Mosbrugger and Utescher (1997) list four basic assumptions that need to be fulfilled (Table 1). The first assumption has never been used in the application of the Coexistence Approach, and the three others superimpose additional uncertainty on the method and are easily violated, particularly if the aim is high accuracy and precision. Notably, none of the assumptions have been tested and verified for taxa commonly used in the Coexistence Approach.

The first assumption is anchored in the ability to define a “systematically close” NLR (Table 1). However, Mosbrugger and Utescher (1997) or Utescher et al. (2014) do not provide a framework on how to quantify systematically close and in what respect systematic closeness should be relevant for the identification of the NLR. A focus on systematic closeness can lead to conflict with the nearest-living-relative principle. This principle is based on overall morphological similarity and not necessarily linked to phylogenetic relatedness, which is the current basis of systematics. Thus, a fossil may be systematically close to a modern species (or group) that has undergone significant shifts in morphology and fundamental niche, and the best modern analogue may be a more distantly related lineage that has been morphologically and ecologically stable (Fig. 2a). In addition, the degree of systematic relatedness of a fossil to an NLR requires the placement of fossils within a phylogenetic framework (i.e. a tree or network) and this has never been explored in any Coexistence Approach study.

There are further issues with Assumption 1 when considering the taxonomic affiliation of an NLR. Given the time span separating ancient assemblages and modern-day taxa, it has been agreed that defining an NLR at the species level is highly problematic (Grimm and Denk, 2012; Utescher et al., 2014). Thus, the Coexistence Approach usually defines an NLR as the genus or family to which the fossil can be assigned, with rare instances of an intrageneric lineage or a modern species (Grimm and Denk, 2012; Utescher et al., 2014; Grimm et al., 2015). For example, the NLR of a fossil oak leaf would be genus Quercus, the NLR of a deciduous, convexly lobed oak leaf would be Quercus Group Quercus (the white oak clade) and the NLRs of a fagaceous fossil of unknown generic affinity would be all Fagaceae. Hence, systematically close, as used in the Coexistence Approach and other nearest-living-relative approaches, translates into simply being a member of the same taxonomic rank (e.g. genus or family), and the actual phylogenetic (i.e. systematic) distances between fossils and their NLRs are never established. Under this implementation, assignment of NLRs to higher taxonomic ranks (above species) includes the taxonomic problems linked to paraphyly (exclusive common origin; Fig. 2b). Fossils of a paraphyletic group will have different systematic distances to the modern members of the specified taxonomic group of NLRs. However, this is not a problem for the combination of mutual climate range approaches and nearest-living-relative principle as long as the assumption of physiological uniformitarianism is fulfilled (Assumption 2). Thus, shared ancestry remains important, but the systematic closeness of Assumption 1 is superfluous for the application of mutual climate range techniques making use of the nearest-living-relative concept.

The second assumption (Table 1) is based upon the concept of physiological uniformitarianism (Tiffney and Manchester, 2001; Tiffney, 2008). Physiological uniformitarianism implies that as long as lineage stays within its environmental niche, it will not accumulate morphological changes. Hence, a modern species with the same, or very similar, morphological traits of a fossil of the same evolutionary lineage should share the same environmental niche. It also implies that members of the lineages that have undergone niche shifts also experienced morphological changes. Assumption 2 is likely to be violated when morphological changes are evident between the fossil and modern members of an evolutionary lineage, and an NLR of a fossil specimen should only be used if there is morphological, not mere taxonomic, similarity and if both have a common origin. This would exclude the use of most modern plant genera and all families as NLRs as they are typically composed of morphologically divergent species.

In addition, the use of morphologically diverse taxonomic groups to represent an NLR usually means that the environmental niche of the NLR is large, likely encompassing the niche of the fossil, but is not “climatically similar” to that of the fossil, thus, directly violating Assumption 2. Novel procedures and methods are required that take cognisance of the fact that the NLR niche is likely to be far broader than can be expected for that of the fossil. The actual assumption, as used by the Coexistence Approach and related mutual climate range methods, is that the climatic niche of a fossil taxon lies somewhere within the range of niches found within the species comprising the NLR. This has two major implications for the set-up and interpretation of reconstructed palaeoclimates using the Coexistence Approach (and other mutual climate range techniques that use NLRs): (1) a high-resolution climate reconstruction should not be possible, especially when only minimum and maximum NLR tolerances are used (Fig. 3a), and (2) mixed floras may not be identified since mutually exclusive species (or communities) have overlapping climate ranges at higher taxonomic levels (Fig. 3b). Thus, highly precise and accurate climate reconstructions can only be obtained using the Coexistence Approach if the critical species within a palaeo-assemblage occupied niches close to the minimum and maximum tolerances of their corresponding modern genus or family level NLRs.

