# Assessing the Extinction Risk of Heterocypris incongruens (Crustacea: Ostracoda) in Climate Change with Sensitivity and Uncertainty Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{2}. This basin is mainly made up of alluvial, deltaic and marine deposits, where the most common lithological types are sedimentary and composed of sand, clay deposits and clay sands and different coarse debris [51].

#### 2.1. Potential Hydroperiod and Hydroperiod Unpredictability

#### 2.2. Clonal Lineages

#### 2.3. Cohen’s Model, Egg Bank Dynamics and Extinction Rate

_{t}) were simulated assuming the exponential growth over 30 time steps (years):

_{t}is the number of resting eggs in the egg bank at time t, Eb

_{0}is the number of resting eggs at time 0 and ln(λ) is the annual egg bank growth rate computed by Cohen’s equation (Equation (2)). It was assumed that there are no effects of competition and predation on the egg bank dynamics. An interval of 30 years of simulation in a specific climate regime between 2020 and 2050 was considered. Climate regime describes the average conditions and the variability of temperature and precipitation in a given region over a period of 30 years. At the last time step, 30 years, the condition of the population egg bank was recorded by binary output. The binary output of the egg bank simulation was expressed as:

#### 2.4. Factor Fixing: Morris’ Method

_{0}), was the least important in determining the extinction or the viability of the egg bank [47]. The least important factor with the lowest interaction level could be fixed at any constant value without loss of information in the model output. Preliminarily, we performed the Morris method, an OAT procedure (one step at a time) [47]. Each factor was sampled 1 time in its own range and the other was kept constant to compute the model output. The ranges of hatching rate (H), probability that the water balance is positive (P) and deterioration rate (D) were set between 0 and 1. The mean number of resting eggs produced per female (Y) was sampled between a minimum value of 0 and a maximum value of 187 [43]. The range of the number of resting eggs at time 0 (Eb

_{0}) was set between 10 and 1000. This procedure was repeated r times (where r = 100), which leads to r(k + 1) = 600 runs, where k = 5 was the number of input factors (H, P, Y, D, and Eb

_{0}). From the application of the Morris method it was estimated: the mean absolute value for elementary effect (µj*) for j-factor, a measure of the importance on dispersion in the model output, and the standard deviation of the elementary effects (σj), a measure of the degree of the interaction effects for the j-factor with other factors. Low values of µj* indicated that one factor was not important in the variation of the model output. High values of σj revealed how strong the interaction with other factors might be. The analysis was performed with R package sensitivity [57]. This analysis revealed that the most important factors with high interaction levels were the probability that the water balance is positive (P), deterioration rate (D) and hatching rate (H) (Figure S1 in Supplementary Materials). The number of resting eggs at time 0 (Eb

_{o}) was the least important factor, with the lowest interaction level. For this reason, in the following analysis, it was set as a fixed factor with a value equal to 10.

#### 2.5. Uncertainty Analysis, Regionalized Sensitivity Analysis (RSA) and Global Sensitivity Analysis (GSA)

## 3. Results

## 4. Discussion

_{0}) was not important for persistence in time but may be in the early stages of the colonization to cope with the random fluctuations of the population and the environment. We assume that this effect loses importance over time, to a negligible effect at the end of the simulation.

## 5. Conclusions

## Supplementary Materials

_{0}is the number of resting eggs at time 0, H is the hatching rate, Y is the mean number of resting eggs produced per female, P is the probability that the water balance is positive and D is the deterioration rate. The x-axis represents the mean absolute value for elementary effect (µ), a measure of the importance on dispersion in model output, and the y-axis represents the standard deviation of the elementary effects (σ), a measure of the degree of the interaction effects between factors. Table S2. For each factor of Cohen equation (Equation (1)) and clonal lineages, distribution and relative parameters were reported for two different climatic conditions: present and climate change. Factors H, D were assumed to be random factors that vary between 0 and 1 in each climatic condition. P and Y distributions were estimated by data [33,43]. R script S1. LHS sampling method and extinction rate estimation. We sample 1000 combinations of factors and we run the simulation for 30 time steps. Table S3. Correlation coefficients and p values estimated from the correlation analysis. The factor’s values were relative to the model output extinction of the egg bank. Figure S2. Hierarchical doughnut chart reported from the center to the border: the two climatic conditions: present and climate change; the factors: hatching rate (H), probability that the water balance is positive (P), the mean number of resting eggs produced per female (Y), and the deterioration rate (D); the clonal lineages: W1, W2, S2, L, I2, S1, and I1; the Sobol first index; and the Sobol total index. Sobol’s indices that differ in importance among clones were reported in the manuscript and they were represented underlined and in bold.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Panel (

**A**) shows the histograms of the annual probability that the water balance is positive (P) under 2 different climatic conditions: present (white) and climate change (grey). The photoperiod of the Po plain was reported as lines and circles. Panel (

**B**) shows the measures of environmental uncertainty: left y-axis is referred to the histograms of the entropy in present condition (white) and climate change (grey). The right y-axis is relative to coefficient of variation (CV) in 2 climatic conditions: present (continuous line and circle) and climate change (dashed line and triangle).

**Figure 2.**Extinction rates obtained by uncertainty analysis for each clone in present (dark grey) and climate change (light grey) conditions.

**Figure 3.**Heatmaps from the Kolmogorov–Smirnov tests for each factor relative to each clone in two conditions: present (

**panel A**) and climate change (

**panel B**). The p-values (α) from the regionalized sensitivity analysis are reported and the ranking criteria labelled with different colors (critical: dark grey; important: light grey; and insignificant: white).

**Figure 4.**Pairwise correlation coefficients (ρ) computed between factors (the hatching rate (H), probability that the water balance is positive (P), mean number of resting eggs produced per female (Y) and deterioration rate (D) for each clone (W1, W2, S2, L, S1, I2, I1) in present and climate change conditions (Table S3).

**Figure 5.**Sobol’s indices: first index (dark grey) and total index (light grey) for each factor (the hatching rate (H), probability that the water balance is positive (P), mean number of resting eggs produced per female (Y) and deterioration rate (D) and each clone (W1, W2, S2, L, I2, S1, I1) in 2 climatic conditions: present (

**panel A**) and climate change (

**panel B**). The error bar represent the standard error estimated from the bootstrap procedure (n = 1000).

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**MDPI and ACS Style**

Bellin, N.; Spezzano, R.; Rossi, V. Assessing the Extinction Risk of *Heterocypris incongruens* (Crustacea: Ostracoda) in Climate Change with Sensitivity and Uncertainty Analysis. *Water* **2021**, *13*, 1828.
https://doi.org/10.3390/w13131828

**AMA Style**

Bellin N, Spezzano R, Rossi V. Assessing the Extinction Risk of *Heterocypris incongruens* (Crustacea: Ostracoda) in Climate Change with Sensitivity and Uncertainty Analysis. *Water*. 2021; 13(13):1828.
https://doi.org/10.3390/w13131828

**Chicago/Turabian Style**

Bellin, Nicolò, Rachele Spezzano, and Valeria Rossi. 2021. "Assessing the Extinction Risk of *Heterocypris incongruens* (Crustacea: Ostracoda) in Climate Change with Sensitivity and Uncertainty Analysis" *Water* 13, no. 13: 1828.
https://doi.org/10.3390/w13131828