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Birth-death identifiability 2

Jeremy Beaulieu and Brian O'Meara
University of Arkansas and University of Tennessee

Diversification analyses: what can we do, and what should we do?

Jeremy Beaulieu and Brian O'Meara
Jeremy Beaulieu and Brian O'Meara

Models have long been used for understanding changing diversification patterns over time. The rediscovery that models with very different rates through time can fit a phylogeny equally well has led to great concern about the use of these models. We share and add to these concerns: even with time heterogeneous models without these issues, the distribution of the data means that estimates will be very uncertain, something which is rarely communicated in empirical studies. Congruence issues such as those established for certain models of diversification also occur in models as basic as Brownian motion and coin flipping, and part of using models is learning when they can and cannot provide insights. The specific concern about lack of information about rates over time does not apply to models primarily seeking to understand rates across taxa (like in many uses of SSE models), but this does not prove immunity to incongruence in general in such models.

John Rhodes
University of Alaska

Identifiability of Multitype Speciation Models

Models of tree generation, building on Yule's classical framework (1925), have played a role in many different sorts of biological studies. However, our understanding of whether the use of the more complex model variants for parameter estimation could be justified has only recently progressed. Although Louca & Pennell's non-identifiablity results (2020) for models with time-dependent speciation and extinction have rightfully received much attention, they do not apply to a different class of tree generation models which allow changes in rates across lineages in the developing tree. Perhaps the best know example of this class is the Binary-State Speciation and Extinction (BiSSE) model of Maddison et al. (2007), in which a changing binary trait determines speciation and extinction dynamics. Extensions to non-binary discrete traits, quantitative traits, and a more complex model with a hidden process determining trait influence, have also been developed and applied. Recently D. Dragomir, E. Allman and I established the first identifiability result among this class of models, for the "pure-birth multitype" model.

In this talk, after explaining the class of models and their uses, I will outline the key ideas in the analysis establishing identifiability. Although the current result applies only to models with no extinction, I will also speculate on prospects for extending it, as well as on possible issues with applications in data analysis.