The third assumption (Table 1), that the distributions of extant species are in equilibrium with their climate, is a topic rich in discussions in the ecological and species distribution modelling literature (Araújo and Pearson, 2005; Bond et al., 2005; Sexton et al., 2009; Franklin, 2010). Species are often not in equilibrium with their climate for abiotic (e.g. soil, fire) or biotic (e.g. competition) reasons, and thus their realised niches do not span their fundamental niches. Thus, species will be plastic in their expression of the realised niche depending on external factors, which would exclude the reconstruction of palaeoclimate with high accuracy. Any change in the abiotic or biotic parameters can affect the distribution of a species (i.e. its realised niche) even if the fundamental niche remains unchanged.

The climatic niche is solely represented by minimum and maximum values in the Coexistence Approach, which are independently compiled for climate parameters in a univariate manner. However, it has been long established that biological climate niches are multidimensional (Köppen, 1936; Hutchinson, 1957; Walter, 1973; Walter and Breckle, 1983–1991; Schroeder, 1998). Using minimum–maximum tolerances along univariate axes can only roughly approximate the multidimensional climatic niche and may be misleading (Klotz, 1999; Thompson et al., 2012). For example, two mutually exclusive taxa, for which Assumption 3 applies, may still have an artificial mutual climate range regarding their minimum and maximum tolerances (Fig. 4a). In this context it is important to note that species distribution modelling started with algorithms that used minimum and maximum values but quickly moved on to methods that better represented the bioclimatic niche of a species (discussed further below). Thus, the use of range values for climatic parameters does not accurately capture the climatic requirements or tolerances of an NLR (Table 1), which will affect the reconstructed palaeoclimate using the Coexistence Approach.

The fourth and last assumption has no apparent theoretical implications. Technical implications have been discussed in Grimm and Denk (2012), Thompson et al. (2012), Utescher et al. (2014) and Grimm et al. (2015). We do, however, wish to highlight that since local climate can substantially vary over short timescales, minimum and maximum tolerances may be unduly affected by the selected observation period of climate stations.

Not formally addressed by Mosbrugger and Utescher (1997) or Utescher et al. (2014) are two more fundamental assumptions of the Coexistence Approach, which distinguish the method from mutual climate range techniques using modern-day species: (1) palaeo-assemblages comprise only taxa that existed as actual communities (i.e. all fossil specimens are autochthonous and from the same point in time); (2) absence of a fossil taxon indicates true absence (i.e. each fossil plant assemblage comprehensively reflects the actual palaeo-community; Table 1). The Coexistence Approach implicitly assumes that only an autochthonous and strictly coeval palaeo-assemblage will result in a single coexistence interval. However, given that two mutually exclusive taxa can share a climate range of minimum and maximum along univariate climate parameters, so too can allochthonous taxa in a fossil assemblage. In addition, the expansion of the climate niche using higher-level NLRs automatically increases the probability of artificial coexistence. Thus, allochthonous assemblages (mixed floras) do not necessarily result in “ambiguous” intervals (Fig. 4b–d; e.g. Utescher et al., 2014) and may very well be the reason for highly precise palaeoclimate estimates (< 1 ∘C for temperature parameters; < 100 mm precipitation per year; < 10 mm precipitation per month) observed in many studies using the Coexistence Approach (Denk et al., 2012; Grimm et al., 2015). Thompson et al. (2012) suggest that a benefit of mutual climate range techniques, in comparison to indicator-species approaches, is that the reconstruction is only affected by the presence of taxa, not their absence. However, this does not apply to the Coexistence Approach, where the mere absence of a taxon can directly affect the outcome of the reconstruction (discussed further below). For instance, the absence of a taxon may eliminate another NLR as a “climatic outlier” rather than producing two ambiguous intervals.

We have outlined a range of probable and inevitable issues of the purported basic assumptions of the Coexistence Approach. These will all, to some unknown degree, decrease the precision and accuracy of any approach that attempts to reconstruct palaeoclimates. In this light, the Coexistence Approach is highly unlikely to reconstruct precise or accurate palaeoclimatic conditions. Utescher et al. (2014) state that it is impossible to test the accuracy of Coexistence Approach reconstructions (but see Grimm and Denk, 2012, for mean annual temperature estimates) but follow the original paper in assuming that violation of the basic assumptions will readily surface in the form of climatic outliers.

