An Alternative Approach to Compute the Likelihood for the DAISIE (Dynamic Assembly of Island Biota Through Speciation, Immigration, and Extinction) Model

Understanding island biodiversity requires studying the processes driving its assembly and examining how these processes vary over time, across lineages, and across different islands. The DAISIE (Dynamic Assembly of Island biota through Speciation, Immigration, and Extinction) framework has been developed for this purpose, and has advanced our understanding of island community assembly by estimating, from phylogenetic data, the contribution of the processes of colonization, speciation and extinction to island community assembly. However, the model assumes uniform colonization and diversification rates across lineages, ignoring potential variation in these rates caused by, for example, lineage-specific traits. This assumption thus restricts the model's capacity to capture complex colonization and diversification dynamics, and may consequently bias inference of colonization and diversification dynamics on islands. An extension of the framework behind these more complex dynamics is therefore desired. However, for this state-dependent colonization and diversification extension, the current computation of the likelihood of the model given phylogenetic data is computationally prohibitive. In this study, we therefore propose an alternative approach to computing the DAISIE likelihood, under the assumption of diversity-independent colonization and diversification. Our novel approach is based on the pruning algorithm that has been used for computing the likelihood of SSE (State-dependent Speciation and Extinction) models, which traces lineage history backward in time from the present day to the root of the tree. We demonstrate that our alternative approach reproduces DAISIE's predictions under diversity-independent colonization and diversification. This provides an additional layer of support to DAISIE in diversity-independent settings, but in doing so also gives more confidence in the results under diversity-dependence. Furthermore, our alternative approach offers greater computational efficiency. Finally, it provides a flexible framework for incorporating state-dependent dynamics in colonization, speciation, and extinction processes.