Remotely sensed spatial heterogeneity as an
exploratory tool for taxonomic and functional
diversity study

Duccio Rocchini ¹,²,³,*, Giovanni Bacaro⁴, Gherardo Chirici⁵,
Daniele Da Re⁴, Hannes Feilhauer⁶, Giles M. Foody⁷,
Marta Galluzzi⁵, Carol X. Garzon-Lopez⁹,
Thomas W. Gillespie¹⁰, Kate S. He¹¹, Jonathan Lenoir¹²,
Matteo Marcantonio¹³, Harini Nagendra¹⁴, Carlo Ricotta¹⁵,
Edvinas Rommel¹⁶, Sebastian Schmidtlein¹⁷,
Andrew K. Skidmore¹⁸, Ruben Van De Kerchove¹⁹,
Martin Wegmann²⁰, Benedetto Rugani²¹

September 27, 2017

¹ Center Agriculture Food Environment, University of Trento, Via E. Mach 1, 38010 S. Michele all'Adige (TN), Italy

² Centre for Integrative Biology, University of Trento, Via Sommarive, 14, 38123 Povo (TN), Italy

³ Fondazione Edmund Mach, Department of Biodiversity and Molecular Ecol-
ogy, Research and Innovation Centre, Via E. Mach 1, 38010 S. Michele al-
l'Adige (TN), Italy

⁴ Department of Life Sciences, University of Trieste, Via L. Giorgieri 10, 34127 Trieste.

⁵ geoLAB - Laboratory of Forest Geomatics Department of Agricultural, Food and Forestry Systems, University of Florence, Via San Bonaventura, 13, 50145 Firenze, Italy

⁵ Institute of Geography, University of Erlangen-Nuremberg, Wetterkreuz 15, 91058 Erlangen, Germany

⁶ University of Nottingham, University Park, Nottingham NG7 2RD, UK
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⁸ Ecology and Vegetation physiology group (EcoFiv), Universidad de los Andes, Cr. 1E No 18A, Bogotá, Colombia

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⁹ Department of Geography, University of California Los Angeles, Los Angeles, CA 90095-1524, USA

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¹⁰ Department of Biological Sciences, Murray State University, Murray, KY 42071, USA

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¹¹ UR “Ecologie et dynamique des systèmes anthropisées” (EDYSAN, FRE3498 CNRS-UPJV), Université de Picardie Jules Verne, 1 Rue des Louvels, 80037 Amiens Cedex 1, France

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¹² Department of Pathology, Microbiology, and Immunology, School of Veterinary Medicine, University of California, Davis, USA

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¹³ Azim Premji University, PES Institute of Technology Campus, Pixel Park, B Block, Electronics City, Hosur Road, Bangalore, 560100, India

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¹⁴ Department of Environmental Biology, University of Rome “La Sapienza”, Rome 00185, Italy

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¹⁵ Department of Biogeography, BayCEER, University of Bayreuth, Universitaetsstr. 30, 95440 Bayreuth, Germany

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¹⁶ Institute of Geography and Geoecology, Karlsruhe Institute of Technology, Kaiserstr. 12, 76131 Karlsruhe, Germany

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¹⁷ Department of Natural Resources, Faculty of Geo-Information Science and Earth Observation (ITC), University of Twente, P.O. Box 217, AE Enschede, 7500, The Netherlands

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¹⁸ VITO (Flemish Institute for Technological Research), Boeretang 200, 2400 Mol, Belgium

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¹⁹ Department of Remote Sensing, Remote Sensing and Biodiversity Research Group, University of Wuerzburg, Wuerzburg, Germany

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²⁰ Luxembourg Institute of Science and Technology (LIST), Dept. Environmental Research and Innovation (ERIN), 41 rue du Brill, L-4422 Belvaux, Luxembourg

