Our sampling design was based on 60 geographical points, randomly located on the Earth's surface using the following protocol. We divided the Earth's surface into 12 sectors, 6 in the Northern and 6 in the Southern hemisphere (see Appendix S1 in Supporting Information, for geographical details). Each sector was a slice of the Earth of 60° of longitude, stretching from the equator to the North or South Pole. We generated 5 random points in each sector, such that all parts of the surface, whether land or sea (hence radically different to existing approaches), had an equal chance of selection. Then, we constructed 5 nested circular plots, centred on each point, with areas (grain sizes) of 104, 105, 106, 107, and 108km2, respectively. This procedure corresponds to a stratified random sampling of nested plots with the same centre (Stohlgren, 2007). For reasons of comparison, we implemented the same number of plots for each grain size (n=60). As the largest plot size covers almost a fifth of the Earth (e.g., Fig. 1e), many of these plots overlap (Fig. 1e). The circular shape was chosen because all points on the edge have the same distance to the centre, minimizing the perimeter/area ratio. We considered this important given that a species’ range must be entirely contained within the sampling unit for that species to be endemic.

Fig. 1.

Example of the nested circle design (NCD). Grain sizes (a) 104km2, (b) 105km2, (c) 106km2, (d) 107km2, and (e) 108km2. All the circles are centred on the point 43 N, 18 E, which is near Dubrovnik. The smallest grain sizes cover parts of Bosnia and Herzegovina and the Croatian coast; the largest includes parts of NE America, Eurasia and Africa (see Appendix S1 in Supporting Information). Note that this illustration is schematic only, showing how the NCD was organized; high resolution maps were utilized for the estimates.

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The NCD provides simple units for estimating the number of endemic plant species, unaffected by the distribution of land and sea, different shapes of sampling units, or biased distributions of plots. Conceptually, if a relatively small sampling unit is centred on the Canary Islands, or the tropical Andes, we conclude that the area has more endemic vascular plant species than is average across the whole planet's surface for a sampling unit of that size. By the same token, if the unit is in the middle of the Antarctic ice cap, or a part of the sea with few or no islands, and therefore contains no endemic vascular plant species, we conclude that this area has fewer endemic species than is average across the whole planet's surface. In both cases, the reasons are well known from biogeography. While these examples may be trivial, they illustrate that our concept of a global endemism reference, provided by the resulting EARs, applies anywhere on Earth.

Since published distributional data of endemic vascular plants for a random sampling at global scales are not available, and in order to achieve the standardization and conceptual harmonization required of the data, we created a database using expert-estimation of the numbers of endemic plant species for each circular plot. Overall, 23 experts participated. For each randomly selected point, five of these experts independently estimated the minimum and maximum number of endemic species in each of the five plots centred on that point. Each expert was provided with the same set of information from existing floras and data, as a reference, but was asked to exercise his/her own judgement from experience of research in this field. The first experts to produce estimates were three of the authors (CH, AC and MJ), who also coordinated the process. Then, 20 other experts were invited to produce independent estimates of randomly allocated plots, without knowing what the other estimates were for those plots. Further, each expert was not aware of the identities of the other experts providing estimates for the same or other plots, ensuring that they did not communicate among themselves about their estimates or about their approach to calculating those estimates. Subsequently, all experts were invited to join the team for proceeding with analyses and writing, and all accepted (becoming co-authors). Part of the group then met in Flensburg, Germany, 2nd–6th February 2018, to plan the rest of the research. The overall procedure was designed to harness the advantages of using expert knowledge, while being aware of typical disadvantages (Araújo and New, 2007; McBride and Burgman, 2012), which we sought to minimize by determining the consensus of expert estimates for each plot.

The procedure resulted in 3000 records, each being an estimate of the number of endemic vascular plant species in a circular plot (i.e., 12 sectors×5 points×5 magnitudes×2min/max×5 experts). Although the dataset produced is not perfect, the estimates are based on the best and most up-to-date available data, and may be considered to represent the current state of knowledge – including the variability among the estimates. The numbers of endemics in many biogeographical analyses or conservation reports are often based on expert opinions that depend on different species concepts (cf. Myers et al., 2000; Mittermeier et al., 2005). Furthermore, many of the published numbers of endemic species within particular regions have recently been adjusted, and these improvements are ongoing. Therefore, we consider the data obtained by our approach to be comparable in quality to data used for other research on endemism at coarse spatial scales (Storch et al., 2012; cf. Tables 5.1–5.5 in Hobohm et al., 2014), with the major advantage of being comparable across the world.

