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. 2012 Aug 22;15(11):1300–1307. doi: 10.1111/j.1461-0248.2012.01853.x

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Copyright © 2012 Blackwell Publishing Ltd/CNRS

Re-use of this article is permitted in accordance with the Creative Commons Deed, Attribution 2.5, which does not permit commercial exploitation.

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The emergence of bistability as host resource levels I_s increase (eqn 3). The higher the host resource input rate I_s, the steeper the Pathogen's nullcline (grey, red online) (A: I_s= 5; B: I_s= 7; C: I_s= 11; black is the Beneficial's nullcline). The system becomes bistable above a critical I_s value. Solid dots indicate stable fixed points, and the empty dot indicates the unstable fixed point (r_p= 2.5, r_b= 2, α = 0.2, k = 1, A_c= 0.1). The antibiotic effect of beneficials on pathogens is scaled by , which is a function of . Increasing I_s increases growth rates of all bacteria but also allows greater antibiotic production, leading to suppression of Pathogens.

Inline graphic — The emergence of bistability as host resource levels I_s increase (eqn 3). The higher the host resource input rate I_s, the steeper the Pathogen's nullcline (grey, red online) (A: I_s= 5; B: I_s= 7; C: I_s= 11; black is the Beneficial's nullcline). The system becomes bistable above a critical I_s value. Solid dots indicate stable fixed points, and the empty dot indicates the unstable fixed point (r_p= 2.5, r_b= 2, α = 0.2, k = 1, A_c= 0.1). The antibiotic effect of beneficials on pathogens is scaled by , which is a function of . Increasing I_s increases growth rates of all bacteria but also allows greater antibiotic production, leading to suppression of Pathogens.