  In this work, we explore the dynamics of species abundances within ecological
communities using the Generalized Lotka-Volterra (GLV) model. At variance with
previous approaches, we present an analysis of stochastic GLV dynamics with
temporal fluctuations in interaction strengths between species. We develop a
dynamical mean field theory (DMFT) tailored for scenarios with annealed colored
noise and simple functional responses. We show that time-dependent interactions
can be effectively modeled as environmental noise in the DMFT and we obtain
analytical predictions for the species abundance distribution that well matches
empirical observations. Our results suggest that environmental noise favors
species coexistence and allows to overcome the complexity-stability paradox,
especially in comparison to dynamics with quenched disorder. This study offers
new insights not only into the modeling of large ecosystem dynamics, but also
proposes novel methodologies for examining ecological systems.
