A rapid and scalable method for multilocus species delimitation using Bayesian model comparison and rooted triplets

Multilocus sequence data provide far greater power to resolve species limits than the single locus data typically used for broad surveys of clades. However, current statistical methods based on a multispecies coalescent framework are computationally demanding, because of the number of possible delimitations that must be compared and time-consuming likelihood calculations. New methods are therefore needed to open up the power of multilocus approaches to larger systematic surveys. Here, we present a rapid and scalable method that introduces two new innovations. First, the method reduces the complexity of likelihood calculations by decomposing the tree into rooted triplets. The distribution of topologies for a triplet across multiple loci has a uniform trinomial distribution when the 3 individuals belong to the same species, but a skewed distribution if they belong to separate species with a form that is specified by the multispecies coalescent. A Bayesian model comparison framework was developed and the best delimitation found by comparing the product of posterior probabilities of all triplets. The second innovation is a new dynamic programming algorithm for finding the optimum delimitation from all those compatible with a guide tree by successively analyzing subtrees defined by each node. This algorithm removes the need for heuristic searches used by current methods, and guarantees that the best solution is found and potentially could be used in other systematic applications. We assessed the performance of the method with simulated, published and newly generated data. Analyses of simulated data demonstrate that the combined method has favourable statistical properties and scalability with increasing sample sizes. Analyses of empirical data from both eukaryotes and prokaryotes demonstrate its potential for delimiting species in real cases

Valuing Energy Options in a One Factor Model Fitted to Forward Prices

In this paper we develop a single-factor modeling framework which is consistent with market observable forward prices and volatilities. The model is a special case of the multi-factor model developed in Clewlow and Stickland [1999b] and leads to analytical pricing formula for standard options, caps, floors, collars and swaptions. We also show how American style and exotic energy derivatives can be priced using trinomial trees, which are constructed to be consistent with the forward curve and volatility structure. We demonstrate the application of the trinomial tree to the pricing of a European and American Asian option. The analysis in this paper extends the results in Schwartz [1997] and Amin, et al. [1995].

Numerical methods for forward curve models in oil and gas markets

Imperial Users onl