Influence of the tree prior and sampling scale on Bayesian phylogenetic estimates of the origin times of language families

Bayesian phylogenetic methods derived from evolutionary biology can be used to reconstruct the history of human languages using databases of cognate words. These analyses have produced exciting results regarding the origins and dispersal of linguistic and cultural groups through prehistory. Bayesian lexical dating requires the specification of priors on all model parameters. This includes the use of a prior on divergence times, often combined with a prior on tree topology and referred to as a tree prior. Violation of the underlying assumptions of the tree prior can lead to an erroneous estimate of the timescale of language evolution. To investigate these impacts, we tested the sensitivity of Bayesian dating to the tree prior in analyses of four lexical data sets. Our results show that estimates of the origin times of language families are robust to the choice of tree prior for lexical data, though less so than when Bayesian phylogenetic methods are used to analyse genetic data sets. We also used the relative fit of speciation and coalescent tree priors to determine the ability of speciation models to describe language diversification at four different taxonomic levels. We found that speciation priors were preferred over a constant-size coalescent prior regardless of taxonomic scale. However, data sets with narrower taxonomic and geographic sampling exhibited a poorer fit to ideal birth–death model expectations. Our results encourage further investigation into the nature of language diversification at different sampling scales.

The length of coastlines in Ptolemy's Geography and in ancient periploi

The lengths of the coastlines in Ptolemy's Geography are compared with the corresponding values transmitted by other ancient sources, presumably based on some lost periploi (literally "voyages around or circumnavigations", a genre of ancient geographical literature describing coastal itineraries). The comparison reveals a remarkable agreement between them, suggesting that Ptolemy relied much more heavily on these or similar periploi than it used to be thought. Additionally, a possible impact of Ptolemy's erroneous estimate of the circumference of the Earth is investigated. It is argued that this error resulted in two interrelated distortions of the coastal outlines in Ptolemy's Geography. First, the north–south stretches of the coast that were tied to particular latitudes are shown compressed relative to the distances recorded in other sources in roughly the same proportion to which Ptolemy's circumference of the Earth is underestimated relative to the true value. Second, in several cases this compression is compensated by a proportional stretching of the adjacent east–west coastal segments. In particular, these findings suggest a simple explanation for the strange shape of the Caspian Sea in Ptolemy's Geography.

Estimates of European uptake of CO₂ inferred from GOSAT X_CO₂ retrievals: sensitivity to measurement bias inside and outside Europe

Estimates of the natural CO2 flux over Europe inferred from in situ measurements of atmospheric CO2 mole fraction have been used previously to check top-down flux estimates inferred from space-borne dry-air CO2 column (XCO2) retrievals. Several recent studies have shown that CO2 fluxes inferred from XCO2 data from the Japanese Greenhouse gases Observing SATellite (GOSAT) and the Scanning Imaging Absorption Spectrometer for Atmospheric CHartographY (SCIAMACHY) have larger seasonal amplitudes and a more negative annual net CO2 balance than those inferred from the in situ data. The cause of this elevated European uptake of CO2 is still unclear, but some recent studies have suggested that this is a genuine scientific phenomenon. Here, we put forward an alternative hypothesis and show that realistic levels of bias in GOSAT data can result in an erroneous estimate of elevated uptake over Europe. We use a global flux inversion system to examine the relationship between measurement biases and estimates of CO2 uptake from Europe. We establish a reference in situ inversion that uses an Ensemble Kalman Filter (EnKF) to assimilate conventional surface mole fraction observations and XCO2 retrievals from the surface-based Total Carbon Column Observing Network (TCCON). We use the same EnKF system to assimilate two independent versions of GOSAT XCO2 data. We find that the GOSAT-inferred European terrestrial biosphere uptake peaks during the summer, similar to the reference inversion, but the net annual flux is 1.40 ± 0.19 GtC a−1 compared to a value of 0.58 ± 0.14 GtC a−1 for our control inversion that uses only in situ data. To reconcile these two estimates, we perform a series of numerical experiments that assimilate observations with added biases or assimilate synthetic observations for which part or all of the GOSAT XCO2 data are replaced with model data. We find that for our global flux inversions, a large portion (60–90 %) of the elevated European uptake inferred from GOSAT data in 2010 is due to retrievals outside the immediate European region, while the remainder can largely be explained by a sub-ppm retrieval bias over Europe. We use a data assimilation approach to estimate monthly GOSAT XCO2 biases from the joint assimilation of in situ observations and GOSAT XCO2 retrievals. The inferred biases represent an estimate of systematic differences between GOSAT XCO2 retrievals and the inversion system at regional or sub-regional scales. We find that a monthly varying bias of up to 0.5 ppm can explain an overestimate of the annual sink of up to 0.20 GtC a−1. Our results highlight the sensitivity of CO2 flux estimates to regional observation biases, which have not been fully characterized by the current observation network. Without further dedicated measurements we cannot prove or disprove that European ecosystems are taking up a larger-than-expected amount of CO2. More robust inversion systems are also needed to infer consistent fluxes from multiple observation types.

On the corrections in the elements of Delambre’s solar tables required by the observations made at the Royal Observatory, Greenwich

The author was desired by the Board of Longitude to examine the discordancies between the right ascensions of the sun, as observed at Greenwich, since the erection of the new transit instrument, and as computed by the solar tables of Delambre, which are used in the computation of the Nautical Almanac; with a view to the discovery of the errors in the elements of those tables. The number of observations from which this comparison was made is 1212, and they extend, with an interruption of only three months, from the end of July 1816 to the end of the year 1826. The result of the comparison at first indicated the necessity of a correction of the epochs of the sun’s longitude, and of the longitude of the perigee, and perhaps also of the equation of the centre. But upon pursuing the examination through a series of years, it became manifest that some other source of irregularity existed, and that this could be no other than an erroneous estimate of the masses of some of the planets, especially of Venus and of Mars. A more critical examination showed, that there was also an error in the assigned mass of the moon. The author proceeds to state the process by which he arrived at the determination of the amount of these several corrections. It was found necessary in these investigations to take into account an error which occurred in the tables with regard to the secular motion. It results from his researches, that the epochs for 1816 and those for 1821 to 25 ought to be increased respectively by 4"·734 and 5"·061; that of the perigee increased by 46"·3, and the greatest equation of the centre diminished by 0"·84. The mass of Venus should be reduced in the proportion nearly of 9 to 8, and that of Mars nearly in the proportion of 22 to 15. On a comparison of these results with those which have been derived from an examination of some of Dr. Maskelyne’s observations, as given by Burkhardt in the Connaissance des Tems for 1816, they are found on the whole to agree in the most satisfactory manner. The principal discordance occurs in the correction of the place of the perigee; a discordance which the author thinks may arise either from want of correctness in the calculation of the term in the motion of the perigee, depending on the square of the time, or, what is more probable, from some undiscovered inequality in the formula, which is a function of the sun’s mean longitude.