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## Abstract

Assessing biodiversity from field-based data is difficult for a number of practical reasons: (i) establishing the total number of sampling units to be investigated and the sampling design (e.g. systematic, random, stratified) can be difficult; (ii) the choice of the sampling design can affect the results; and (iii) defining the focal population of interest can be challenging. Satellite remote sensing is one of the most cost-effective and comprehensive approaches to identify biodiversity hotspots and predict changes in species composition. This is because, in contrast to field-based methods, it allows for complete spatial coverages of the Earth's surface under study over a short period of time. Furthermore, satellite remote sensing provides repeated measures, thus making it possible to study temporal changes in biodiversity. While taxonomic diversity measures have long been established, problems arising from abundance related measures have not been yet disentangled. Moreover, little has been done to account for functional diversity besides taxonomic diversity measures. The aim of this manuscript is to propose robust measures of remotely sensed heterogeneity to perform exploratory analysis for the detection of hotspots of taxonomic and functional diversity of plant species.

Keywords: cartograms; functional diversity; remote sensing; Rao's quadratic diversity; satellite imagery; spectral rarefaction; taxonomic diversity.

# 1 Introduction

The assessment of biodiversity for a conservation purpose is difficult to undertake via field survey (Palmer, 1995). Species richness is the simplest, most intuitive and most frequently used measure for characterizing the diversity of an assemblage (Chiarucci et al., 2012; Chao et al., 2016). In nearly all biodiversity studies, however, the compilation of complete species census and inventories often requires extraordinary efforts and is an almost unattainable goal in practical applications. There are undiscovered species in almost every taxonomic survey or species inventory (Palmer, 1995). Consequently, a simple count of species (observed richness) in a sample underestimates the true species richness (observed plus undetected), with the magnitude of the negative bias possibly substantial. In addition, empirical richness strongly depends on sampling effort and thus also depends on sample completeness. Statistically sound sampling of biodiversity requires several assumptions to be fulfilled in order to allow reproducibility and credible estimation. The
crucial assumption is a random sampling design, i.e. the random spatial dis-
tribution of samples based on stanrdadised statistical sampling procedures,
which generally hampers rapid sampling mainly due to logistic problems. In
fact, complex ecosystems might not be systematically surveyed or temporar-
ily monitored by conventional biodiversity surveys because of high costs,
challenges to access the sampling sites or the lack of historical data (Roy and
Tomar, 2000).

From this point of view, remote sensing is an efficient tool allowing to
cover large areas over a short period of time, hence providing key information
on the spatio-temporal variation of biodiversity.

This is overall true (from a biodiversity conservation viewpoint), con-
sidering the fact that recent Life Cycle Impact Assessment (LCIA) studies
acknowledged the importance of understanding the human induced cause-
effect mechanisms shaping the decline or improvement of biodiversity and
thus the provision of biodiversity-related ecosystem services (Moran et al.,
2016).

Recently, Souza et al. (2015) explicitly observed that landscape-oriented
approaches to evaluate biodiversity loss in a LCIA context are still lacking
(Scheiner et al., 2000; Dungan et al., 2002). Changing the focus from indi-
viduals to communities, entire ecosystems and biomes might represent a key
concept to a correct and widely usable LCIA model.

The aim of this paper is to propose novel approaches using remote sensing
to perform exploratory analysis for the detection of hotspots of taxonomic
and functional diversity of plant species. The complete R code (R Core
Team, 2017) used to implement all the presented algorithms is available in
Appendix 1.

2 Heterogeneity measurement from remote sensing and the relationship with taxonomic diversity

According to the spectral variation hypothesis (Palmer et al., 2002) the larger
the spectral heterogeneity the higher will be the niche availability for different
organisms to survive. Hence, the higher the spectral variability of an envi-
ronment the higher might be its biodiversity. Such a hypothesis has been
widely tested with taxonomic data (Rocchini, 2007; Rocchini et al., 2016;
Schmeller et al., 2017) and often resulted in a positive statistical relationship
although the link does not always hold true (Schmidtlein and Fassnacht ,
2017).
The variability over space is generally tested relying on a local calculation of heterogeneity based on a moving window in a satellite image and connecting it to human-related and ecological / geographical drivers shaping biodiversity in the field.

