization is
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used in Fig. 4 of the main text, except for the parameters L0, S and qR,I., as indicated in the figure
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legend.
,gR,I= 0.25 day-1, kR,N= 30 mg.kg-1, kR,I= 35 mg.kg-1, mN=0.005 day-1, mI=0.01 day-1, a= 0.005
,αR,N= 0.7, αR,I= 0.7, dN= 0.003 day-1, dI= 0.003 day-1, L0= 50 mol.m-2.day-1, γL,N= 0.03 m2.g-1,
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2