Incongruences between gene trees and corresponding species trees are common. Gene duplication, gene loss, and lateral gene transfer are three types of evolutionary events that can cause such incongruences. I will first describe our probabilistic model of nucleotide substitutions, gene duplication, gene loss, and lateral gene transfer. This model requires a dated species tree and can be used to reconstruct a gene tree for a gene family of interest and simultaneously reconcile the gene tree with the species tree. I will then describe how we used our MCMC framework PrIME, based on the model, to analyze gene families from Mollicutes and Cyanobacteria as well as the results obtained.