# Measuring Alpha and Beta Diversity by Field and Remote-Sensing Data: A Challenge for Coastal Dunes Biodiversity Monitoring

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data Collection and Analysis

#### 2.2.1. Data Collection

#### Field Data Collection

#### Remote-Sensing Data

#### 2.2.2. Alpha Diversity Analysis

#### 2.2.3. Beta Diversity Analysis

#### 2.2.4. Spectral Variability Hypothesis Test

^{2}(Figure 2, box d) [9,19,75]. Since alpha diversity indices are not normally distributed, we fit linear regressions where coefficients significance was evaluated by randomly permuting observations in the data. This approach has the substantial advantage of relaxing the normality assumption of linear regression [83], thus resulting particularly appropriate in our analytical context. Permutational marginal regressions were calculated using the R package “permuco” (function lmperm), allowing 5000 random permutations among observations [84].

## 3. Results

#### 3.1. Spectral Variability Hypothesis (SVH) Alpha Diversity

^{2}= 0.383), followed by Inverse Simpson index (R

^{2}= 0.342) and Shannon index (R

^{2}= 0.322, Table 5). The interaction effects suggested that the abovementioned positive relationship is true for all the analyzed vegetation types (Shifting, Transition and Invaded dunes, Figure 3). The regression model for species richness showed a highly significant relationship, with positive coefficients for all three vegetation categories (Table 5). Similarly, the models for inverse Simpson and Shannon indices reported significant relationships for the three analyzed vegetation categories (Table 5). Permutation regressions confirmed significant relationships for all the considered alpha diversity indices (Table S2).

_{N14}= 1–13), Shannon index (H’

_{N14}= 0.000–2.259) and Inverse Simpson index (D

_{N14}= 1.000–7.376, Figure 3). The regression lines for transition fixed dunes (EUNIS-N16) and invaded vegetation (Invaded dunes) showed similar trends and ranges, slightly differentiating only in species numbers (S

_{N16}= 2–15; S

_{I}= 4–18, Figure 3), whereas in both the Shannon index and inverse Simpson index the trends and ranges resulted almost identical (H’

_{N16}= 0.64–2.450, H’

_{I}= 1.077–2.502, D

_{N16}= 1.830–10.960, D

_{I}= 2.117–9.212).

#### 3.2. SVH Beta Diversity

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Workflow describing the procedure followed for investigating the potential of the spectral variability hypothesis for depicting alpha and beta diversity levels on herbaceous coastal dune vegetation.

**Figure 3.**Linear regression models of alpha floristic diversity: species richness (

**a**), Shannon (

**b**) and inverse Simpson (

**c**) vs. spectral heterogeneity: mean distance from spectral principal component analysis (PCA) centroid. Shifting dunes: N14 EUNIS category; Transition dunes: N16 EUNIS category: Invaded dunes: coastal dune vegetation with the presence Carpobrotus sp. covering more than 25 percent.

**Figure 4.**Distance decay models of Jaccard (

**a**) and Bray–Curtis (

**b**) species similarity versus spectral distance (spectral pairwise Euclidean distance). The linear regression is described by solid line, the quantile regressions considering four different τ (from upper to lower lines: 0.99, 0.95, 0.90, 0.75) are reported by dashed lines. Gray dots represent the sampling plots.

**Table 1.**Description of herbaceous dune communities referred to EUNIS (European Nature Information Systems) categories, along with their corresponding European Union (EU) habitat (ex Annex I 92/43/EEC) and the respective number of sampling plots. Coastal dune vegetation with the presence Carpobrotus sp. covering more than 25% are also reported.

Acronym/Vegetation Categories | Description and Correspondence with EU Habitats (Ex Annex I 92/43/EEC) | Number of Plots |
---|---|---|

Shifting dunes/EUNIS-N14 | Mobile coastal sand ridges including embryonic dunes characterized by Elymus farctus and semi-permanent dune systems dominated by Ammophila arenaria subsp. australis (EU habitat code: 2110, 2120). | 79 |

Transition dunes/EUNIS-N16 | Fixed dune grasslands including chamaephytic communities of the inland dunes dominated by Crucianella maritima and annual species-rich communities colonizing dry interdunal depressions. (EU habitat code: 2210, 2230). | 41 |

Invaded dunes | Herbaceous vegetation with the presence Carpobrotus spp. covering more than 25 percent. | 43 |

**Table 2.**Spectral variables selected for analyzing alpha and beta spectral diversity along with their related bandwidth/equation, index proxy and references.