The minimum and maximum number of endemic plant species in each circle of the NCD are here made available for future studies (see Appendix S1 in Supporting Information). For each circle, we used median values across the experts to eliminate the influence of outliers and improve the estimate (Bates and Granger, 1969). The variability among estimates by experts for the same circle was calculated by using standardized Analysis of Variance (Fox et al., 2015).

To model the number of endemic species as a function of area, we calculated linear, power and polynomial EARs (Storch et al., 2012). The Arrhenius (1921) power function, which is the most frequently used model in the context of SARs (species–area relationships) and EARs (Drakare et al., 2006), was the best fitting curve to the series of estimates presented here (see Results). Since the number of endemics in a large number of plots was estimated as zero, we used the non-logarithmic form of the Arrhenius equation:

where E is the number of endemic vascular plant species, A is the surface area of the circle, in km2, c and z are two fitted parameters representing the intercept (i.e. the number of endemic species per unit area) and the exponent (which is also the slope of the increase of the log (number of endemic species) per unit increase in log(area)), respectively. We fitted Equation (1) using three different data sets extracted by the ten estimates provided by the experts per each circle (5 experts×2 values): the first composed by the median values (n=300), the second composed by the minimum values (n=300) and the third composed by the maximum values (n=300). Model fitting was performed using the non-linear modelling procedure of the SSArrhenius function contained in the Vegan R package (Oksanen et al., 2016).

Global species–area relationships (SARs) and EARs can be validated to some extent by extrapolating from the dataset to the whole planet, and comparing the results with those derived from other ways of estimating the total number of vascular plant species on Earth, as done by Storch et al. (2012) for vertebrates. For the entire Earth, the number of endemic species (E) equals the total number of species (S). We used our models to calculate the number of endemic vascular plant species for the Earth, by extrapolating to A=510,000,000km2. We also used the models to calculate the average area harbouring one single endemic species. We compared the results with published estimates of the total number of vascular plant species.

Of the 3000 estimates of the number of endemic species in a circular plot in our dataset, about 40% were zero. Most of these zero estimates were for plots of the finer grain sizes and centred on points in the sea (Table 1). Overall, about 51% of the estimates in plots centred in the sea and about 83% of those in plots centred on land include endemics (Table 1). As expected from the wide range of biogeographical and ecological features of different regions on Earth, the estimates of numbers of endemic plant species in plots of the same size differ considerably (Fig. 2, Table 2; also see Appendix S1 in Supporting Information). The highest coefficient of variation, with a value of 2.236 (223.6%), resulted when four of the five estimates for a certain plot and magnitude were zero endemics and the other estimate was one or more endemics. Despite the high coefficient of variation, these frequent cases represent small absolute differences in estimates. Despite the high variance within each grain size and the uncertainty inherent to the estimates, values estimated by different experts are in general surprisingly similar, as shown by the mean of the coefficients of variation calculated on the values provided by the five experts for each circle (Table 2).

Fig. 2.

Minimum and maximum estimates (median estimate for each plot) of the number of endemic vascular plant species for the various plot sizes based on the estimates provided by the experts. The largest plot size represents values for the whole Earth (see text). Boxes indicate inter-quartile ranges while whiskers indicate the ranges. Richness values have been added to 1 to allow plotting on a log scale.

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Fig. 3 illustrates the variation of endemic species richness in space and across grain sizes. One notable feature is how the spatial patterns in the richness of endemics change with the grain size.

Fig. 3.

a-e Maps showing the position of the circular plots and estimates of the diversity of endemic vascular plants (medians, as log (e+1)) in circular plots of 104 (a) to 108km2 (e). Sizes of small circles in (a) and (b) are exaggerated to aid interpretation and, in each panel, one point centre is covered by the legend. Colours reflect the amount of endemism; blue indicating low and red high numbers. The distortion of the circular plots towards ellipses in high latitudes is an artefact of the cartographic reference we used, hat based on geographic co-ordinates provided by WorldClim (WGS84 Datum)..

