Ignorance maps of raw data accessed from species observation databases

Worldwide; example data from Sweden​

Rationale and assumptions

The aim is to provide ignorance maps that are easily comparable and easily scalable, to report the spatial distribution of sampling effort (or lack of it). Therefore the obvious choice is to represent ignorance on a scale of 0 to 1 (1 being absolute ignorance and 0 being absolute certainty or credibility in the data). There are several approaches to incorporate sampling effort to different analysis of richness, species distributions and trends in population abundance (Hill 2012, Jeppsson et al. 2010, Ponder et al. 2001, Prendergast et al. 1993, Schulman et al. 2007, Snäll et al. 2011). However, most of these methods require several assumptions that constrain their generality and comparability. Conversely, the aim of this approach is to express ignorance solely based on raw data summarized per grid cell in order to rely on the fewest assumptions possible. The aim is not to include any covariates or correlation and to avoid prediction, estimation and interpolation methods (see e.g. Ponder et al. 2001). These basic criteria will give the end-user more freedom to adapt the ignorance maps to their own research question.

Observations are reported by people with varied field skills and accuracy. Because of the intrinsic characteristics of the reports (e.g. voluntary, non-systematic), biodiversity datasets have a considerable spatial and temporal bias. However, observers are assumed to be fond of or specialist on one or more taxonomic groups (e.g. family, order), rather than on individual species. Since it is likely that an entire group of species observed by similar methods (henceforth a reference taxonomic group) will share similar bias (Phillips et al. 2009), it is appropriate to use species’ groups as a surrogate for sampling effort (Phillips et al. 2009, Ponder et al. 2001). Therefore, it is straightforward to assume that the lack of reports of any species from the reference taxonomic group (e.g. birds) at a particular location is likely due to a lack of ornithologists on that specific location, rather than to the total absence of birds. The inverse logic also holds true. That is, the larger the number of observations of species from the reference taxonomic group in a grid cell, the more likely it is that the lack of reports of a particular species reflects a true absence of that species from the grid cell (i.e. larger certainty).

There are some considerations to take into account before describing the algorithms. First, the reference target group should only include species that are assumed to be sampled with the same methodology, to keep the sampling bias consistent (Ponder et al. 2001). For example, reference taxonomic groups should not include all species in the Order Lepidoptera because butterflies sensu stricto (superfamily Papilionoidea) are sampled in very different ways than all other species of Lepidoptera (mainly moths). Alternatively, interacting species could be included for specialist and symbiont species. Second, it has been pointed out that in case that ignorance maps are to be used to correct the sampling bias of background information (for software packages like MaxEnt; http://www.cs.princeton.edu/~schapire/maxent/), the target species should be removed from the reference taxonomic group if it is known that the species has been heavily sampled at a particular location but has few records in the vicinity (Ponder et al. 2001). In the case of allopatric species, however, removing the target species will leave “holes” in the ignorance maps (Ponder et al. 2001). Finally, it is preferred to calculate ignorance maps including observations over long time periods to reduce temporal variability in sampling effort (Snäll et al. 2011). Of course, this is only valid as long as there is no significant change to the underlying habitat that holds the species, and time itself is not a covariate to be included in the analysis of the data.

Algorithms overview

The sampling behaviour that characterizes observers differs among reference taxonomic groups. For some groups like vascular plants or bryophytes observers typically inventory confined areas (sites) reporting every species they observe, aiming to cover as many sites as possible. In these cases, raw observation counts per grid cell i (N_i) better represent the sampling intensity and species discovery (Fig. 1a). For other groups like birds, observers aim to complete a species list and often have preferred observation sites. Also, common species within these groups are often not reported by voluntary citizen scientists (Snäll et al. 2011). In these cases, a species observation index \(O{i} = \left\{\begin{array}{l l} 0, & N_{i} = 0\\ N_{i}/R_{i}, & N_{i} > 0 \end{array} \right.;\) is preferred, where R_i is the number of species observed in grid cell i. The species observation index O_i offsets the sampling effort relative to the number of species reported per grid cell. The relationship between the number of observations and the species observation index is shown in Fig. 1b for different reference taxonomic groups including mammals (land mammals without bats), birds, butterflies (superfamily Papilionoidea) and vascular plants (Tracheophyta). The use of N_i or O_i is optional to the researcher, and its consequences can be further explored using the HTML application run through R that can be downloaded from the projects webpage (http://alejandroruete.github.io/IgnoranceMaps). For simplicity, in this article “number of observations” will also refer to the species observation index.

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Figure 1.

a) Species discovery plot (N_i vs R_i) and b) species observation index (O_i) as a function of the number of observations per grid cell (N_i; Suppl. materials 1, 2). Each dot shows the data summarized per grid cell over 2000-2014 in Sweden. The dotted line indicates the 1:1 ratio of the number of observations versus the number of observed species (a), which is equal to a species observation index of 1 (b). Note the break in the x-axis and the change of scale of the secondary y-axis in b).

