A Time-Inhomogeneous Prendiville Model with Failures and Repairs

We consider a time-inhomogeneous Markov chain with a finite state-space which models a system in which failures and repairs can occur at random time instants. The system starts from any state j (operating, F, R). Due to a failure, a transition from an operating state to F occurs after which a repair is required, so that a transition leads to the state R. Subsequently, there is a restore phase, after which the system restarts from one of the operating states. In particular, we assume that the intensity functions of failures, repairs and restores are proportional and that the birth-death process that models the system is a time-inhomogeneous Prendiville process.

At the Crossroads of Memory and Imagination: a Poetic Image of a Window at Night in Samuel Beckett’s "A Piece of Monologue"

The pivotal objective of this research is to analyse a poetic image of an imaginary window at night as well as a “ghost” room in Samuel Beckett’s play A Piece of Monologue through the binary lens of Gaston Bachelard’s The Poetics of Space, and Beckett’s biography. An absent onstage window, being part of an imagined reality created by the Speaker, becomes the nexus of this short play, and is discussed in relation to its locus, the writer’s memory, and material imagination. Tightly linked to Beckett’s life, childhood home and the instance of his birth, this image becomes a multi-layered construct, which gains a life of its own in the play and represents the universal themes of birth, death, loss of loved ones and mourning.

Distributions of extinction times from fossil ages and tree topologies: the example of mid-Permian synapsid extinctions

Given a phylogenetic tree that includes only extinct, or a mix of extinct and extant taxa, where at least some fossil data are available, we present a method to compute the distribution of the extinction time of a given set of taxa under the Fossilized-Birth-Death model. Our approach differs from the previous ones in that it takes into account (i) the possibility that the taxa or the clade considered may diversify before going extinct and (ii) the whole phylogenetic tree to estimate extinction times, whilst previous methods do not consider the diversification process and deal with each branch independently. Because of this, our method can estimate extinction times of lineages represented by a single fossil, provided that they belong to a clade that includes other fossil occurrences. We assess and compare our new approach with a standard previous one using simulated data. Results show that our method provides more accurate confidence intervals. This new approach is applied to the study of the extinction time of three Permo-Carboniferous synapsid taxa (Ophiacodontidae, Edaphosauridae, and Sphenacodontidae) that are thought to have disappeared toward the end of the Cisuralian (early Permian), or possibly shortly thereafter. The timing of extinctions of these three taxa and of their component lineages supports the idea that the biological crisis in the late Kungurian/early Roadian consisted of a progressive decline in biodiversity throughout the Kungurian.

Impacts of Taxon-Sampling Schemes on Bayesian Molecular Dating under the Unresolved Fossilized Birth-Death Process

Evolutionary timescales can be estimated using a combination of genetic data and fossil evidence based on the molecular clock. Bayesian phylogenetic methods such as tip dating and total-evidence dating provide a powerful framework for inferring evolutionary timescales, but the most widely used priors for tree topologies and node times often assume that present-day taxa have been sampled randomly or exhaustively. In practice, taxon sampling is often carried out so as to include representatives of major lineages, such as orders or families. We examined the impacts of these diversified sampling schemes on Bayesian molecular dating under the unresolved fossilized birth-death (FBD) process, in which fossil taxa are topologically constrained but their exact placements are not inferred. We used synthetic data generated by simulation of nucleotide sequence evolution, fossil occurrences, and diversified taxon sampling. Our analyses show that increasing sampling density does not substantially improve divergence-time estimates under benign conditions. However, when the tree topologies were fixed to those used for simulation or when evolutionary rates varied among lineages, the performance of Bayesian tip dating improves with sampling density. By exploring three situations of model mismatches, we find that including all relevant fossils without pruning off those inappropriate for the FBD process can lead to underestimation of divergence times. Our reanalysis of a eutherian mammal data set confirms some of the findings from our simulation study, and reveals the complexity of diversified taxon sampling in phylogenomic data sets. In highlighting the interplay of taxon-sampling density and other factors, the results of our study have useful implications for Bayesian molecular dating in the era of phylogenomics.

Fossils Do Not Substantially Improve, and May Even Harm, Estimates of Diversification Rate Heterogeneity

There is a prevailing view that the inclusion of fossil data could remedy identifiability issues related to models of diversification, by drastically reducing the number of congruent models. The fossilized birth-death (FBD) model is an appealing way of directly incorporating fossil information when estimating diversification rates. Here we explore the benefits of including fossils by implementing and then testing two-types of FBD models in more complex likelihood-based models that assume multiple rate classes across the tree. We also assess the impact of severely undersampling, and even not including fossils that represent samples of lineages that also had sampled descendants (i.e., k-type fossils), as well as converting a fossil set to represent stratigraphic ranges. Under various simulation scenarios, including a scenario that exists far outside the set of models we evaluated, including fossils rarely outperforms analyses that exclude them altogether. At best, the inclusion of fossils improves precision but does not influence bias. We also found that severely undercounting the number of k-type fossils produces highly inflated rates of turnover and extinction fraction. Similarly, we found that converting the fossil set to stratigraphic ranges results in turnover rates and extinction fraction estimates that are generally underestimated. While fossils remain essential for understanding diversification through time, in the specific case of understanding diversification given an existing, largely modern tree, they are not especially beneficial.