Organismal traits can evolve in a coordinated way, with correlated patterns of gains and losses reflecting important evolutionary associations. Phylogenetic profiles treat individual genes as traits distributed across sets of genomes and can be used to identify functionally linked genes or lateral gene transfer. We propose the Community Coevolution Model (CCM) to analyze the evolutionary associations of traits (genes) based on phylogenetic profiles with traits evolving as a community with interactions, and the transition rate for each trait depends on the current states of other traits. We show that CCM is more efficient and fits real data better than other methods resulting in higher likelihood scores with fewer parameters. We further introduce a machine learning method (CNN-CCM) to estimate the parameters for large community CCM and demonstrate its efficiency through both simulations and real data.