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.

中文翻译：

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从生物组合重建过去气候的改进统计方法

过去气候的定量重建是评估气候模型再现气候变化效果的重要资源。一种从化石生物组合进行此类重建的广泛使用的统计方法是加权平均偏最小二乘回归 (WA-PLS)。然而，WA-PLS 有一种已知的趋势，即产生向用于校准的气候范围中心压缩的重建，这可能会使重建的过去气候产生偏差。我们通过假设提出了 WA-PLS 的改进：（i）每个分类单元的理论丰度相对于所考虑的气候变量是单峰的；(ii) 观察到的分类群丰度遵循多项分布，其中样本的总丰度在气候方面没有信息；(iii) 对给定地点和时间的气候值的估计使观测最有可能，即它最大化对数似然函数。该气候估计是通过对 WA-PLS 中的分类群丰度按其气候耐受性的平方反比加权来近似得出的。我们通过考虑训练数据集中气候变量的频率 (fx) 来进一步改进该方法。与 WA-PLS 相比，具有 fx 校正的容差加权 WA-PLS 大大降低了压缩偏差，并提高了基于广泛的现代花粉数据集的重建模型性能。我们通过考虑训练数据集中气候变量的频率 (fx) 来进一步改进该方法。与 WA-PLS 相比，具有 fx 校正的容差加权 WA-PLS 大大降低了压缩偏差，并提高了基于广泛的现代花粉数据集的重建模型性能。我们通过考虑训练数据集中气候变量的频率 (fx) 来进一步改进该方法。与 WA-PLS 相比，具有 fx 校正的容差加权 WA-PLS 大大降低了压缩偏差，并提高了基于广泛的现代花粉数据集的重建模型性能。