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Fitting the Arrhenius power function (Table 3) to the data set comprising the median values of all estimates produce an R2 values of 0.68. Fitting the function to the minimum and maximum expert estimates gave R2 values of 0.65 and 0.67, respectively. The c value, i.e. the number of endemic species per unit of area (here 1km2), is extremely small, as expected. Also as expected, the z values are always a little larger than 1. The best-fitting EAR (for all median values) is described by the formula E=0.00001227·A1.195.

Extrapolating to the surface area of the Earth, the model estimates 312,243 vascular plant species. Using the model for the medians of the minimum estimates gives a total of 284,493 species, while using the model for the medians of the maxima the estimate gives a total of 398,364 species. The associated average area to find a single endemic species (Table 3) is estimated as 12,875km2, ranging from 9675 to 20,529km2 (median values for maxima and minima, respectively).

At biogeographical scales, numbers of species are typically counted, estimated and assembled by many researchers using heterogeneous sources, and as a result they can be heterogeneous and variable in quality (Chiarucci et al., 2011). For many regions on Earth, it is still impossible to get accurate data on the number of endemic vascular plant species, and even where reasonable data exist, differences in methodology and species concepts cause large variation in estimates or counts for the same region (Hobohm, 2014).

Most of the published data on the number of endemic species are related to political units, such as countries or provinces. Very often, when numbers do refer to natural biogeographical units, they refer specifically to islands, archipelagos or mountain ranges (cf. Hobohm, 2014). Many large countries at high latitudes or in arid regions are relatively poor in endemics, while many islands in tropical and subtropical regions are extraordinarily rich in endemics (Groombridge and Jenkins, 2002; Kier et al., 2009). Using these data, which are strongly biased in spatial representativeness, does not guarantee a model reflecting the real and highly uneven distribution of endemic plants on Earth.

The sequences count – estimate – guess and fact – hypothesis – speculation are often considered to indicate an order from scientific certainty to weak conjecture (Franklin, 2009; Burgman et al., 2011). Expert knowledge is sometimes associated with the weaker side of science, though species’ range maps are often based in large part on such knowledge. Nobody knows the exact number of endemic species in a circular plot constituting 20% of the Earth's surface and including parts of different continents and many islands. However, in the absence of ideal data (exacerbated by the recent, widespread reduction in support for systematics, taxonomy and other areas of basic science), the use of expert knowledge is increasingly important, especially in nature conservation science and practice (Maddock and Samways, 2000; Drescher et al., 2013; Grêt-Regamey et al., 2013). This is for at least two reasons. First, nature conservation practice cannot wait until all individuals and species of all taxonomic groups in a region are counted or identified; nature conservation management often has to act on the basis of imperfect data, or despite a lack of knowledge. We used expert knowledge simply because of the lack of a dataset appropriate for calculating global plant EARs for areas of standardized grain and shape. As we outline in the Introduction, the counts that do exist cannot be compared or combined and analysed without biased results. Our first global vascular plant EAR can certainly be improved in the future, but for now addresses the lack of such a tool with a reasonable model. Second, measures of uncertainty can be built into the use of expert knowledge, as herein. When this is done, expert knowledge does not necessarily result in weaker conclusions than models based on incomplete or biased occurrence data (cf. Yamada et al., 2003; Perera et al., 2012; Tara et al., 2012; Reside et al., 2019).

We therefore consider that harnessing expert knowledge is the best approach to overcoming the lack of accurate empirical data and biased results. We accounted for uncertainties associated with data deficiencies and varying species concepts by estimating minimum and maximum values for the number of endemics in each plot. Further, our combination of estimates by five randomly selected experts per plot reduces errors associated with the subjective part of this process (McBride and Burgman, 2012). In our data, the highest variability among experts’ estimates was observed at plot sizes in the range 100,000–10,000,000km2, for both the minimum and maximum values of endemic species richness. Because the plots of the smallest size (10,000km2) often represent areas without vegetation, or with minimal vegetation, many estimates were zero at this scale. At intermediate plot sizes (100,000–10,000,000km2), many of the circles had zero and non-zero estimates, resulting in relatively high proportional variation between estimates. For many islands and countries, official estimates of numbers of endemic species have had to be adjusted in recent decades because of better knowledge and changing taxonomies (Hobohm, 2014). The largest circles in our analysis, on the other hand, usually contain entire endemic-rich floristic regions, no zero-endemic estimates, and thus, the variation between them was relatively low.

