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Quantitative reconstructions of past climates are an important resource for evaluating how well climate models reproduce climate changes. One widely used statistical approach for making such reconstructions from fossil biotic assemblages is weighted averaging partial least-squares regression (WA-PLS). There is however a known tendency for WA-PLS to yield reconstructions compressed towards the centre of the climate range used for calibration, potentially biasing the reconstructed past climates. We present an improvement of WA-PLS by assuming that: (i) the theoretical abundance of each taxon is unimodal with respect to the climate variable considered; (ii) observed taxon abundances follow a multinomial distribution in which the total abundance of a sample is climatically uninformative; and (iii) the estimate of the climate value at a given site and time makes the observation most probable, i.e. it maximizes the log-likelihood function. This climate estimate is approximated by weighting taxon abundances in WA-PLS by the inverse square of their climate tolerances. We further improve the approach by considering the frequency (fx) of the climate variable in the training dataset. Tolerance-weighted WA-PLS with fx correction greatly reduces the compression bias, compared with WA-PLS, and improves model performance in reconstructions based on an extensive modern pollen dataset. [ABSTRACT FROM AUTHOR]

Many studies have failed to show an increase in the radial growth of trees in response to increasing atmospheric CO 2 concentration [CO 2 ] despite the expected enhancement of photosynthetic rates and water-use efficiency at high [CO 2 ]. A global light use efficiency model of photosynthesis, coupled with a generic carbon allocation and tree-growth model based on mass balance and tree geometry principles, was used to simulate annual ring-width variations for the gymnosperm Callitris columellaris in the semi-arid Great Western Woodlands, Western Australia, over the past 100 years. Parameter values for the tree-growth model were derived from independent observations except for sapwood specific respiration rate, fine-root turnover time, fine-root specific respiration rate and the ratio of fine-root mass to foliage area (ζ), which were calibrated to the ring-width measurements by approximate Bayesian optimization. This procedure imposed a strong constraint on ζ. Modelled and observed ring-widths showed quantitatively similar, positive responses to total annual photosynthetically active radiation and soil moisture, and similar negative responses to vapour pressure deficit. The model also produced enhanced radial growth in response to increasing [CO 2 ] during recent decades, but the data do not show this. Recalibration in moving 30-year time windows produced temporal shifts in the estimated values of ζ, including an increase by ca 12% since the 1960s, and eliminated the [CO 2 ]-induced increase in radial growth. The potential effect of CO 2 on ring-width was thus shown to be small compared to effects of climate variability even in this semi-arid climate. It could be counteracted in the model by a modest allocation shift, as has been observed in field experiments with raised [CO 2 ]. [ABSTRACT FROM AUTHOR]