# Relevance of the Cell Neighborhood Size in Landscape Metrics Evaluation and Free or Open Source Software Implementations

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## Abstract

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## 1. Introduction

## 2. Literature Review

- 70 (65.1%) papers cited FRAGSTATS as software for the evaluation of landscape metrics;
- 16 (14.9%) papers cited LecoS as QGIS add-on used for the calculation of the landscape metrics;
- Four (3.7%) papers cited r.li/r.le as GRASS modules for the assessment of the metrics;
- Three (2.8%) papers cited other software for the assessment of the metrics;
- Two papers developed new software for the evaluation of landscape metrics, using as reference for the calculations FRAGSTATS (these papers have been counted in the 70 articles citing FRAGSTATS).

- papers that deal with landscape fragmentation as an issue in itself;
- papers that deal with landscape fragmentation as an issue for habitat connectivity;
- papers that investigate which landscape metric could explain other metrics;
- papers that investigate the size of a moving window algorithm and how it affects landscape analysis;
- papers that present new software for landscape metrics calculation, basing their structure and methods on FRAGSTATS.

## 3. Materials and Methods

#### 3.1. Test Software

`landscapemetrics`it is now possible to perform landscape analysis on rasters inside the R environment [51].

#### 3.2. Landscape Metrics

**Patch****Number****(NP)**- is the number of patches of each type; it is an adimensional metric. It is defined as:$$NP={N}_{k},$$
- N is the number of patches in the k-th category.

**Patch****density****(PD)**- equals the number of patches of the corresponding patch type divided by total landscape area [m], multiplied by 10,000 and 100 (to convert to 100 hectares). The unit of measure is number of patches per 100 hectares. It is expressed as:$$PD=\frac{N}{A}\left({10}^{4}\right)\left(100\right),$$
- N is the number of patches in the landscape;
- A is the total landscape area in [m${}^{2}$];
- ${10}^{4}$ and 100 are constant and used to express the index in (100) ha.

**Mean****patch****size****(MPS)**- is the average area of all the patches of a given type. It is measured in square meters. When used in combination with NP, MPS gives information about how the patches of a given land use class are growing or merging over time [53]. It is defined as:$$MPS=\frac{A}{NP},$$
- A is the area of the patches in [m${}^{2}$];
- $NP$ is the number of patches.

**Edge****density****(ED)**- equals the sum of the lengths (m) of all edge segments involving the corresponding patch type, divided by the total landscape area (m), multiplied by 10,000 (to convert to hectares). The unit is meters per hectare. ED > 0. This index is useful in ecological studies dealing with ecotone species. It is expressed as:$$ED=\frac{{\sum}_{k=1}^{m}{\sum}_{i=1}^{n}{e}_{ik}}{A}\left({10}^{4}\right),$$
- k is the category of the patches;
- m is the total number of different categories of patches;
- n is the number of boundary edges for the patch;
- ${e}_{ik}$ is the total length of boundary edges for the k-th category of patches;
- A is the total landscape area;
- ${10}^{4}$ is a constant to convert the index in [m/ha].

**Landscape****shape****index****(LSI)**- measures the perimeter-to-area ratio for the landscape as a whole. All edge segments (m) within the landscape boundary involving the corresponding patch type are divided by the square root of the total landscape area (m). LSI > 1, adimensional. This index is a measure of the overall geometric complexity of the landscape and is defined as:$$LSI=0.25\frac{E}{\sqrt{A}},$$
- E is the sum of the lengths of all the boundary edges of the patches;
- A is the sum of all the areas of the patches;
- 0.25 is a adjustment coefficient.

**Aggregation****index****(AI)**- equals the number of adjacent patches involving the corresponding class, divided by the maximum possible number of like adjacencies, which is achieved when the class is maximally clumped into a single, compact patch, multiplied the proportion of the landscape comprised of the corresponding class, summed over all classes and multiplied by 100 (to convert to a percentage). Unit: Percent, range 0 < AI < 100 [45]. It is useful to quantify spatial patterns and fragmentation of the landscape. It is defined as:$$AI=\left[{\displaystyle \frac{{g}_{ii}}{max\left({g}_{ii}\right)}}\right]\left(100\right),$$
- ${g}_{ii}$ is the number of like adjacencies between pixels of patch class i based on the single-count method;
- $max\left({g}_{ii}\right)$ is the maximum number of like adjacencies between pixels of patch class i based on the single-count method;
- 100 is a constant used to express the index as percentage.

