Bhutan has measured citizens' well-being using gross national happiness since 2008 (left); GDP has been in use since the 1944 Bretton Woods meeting (right).

Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data sets from the model. In this paper we show that under the assumption of the existence of a uniform additive model error term, ABC algorithms give exact results when sufficient summaries are used. This interpretation allows the approximation made in many previous application papers to be understood, and should guide the choice of metric and tolerance in future work. ABC algorithms can be generalized by replacing the 1 0-1 cut-off with an acceptance probability that varies with the distance of the simulated data from the observed data. The acceptance density gives the distribution of the error term, enabling the uniform error usually used to be replaced by a general distribution. This generalization can also be applied to approximate Markov chain Monte Carlo algorithms. In light of this work, ABC algorithms can be seen as calibration techniques for implicit stochastic models, inferring parameter values in light of the computer model, data, prior beliefs about the parameter values, and any measurement or model errors.

Estimation of divergence times is usually done using either the fossil record or sequence data from modern species. We provide an integrated analysis of palaeontological and molecular data to give estimates of primate divergence times that utilize both sources of information. The number of preserved primate species discovered in the fossil record, along with their geological age distribution, is combined with the number of extant primate species to provide initial estimates of the primate and anthropoid divergence times. This is done by using a stochastic forwards-modeling approach where speciation and fossil preservation and discovery are simulated forward in time. We use the posterior distribution from the fossil analysis as a prior distribution on node ages in a molecular analysis. Sequence data from two genomic regions (CFTR on human chromosome 7 and the CYP7A1 region on chromosome 8) from 15 primate species are used with the birth-death model implemented in mcmctree in PAML to infer the posterior distribution of the ages of 14 nodes in the primate tree. We find that these age estimates are older than previously reported dates for all but one of these nodes. To perform the inference, a new approximate Bayesian computation (ABC) algorithm is introduced, where the structure of the model can be exploited in an ABC-within-Gibbs algorithm to provide a more efficient analysis.

Lobsters are a ubiquitous and economically important group of decapod crustaceans that include the infraorders Polychelida, Glypheidea, Astacidea and Achelata. They include familiar forms such as the spiny, slipper, clawed lobsters and crayfish and unfamiliar forms such as the deep-sea and "living fossil" species. The high degree of morphological diversity among these infraorders has led to a dynamic classification and conflicting hypotheses of evolutionary relationships. In this study, we estimated phylogenetic relationships among the major groups of all lobster families and 94% of the genera using six genes (mitochondrial and nuclear) and 195 morphological characters across 173 species of lobsters for the most comprehensive sampling to date. Lobsters were recovered as a non-monophyletic assemblage in the combined (molecular + morphology) analysis. All families were monophyletic, with the exception of Cambaridae, and 7 of 79 genera were recovered as poly- or paraphyletic. A rich fossil history coupled with dense taxon coverage allowed us to estimate and compare divergence times and origins of major lineages using two drastically different approaches. Age priors were constructed and/or included based on fossil age information or fossil discovery, age, and extant species count data. Results from the two approaches were largely congruent across deep to shallow taxonomic divergences across major lineages. The origin of the first lobster-like decapod (Polychelida) was estimated in the Devonian (∼409-372 Ma) with all infraorders present in the Carboniferous (∼353-318 Ma). Fossil calibration subsampling studies examined the influence of sampling density (number of fossils) and placement (deep, middle, and shallow) on divergence time estimates. Results from our study suggest including at least 1 fossil per 10 operational taxonomic units (OTUs) in divergence dating analyses. [Dating; decapods; divergence; lobsters; molecular; morphology; phylogenetics.].

How to cite:Holden, Philip B.; Edwards, N. R.; Oliver, K. I. C.; Lenton, T. M. and Wilkinson, R. D. (2010). A probabilistic calibration of climate sensitivity and terrestrial carbon change in GENIE-1. Climate Dynamics, 35 (5) AbstractIn order to investigate Last Glacial Maximum and future climate, we "precalibrate" the intermediate complexity model GENIE-1 by applying a rejection sampling approach to deterministic emulations of the model. We develop ~1,000 parameter sets which reproduce the main features of modern climate, but not precise observations. This allows a wide range of large-scale feedback response strengths which generally encompass the range of GCM behaviour. We build a deterministic emulator of climate sensitivity and quantify the contributions of atmospheric (±0.93ºC, 1σ) vegetation (±0.32ºC), ocean (±0.24ºC) and sea-ice (±0.14ºC) parameterisations to the total uncertainty. We then perform an LGM-constrained Bayesian calibration, incorporating data-driven priors and formally accounting for structural error. We estimate climate sensitivity as likely (66% confidence) to lie in the range 2.6 to 4.4ºC, with a peak probability at 3.6ºC. We estimate LGM cooling likely to lie in the range 5.3 to 7.5ºC, with a peak probability at 6.2ºC. In addition to estimates of global temperature change, we apply our ensembles to derive LGM and 2xCO 2 probability distributions for land carbon storage, Atlantic overturning and sea-ice coverage.Notably, under 2xCO 2 we calculate a probability of 37% that equilibrium terrestrial carbon storage is reduced from modern values, so the land sink has become a net source of atmospheric CO 2 .