Exact simulation of the Wright-Fisher diffusion

The Wright-Fisher family of diffusion processes is a widely used class of evolutionary models. However, simulation is difficult because there is no known closed-form formula for its transition function. In this article we demonstrate that it is in fact possible to simulate exactly from a broad class of Wright-Fisher diffusion processes and their bridges. For those diffusions corresponding to reversible, neutral evolution, our key idea is to exploit an eigenfunction expansion of the transition function; this approach even applies to its infinite-dimensional analogue, the Fleming-Viot process. We then develop an exact rejection algorithm for processes with more general drift functions, including those modelling natural selection, using ideas from retrospective simulation. Our approach also yields methods for exact simulation of the moment dual of the Wright-Fisher diffusion, the ancestral process of an infinite-leaf Kingman coalescent tree. We believe our new perspective on diffusion simulation holds promise for other models admitting a transition eigenfunction expansion.Comment: 36 pages, 2 figure, 2 tables. This version corrects an error in the proof of Lemma 6.

Consistency of Bayesian nonparametric inference for discretely observed jump diffusions

We introduce verifiable criteria for weak posterior consistency of identifiable Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient and uniformly Lipschitz drift and jump coefficients in arbitrary dimension. The criteria are expressed in terms of coefficients of the SDEs describing the process, and do not depend on intractable quantities such as transition densities. We also show that products of discrete net and Dirichlet mixture model priors satisfy our conditions, again under an identifiability assumption. This generalises known results by incorporating jumps into previous work on unit diffusions with uniformly Lipschitz drift coefficients.Comment: 20 page

Dual process in the Two-parameter Poisson-Dirichlet diffusion

The two-parameter Poisson--Dirichlet diffusion takes values in the infinite ordered simplex and has a two-parameter Poisson-Dirichlet stationary distribution ${\cal PD}(\alpha, \theta)$ . The dual process is in terms of a line-of-descent process which tracks the evolution of non-mutant frequencies from time zero, and Remarkably does not depend on the parameter $\alpha$. Methods of proof use the sampling distributions associated to the two-parameter Poisson-Dirichlet process. We also exploit a connection between the sampling distribution and a generalized Blackwell and MacQueen P{\'o}lya urn model to obtain a direct derivation of the transition density

Excursion theory for the Wright-Fisher diffusion

In this work, we develop excursion theory for the Wright-Fisher diffusion with recurrent mutation. Our construction is intermediate between the classical excursion theory where all excursions begin and end at a single point and the more general approach considering excursions of processes from general sets. Since the Wright-Fisher diffusion has two boundary points, it is natural to construct excursions which start from a specified boundary point, and end at one of two boundary points which determine the next starting point. In order to do this we study the killed Wright-Fisher diffusion, which is sent to a cemetery state whenever it hits either endpoint. We then construct a marked Poisson process of such killed paths which, when concatenated, produce a pathwise construction of the Wright-Fisher diffusion.Comment: 19 pages, 3 figure

The FLUXNET2015 dataset and the ONEFlux processing pipeline for eddy covariance data

The FLUXNET2015 dataset provides ecosystem-scale data on CO2, water, and energy exchange between the biosphere and the atmosphere, and other meteorological and biological measurements, from 212 sites around the globe (over 1500 site-years, up to and including year 2014). These sites, independently managed and operated, voluntarily contributed their data to create global datasets. Data were quality controlled and processed using uniform methods, to improve consistency and intercomparability across sites. The dataset is already being used in a number of applications, including ecophysiology studies, remote sensing studies, and development of ecosystem and Earth system models. FLUXNET2015 includes derived-data products, such as gap-filled time series, ecosystem respiration and photosynthetic uptake estimates, estimation of uncertainties, and metadata about the measurements, presented for the first time in this paper. In addition, 206 of these sites are for the first time distributed under a Creative Commons (CC-BY 4.0) license. This paper details this enhanced dataset and the processing methods, now made available as open-source codes, making the dataset more accessible, transparent, and reproducible.Peer reviewe

Geothermobarometry of Al-silicate-bearing migmatites from the Variscan chain of NE Sardinia, Italy: a P-T pseudosection approach

