# Simulation Modeling Unveils the Unalike Effects of Alternative Strategies for Waterbird Conservation in the Coastal Wetlands of Sardinia (Italy)

^{*}

## Abstract

**:**

## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Field Surveys

#### 2.2. Model Setup and Validation

_{1}, X

_{2},…, X

_{n}), and the conditional correlations are calculated using the normal copula [17]. By using Sklar’s theorem [18], any joint cumulative distribution function (here denoted F

_{1}…F

_{n}) of variables X

_{1}…X

_{n}can be rewritten as a function of the corresponding copula C:

_{1...n}(X

_{1}...X

_{n}) = C(F

_{1}(X

_{1})...F

_{n}(X

_{n}))

_{i}(X

_{i}) is the marginal distribution of the i-th variable. The normal copula is expressed as:

_{ρ}(u

_{1}...u

_{n}) = Φ

_{R}(Φ

^{−1}(u

_{1})...Φ

^{−1}(u

_{n}))

^{−}

^{1}denotes its inverse, and Φ

_{ρ}is the bivariate Gaussian cumulative distribution with conditional correlation ρ between the two marginal uniform variables u and v.

_{ER}(determinant of the empirical rank correlation matrix; i.e., the dependence structure of the original data) and the D

_{NR}(determinant of the empirical normal rank correlation matrix), calculated as

^{4}simulations) the sampling distribution of D

_{NR}and checking whether D

_{ER}was within the 90% confidence band of D

_{NR}; if so, the normal copula assumption could not be rejected at the 10% significance level [16]. The empirical rank correlation matrix was calculated by using Spearman’s rho correlation coefficient

_{i}is the rank of the i-th wetland in the first variable minus the rank of the i-th wetland in the second variable.

#### 2.3. Baseline, Counterfactual, Management, and Mixed Scenarios

## 3. Results

_{ER}fell within the 90% confidence band of D

_{NR}(Figure 4).

## 4. Discussion

#### 4.1. Model Properties and Assumptions

#### 4.2. Implications for Waterbird Conservation

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Study area (Sardinia, Italy). The total surface area of the 22 wetlands under study is 5545 ha, and the average inter-distance is 12.6 km. With the exception of Tartanelle and Tortoli, all wetlands belong to the Natura 2000 network.

**Figure 2.**The conceptual model (expert knowledge) of the level of avian diversity (green ellipse) in the Sardinian wetlands as a function of spatial (yellow ellipses), anthropic (red ellipses), and hydrological (blue ellipses) variables. Arrows denote the hypothesized direct influences of the source variables upon the destination variables. Blue and red arrows indicate positive and negative effects, respectively.

**Figure 3.**The estimated non-parametric Bayesian network used to predict the effects of counterfactual, management, and mixed scenarios on the level of avian diversity in the Sardinian wetlands.

**Figure 4.**Model validation. The determinant of the empirical rank correlation matrix (D

_{ER}) fell between the 0.75 and 0.80 quantiles (red bin) of the confidence band of the empirical normal rank correlation matrix (D

_{NR}).

**Figure 5.**Baseline (

**a**) and worst-case (

**b**–

**h**) scenarios. The letters associated with the scenarios have the same meaning as per Table 2. On the x-axis, the expected distribution of the avian diversity (expressed as number of bird species in 10 equal-size intervals) is reported. On the y-axis, the proportion (in %) of wetlands that are expected to fall into each range of avian diversity is shown. For each scenario, the Greek letters indicate the mean (µ, i.e., alpha diversity) and standard deviation (σ) of the expected number of bird species per wetland.

**Figure 6.**Baseline (

**a**) and best-case (

**i**–

**o**) scenarios. The letters associated with the scenarios have the same meaning as per Table 2. On the x-axis, the expected distribution of the avian diversity (expressed as number of bird species in 10 equal-size intervals) is reported. On the y-axis, the proportion (in %) of wetlands that are expected to fall into each range of avian diversity is shown. For each scenario, the Greek letters indicate the mean (µ, i.e., alpha diversity) and standard deviation (σ) of the expected number of bird species per wetland.

**Figure 7.**Baseline (

**a**) and mixed (

**p**–

**r**) scenarios. The letters associated with the scenarios have the same meaning as per Table 2. On the x-axis, the expected distribution of the avian diversity (expressed as number of bird species in 10 equal-size intervals) is reported. On the y-axis, the proportion (in %) of wetlands that are expected to fall into each range of avian diversity is shown. For each scenario, the Greek letters indicate the mean (µ, i.e., alpha diversity) and standard deviation (σ) of the expected number of bird species per wetland.

