Figure 29. Diagrammatic representations of remaining two of four patterns of gene frequency changes in hypothetical host-parasite models. C. Stable limit cycle: if gene frequencies start anywhere on the closed trajectory represented by the circle with the solid line, they remain in that trajectory as they cycle around the internal equilibrium point (EP). Gene frequencies starting outside the limit cycle (for example at point 0), spiral inward toward the limit cycle. Gene frequencies starting inside the limit cycle (e.g., point I) spiral outward toward the limit cycle. D. Unstable limit cycle: gene frequencies starting on an unstable limit cycle continue in its closed trajectory, but gene frequencies that start outside the unstable limit cycle (e.g. point 0) spiral outward toward fixation of virulence and loss of resistance. Gene frequencies that start inside the unstable limit cycle (e.g. point I) spiral inward toward the internal equilibrium point (EP). For a very large unstable limit cycle whose trajectory essentially follows the boundaries of the phase plane, nearly any initial frequencies of resistance and virulence genes lead to an inward spiral toward the internal EP.

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