We examined 26 herbarium specimens in the herbaria listed in the text. These were combined with our field observations from Peru in the identification and description of the new taxon (see Taxonomy below). All specimens are cited in the text and full data is provided in the supplemental file and on Solanaceae Source (www.solanaceaesource.org ). We included all specimens examined in the model-based analysis.

Following the MBS approach by Guisan et al. (2006), we used a SDM method to identify potentially suitable habitat areas for Solanum pseudoamericanum. We chose the machine learning algorithm MAXENT version 3.3.3e (Phillips et al. 2006) for developing the habitat suitability maps. MAXENT uses the principle of maximum entropy to discriminate the range of environments associated with species occurrences from the range of environmental conditions present across the landscape and finds the smoothest climatic envelope that describes the presence points. MAXENT is considered one of the most reliable methods when working with a small number of potentially biased occurrence records (Hernandez et al. 2006; Pearson et al. 2007; Wisz et al. 2008; Elith et al. 2006), and has been found to outperform other SDM methods in complex but poorly collected areas (Hernandez et al. 2008). MAXENT requires presence points only and can hence be used for modelling poorly known species for which reliable absence records cannot be derived.

We first ran MAXENT based on the four observed collections from 2012 from southern Peru to identify potential suitable habitat areas for the target species (Model 1). The model was run with default settings (allowing for transformations of the covariates with the default thresholds for conversion, removing duplicate presence records, maximum number of background points = 10, 000, maximum number of iterations = 500; convergence threshold = 0.00001; fit regulization parameter = 1; default prevalence = 0.5). To evaluate model performance, we ran it with cross-validation, where the occurrence data is randomly split into two equal-sized groups and one of them is then used for creating the model whilst the other is used for validating the model. We chose cross-validation approach because it uses all of the data for validation, unlike a single training/test split, and is hence more suitable when working with small numbers of occurrence points across a complex landscape (Hernandez et al. 2008).

The model was run with 11 bioclimatic variables at 30 arc second spatial resolution (c. 1 km²) (Hijmans et al. 2005; http://www.worldclim.org ). Variables used in models as predictors should optimally be independent. In order to avoid colinearity between the climatic variables, we tested for correlations between all the 19 BioClim and the digital elevation model (SRTM) using Principal Component Analyses, and excluded nine variables that were found to be highly correlated with Pearson correlations coefficients of 0.75 or higher (Table 1). The remaining 11 variables included layers describing the seasonality of the habitat (Mean Diurnal Range, Temperature Seasonality, Temperature Annual Range and Precipitation Seasonality) and precipitation and water availability (Precipitation of Wettest Quarter, Precipitation of Driest Quarter, Precipitation of Warmest Quarter, Max Temperature of Warmest Month, Mean Temperature of Driest Quarter) (Table 1). The model was trained using southern Peru alone (-76, -70, -15.2, -12), and the results of the training were then projected over the whole of Peru (-81.6, -68.0, -18.5, 0). This approach of limiting the model training extent avoids model overfitting which leads to underestimation of species’ distribution areas (Barve et al. 2011).

The Model 1 output was ground-truthed with additional field work. To target areas where potential new populations of Solanum pseudoamericanum could be encountered, we chose to interpret the Model 1 cumulative output. We chose not to use a threshold approach, where the prediction is divided into a binary map of presence or absence, due to the fact that only four records were used for building the model and hence using a threshold approach would discard valuable data. The cumulative output indicates relative suitability, not probability, of occurrence with values ranging from 0 to 100. Grid cell values are calculated as the sum of the cells with equal or lower probability, multiplied by 100 to give a percentage (Phillips et al. 2006). All areas identified in the Model 1 with a relative suitability of more than 40% were considered as high priority areas for ground-truthing during the second field season in April-June 2013. Further occurrence records for the new species were identified through herbarium visits and loans. Local Peruvian herbaria were visited in Arequipa (HUSA), Lima (MOL, USM), Trujillo (HUT) and Cajamarca (CPUN), and loans from several international herbaria were examined (F, MO, US, S, NY).

We ran a second model after the second field season, where all new localities identified through field work and herbarium visits and loans were included. Model 2 was run using a total of 26 records, of which four were from our first field trip in 2012, 17 were from our second field trip in 2013, and five from herbarium records (SI File 1 Occurrence data). The same 11 climatic predictors and MAXENT parameters were used as in Model 1 (see above). The model was trained using Peru as the study extent, and results were projected to an area that covered the whole of Ecuador and northern Bolivia (-81.0, 65.6, -19.5, 0). A final potential distribution map for Solanum pseudoamericanum was produced based on the cumulative output of Model 2, where all areas with relative suitability above 0.4 (logistic output) were considered as potential areas of occurrence for the species.

Previous studies have clearly demonstrated how the use of SDM can dramatically increase detection rates of rare species in the field (Guisan et al. 2006; Raxworthy et al. 2003; Edwards et al. 2005; Boetsch et al. 2003). Our case study adds to this list of studies where records of rare species are used to locate new populations via SDM. Once new populations are found, new models are reiteratively run to enhance the distribution models (La Ley et al. 2010). Our example demonstrates that the MBS approach can be used even in more complex and poorly collected areas such as the Andes, and can greatly help in increasing our knowledge of species distribution patterns in highly diverse systems. It is clear from the continuing rates of species discovery in plants (Joppa et al. 2011) as well as in mammals and birds in the tropical Andes (Hosner et al. 2013; Seeholzer et al. 2012; Jiménez et al. 2013; Helgen et al. 2013) that tools such as SDM should be used to predict diversity patterns from the existing sparse data.

