Fig. 4: Map phase transition.

a shows the transition of the fraction of scores which converge to positive values of the plant-pollinator matrix Robertson 1929 (see Sec. “Datasets''). The four red circles above the blue line of the plot on the left are associated to the four plots on the right, which show the x-score trajectories for different exponents. The line colors refer to the node degree. b displays the absolute value of the transition exponent, γ_c, for the x-score as a function of the size and the density in uniform random matrices. Different line colors and styles represent different matrix densities on the left and different matrix sizes on the right. Each point is computed as an average over five matrices generated with the same parameters. c shows the scatter plot of the exponent which maximizes the extinction area, γ_EA and the exponent of the phase transition, γ_c, for uniform random matrices and the 20 largest ecological matrices (red points). The other three colors are different shapes of uniform random matrices: horizontal N = s/1.5, M = s*1.5 in blue, vertical N = s*1.5, M = s/1.5 in orange, and squared N = M = s in green. The considered matrices have been generated with different sizes s, between 50 and 200, and different densities between 0.2 and 0.4.