A recent study of a pair of sympatric species of palms on the Lord Howe Island is viewed as providing probably one of the most convincing examples of sympatric speciation to date. Here we describe and study a stochastic, individual-based, explicit genetic model tailored for this palms system. Overall, our results show that relatively rapid (<50,000 generations) colonization of a new ecological niche, and sympatric or parapatric speciation via local adaptation and divergence in flowering periods are theoretically plausible if (i) the number of loci controlling the ecological and flowering period traits is small; (ii) the strength of selection for local adaptation is intermediate; and (iii) an acceleration of flowering by a direct environmental effect associated with the new ecological niche is present. We discuss patterns and time-scales of ecological speciation identified by our model, and we highlight important parameters and features that need to be studied empirically in order to provide information that can be used to improve the biological realism and power of mathematical models of ecological speciation.