Here we describe a new species and provide both an observed distribution map as well as a modelled distribution range for the species. With increasing ease of SDM through publicly supported online portals such as BioVel (http://www.biovel.eu ), the tools are now available for non-specialists to analyse models prior to species publication. Generally, SDMs are still created by GIS specialists rather than taxonomic specialists, but the availability of online portals will hopefully increase the use of SDM amongst taxonomists who are best informed to run such models because of their expert knowledge of species’ ecology.

Modelled distribution maps have large benefits over observed distribution maps. Modelled maps, although still incomplete, can be argued to provide a more realistic picture of the actual species’ distribution area. This is because modelled maps are less biased by collection densities, and although nowhere near complete, provide a step towards representing species distributions in a more realistic manner. Such maps will also aid in targeting field collecting efforts and provide additional information for planning conservation areas compared to traditional maps.

Whilst advocating the publication of modelled distributions for new species, we fully acknowledge that species distributions are not guided by simple factors such as climate alone. Many factors govern range size, including dispersal limitation, competitive exclusion, habitat destruction, urbanisation and agriculture, as well as species interactions. These complex factors are often dismissed in simplistic SDMs where only bioclimatic predictors are included. Simple SDMs can, however, be used as a starting point for evaluating rare species (e.g., Simon et al. 2011). Firstly, SDMs can be used to establish whether species are truly restricted in their distributions by reducing sampling artefacts such as those presented here. Secondly, simple SDMs can be used as null models to examine whether bioclimatic factors restrict species’ distributions or whether other factors, such as dispersal limitation or habitat destruction, are likely at play.

In the case of Solanum pseudoamericanum, the MBS approach helped us to extent the range size of the newly described species, changing our view of the target taxon from a narrow endemic species restricted to only two river valleys in southern Peru to a relatively widespread species that is distributed across Peru. The large increase in the actual observed distribution range of the new species demonstrates not only how poorly collected the Peruvian Andes is for vascular plants, but also how MBS can work with extremely low number of collection records across a complex landscape. This extension of the observed occurrence area of the newly described species was despite the relatively large model training area that was used, where the whole of Peru was considered. The use of relatively large training areas in model training leads to model overfitting and underprediction of distribution areas (Barve et al. 2011), which in our case means that there is likely to be a bias towards underestimating the true potential habitat area of Solanum pseudoamericanum. But is our case study an exception?

Our null hypothesis was that MBS approach cannot be used in such a highly variable landscape as the Andes with as few records as we had available. Our expectations were low for two reasons. Firstly, the climate data available for the Andes through WorldClim suffers from high uncertainty because only a few weather stations were used to interpolate the data (Hijmans et al. 2005). Hence, we expected that the climatic data might not be adequate to produce good models for Andean species. Secondly, we expected poor model performance due to the low number of records used. Although some algorithms, such as MAXENT which was used here, have been found to be less sensitive to small sample sizes than other methods, they still require generally more than 30 records to obtain accurate results (Wisz et al. 2008; Kadmon et al. 2003).

Results from our case study indicate that both assumptions might not be correct. The high AUC scores shown by our models indicate that informative models can be run with as little data as used here and with climate predictors alone. The climate data appears to be of high enough quality to reveal broad patterns that can be used to identify suitable habitats across poorly explored regions. Variation in climate, and the associated elevational gradients, seem to explain large parts of plant distribution patterns in the Andes (Killeen et al. 2007), and hence such simple bioclimatic models can perform well. This is in contrast to lowland Amazonia where climatic variation, as well as elevational gradients, are much reduced and where the importance of soil in explaining diversity patterns has been highlighted (Hoorn et al. 2010; Higgins et al. 2011; Tuomisto et al. 2003).

Another question is the minimum number of occurrence records required for building accurate distribution models. While it is well established that more data produce better, more accurate models (Wisz et al. 2008; Kadmon et al. 2003), the question remains how little is enough to produce an informative SDM? The good news based on our case study is that the actual number of records might not be the only thing that matters. As exemplified by Solanum pseudoamericanum, a small number of records can be enough to characterize the climatic niche of a species, given that the few records available adequately describe the environment that the species occupies. In other words, it is not only the pure number of records but the information content that the locality points provide that matters (Kadmon et al. 2003). Optimally, occurrence records should be spatially spread and represent the environmental extremes that the species occupies (Syfert et al. 2013). Because the information content of the occurrence points is often hard to know a priori, our case study demonstrates the value of running preliminary SDM analyses even when only a handful of records are available. Caution has to be given to how SDM analyses are run with limited data, and care should be especially be given to interpreting AUC values which can be inflated due to small number of records (Wisz et al. 2008), especially when sampling bias is present (Raes and ter Steege 2006). Despite this caution, our results presented here are encouraging and we see SDMs as a tool that can offer much needed help in our efforts to describe diversity in poorly explored areas such as the Andes.