For instance, spectral heterogeneity measurements, based on the calculation of indices of variability of neighbouring pixels in an image have been recently proposed as a possible solution to support the assessment of land use impacts on biodiversity (Rugani and Rocchini, 2017). Such approaches might help detecting the geographical location of hotspots of diversity and their temporal changes in a straightforward manner. Figure 1 shows as an example the Rao's quadratic diversity in two dimensions over the world, theoretically depicted by (Rocchini et al., 2017), calculated from Normalized Difference Vegetation Index (hereafter NDVI) based on Moderate Resolution Imaging Spectroradiometer (MODIS) satellite data. As far as we know, this is the first application of Rao's Q metric to satellite data covering the whole world. The complete R code is available in Appendix 1.

Given a certain number of reflectance values in a portion of a remotely sensed image (usually a moving window of n x n pixels), such metric is defined as the expected difference in reflectance values between two pixels drawn randomly with replacement from the set of pixels:

$$Q = \sum \sum d_{ij} \times p_i \times p_j \qquad (1)$$

where $d_{ij}$ is the spectral distance between pixel i and j and $p_i$ is the relative proportion of pixel i (i.e. in a window of n x n pixels $p_i = 1/n^2$). The spectral distance $d_{ij}$ can be calculated either for a single band or in a multispectral system, thus allowing to consider more than one band at a time (Rocchini et al., 2017). If Q is calculated for a single band, the resulting value can be directly related to the variance of the reflectance values within the considered set of pixels, a well-known metric for summarizing the spatial complexity of remotely sensed images (Rocchini et al., 2010). Rao's Q metric weights the distance among pixel values in a spectral space and their evenness. In practice, higher diversity in this example is related to the relative distance of NDVI spectral values and to relative evenness in the distribution of such values.

Once applied at large spatial scales, Rao's quadratic diversity might reveal differences among different countries, areas, habitats or land use types to be potentially linked to related ecosystem services.

In this view, the use of cartograms (Figure 2, Gastner and Newman (2004)) can help to show the differences among units (in this case, different countries are shown, as an example) in terms of Rao's Q, by distorting
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each unit depending on the relative value of the entropy index reported in
Figure 1 (restricted to Europe in Figure 2).

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Using multitemporal remotely-sensed imagery, such a map might prove
useful to detect abrupt changes, referred to as “catastrophic regime shifts”,
which can lead to an alteration in the provision of ecosystem services, such
as water provision (Gutral and Jayaprakash, 2009). An example is provided
in Figure 3 in which MODIS tiles (NDVI, 16-days product, June, Appendix
1) have been used to calculate Rao’s Q at a spatial resolution of 1 km.
Care might be taken considering the first years after the launch of the Terra
MODIS satellite (launched December 18th 1999), in which calibration was
still in process but provisional data were acquired (e.g. year 2000). As
pointed out by Rocchini et al. (2017) variations at large spatial scales (large
extent) are mainly due to the variability of climatic conditions, e.g. the high
variability at higher latitudes (Figures 3a and 3b), while local scale variability
could be related to processes like local management practices, urban spread,
agricultural land conversion or disturbance. Rao’s Q applied over multiple
dates (also potentially including different seasons) might help detecting local
to global scale changes in heterogeneity.

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Furthermore, the so-called global disparities and habitat losses might be
also detected once applying proper diversity measures at global spatial scales.
Major disparities between habitat loss and conservation lead some areas of
the world to be more sensible to environmental change. In such a case, mea-
suring diversity from satellites can help to anticipate habitat loss, providing
useful tools to further improve management actions (Hoekstra et al., 2005).

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The spectral variation approach has been observed to be complementary
to the current state-of-the-art practice in LCIA of land use on biodiver-
sity, where characterization models are mainly based on the consideration
of species-area relationships (De Schryver et al., 2010; De Baan et al., 2013;
Elshout et al., 2014; Chaudhary et al., 2015; Verones et al., 2015). Assessing
spectral heterogeneity seems also a complementary approach to the study
of (Human Appropriation of) Net Primary Production ((HA)NPP, Haberl
et al. (2014)). Indeed, detecting heterogeneity through the processing of
remotely sensed imagery allows to capture possible changes associated with
plant species diversity loss or gain over time and at various spatial resolutions
and extents, while (HA)NPP indicators can provide a quantitative measure
of the impact associated with spatial variability patterns.