The first and easiest way to transform observation counts into a 0-1 scale of ignorance (I) is by using normalized data (henceforth the Normalization approach): \(I_{i}=1-N_{i}/N_{m}\) where N_m is the maximum number of observations per grid cell of the dataset. Then 0 represents the maximum certainty of the data corresponding to the maximum number of observations recorded in the entire dataset (Fig. 2) and 1 represents absolute ignorance. The normalization algorithm is recommended when the maximum number of observations is not too different from the mean number of observations, and particularly for areas with low variability. However, it is not recommended when the probability distribution of number of observations per grid cells presents a long right tail (i.e. many grid cells with none or few observations and few cells with extremely high number of observations).

Figure 2.  

Ignorance scores as a function of the number of observations per grid cell. The curves for the half-ignorance algorithm (red lines) are calculated for three values of O_0.5 = 1, 5, and 10 (i.e. enough number of observations to reduce the ignorance score by half).

In many cases there are sites that are more than sufficiently sampled (i.e. long right tails in the probability distribution of observations) but the relative influence of these sites on our certainty may not be linear. In these cases, when it is relevant to separate sites with “few” observations from sites with “enough” observations, logarithmic transformations are preferred (Fig. 2). Then, ignorance is equal to one minus the normalization of the natural logarithm of the data (henceforth the Log-Normalization approach) \(I_{i}=1-\log(N_{i}+1) / \log(N_{m}+1)\). A unit is added before log-transforming the data so that grid cells without observations are transformed to the highest ignorance score, i.e. 1. In both algorithms presented so far the minimum ignorance score, i.e. 0, is relative to the maximum number of observations for the reference taxonomic group. Therefore, ignorance maps produced with these algorithms are highly sensitive to the spatial and temporal extent of the data because the absolute maximum may not be included in subsets of the dataset.

An alternative approach is an algorithm independent of the maximum number of observations. It estimates ignorance scores making data relative to a reference number of observations that is considered to be enough to reduce the ignorance score by half (henceforth the Half-ignorance approach). In this case, ignorance scores are defined as \(I_{i} = O_{0.5}/(N_{i}+O_{0.5})\) (Fig. 2). In other words, setting the reference number O_0.5 = 1 means that one observation is enough to consider that the absence of reports of a target species from any grid cell is 50% due to true absence from the site and 50% due to failure to detect the species. Setting O_0.5 < 1 denotes more confidence on every single observation, not gaining much information from a higher number of observations. In this case, setting O_0.5 = 0.5 assumes that the first single observation (of any species in the reference taxonomic group) reduces our ignorance to 0.333. Conversely, setting O_0.5 > 1 denotes the need for more than one observation per grid cell to rely on such information (i.e. to significantly reduce the ignorance score). For example, setting O_0.5 = 5 assumes that we need at least five observations to partially trust on the sampling effort spent in any particular grid cell. This algorithm allows the researcher to customize its credibility on each observation in a way that the ignorance score approaches asymptotically to 0 as the number of observation increases. However, the bigger the O_0.5 the slower ignorance scores will approach 0 (Fig. 2). This approach is specially recommended when i) there are particular assumption about the confidence on each observation, and ii) when the aim is to compare datasets with very different maximum number of observaitons. As an illustration raw observational data for the superfamily Papilionoidea (Fig. 3a) is compared to ignorance maps produced with the three different algorithms: Normalization (Fig. 3b), Log-Normalization (Fig. 3c) and Half-Ignorance algorithms, setting O_0.5 = 1, 5, and 10 (Fig. 3d, e, f respectively). For more examples on different reference taxonomic groups download and run the interactive examples available in http://alejandroruete.github.io/IgnoranceMaps.

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Figure 3.

Raw observations (a; Suppl. material 1​) and ignorance maps (b,c,d,e,f) for the superfamily Papilionoidea over Sweden for the period 2000-2014, produced with the three proposed algorithms. The inset in panel 3a. shows Sweden in Europe. The black contour shows a 10 km buffer around Sweden’s land surface. Grid resolution is 10 x 10 km. Panels 3d,e,f: O_0.5 = 1, 5, and 10; respectively.

It is important to highlight that the size of the grid cells (i.e. resolution) will affect the results of all implemented algorithms. For example, consider the simple case where one large grid cell is made up of four smaller cells of which three cells are empty and only one cell scores all the reported observations. In this case the spatial distribution of recording effort will look very different when mapped at a high or low resolution. Sensitivity to spatial resolution is a common problem on studies summarizing biodiversity data on arbitrary grid cells, and the relevance of this problem has to be evaluated for each study in light of the question or hypothesis tested (Hurlbert and Jetz 2007). The algorithms allow the user to specify the temporal and spatial extent and resolution in order to produce ignorance maps that are relevant to the species biology and researchers needs (note: to do so with the R scripts provided on the project website, the user has to simply replace the raster images with the number of observations and the number of species with the desired ones). Some solutions have been developed to produce scale and resolution independent maps of the sampling effort (i.e. the opposite of ignorance; Schulman et al. 2007). However, because the algorithms suggested by Schulman et al. 2007 are based on Thiessen polygons and interpolations computed for individual observation points (i.e. instead of summaries per grid cells) these solutions are not flexible enough and are too computationally intensive to provide custom web-based results over large datasets.

This project was framed within and funded by the Swedish LifeWatch.