- FRAGSTATS allows the user to choose between the two definitions [42].

#### 3.3. Artificial Maps

#### 3.4. Real Maps

## 4. Results

## 5. Aggregation Index

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

AI | aggregation index |

CN | cell neighborhood |

ED | edge density |

GIS | geographic information system |

GPL | Gnu Public License |

FOSS | free and open source software |

LSI | landscape shape index |

MPS | mean patch size |

NP | number of patches |

PD | patch density |

## Appendix A. Available Metrics

**Table A1.**Software features: cell neighborhood and available area and edge metrics for FRAGSTATS, GRASS (r.li), and QGIS (LecoS).

FRAGSTATS | GRASS | QGIS | |
---|---|---|---|

Cell neighborhood | 4 or 8 cells | 4 cells | 8 cells |

Patch Metrics | |||

Patch Area (AREA) | ✓ | ✓ | |

Patch Perimeter (PERIM) | ✓ | ||

Radius of Gyration (GYRATE) | ✓ | ||

Class Metrics | |||

Total (Class) Area (CA) | ✓ | ✓ | |

Percentage of Landscape (PLAND) | ✓ | ✓ | ✓ |

Largest Patch Index (LPI) | ✓ | ||

Total Edge (TE) | ✓ | ✓ | |

Edge Density (ED) | ✓ | ✓ | ✓ |

Patch Area Distribution(AREA_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Radius of Gyration Distribution(GYRATE_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Landscape Metrics | |||

Total Area (TA) | ✓ | ✓ | |

Largest Patch Index (LPI) | ✓ | ✓ | |

Total Edge (TE) | ✓ | ||

Edge Density (ED) | ✓ | ✓ | |

Patch Area Distribution(AREA_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ✓ | |

Radius of Gyration Distribution(GYRATE_MN, _AM, _MD, _RA, _SD, _CV) | ✓ |

FRAGSTATS | GRASS | QGIS | |
---|---|---|---|

Patch Metrics | |||

Perimeter-Area Ratio (PARA) | ✓ | ||

Shape Index (SHAPE) | ✓ | ✓ | ✓ |

Fractal Dimension Index (FRAC) | ✓ | ✓ | |

Related Circumscribing Circle (CIRCLE) | ✓ | ||

Contiguity Index (CONTIG) | ✓ | ||

Class Metrics | |||

Perimeter-Area Fractal Dimension (PAFRAC) | ✓ | ||

Perimeter-Area Ratio Distribution(PARA_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Shape Index Distribution(SHAPE_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ✓ | |

Fractal Index Distribution(FRAC_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Linearity Index Distribution(LINEAR_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Related Circumscribing Square Distribution(SQUARE_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Contiguity Index Distribution(CONTIG_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Landscape Metrics | |||

Perimeter-Area Fractal Dimension (PAFRAC) | ✓ | ||

Perimeter-Area Ratio Distribution(PARA_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Shape Index Distribution(SHAPE_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ✓ | |

Fractal Index Distribution(FRAC_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Linearity Index Distribution(LINEAR_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Related Circumscribing Square Distribution(SQUARE_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Contiguity Index Distribution(CONTIG_MN, _AM, _MD, _RA, _SD, _CV) | ✓ |

**Table A3.**Software features: available core area metrics for FRAGSTATS, GRASS (r.li), and QGIS (LecoS).

FRAGSTATS | GRASS | QGIS | |
---|---|---|---|

Patch Metrics | |||

Core Area (CORE) | ✓ | ||

Number of Core Areas (NCA) | ✓ | ||

Core Area Index (CAI) | ✓ | ||

Class Metrics | |||

Total Core Area (TCA) | ✓ | ✓ | |

Core Area Percentage of Landscape (CPLAND) | ✓ | ||

Number of Disjunct Core Areas (NDCA) | ✓ | ||

Disjunct Core Area Density (DCAD) | ✓ | ||

Core Area Distribution(CORE_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Disjunct Core Area Distribution(DCORE_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Core Area Index Distribution(CAI_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Landscape Metrics | |||

Total Core Area (TCA) | ✓ | ||

Number of Disjunct Core Areas (NDCA) | ✓ | ||

Disjunct Core Area Density (DCAD) | ✓ | ||

Core Area Distribution(CORE_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Disjunct Core Area Distribution(DCORE_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Core Area Index Distribution(CAI_MN, _AM, _MD, _RA, _SD, _CV) | ✓ |