This paper investigates Al-silicate-bearing migmatite from NE Sardinia by using the P-T pseudosection approach with the aim to determine the P-T conditions of partial melting and those of melt crystallization. P-T pseudosections were calculated in the NCKFMASH system within the P-T range 500-800°C, 0.1-1.5 GPa by using the average compositions of metapelitic greywacke, average mesosome and average trondhjemitic leucosome, respectively. The P-T pseudosections calculated for the average metapelitic greywacke and for the average mesosome, contoured for melt volume %, Si/Al and Na/K molar ratios in melt point to P–T conditions 700-740°C, 1.1-1.3 GPa which are indicative of partial melting. The P-T pseudosection calculated for the average composition of trondhjemitic leucosomes, contoured for kyanite and biotite modal content and for XMg ratio in biotite indicates P-T conditions of 660-730°C, 0.75-0.90 GPa for the crystallization of the melt. The comparison between the Na/K and Si/Al ratios in leucosomes, and the same ratios modeled for the anatectic melt by an haplogranitic melt model is thus a powerful tool for the reconstruction of P-T conditions of partial melting also in pelitic rocks, provided that leucosomes represent pure melts and are not contaminated by restitic phases or feldspar cumulates

Petrophysical properties of Variscan mylonitic leucogranite of Monte Grighine, west-central Sardinia

Abstract: Monte Grighini Complex consist of a pile of variscan Nappes and of a suite of granitoid rocks, mostly monzogranite and leucogranite (Musumeci, 1992), that intrudes the tectonic unit of Monte Grighini. Rb/Sr and Ar/Ar radiometric data give, for granitoid rocks, an age of about 305-300 Ma (Carmignani et al., 1987; Laurenzi et al., 1991). A late variscan shear zone affects the SW side of the complex and produces a wide cataclastic and mylonitic zone, along which leucogranite can be mostly found. In this zone an outcrop, that shows a rapid change in the intensity of mylonitic deformation, has been investigated in detail. The outcrop is affected by a pervasive N162-170° foliation dipping 60-65° W. Petrographic and XRD analysis show the following mineralogical assemblage: quartz, k-felspar, plagioclase (albite), muscovite, biotite, iron oxides and ± tourmaline ± apatite ± zircon ± epidote. Almost all samples are characterized by k-feldspar porphyroclasts in a quartz-phyllosilicate matrix. On the basis of porphyroclast/matrix ratio protomylonite, mylonite and ultramylonite layers have been identified. In protomylonitic layers k-felspar phenocrysts are fractured and sometimes perthitic. Quartz occurs in microcrystalline lens and bands following the foliation. Phyllosilicate matrix consists of biotite, subordinate muscovite and chlorite. Mylonitic layers are similar to the previous ones but show a decrease in grain-size. Ultramylonitic layer consists of rare k-feldspar relics in a very fine-grained phyllosilicate matrix. The following physical properties have been determined in 12 series of samples with varying degree of deformation: the open porosity, the total porosity, the real and apparent density, the water imbibition coefficient, and the water saturation index. To calculate the closed and total porosity the real density of ground samples were determined. The ultrasonic velocity of the studied samples has been determined in three directions: 1) perpendicular to the foliation, 2) parallel to the foliation and to the direction of mineral stretching lineation, 3) parallel to the foliation and perpendicular to the direction of mineral stretching lineation. The overall results indicate that the samples of protomylonite, mylonite and ultramylonite have different physical properties values. The average values of the real density of samples vary from a minimum of 2.66±0.02 g/cm3 in the protomylonitic samples, to a maximum of 2.72±0.01 g/cm3, in the ultramylonitic samples. The mylonitic samples show intermediate values with an average of 2.68±0.01 g/cm3. The open porosity shows a similar trend; it ranges from 4.1±0.2% in the protomylonitic samples, to 6.3±0.9% in the mylonitic samples, to 9.2±0.5% in the ultramylonitic samples. Therefore, there is a positive correlation between the degree of mylonitization and these physical parameters. The ultrasonic velocity values show on one side of the greater porosity of ultramylonites than proto-mylonites and mylonites, on the other side confirm a higher anisotropy degree in the ultramylonitic samples releaved perpendicular to the foliation. Preliminary results seem to suggest a relationship between the petrographic and petrophysical characteristics of the layers. References Carmignani L., Cherchi G.P., Del Modo A., Franceschelli M., Ghezzo C., Musumeci G. & Pertusati P.C. (1987). IGCP project n°5. Newsletter. Higgins M. W. (1991). USGS Prof. Paper 687. Laurenzi M.A., Del Moro A., Musumeci G. & Pardini G. (1991). Terra abstract, 3, 1, p. 501-502. Musumeci G. (1992). Geodinamica Acta: 5, 119-133, Paris