According to Utescher et al. (2014) the “Coexistence Approach by Mosbrugger and Utescher (1997) is a nearest-living-relative method, which relies only on the presence or absence of a plant taxon within a fossil assemblage and the climatic requirements of its modern relatives. It avoids any statistical processing or further assumptions, except those given in Mosbrugger and Utescher (1997) [i.e. the four basic assumptions, see Table 1]”. In the original paper, no means of statistical processing were proposed; hence, the Coexistence Approach defines an interval for a past climate parameter assuming that statistical effects do not exist or are negligible. The Coexistence Approach discounts the majority of the community information because the reconstructed climate interval is always solely defined by the pair of the two most divergent but putatively coexisting NLRs. Usually one member of the pair is an exotic element; here we define exotic as any NLR whose niche is at odds with the majority of the assemblage (e.g. Fig. 5). The likelihood of potential oddities, errors or violations of assumptions increases with assemblage size or depositional age. The Coexistence Approach relies, however, on the presumption that any violation will readily surface in the form of so-called climatic outliers (Mosbrugger and Utescher, 1997; Utescher et al., 2014). This exposes palaeoclimate reconstructions using this approach to the vagaries of statistical outliers and exotic elements (see Grimm and Denk (2012) and Grimm et al. (2015) for real-world data examples).

A climatic outlier is identified as an NLR or small number of NLRs that do not share the climate space of a given parameter with a slightly higher number of other NLRs (Fig. 5). In those cases where there is more than one interval that can be reconstructed using the same maximum possible number of NLRs, then alternative (ambiguous) intervals are reported; each of these intervals recognises a different set of climatic outliers. Ambiguous intervals are interpreted by Utescher et al. (2014) as the only evidence for mixed floras rather than a violation of any of the assumptions discussed above. Taxa identified as climatic outliers are typically removed from a Coexistence Approach analysis for a given palaeo-assemblage and parameter. We wish to highlight that a climatic outlier is simply an NLR that is seemingly at odds with a few other NLRs and must not be confused with a statistical outlier (Fig. 5).

There are two paramount problems with the outlier elimination strategy used by the Coexistence Approach. First, two taxa violating the assumptions behind the Coexistence Approach may eliminate one taxon that is not. A typical situation is illustrated in Fig. 5, where an NLR occupying a climate range that is in general agreement with the rest of the flora would be identified and eliminated as a climatic outlier because of the presence of two deviant taxa that are at odds with the overall NLR community. Second, taxa identified as climatic outliers for one climatic parameter and therefore removed from the assemblage for estimating that parameter are still, in most cases, kept for analysing other parameters for the same assemblage. In some cases, these climatic outliers even define the coexistence interval in another parameter (Grimm et al., 2015). If we follow the logic that climatic outliers represent violations of the basic assumptions of the Coexistence Approach (Utescher et al., 2014), then it is imperative that they are removed from all reconstructions for a given assemblage or in general (Table 2). This has been rarely applied in any study that has identified climatic outliers in the Coexistence Approach, mainly to avoid wide, and thus uninformative, coexistence intervals (Grimm and Denk, 2012; Grimm et al., 2015). It could be argued that any palaeo-assemblage represented by mutually exclusive NLRs should be ignored until the reason for the non-coexistence can be identified and corrected for.

Any mutual climate range approach needs a framework to identify statistical outliers as the assumptions will inevitably be violated, and establishing the degree of violation (e.g. degree of niche shifts) is not feasible based on current knowledge. Many palaeo-assemblages will comprise mixed floras with elements from different climate niches, and this would need to be explicitly addressed before reconstructing coexistence intervals. As stated above, the Coexistence Approach lacks any framework to identify exotic elements or allochthonous assemblages, unless they are sufficiently divergent to generate climatic outliers. Allochthonous assemblages comprising mutually exclusive species can share a climate interval (Fig. 4b), and this problem of pseudo-coexistence is exacerbated by the use of higher-level taxa (genera, families) as NLRs of a fossil species or morphotypes. Any slightly conflicting, but exotic, element in an assemblage will have a disproportionally high influence on the palaeoclimate estimates (Fig. 5). It is clear that not only climatic outliers and ambiguous intervals should be indicative of mixed floras, errors in the data or violations in the assumptions but also any narrow coexistence interval (see Grimm and Denk, 2012; Grimm et al., 2015, for real-world examples).

