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Fig. 11 | Biology Direct

Fig. 11

From: What can ecosystems learn? Expanding evolutionary ecology with learning theory

Fig. 11

In the long term the two-attractor system breaks down. Monte Carlo sampling of the ecological attractor states from random initial species densities during evolutionary time. Initially, all attractor states contain species densities that are only minor deviations from the default attractor (E 0) in Euclidean distance. The signed pattern of the attractor state, i.e. in terms of +/− with respect to the mean species densities, either matches E 1 (blue) or E 2 (green). As the two-attractor state emerges, at around generation 525 (a classic pitchfork bifurcation, but the unstable fixed point is not shown), the magnitudes (as well as signs) of the attractor states closely match the two targets. In the long term, one of the attractors, in this case E 1, outcompetes the other and becomes the only attractor. Eventually (after ∼575 generations), this attractor also degrades, i.e. the equilibrium magnitudes no longer match the original target closely (Fig. 10)

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