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The Coexistence Approach has been used to infer palaeoclimates for manyEurasian fossil plant assemblages. However, the theory that underpins themethod has never been examined in detail. Here we discuss acknowledged andimplicit assumptions and assess the statistical nature and pseudo-logic ofthe method. We also compare the Coexistence Approach theory with the activefield of species distribution modelling. We argue that the assumptions willinevitably be violated to some degree and that the method lacks anysubstantive means to identify or quantify these violations. The absence of astatistical framework makes the method highly vulnerable to the vagaries ofstatistical outliers and exotic elements. In addition, we find numerouslogical inconsistencies, such as how climate shifts are quantified (the useof a "centre value" of a coexistence interval) and the ability toreconstruct "extinct" climates from modern plant distributions. Given theproblems that have surfaced in species distribution modelling, accurate andprecise quantitative reconstructions of palaeoclimates (or even climateshifts) using the nearest-living-relative principle and rectilinear niches(the basis of the method) will not be possible. The Coexistence Approach canbe summarised as an exercise that shoehorns a plant fossil assemblage intocoexistence and then assumes that this must be the climate. Given thetheoretical issues and methodological issues highlighted elsewhere, wesuggest that the method be discontinued and that all past reconstructions bedisregarded and revisited using less fallacious methods. We outline six stepsfor (further) validation of available and future taxon-based methods andadvocate developing (semi-quantitative) methods that prioritise robustnessover precision

Fallacies and fantasies: the theoretical underpinnings of the Coexistence Approach for palaeoclimate reconstruction