Variable | Unit of Measure | Range | Description |
---|---|---|---|

Wetland size | hectares | 13.3–2048 | |

Isolation | meters | 296–54,472 | |

Distance to the coastline | meters | 0–2050 | |

Mean water level | dimensionless | 1–11 | 1 = from 0 to 10 cm; 2 = from 10 to 20 cm; 3 = from 20 to 30 cm, etc. |

Water salinity | dimensionless | 0–3 | 0 = absent; 1 = localized; 2 = scattered; 3 = widespread |

Water diversions | dimensionless | 0–3 | 0 = absent; 1 = localized; 2 = scattered; 3 = widespread |

Water discharges | dimensionless | 0–2 | 0 = absent; 1 = localized; 2 = scattered |

Tourism pressure | dimensionless | 0–3 | 0 = absent; 1 = localized; 2 = scattered; 3 = widespread |

Anthropization | dimensionless | 0–2 | 0 = absent; 1 = localized; 2 = scattered |

Number of species | dimensionless | 2–32 |

**Table 2.**Description of the 18 scenarios simulated to predict their effects on the level of avian diversity in the 22 Sardinian wetlands under study.

Scenario Type | Code | Conditionalization | Outcome |
---|---|---|---|

Baseline scenario | (a) | none | the baseline level of avian diversity |

Worst-case scenario | (b) | tourism pressure = 3 | the expected level of avian diversity if tourism pressure becomes widespread in all wetlands |

Worst-case scenario | (c) | water salinity = 3 | the expected level of avian diversity if water salinity becomes widespread in all wetlands |

Worst-case scenario | (d) | water discharges = 2 | the expected level of avian diversity if water discharges become scattered in all wetlands |

Worst-case scenario | (e) | anthropization = 2 | the expected level of avian diversity if anthropization becomes scattered in all wetlands |

Worst-case scenario | (f) | water level = 11 | the expected level of avian diversity if water level exceeds 100 cm in all wetlands |

Worst-case scenario | (g) | water diversions = 0 | the expected level of avian diversity if water diversions become null in all wetlands |

Worst-case scenario | (h) | scenarios b–g together | the expected level of avian diversity if scenarios from b to g occur all together |

Best-case scenario | (i) | tourism pressure = 0 | the expected level of avian diversity if tourism pressure becomes null in all wetlands |

Best-case scenario | (j) | water salinity = 0 | the expected level of avian diversity if water salinity becomes null in all wetlands |

Best-case scenario | (k) | water discharges = 0 | the expected level of avian diversity if water discharges become null in all wetlands |

Best-case scenario | (l) | anthropization = 0 | the expected level of avian diversity if anthropization becomes null in all wetlands |

Best-case scenario | (m) | water level = 3 | the expected level of avian diversity if water level is between 20 and 30 cm in all wetlands |

Best-case scenario | (n) | water diversions = 3 | the expected level of avian diversity if water diversions become widespread in all wetlands |

Best-case scenario | (o) | scenarios i–n together | the expected level of avian diversity if scenarios from i to n occur all together |

Mixed scenario | (p) | same as scenario h but tourism pressure = 0 | the expected level of avian diversity if all conditions deteriorate except for tourism pressure that becomes null |

Mixed scenario | (q) | same as scenario h but water salinity = 0 | the expected level of avian diversity if all conditions deteriorate except for water salinity that becomes null |

Mixed scenario | (r) | same as scenario h but water discharges = 0 | the expected level of avian diversity if all conditions deteriorate except for water discharges that become null |

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**MDPI and ACS Style**

Ferrarini, A.; Gustin, M.; Celada, C.
Simulation Modeling Unveils the Unalike Effects of Alternative Strategies for Waterbird Conservation in the Coastal Wetlands of Sardinia (Italy). *Biology* **2023**, *12*, 1440.
https://doi.org/10.3390/biology12111440

**AMA Style**

Ferrarini A, Gustin M, Celada C.
Simulation Modeling Unveils the Unalike Effects of Alternative Strategies for Waterbird Conservation in the Coastal Wetlands of Sardinia (Italy). *Biology*. 2023; 12(11):1440.
https://doi.org/10.3390/biology12111440

**Chicago/Turabian Style**

Ferrarini, Alessandro, Marco Gustin, and Claudio Celada.
2023. "Simulation Modeling Unveils the Unalike Effects of Alternative Strategies for Waterbird Conservation in the Coastal Wetlands of Sardinia (Italy)" *Biology* 12, no. 11: 1440.
https://doi.org/10.3390/biology12111440