In some cases, the heterogeneity measured from space might be directly
related to human-based processes, like urban spread, which seem to affect
both ecosystem functioning and the provision of ecosystem services (Tratalos
et al., 2007). As an example, Figure 4 represents the number of accumulated
spectral values once increasing the extent of analysis (sampling effort), at-
tained by calculating a rarefaction curve on the spectral values of a Landsat 8 image (pixel resolution = 30m) in the Tenerife island (Canary Islands) as in Rocchini et al. (2011). After i) superimposing a grid of 500x500m on the Landsat 8 image and ii) extracting the first principal component (Appendix 1), the amount of spectral values accumulated by increasing the extent (number of grid cells) was calculated as:

$$E(S) = S - \frac{\sum_{i=1}^{S} \binom{N - N_i}{n}}{\binom{N}{n}} \quad (2)$$

where S = total number of spectral values, Nᵢ = number of grid cells in which the spectral value i is found, n = number of randomly chosen grid cells. Reader is referred to Shinozaki et al. (2016) and Kobayashi (1974) for the original formulation of the rarefaction curve algorithm, and to Ugland et al. (2003) and Chiarucci et al. (2008) for a critique on its application to ecological data (species rarefaction), and further to Rocchini et al. (2011) for its application to remote sensing data (spectral rarefaction). In this example, human-related land use, mainly related to urban spread, is concentrated in the arid coastal (vegetation) belt at low elevations (Fernandez-Palacios and Nicolás, 1995), leading to a higher spectral heterogeneity caused by a mixed anthropic-natural landscape which is described by a higher number of accumulated spectral values.

## 3 The importance of estimating functional diversity

Beside taxonomic diversity, the combination of different traits is generally investigated by remote sensing to find indirect measures of functional diversity from a remote sensing perspective (Schmidtlein et al., 2012; Kattenborn et al., in press).

The underlying assumption for the use of taxonomic diversity as a proxy of general biodiversity of an area is that the taxa are equally distinct from one another, disregarding the fact that communities are composed by species with different evolutionary history and a diverse array of ecological functions. More recently, the concept of functional diversity has received considerable attention because it captures information on species functional traits, which is absent in traditional measures of species diversity (Violle et al., 2007; Bartha, 2008; Lavorel et al., 2008; Ricotta et al., 2014). Functional traits
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are morphological, physiological, and phenological attributes, which impact
individual fitness via their effects on growth, reproduction and survival.

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There is an increasing body of literature demonstrating that functional diversity tends to correlate more strongly than traditional species diversity with ecosystem functions such as productivity (Loreau, 2000; Petchey et al., 2004; Hooper et al., 2005; Cardoso et al., 2014), resilience to perturbations (Moretti and Legg, 2009; Mori et al., 2013), or regulation of biogeochemical fluxes (Waldbusser et al., 2004; Legendre et al., 2005). Functional diversity might also be a tool for predicting the functional consequences of human-induced biotic change (Ricotta et al., 2012).

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The observed relationships between functional diversity and ecosystem functioning raise the question of how to measure functional diversity in meaningful ways. One of the most established systems for plant functional types is the strategy types proposed by Grime (Grime, 1974, 1977). The CSR plant strategy type system categorizes plants according to their abilities to compete for resources (C strategists), tolerate stress (S strategists) and survive disturbance (R strategists), recognizing the interplay of plant functional types, plant functional traits and ecosystem functions (Schweiger et al., 2016).

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However, as for species inventories, field measurements of plant functional traits are costly, time-consuming and notoriously difficult to acquire, especially in remote areas. In contrast, plant functional types can be deduced from botanical inventories (releve data) and corresponding trait databases, which are more widely available than plant functional trait measurement.

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Recently, increasing efforts have been devoted in assessing existing links between plant species spectral signatures (Asner and Martin, 2008) and plant community functional diversity. Imaging spectroscopy could enable modelling and predicting plant functional types at the vegetation community scale with high accuracy and greater consistency than plant life/growth forms (Schmidtlein et al., 2012; Schweiger et al., 2016; Kattenborn et al., in press). Based on these results, it can be affirmed that remote sensing methods mainly proposed for estimating biodiversity at the taxonomic level could even be related to the variation of community functional characteristics: in other words, the spectral signature of plant functional types is preserved in the vegetation community's spectral response.