**Table A4.**Software features: available contrast metrics for FRAGSTATS, GRASS (r.li), and QGIS (LecoS).

FRAGSTATS | GRASS | QGIS | |
---|---|---|---|

Patch Metrics | |||

Edge Contrast Index (ECON) | ✓ | ||

Class Metrics | |||

Contrast-Weighted Edge Density (CWED) | ✓ | ✓ | |

Total Edge Contrast Index (TECI) | ✓ | ||

Edge Contrast Index Distribution(ECON_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Landscape Metrics | |||

Contrast-Weighted Edge Density (CWED) | ✓ | ✓ | |

Total Edge Contrast Index (TECI) | ✓ | ||

Edge Contrast Index Distribution(ECON_MN, _AM, _MD, _RA, _SD, _CV) | ✓ |

**Table A5.**Software features: available aggregation metrics for FRAGSTATS, GRASS (r.li), and QGIS (LecoS).

FRAGSTATS | GRASS | QGIS | |
---|---|---|---|

Patch Metrics | |||

Euclidean Nearest Neighbor Distance (ENN) | ✓ | ✓ | |

Proximity Index (PROX) | ✓ | ||

Similarity Index (SIMI) | ✓ | ||

Class Metrics | |||

Interspersion & Juxtaposition Index (IJI) | ✓ | ||

Percentage of Like Adjacencies (PLADJ) | ✓ | ✓ | |

Aggregation Index (AI) | ✓ | ||

Clumpiness Index (CLUMPY) | ✓ | ||

Landscape Shape Index (LSI) | ✓ | ||

Normalized Landscape Shape Index (nLSI) | ✓ | ||

Patch Cohesion Index (COHESION) | ✓ | ✓ | |

Number of Patches (NP) | ✓ | ✓ | ✓ |

Patch Density (PD) | ✓ | ✓ | ✓ |

Landscape Division Index (DIVISION) | ✓ | ✓ | |

Splitting Index (SPLIT) | ✓ | ✓ | |

Effective Mesh Size (MESH) | ✓ | ✓ | |

Euclidean Nearest Neighbor Distance Distribution(ENN_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Proximity Index Distribution(PROX_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Similarity Index Distribution(SIMI_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Connectance (CONNECT) | ✓ | ||

Landscape Metrics | |||

Contagion (CONTAG) | ✓ | ||

Interspersion & Juxtaposition Index (IJI) | ✓ | ||

Percentage of Like Adjacencies (PLADJ) | ✓ | ||

Aggregation Index (AI) | ✓ | ||

Landscape Shape Index (LSI) | ✓ | ||

Patch Cohesion Index (COHESION) | ✓ | ||

Number of Patches (NP) | ✓ | ||

Patch Density (PD) | ✓ | ||

Landscape Division Index (DIVISION) | ✓ | ||

Splitting Index (SPLIT) | ✓ | ||

Effective Mesh Size (MESH) | ✓ | ||

Euclidean Nearest Neighbor Distance Distribution(ENN_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Proximity Index Distribution(PROX_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Similarity Index Distribution(SIMI_MN, _AM, _MD, _RA, _SD, _CV) | ✓ | ||

Connectance (CONNECT) | ✓ |

**Table A6.**Software features: available diversity indexes for FRAGSTATS, GRASS (r.li), and QGIS (LecoS).

FRAGSTATS | GRASS | QGIS | |
---|---|---|---|

Landscape Metrics | |||

Patch Richness Density (PRD) | ✓ | ✓ | |

Relative Patch Richness (RPR) | ✓ | ||

Shannon’s Diversity Index (SHDI) | ✓ | ✓ | ✓ |

Simpson’s Diversity Index (SIDI) | ✓ | ✓ | ✓ |

Modified Simpson’s Diversity Index (MSIDI) | ✓ | ||

Shannon’s Evenness Index (SHEI) | ✓ | ✓ | |

Simpson’s Evenness Index (SIEI) | ✓ | ||

Modified Simpson’s Evenness Index (MSIEI) | ✓ |

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**Figure 4.**Scheme of the configuration of the second artificial test map, consisting of two large patches separated by a single column of 0 values.

**Figure 5.**Scheme of the configuration of the third artificial test map, consisting of a single large patch occupying the left half of the map.

