Global gyrokinetic simulations find that realistic density gradients of energetic particles can simultaneously excite low frequency Alfven eigenmodes in toroidal geometry, beta-induced Alfven-acoustic eigenmode (BAAE) and beta-induced Alfven eigenmode (BAE), with similar radial mode widths and comparable linear growth rates even though damping rate of BAAE is much larger than BAE in the absence of energetic particles. This surprising result is attributed to non-perturbative effects of energetic particles that modify ideal BAAE mode polarizations and nonlocal geometry effects that invalidate radially local dispersion relation. Dominant mode changes from BAAE in a larger tokamak to BAE in a smaller tokamak due to the dependence of wave-particle resonance condition on the tokamak size.