Acronym | Name | Bandwidth/Equation | Index of | Reference |
---|---|---|---|---|

B | Blue band | 455–515 nm | – | [61] |

G | Green band | 500–590 nm | – | [61] |

R | Red band | 590–670 nm | – | [61] |

NIR | Near Infrared band | 780–860 nm | – | [61] |

MSAVI2 | Modified Soil Adjusted Vegetation Index 2 | $\frac{2\ast \mathrm{NIR}+1-\sqrt{{(2\ast \mathrm{NIR}+1)}^{2}-8\ast (\mathrm{NIR}-\mathrm{RED})}}{2}$ | photosynthetic biomass | [63] |

CI | Colouration index | $\frac{\mathrm{RED}-\mathrm{GREEN}}{\mathrm{RED}+\mathrm{GREEN}}$ | organic content level in soil | [66] |

**Table 3.**Alpha diversity indices used for analyzing field vegetation data along with the formula and references. N = total number of species; n

_{i}= each species; p

_{i}= abundance value of i-species.

Acronym | Name | Formula | References |
---|---|---|---|

S | Species Richness | $\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{N}}}{\mathrm{n}}_{\mathrm{i$ | [73] |

H’ | Shannon index | $-{\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{N}}}{\mathrm{p}}_{\mathrm{i}}\mathrm{x}\mathrm{ln}\left({\mathrm{p}}_{\mathrm{i}}\right)$ | [74] |

D | Inverse Simpson index | $1/{\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{N}}}{\mathrm{p}}_{\mathrm{i}}^{2}$ | [76] |

**Table 4.**Beta diversity indices used for analyzing field floristic data along with the formula and references. In the Jaccard similarity between plots (p, q), a = number of species shared between p and q vegetation plots, b = number of unique species in the p vegetation plot, c = number of unique species in q plot. In the Bray–Curtis similarity between plots (p, q), x

_{pi}= the abundance value of the i-species on plot p and x

_{qi}the abundance value of the i-species on plot q.

Acronym | Name | Formula | References |
---|---|---|---|

J | Jaccard similarity index | $\frac{{a}_{pq}}{{a}_{pq}+{b}_{p}+{c}_{q}}$ | [79] |

BC | Bray-Curtis similarity index | $1-\frac{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{|\mathrm{x}}_{\mathrm{pi}}{-\mathrm{x}}_{\mathrm{qi}}|}{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{(\mathrm{x}}_{\mathrm{pi}}{+\mathrm{x}}_{\mathrm{qi}})}$ | [81] |

**Table 5.**Summary of linear regressions for alpha floristic diversity (species richness, Shannon and inverse Simpson) vs. spectral heterogeneity (distance from spectral centroid index). Shifting dunes: N14 EUNIS category; Transition dunes: N16 EUNIS category: Invaded dunes: coastal dune vegetation with the presence Carpobrotus sp. covering more than 25%. p-value: * <0.05; ** <0.01; *** <0.001.

Species Richness—Distance to Centroid | R^{2} = 0.383 | ||

Linear Model with Interactions | Estimate | Std. Error | p-Value |

Distance to centroid: Shifting dunes | 3.937 × 10^{−3} | 9.512 × 10^{−4} | 5.362 × 10^{−5} *** |

Distance to centroid: Transition dunes | 4.554 × 10^{−3} | 8.794 × 10^{−4} | 6.666 × 10^{−7} *** |

Distance to centroid: Invaded dunes | 4.746 × 10^{−3} | 8.903 × 10^{−4} | 3.311 × 10^{−7} *** |

Shannon Index—Distance to Centroid | R^{2} = 0.322 | ||

Linear Model with Interactions | Estimate | Std. Error | p-Value |

Distance to centroid: Shifting dunes | 4.202 × 10^{−4} | 1.754 × 10^{−4} | 0.018 * |