**Figure 6.**Scheme of the configuration of the fourth artificial test map, consisting of a single patch of one pixel at the center of the map.

**Figure 7.**Location of Trentino region, in orange (in Italy), the Val di Fassa, in red (in the Trentino region), and the forest area in green (in Val di Fassa).

**Figure 8.**Maps of the forest coverage of Val di Fassa in 2006, original map (left), filtered with the third quartile (center) and first quartile (right).

**Figure 10.**Variation of number of patches, patch density, and mean patch size landscape metrics as a function of AI for CN values of 4 and 8, left scale, and their difference in percentage, right scale, evaluated on the map representing the forest coverage in Val di Fassa in 2006 and the two maps obtained by applying a low pass filter with a 3 × 3 pixels window, assigning the first and the third quartile.

**Figure 11.**Difference in number of patches using 4 and 8 cells CN in percentage as a function of AI for the six forest maps.

Metric | Number of Citing Papers | Percentage of Citing Papers |
---|---|---|

Patch Number | 47 | 51.1% |

Patch density | 31 | 33.7% |

Mean patch size | 51 | 55.4% |

Edge density | 34 | 37.0% |

Landscape shape index | 32 | 34.8% |

Aggregation index | 21 | 22.8% |

GRASS | FRAGSTATS | QGIS | ||
---|---|---|---|---|

Cell neighborhood | 4 cells | 4 cells | 8 cells | 8 cells |

N patches | 5000 | 5000 | 1 | 1 |

Patch density [patches/100 ha] | 10,000 | 10,000 | 2 | 2 |

Mean patch size [m${}^{2}$] | 0.01 | 0.01 | 50 | 50 |

Edge density [m/ha] | 4000 | 4000 | 4000 | 4000 |

Landscape shape index | 70.71 | 70.42 | 70.42 | 70.71 |

GRASS | FRAGSTATS | QGIS | ||
---|---|---|---|---|

Cell neighborhood | 4 cells | 4 cells | 8 cells | 8 cells |

N patches | 2 | 2 | 2 | 2 |

Patch density [patches/100 ha] | 2.02 | 2.02 | 2.02 | 2.02 |

Mean patch size [m${}^{2}$] | 49.5 | 49.5 | 49.5 | 49.5 |

Edge density [m/ha] | 60.4 | 60.4 | 60.4 | 60.4 |

Landscape shape index | 1.5 | 1.5 | 1.5 | 1.5 |

GRASS | FRAGSTATS | QGIS | ||
---|---|---|---|---|

Cell neighborhood | 4 cells | 4 cells | 8 cells | 8 cells |

N patches | 1 | 1 | 1 | 1 |

Patch density [patches/100 ha] | 2 | 2 | 2 | 2 |

Mean patch size [m${}^{2}$] | 50 | 50 | 50 | 50 |

Edge density [m/ha] | 60 | 60 | 60 | 60 |

Landscape shape index | 1.06 | 1.06 | 1.06 | 1.06 |

GRASS | FRAGSTATS | QGIS | ||
---|---|---|---|---|

Cell neighborhood | 4 cells | 4 cells | 8 cells | 8 cell |

N patches | 1 | 1 | 1 | 1 |

Patch density [patches/100 ha] | 10,000 | 10,000 | 10,000 | 10,000 |

Mean patch size [m${}^{2}$] | 0.01 | 0.01 | 0.01 | 0.01 |

Edge density [m/ha] | 4000 | 4000 | 4000 | 4000 |

Landscape shape index | 1 | 1 | 1 | 1 |

GRASS | FRAGSTATS | QGIS | ||
---|---|---|---|---|

Cell neighborhood | 4 cells | 4 cells | 8 cells | 8 cells |

N patches | 43,594 | 43,594 | 21,094 | 21,094 |

Patch density [patches/100 ha] | 368.3626 | 368.2583 | 178.1906 | 178.2262 |

Mean patch size [m${}^{2}$] | 0.2715 | 0.2715 | 0.5611 | 0.5611 |

Edge density [m/ha] | 728.6887 | 728.5863 | 728.5863 | 728.6592 |

Landscape shape index | 198.1790 | 198.1631 | 198.1631 | 198.1792 |

**Table 7.**Aggregation index and difference in the number of patches using cell neighbourhood (CN) values of 4 and 8 for the 4 artificial maps.

