  We study species abundance in the empirical plant-pollinator mutualistic
networks exhibiting broad degree distributions, with uniform intra-group
competition assumed, by the Lotka-Volterra equation. The stability of a fixed
point is found to be identified by the signs of its non-zero components and
those of its neighboring fixed points. Taking the annealed approximation, we
derive the non-zero components to be formulated in terms of degrees and the
rescaled interaction strengths, which lead us to find different stable fixed
points depending on parameters, and we obtain the phase diagram. The selective
extinction phase finds small-degree species extinct and effective interaction
reduced, maintaining stability and hindering the onset of instability. The
non-zero minimum species abundances from different empirical networks show data
collapse when rescaled as predicted theoretically.
