Biodiversity is in decline and conservation is becoming increasingly important in today's society. The process of speciation, how new species evolve, is fundamental to biodiversity maintenance but is not fully understood. Phylogenetic trees show the origins of present day diversity, pinpointing when species evolved and describing their relatedness. They are also used in modeling the different strains of diseases such as flu. A lot of research has taken place with the aim of interpreting speciation and phylogenetic trees by evaluating various models. In this project, we use neutral models, which make the controversial assumption that all individuals interact with the system in an identical manner regardless of their species. Despite their assumptions, these models match ecological data with astounding precision, attracting a lot of research attention. For modeling phylogenetic trees, neutral models improve on many earlier models because the probability of a species becoming extinct becomes proportional to the number of representative individuals. Point mutation is one of three modes of speciation regularly used in these models. It states that every newborn individual has a constant probability being a new species. A powerful computational method based on coalescence traces the ancestry of individuals backwards in time. This solves the problems of waiting for equilibrium and restrictive simulation sizes associated with alternative forwards simulations. Point mutation creates a lot of species with only one member, which is not observed in reality. The phylogenetic trees it generates consequently appear unrealistic having many passing mutations counted as novel species. The other two mechanisms are random fission and peripheral isolate speciation where new species arrive as a small founding population. This approach is promising but the coalescence simulations cannot be used for these modes of speciation. This is extremely restrictive and prevents detailed studies. We will develop novel modification of coalescence to make it suitable for investigating the random fission and peripheral isolate modes of speciation. Speciation in nature is a gradual process but all three existing mechanisms assume a sudden speciation event. We propose a novel speciation mechanism where each individual has a simple genome including two genes. This solves the problem of passing mutations in a different way; they exist but would never be defined as a distinct species because the passing mutation would only influence one of the two genes. This mechanism of speciation is gradual because time passes between the mutation of the first gene and mutation of the second gene. It is mutation of the second gene that completes the speciation process. We will fully investigate this mode of speciation and the phylogenetic trees it generates. We have a number of exciting applications for these novel methods, each of which requires a different spatially explicit structure in the model. A two dimensional spatially explicit version of the model is suitable for comparison with empirical phylogenies from collaborator Stephen Hubbell. We have access to a further dataset collected across a rainfall gradient. This will give us the opportunity to test a version of the model that includes habitat heterogeneity. A network of distinct communities is an appropriate spatial structure for many applications including archipelagos and disease dynamics. For example, our collaborator Luke Harmon has zooplankton data collected from fresh water lakes, where a comparison with neutral models would be insightful. A medical application also exists regarding bioflms. These are adhesive matrices and infections that are untreatable with antibiotics. Recent research has shown an extreme rate of diversification in these biofilms. A test using a three dimensional neutral model would be insightful research in understanding within biofilm competition.