Art. Map 1 | Art. Map 2 | Art. Map 3 | Art. Map 4 | |
---|---|---|---|---|

Aggregation Index [%] | 0 | 99.49 | 99.92 | N/A |

N patches (4 cells) | 5000 | 2 | 1 | 1 |

N patches (8 cells) | 1 | 2 | 1 | 1 |

Difference % N patches | 99.98% | 0 | 0 | 0 |

Original Map | Third Quartile | First Quartile | ||||
---|---|---|---|---|---|---|

4 cells | 8 cells | 4 cells | 8 cells | 4 cells | 8 cells | |

N patches | 43,594 | 21,094 | 24,859 | 15,497 | 9037 | 7768 |

Patch density [patches/100 ha] | 368.26 | 178.19 | 175.61 | 109.47 | 57.31 | 49.26 |

Mean patch size [m${}^{2}$] | 0.27 | 0.56 | 0.57 | 0.91 | 1.74 | 2.03 |

Edge Density [m/ha] | 728.59 | 728.59 | 271.82 | 271.82 | 173.02 | 173.02 |

Landscape shape index | 198.16 | 198.16 | 80.83 | 80.83 | 54.30 | 54.30 |

Aggregation index [%] | 81.86 | 81.86 | 93.28 | 93.28 | 95.75 | 95.75 |

**Table 9.**Differences for number of patches, patch density (PD) (number of patches/100 ha) and mean patch size (MPS) (ha) for the two values of CN (4 or 8 cells) for the map representing the forest coverage in Val di Fassa in 2006 and the two maps obtained by applying a low pass filter with a 3 × 3 pixels window, assigning the first and the third quartile.

Original Map | Third Quartile | First Quartile | |
---|---|---|---|

Aggregation index [%] | 81.86 | 93.28 | 95.75 |

N patches (4 cells) | 43,594 | 24,859 | 9037 |

N patches (8 cells) | 21,094 | 15,497 | 7768 |

Difference % N patches | 51.6% | 37.6% | 14.0% |

Patch density (4 cells) [patches/100 ha] | 368.26 | 175.61 | 57.31 |

Patch density (8 cells) [patches/100 ha] | 178.19 | 109.47 | 49.26 |

Difference % PD | 51.6% | 37.6% | 14.0% |

Mean patch size (4 cells) [m${}^{2}$] | 0.27 | 0.57 | 1.74 |

Mean patch size (8 cells) [m${}^{2}$] | 0.56 | 0.91 | 2.03 |

Difference % MPS | −107.4% | −59.6% | −16.7% |

**Table 10.**Differences of number of patches for the two values of CN (4 or 8 cells) for the three forest maps of Val di Fassa in 1954, 1974, and 1994.

1954 Map | 1974 Map | 1994 Map | |
---|---|---|---|

Aggregation index [%] | 85.90 | 76.66 | 88.31 |

N patches (4 cells) | 33,361 | 135,505 | 90,090 |

N patches (8 cells) | 16,624 | 54,350 | 47,416 |

Difference % N patches | 50.17% | 59.89% | 47.37% |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zatelli, P.; Gobbi, S.; Tattoni, C.; Cantiani, M.G.; La Porta, N.; Rocchini, D.; Zorzi, N.; Ciolli, M.
Relevance of the Cell Neighborhood Size in Landscape Metrics Evaluation and Free or Open Source Software Implementations. *ISPRS Int. J. Geo-Inf.* **2019**, *8*, 586.
https://doi.org/10.3390/ijgi8120586

**AMA Style**

Zatelli P, Gobbi S, Tattoni C, Cantiani MG, La Porta N, Rocchini D, Zorzi N, Ciolli M.
Relevance of the Cell Neighborhood Size in Landscape Metrics Evaluation and Free or Open Source Software Implementations. *ISPRS International Journal of Geo-Information*. 2019; 8(12):586.
https://doi.org/10.3390/ijgi8120586

**Chicago/Turabian Style**

Zatelli, Paolo, Stefano Gobbi, Clara Tattoni, Maria Giulia Cantiani, Nicola La Porta, Duccio Rocchini, Nicola Zorzi, and Marco Ciolli.
2019. "Relevance of the Cell Neighborhood Size in Landscape Metrics Evaluation and Free or Open Source Software Implementations" *ISPRS International Journal of Geo-Information* 8, no. 12: 586.
https://doi.org/10.3390/ijgi8120586