Distance to centroid: Transition dunes | 5.556 × 10^{−4} | 1.622 × 10^{−4} | 7.697 × 10^{−4} *** |

Distance to centroid: Invaded dunes | 5.702× 10^{−4} | 1.642 × 10^{−4} | 6.624 × 10^{−4} *** |

Inverse Simpson Index—Distance to Centroid | R^{2} = 0.342 | ||

Linear Model with Interactions | Estimate | Std. Error | p-value |

Distance to centroid: Shifting dunes | 1.695 × 10^{−3} | 6.450 × 10^{−4} | 9.426 × 10^{−3} ** |

Distance to centroid: Transition dunes | 2.231 × 10^{−3} | 5.963 × 10^{−4} | 2.547 × 10^{−4} *** |

Distance to centroid: Invaded dunes | 2.239 × 10^{−3} | 6.038 × 10^{−4} | 2.885 × 10^{−4} *** |

**Table 6.**Results of distance decay models calculated by linear and quantile regressions at four different τ values (from upper to lower lines: 0.99, 0.95, 0.9, 0.75). p-value: *** < 0.001.

Jaccard Similarities—Uclidean Distance | |||||

Regression Type | τ | Intercept | Intercept Boundaries (99%) | Decay Rate (10^{−2}) | Decay Rate (10^{−2}) Boundaries (99%) |

Linea regression | – | 0.145 *** | 0.138–0.152 | −1.207 *** | −1.405–−1.009 |

Quantile regressions | 0.75 | 0.211 *** | 0.202–0.220 | −1.665 *** | −1.892–−1.412 |

0.90 | 0.318 *** | 0.306–0.330 | −2.312 *** | −2.655–−2.009 | |

0.95 | 0.377 *** | 0.361–0.393 | −2.426 *** | −2.83–−1.927 | |

0.99 | 0.521 *** | 0.491–0.564 | −2.226 *** | −3.208–−0.849 | |

Bray-Curtis Similarities—Euclidean Distance | |||||

Regression Type | τ | Intercept | Intercept Boundaries (99%) | Decay Rate (10^{−2}) | Decay Rate (10^{−2}) Boundaries (99%) |

Linear regression | – | 0.235 *** | 0.207–0.257 | −1.814 *** | −2.106–−1.522 |

Quantile | 0.75 | 0.353 *** | 0.339–0.367 | −2.529 *** | −2.867–−2.200 |

0.90 | 0.489 *** | 0.473–0.505 | −3.082 *** | −3.529–−2.614 | |

0.95 | 0.552 *** | 0.533–0.573 | −2.938 *** | −3.581–−2.206 | |

0.99 | 0.686 *** | 0.659–0.726 | −2.030 *** | −3.123–−0.699 |

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**MDPI and ACS Style**

Marzialetti, F.; Cascone, S.; Frate, L.; Di Febbraro, M.; Acosta, A.T.R.; Carranza, M.L.
Measuring Alpha and Beta Diversity by Field and Remote-Sensing Data: A Challenge for Coastal Dunes Biodiversity Monitoring. *Remote Sens.* **2021**, *13*, 1928.
https://doi.org/10.3390/rs13101928

**AMA Style**

Marzialetti F, Cascone S, Frate L, Di Febbraro M, Acosta ATR, Carranza ML.
Measuring Alpha and Beta Diversity by Field and Remote-Sensing Data: A Challenge for Coastal Dunes Biodiversity Monitoring. *Remote Sensing*. 2021; 13(10):1928.
https://doi.org/10.3390/rs13101928

**Chicago/Turabian Style**

Marzialetti, Flavio, Silvia Cascone, Ludovico Frate, Mirko Di Febbraro, Alicia Teresa Rosario Acosta, and Maria Laura Carranza.
2021. "Measuring Alpha and Beta Diversity by Field and Remote-Sensing Data: A Challenge for Coastal Dunes Biodiversity Monitoring" *Remote Sensing* 13, no. 10: 1928.
https://doi.org/10.3390/rs13101928