Phase portraits obtained numerically from <b>Eqs. (1)</b>–<b>(2)</b> displaying the dynamics in the phase plane (<i>x</i>₁, <i>x</i>₂), with <i>x</i>₁+<i>x</i>₂ = 1, and the stability of the fixed points: <i>P</i>₁^*, <i>P</i>₂^*, <i>P</i>₃^*, and <i>P</i>₄^* (stable and unstable equilibria are shown, respectively, in black and white circles).

<p>In (a) we use the experimental values used in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0017917#pone-0017917-g004" target="_blank">Fig. 4 (a)</a> right. In (b) we use the same values of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0017917#pone-0017917-g004" target="_blank">Fig. 4(b)</a> left. In both cases the origin is a repeller; <i>P</i>₃^* is a saddle; <i>P</i>₂^* (outcompetition of <i>x</i>₂ by <i>x</i>₁) is stable and the equilibrium <i>P</i>₄^* is outside the phase plane. In (c) we show the asymptotic coexistence scenario, where <i>P</i>₂^* becomes a saddle and the fixed point <i>P</i>₄^*, which is stable, is inside the phase plane (here we use <i>r_max</i>_,1 = 1.07, <i>r_max</i>_,2 = 0.621, <i>K</i>₁ = 0.8 and <i>K</i>₂ = 0.2). The arrows in all the plots indicate the directions of the flows.