Mutual climate range techniques that apply simple statistics to filter exotic taxa, such as the Bioclimatic Approach (Greenwood et al., 2005), will be less susceptible to the presence and absence of a few exotic taxa but will also usually fail to recognise mixed floras. The problem of mixed floras can only be overcome, to some degree, by using alternative mutual climate range techniques that make use of the full spectrum of distributional information and thus include the climatic preference of all constituent elements of a palaeo-assemblage (e.g. by using the niche curves in Fig. 5). This includes methods such as the weighted mutual climate range approach (Thompson et al., 2012), the probability density function method (Chevalier et al., 2014) and the coexistence likelihood estimation method (Harbert and Nixon, 2015). However, these methods will probably begin to break down when the nearest-living-relative principle is needed to link fossils with extant lineages (Thompson et al., 2012; Harbert and Nixon, 2015), and this may explain why their application has been limited to Quaternary assemblages.

We wish to highlight four additional points regarding the use of the Coexistence Approach that lack any (bio)logical basis, specifically: (1) the use of the centre value to identify and quantify climatic shifts, (2) that the reconstructed climate is based on only two nominally coexisting elements, (3) that the reconstructed climate is highly dependent on the presence or absence of a single or few taxa, and (4) the reconstruction of extinct climates. We elaborate on each of these points below.

The conclusions of most Coexistence Approach studies rely on shifts observed in the so-called centre value. This value is simply the arithmetic mean of the upper and lower boundary of the coexistence interval. Practical tests have shown that there is little correlation between the actual climate and the centre value (Klotz, 1999; Grimm and Denk, 2012). The use of this value highlights a fundamental misunderstanding of the niche concept. If we imagine the coexistence interval to be correct, then all values within the interval should be equally probable as no other information is incorporated regarding the probabilities of occurrence of the assemblage. Selecting the centre value as an indicator of a shift in climate makes no statistical or biological sense. For example, Fig. 6a shows two plant assemblages that differ only by the climatic preference of a single NLR. The replacement of one NLR by another with a preference towards lower values gives rise to a reconstructed climate shift towards higher values using the centre value.

Many Coexistence Approach reconstructions rely on the presence of NLRs that nominally coexist, even if these elements have climate tolerances that are at odds with the rest of the assemblage (Fig. 5; cf. Grimm and Denk, 2012; Grimm et al., 2015). In extreme cases the same coexistence interval can be reconstructed based on plant assemblages with contrary climate tolerances (Fig. 6b). In Fig. 6b, the elements of two plant assemblages have contrary climate tolerances and it is the two exotic taxa in each assemblage that ensure that the reconstructed coexistence intervals are the same. Thus, the precision of the reconstructed palaeoclimates is often entirely dependent on the presence or absence of specific, usually exotic NLRs. Across Coexistence Approach studies, a handful of NLRs that occur towards the tolerance margins over the entirety of all palaeo-floras usually determine the coexistence intervals; it is these few NLRs that give rise to the praised precision of the technique (Grimm and Denk, 2012; Grimm et al., 2015).

The presence or absence of individual NLRs is generally at the root of reconstruction uncertainty in coexistence interval – we term this the Heisenberg effect. Figure 6c shows two very similar assemblages where the presence or absence of the two highlighted taxa changes the coexistence interval reconstructed by the Coexistence Approach to a degree that would be interpreted as a trend towards higher values. The Heisenberg effect renders palaeoclimate estimates obtained with the Coexistence Approach protocol highly susceptible to taxon-bias effects. The reconstructed climate is exceedingly dependent on what fraction of the actual vegetation has been captured by the fossil assemblages (note that in Fig. 6c all NLRs have a mutually shared climate range). Thus, even if all assumptions needed for a mutual climate range approach that also uses the nearest-living-relative principle are fulfilled, the Heisenberg effect will lead to unstable, even random, climate reconstructions when the Coexistence Approach is used.

Utescher et al. (2014) explicitly state that, as each parameter is independently reconstructed, the Coexistence Approach has the potential to reconstruct a climate that does not exist today: an extinct climate. It is hard to grasp how this can be logically accommodated within the basic assumptions of the Coexistence Approach and the actuo-palaeontological nearest-living-relative principle in general (Fig. 7). An extinct climate for a palaeo-assemblage would indicate that the present-day niches of the NLRs are not representative of the fossils and therefore would indicate direct violations of Assumptions 2 and 3 discussed above (Table 1). In addition, it is not possible to construct an extinct climate using species that are restricted to present-day climates if the principle of physiological uniformitarianism applies. Reasons why extinct climates are reconstructed using the Coexistence Approach include violations of basic assumptions, pseudo-coexistence, the inconsistent identification of climatic outliers within an assemblage across climate variables and the single-dimension effect where climate parameters are analysed in isolation and are assumed to be unlinked. The reconstruction of an extinct climate should be seen as a direct indication of error and not lauded as a benefit of the method.