In comparison to ‘strictly nested quadrat’ (SNQ) and ‘continental shape’ (CS) designs (Storch et al., 2012; Storch, 2016), the NCD has no plot large enough to include the whole or almost the whole surface of the Earth. However, the number of NCD sampling units per grain size is kept constant (n=60 in this application), whereas the number of sampling units declines with increasing grain size both in the SNQ and CS designs. Having the same number of sampling units per grain size, NCD allows more spatially representative estimates.

There are currently few published EAR models for vascular plants (Cowling and Samways, 1995; Hobohm, 2003; Georghiou and Delipetrou, 2010; Hobohm and Tucker, 2014). Curves for the Greek mainland and island regions were relatively steep, with z-values of 1.49 and 1.15, respectively (Georghiou and Delipetrou, 2010). The curve for a combination of mainland and archipelagos (Georghiou and Delipetrou, 2010), in contrast, was shallow (z-value of 0.42). This example shows how the sampling of geographical units can strongly affect the resulting EAR, when checklists are combined. Our z-values are slightly higher than 1, as expected for EARs at this scale (Storch et al., 2012). Our method, coupled with the use of ensembles of expert-derived estimates to generate the data, is intended to provide a standardized estimate of endemic species richness per unit area that is unbiased and directly comparable in terms of grain size and shape, thus reducing relating problems of inconsistency. The results of the variance analysis, the comparison with theoretical expectations (Kier et al., 2009; Storch et al., 2012; Storch, 2016; Hobohm and Tucker, 2014), and the results produced by extrapolating to the total number of vascular plant species on Earth, indicate that our model is reasonable, and has potential for further applications.

Because of the new sampling design, the results of the models we present are not directly comparable to formerly published models. Recently published curves (Storch et al., 2012; Storch, 2016) show a slightly ascending EAR to the right hand side in log–log space at global. This can be explained by the lesser representation of regions at the edges of continents, which are often more rich in endemics than the more inland regions (David Storch, pers. comm., 2016). The NCD does not show such an effect because the number of units for every plot size is the same (n=60), and probably also because the circle design incorporates these geographical gradients, as discussed in the next section.

It might not seem useful or appropriate to include areas without terrestrial vegetation in our analysis. However, should plots with no endemic plant species, such as regions of the ocean without islands, be excluded from sampling or analyses? If yes, then what about other water bodies within countries, some of which do not contain endemic vascular plants, that are not usually excluded from calculations or estimates? Or what about ice caps, bare rock or unvegetated desert? Further, seagrasses show that vascular plants can live in the oceans. However, almost all seagrass-beds are species-poor and dominated by widespread species, giving very low numbers of endemics in any local marine area. This is part of the global pattern of vascular plant endemism. Our approach therefore highlights that the areas covered by seas are not qualitatively very different from areas covered by lakes, ice caps, or sandy deserts, from the point of view of plant species diversity and endemism.

While it may seem trivial that most plots containing no habitable land have no endemic vascular plants, the isolation created by these regions that are inhospitable to vascular plants is key to why many islands in the ocean have so many endemics. The same applies, to a lesser extent, around coastlines. Our approach does not exclude those influences, thus bringing the physical geography of the Earth into our modelling and into the resulting reference values for the numbers of endemics. The distribution of endemics is a pattern that develops over long time-periods, of which the present-day is a snapshot, and is affected by evolutionary processes related to continental drift and changing ecological conditions, by isolation and dispersal, and thus, by the distribution patterns of land and sea (e.g. Huston, 1994; Gaston, 1996). To produce a global reference and to help in understanding the patterns, it is appropriate to include all these areas in the models. Our approach therefore has strengths not shared by others, including overcoming some of the biases affecting other approaches, such as the continental-edge bias identified by David Storch (pers. comm., 2016).