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Using remotely sensed spectral heterogeneity might lead to an estimate of functional diversity. As an example, the previously mentioned Rao's Q has been extensively used in functional diversity applications (Botta-Dukat, 2005; Ricotta et al., 2014; Marcantonio et al., 2014). Functional ecologists make use of a wide set of functional traits (plants functional characteristics) to assess the diversity of natural systems. Rao's Q has been shown to be a valid candidate to summarize them in a single diversity value (Botta-Dukat,

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## 4 Conclusion and outlook

When assessing impacts associated with land use, biodiversity loss in terms of species richness and vulnerability is explicitly considered to have an intrinsic value for the ecosystem quality, while ecosystem services are reflected to have rather an instrumental value.

However, heterogeneity measurements can only capture spatial variability at different scales of complexity. Therefore, in the absence of field data it is difficult if not impossible to find the best solution to assess other functional biodiversity related issues, such as issues vulnerability resilience and recoverability of e.g., species or ecosystems.

This said, the use of remotely-sensed diversity might prove useful since in most cases satellite imagery is directly related to variables connected to ecosystem services. As an example, NDVI, which has been used to measure diversity from space in a number of papers (Gillespie, 2005; He and Zhang, 2009) is directly linked to the photosynthetic activity of the vegetation and thus indirectly to vegetation biomass (Krishnaswamy et al., 2009).

It might be clear that ecosystems biodiversity provides ecosystem services which also regulate human livelihood, like, as previously stated, water and carbon cycle regulation or soil erosion prevention. In this sense, remote sensing and the analysis of satellite data provide spatial models which are crucial for assessing the current (and predicting the future) conditions of habitats (Newton et al., 2009).

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<figure><img src="image_1.png" /><figcaption>Figures</figcaption></figure>

Figure 1: Rao's quadratic diversity metric applied to an NDVI map of the world (date 2016-06-06, http://land.copernicus.eu/global/products/ndvi), resampled at 2km resolution with a moving window of 5 pixels. As far as we know, this is the first application of Rao's Q metric to satellite data covering the whole world. The complete R code is provided in Appendix 1.
<figure><img src="image_2.png" /><figcaption>Figure 2: Cartograms showing univariate statistics of the Rao'S Q metric in Europe, distorting the shape of units (in this case, as an example, countries) depending on the relative value of the index. ci = confidence interval at 95%, se = standard error, sd = standard deviation. The free software ScapeToad (https://scapetoad.choros.ch/) was used to generate the cartograms.</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>Figure 3: Multi spatio-temporal comparison of Rao index on NDVI images: (a) spatial pattern of heterogeneity at European scale, (b) temporal-latitude profile of Rao's Q index with an increase of heterogeneity between 60 and 70 degrees (i.e. mainly in the Scandinavian region), principally due to the variability related to temporary snow cover. Once data on different phenological seasons are attained, different patterns are also expected.</figcaption></figure>
<figure><img src="image_4.png" /></figure>

Figure 4: Applying rarefaction techniques to a Landsat 8 image might reveal the diversity of different land use classes which can be related to human-based processes. As an example, in Tenerife (a), human-related land use, mainly related to urban spread, is concentrated in the arid coastal (vegetation) belt at low elevations (b). This leads to a higher spectral heterogeneity caused by a mixed anthropic-natural landscape which is described by a higher number of accumulated spectral values (c).
<figure><img src="image_5.png" /><figcaption>Figure 5: Rao's Q calculated on a set of C (competitive species), S (stress-tolerative species), R (ruderal species) score maps (derived from (Schmidtlein et al., 2012)) to estimate the diversity of functional types probability in space. In the numeric space (left), the C, S, R maps can be viewed as score matrices in two dimensions; in the Rao's Q formula the distance between such scores is used together with their relative abundance.</figcaption></figure>