A covariate adjustment for zero-truncated approaches to estimating the size of hidden and elusive populations

In this paper we consider the estimation of population size from onesource capture–recapture data, that is, a list in which individuals can potentially be found repeatedly and where the question is how many individuals are missed by the list. As a typical example, we provide data from a drug user study in Bangkok from 2001 where the list consists of drug users who repeatedly contact treatment institutions. Drug users with 1, 2, 3, . . . contacts occur, but drug users with zero contacts are not present, requiring the size of this group to be estimated. Statistically, these data can be considered as stemming from a zero-truncated count distribution.We revisit an estimator for the population size suggested by Zelterman that is known to be robust under potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood estimator for a locally truncated Poisson likelihood which is equivalent to a binomial likelihood. This result allows the extension of the Zelterman estimator by means of logistic regression to include observed heterogeneity in the form of covariates. We also review an estimator proposed by Chao and explain why we are not able to obtain similar results for this estimator. The Zelterman estimator is applied in two case studies, the first a drug user study from Bangkok, the second an illegal immigrant study in the Netherlands. Our results suggest the new estimator should be used, in particular, if substantial unobserved heterogeneity is present.

Decadal-scale rainfall variability in Ethiopia recorded in an annually laminated, Holocene-age, stalagmite

An annually laminated, uranium-series dated, Holocene stalagmite from southeast Ethiopia has been analysed for growth rate and δ13C and δ18O variations at annual to biennial resolution, in order to provide the first long duration proxy record of decadal-scale rainfall variability in this climatically sensitive region. Our study site (10°N) is climatically influenced by both summer (June—August) and spring (March—May) rainfall caused by the annual movement of the Inter-Tropical Convergence Zone (ITCZ) and modulated by large-scale anomalies in the atmospheric circulation and in ocean temperatures. Here we show that stalagmite growth, episodic throughout the last 7800 years, demonstrates decadal-scale (8—25 yr) variability in both growth rate and δ 18O. A hydrological model was employed and indicates that this decadal variability is due to variations in the relative amounts of rainfall in the two rain seasons. Our record, unique in its combination of length (a total of ~1000 years), annual chronology and high resolution δ18O, shows for the first time that such decadal-scale variability in rainfall in this region has occurred through the Holocene, which implies persistent decadal-scale variability for the large-scale atmospheric and oceanic driving factors.

Radiative forcing due to changes in ozone and methane caused by the transport sector

The year 2000 radiative forcing (RF) due to changes in O3 and CH4 (and the CH4-induced stratospheric water vapour) as a result of emissions of short-lived gases (oxides of nitrogen (NOx), carbon monoxide and non-methane hydrocarbons) from three transport sectors (ROAD, maritime SHIPping and AIRcraft) are calculated using results from five global atmospheric chemistry models. Using results from these models plus other published data, we quantify the uncertainties. The RF due to short-term O3 changes (i.e. as an immediate response to the emissions without allowing for the long-term CH4 changes) is positive and highest for ROAD transport (31mWm-2) compared to SHIP (24 mWm-2) and AIR (17 mWm-2) sectors in four of the models. All five models calculate negative RF from the CH4 perturbations, with a larger impact from the SHIP sector than for ROAD and AIR. The net RF of O3 and CH4 combined (i.e. including the impact of CH4 on ozone and stratospheric water vapour) is positive for ROAD (+16(±13)(one standard deviation) mWm-2) and AIR (+6(±5) mWm-2) traffic sectors and is negative for SHIP (-18(±10) mWm-2) sector in all five models. Global Warming Potentials (GWP) and Global Temperature change Potentials (GTP) are presented for AIR NOx emissions; there is a wide spread in the results from the 5 chemistry models, and it is shown that differences in the methane response relative to the O3 response drive much of the spread.