Eliminating zero-endemic plots, especially at the smallest size, would increase the average number of endemics of the smaller sizes and flatten the curve (cf. Cowling and Samways, 1995; Williams, 1996). We consider it inappropriate because the sampling design must have priority and should be independent of the result; the distribution of plots with and without endemics is the result. Moreover, previous SARs and EARs have used samples with zero vascular plant species or zero endemic plant species, respectively (Green and Ostling, 2003; Werner and Buszko, 2005; Dengler and Boch, 2008; Duarte et al., 2008; Georghiou and Delipetrou, 2010; Storch et al., 2012; Polyakova et al., 2016). Since we were developing a global EAR, we wanted to represent the overall global pattern of endemics, including regions with many or few endemics, as well as arid or cold regions, glaciers or ocean, where we did not expect to find any endemic plants.

For all these reasons, we consider that there is no biogeographical argument to exclude zero-endemic plots from our sampling or analyses. Further, we suggest that the resulting models reflect the total number of vascular plant species well (see next section) in part because we did not exclude zero-endemic plots from sampling.

At present, the total number of vascular plant species estimated on Earth varies a lot between published estimates, depending on the data sources and the associated taxonomic or other biases. The number of seed plants has been estimated as 223,300 (Govaerts, 2001), 352,000 (Scotland and Wortley, 2003) and 422,127 (Paton et al., 2008), for example. Estimates of 308,312 (Christenhusz and Byng, 2016), 315,903 (Kier et al., 2009) and 383,671 (Nic Lughadha et al., 2016) were calculated for the total number of vascular plant species, and 298,000 (Mora et al., 2011) and 320,000 (Groombridge and Jenkins, 2002) for all plants. Clearly, present knowledge is very incomplete and needs further data gathering and integration. Furthermore, it is difficult to calculate potential overestimation and underestimation resulting from taxonomic or nomenclatural artefacts, and potential underestimation reflecting the likelihood of ongoing exploration and discovery (Ungricht, 2004). Bearing these limitations in mind, and assuming that pteridophytes comprise c. 13,000–14,000 species (Nic Lughadha et al., 2016), estimates for all vascular plant species on Earth thus range between c. 236,000 and c. 436,000. The values we estimated here fit squarely within that range of published numbers, giving us some confidence in the quality of our assembled data and models.

Extrapolating in the other direction, our models give values ranging from 9675 (medians of maxima) to 20,529km2 (medians of minima) for the reference area to include only one endemic species (Table 3). These values represent the average expectations of our models for the whole surface of the Earth, including marine and terrestrial regions. According to the formula in Georghiou and Delipetrou (2010) for mainland Greece (a Mediterranean region known for being rich in endemics), one endemic plant species can typically be expected in an area of 1374km2. Appropriately, according to our models, that area is endemic-rich. From theoretical assumptions, Hobohm and Tucker (2014) found that the terrestrial regions (island or mainland) harbouring a single endemic plant species should be larger than 493km2. Again, these estimates can be improved with further research.

In general, SARs and EARs, such as those we produced, can be used to identify areas that are significantly richer or poorer in species or endemic species than average. As Lomolino (1982) has shown, the regression residuals give the possibility to quantify the diversity of endemics in a region as log-distance to the regression line for every size of area (see also Hobohm, 2003; Duarte et al., 2008). Thus, the models presented here can be considered as average theoretical expectations, or reference values, for comparing and analysing the distribution patterns of vascular plant endemism on Earth in areas of standardized circular area. As an example, the area of Hawaii (Big Island) is slightly larger than 10,000km2 and hosts 82 endemic plant species (Price, 2004), thus having c. 81 more endemic species than expected for a circular area of 10,000km2 and between 65 and 74 endemic species more than expected for a circular area of 100,000km2. From this, we infer that there is a strong concentration of endemism in this island – in line with received wisdom, and demonstrating our approach. On the other hand, many regions on Earth, such as parts of the oceans, cold or even temperate regions such as many lowland regions in Europe (Hendrych, 1982), have very few or even no endemic vascular plant species in relatively large areas.