Leaving aside these logical inconsistencies in the conception and application of the method, the Coexistence Approach still cannot be expected to reproduce a robust quantitative reconstruction of the palaeoclimate, as (1) assumptions are likely to be violated but cannot be detected, (2) one cannot avoid using higher-level taxa to represent fossil species or morphotypes, and (3) the fossil record will always be incomplete to different degrees and this will affect the calculated coexistence interval.

There are already a range of potential methods available for palaeoclimate reconstruction using plant fossils as proxies in a univariate manner that have been rarely used or recently proposed (e.g. Greenwood et al., 2005; Boyle et al., 2008; Thompson et al., 2012; Chevalier et al., 2014; Harbert and Nixon, 2015), and there are avenues ripe for exploration (see, e.g., Broennimann et al., 2012; Denk et al., 2013). However, all of these methods require (further) testing and then careful, well-documented usage when reconstructing palaeoclimates. The development of the physiognomic approach (CLAMP, Climate Leaf Analysis Multivariate Program) within the last 2 decades may serve as an example regarding validation, advancement and, most importantly, documentation and transparency. The various publications demonstrate a constant effort to reach higher precision and counter known problems (e.g. Kovach and Spicer, 1995; Herman and Spicer, 1997; Spicer et al., 2009; Yang et al., 2015; Li et al., 2016). All primary data are made freely accessible and means are implemented allowing for quick application (CLAMP online; Yang et al., 2011). CLAMP online not only provides data, guidelines and templates for application but also pinpoints shortcomings and ideas on how to deal with them. No method is or will be perfect. Nevertheless, it is crucial to define the principal accuracy and precision of any quantitative method. If this is not possible, as in the case of the Coexistence Approach (Utescher et al., 2014, p. 61), it must not be used. Therefore, we suggest that any current or future taxon-based method be

tested against the modern flora (e.g. Boyle et al., 2008; Thompson et al., 2012; Chevalier et al., 2014; Harbert and Nixon, 2015).

After such a series of tests, the method can be considered an alternative means to reconstruct past climates for further exploration. However, the ultimate limitations of mutual climate range techniques or other nearest-living-relative methods for palaeoclimate reconstruction do not lie in the methodological framework to estimate, for example, the coexistence space but rather in the applicability of the nearest-living-relative principle. When it comes to application in the more distant past, the basic assumption of any method must be that the nearest-living-relative principle will be violated to an unknown degree. The degree of violation will likely increase with time and may not necessarily surface during the application or testing phase. Bivariate or multivariate approaches, which can tackle the problem of pseudo-coexistence (e.g. Fig. 4), will be more sensible in this respect. The capability to accurately and precisely predict palaeoclimate will not only deteriorate with increasing age but also with compositional change of the fossil plant assemblages relative to the modern-day situation. Precise, highly sophisticated methods (e.g. Punyasena, 2008; Harbert and Nixon, 2015) or methods using few, overly precise, values to characterise the niche space of the NLR (e.g. Greenwood et al., 2005) run a higher risk of being affected by violations of the nearest-living-relative principle than methods that use semi-quantitative approximations of the niche (e.g. Thompson et al., 2012; Denk et al., 2013).

Taking into account all theoretical and practical issues involved, we suspect that quantitative palaeoclimate estimates at a high precision and accuracy are an impossible goal when the nearest-living-relative principle is be applied. Therefore, our opinion is that method development should not focus on high (or higher) precision, as the basis of this precision is undermined as the temporal difference between fossil and NLR increases, but rather on establishing climate change trends in a robust and reproducible manner. Semi-quantitative approaches can detect such changes and may prove to be more robust (e.g. the Köppen signature approach proposed by Denk et al., 2013). Furthermore, the application of any nearest-living-relative method to palaeo-floras will always depend on the thoughtful filtering of a fossil assemblage for elements that have been shown to have a high likelihood of niche conservatism. Fossil–NLR associations must be carefully selected to ensure that the principle of physiological uniformitarianism applies, in contrast to the current practice of seemingly data-naive bulk analyses.