Minimum convex polygons (convex hulls) are an internationally accepted, standard method for estimating species' ranges, particularly in circumstances in which presence-only data are the only kind of spatially explicit data available. One of their main strengths is their simplicity. They are used to make area statements and to assess trends in occupied habitat, and are an important part of the assessment of the conservation status of species. We show by simulation that these estimates are biased. The bias increases with sample size, and is affected by the underlying shape of the species habitat, the magnitude of errors in locations, and the spatial and temporal distribution of sampling effort. The errors affect both area statements and estimates of trends. Some of these errors may be reduced through the application of α-hulls, which are generalizations of convex hulls, but they cannot be eliminated entirely. α-hulls provide an explicit means for excluding discontinuities within a species range. Strengths and weaknesses of alternatives including kernel estimators were examined. Convex hulls exhibit larger bias than α-hulls when used to quantify habitat extent and to detect changes in range, and when subject to differences in the spatial and temporal distribution of sampling effort and spatial accuracy. α-hulls should be preferred for estimating the extent of and trends in species' ranges.

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Papua New Guinea (PNG) has become the focus of climate change mitigation initiatives such as reducing emissions from deforestation and forest degradation, but defensible estimates of forest carbon are lacking. Here we present a methodology for estimating aboveground forest carbon, and apply it to a large Permanent Sample Plot system maintained by Papua New Guinea Forest Research Institute. We report the first estimates of forest carbon in lowland tropical forest in PNG. Average aboveground carbon in stems 4 10 cm diam. for 115 selectively harvested 1-ha plots in lowland tropical forest was 66.3 AE 3.5 Mg C/ha (95% CI) while for 10 primary forest plots the average was 106.3 AE 16.2 Mg C/ha. We applied ratios based on field observations, in-country studies, and the literature to estimate unmeasured pools of aboveground carbon (stems o 10 cm diam., fine litter and coarse woody debris). Total aboveground carbon was estimated at 90.2 and 120.8 Mg C/ha in selectively harvested and primary lowland forest, respectively. Our estimate for primary tropical forest is lower than biome averages for tropical equatorial forest, and we hypothesize that frequent disturbances from fire, frost, landslides, and agriculture are limiting carbon stock development. The methodology and estimates presented here will assist the PNG government in its preparedness for mitigation initiatives, are of interest to communities that are seeking to participate in voluntary carbon markets, and will encourage transparency and consistency in the estimation of forest carbon.