# Uncertainty in Various Habitat Suitability Models and Its Impact on Habitat Suitability Estimates for Fish

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{2}. Consistent with previous studies, Sicyopterus japonicas, an amphidromous gobiid, was the focal species, as it has often been identified as a habitat quality indicator species [5,31,32,33]. Lin et al. (2011) [5,32] have described the study area and the method for collecting data in more detail. Figure 1 presents the study area and sampling locations as well as the number of Sicyopterus japonicas observed.

**Figure 1.**(

**a**) Study site; (

**b**) sample locations and number of Sicyopterus japonicas observed; and (

**c**) Sicyopterus japonicas observations and corresponding stream velocity and depth.

#### 2.1. Hydraulic Model and Model Units

^{2}. River 2D is a free-source two-dimensional depth-averaged finite element hydrodynamic model that is used in fish habitat evaluation studies [2]. During the flow condition simulation, geo-referenced topographic measurements and boundary conditions, including flow rate as well as upstream and downstream water levels, were used as input data. The terrain model was based on a triangular network of elements (cells). The sizes of the substrates in the study area were homogeneous and were neglected in estimating HSI.

#### 2.2. Ensemble Modeling of Species Distribution and Model Evaluations

#### 2.3. Weighted Usable Area

^{th}cell; $WU{A}_{i}=$ weighted useable habitat area in i

^{th}cell; and ${A}_{i}=$ water surface area in i

^{th}cell. The WUA values were calculated as a basis of discussing the total potential useable habitat areas and their various discharges. A nonparametric Kruskal–Wallis test and a multiple comparison test were performed to determine whether the median WUA derived from the outputs of the six SDMs differed significantly.

#### 2.4. Spatial Heterogeneity of Flow Conditions and Habitat Suitability

_{cat}is the number of parameter categories considered, and p

_{i}is the proportional frequency of the considered parameter in category i. In this case, the entropies of V, D, V + D and HSI were evaluated for each SDM. V ranged from 0.05 to 1.25 m/s and was classed into 12 categories, each with a range of 0.1 m/s. Similarly, D was grouped into ten categories from 0.05 to 1.05 m, defined in 0.1 m increments. HSI was grouped into ten categories from 0 to 1, defined in 0.1 increments. The range of values of information entropy is from zero to one. An entropy value of close to 1 indicates that the considered parameter is distributed uniformly across all categories, indicating high spatial heterogeneity. A value of zero indicates that the considered parameter is concentrated in a single category, indicating a low spatial heterogeneity.

#### 2.5. Quantifying Variability in Habitat Suitability Index for Each Model

## 3. Results

#### 3.1. River 2D Simulations of Flow Conditions

^{3}/s, which was the average of a nearby flow meter. This model was calibrated and validated with the field measurements of flow conditions and its simulation performance are shown in terms of Coefficient of Determination (R

^{2}) and Nash–Sutcliffe efficiency coefficient (Eff) [5]. For current velocity, the calibration projection showed an R

^{2}= 0.93 and an Eff = 0.92; the validation dataset showed an R

^{2}= 0.85 and an Eff = 0.84. For water depth, the calibration projection had an R

^{2}= 0.98, and an Eff = 0.98, and the validation projection had an R

^{2}= 0.95, and an Eff = 0.96.

**Figure 2.**Maps of (

**a**) current velocity (m/s) and (

**b**) depth (m) over the study area. Note: flow direction: South to North.

#### 3.2. HSI Obtained from SDMs and Ensemble Models

**Table 1.**Mean ± standard error of validation root mean square error, Akaike information criterion (AIC) and Kullback–Leibler divergence (KL) in 1000 realizations as well as the partial explanations power. * from velocity and depth in the training model.

Model Performance | GLM | GAM | RF | SVM | ANN | Ensemble |
---|---|---|---|---|---|---|

RMSE | 1.551 ± 0.212 | 1.518 ± 0.218 | 1.562± 0.221 | 1.531 ± 0.221 | 1.517 ± 0.208 | 1.505 ± 0.206 |

AIC | 72.445 ± 3.814 | 74.313 ± 3.846 | – | 63.661 ± 7.407 | 34.805 ± 5.555 | – |

KL | 0.250 ± 0.088 | 0.240 ± 0.086 | 0.247 ± 0.084 | 0.249 ± 0.093 | 0.234 ± 0.081 | 0.232 ± 0.081 |

V+ D* | 30.90% | 39.00% | 74.10% | 33.80% | 32.60% | 37.20% |

V* | 22.60% | 23.20% | 62.90% | 21.70% | 19.30% | 22.50% |

D* | 8.30% | 15.80% | 11.60% | 12.10% | 13.70% | 14.60% |

**Figure 3.**Maps of average Habitat suitability index (HSI) derived from (

**a**) GLM; (

**b**) GAM; (

**c**) RF; (

**d**) SVM and (

**e**) ANN; as well as (

**f**) the ensemble model, and maps of standard deviation of HSI derived from (

**g**) GLM; (

**h**) GAM; (

**i**) RF; (

**j**) SVM and (

**k**) ANN; as well as (

**l**) the ensemble model.

**Figure 4.**Habitat suitability surfaces obtained using six species distribution models, (

**a**) GLM; (

**b**) GAM; (

**c**) RF; (

**d**) SVM; (

**e**) ANN; and (

**f**) ensemble model as well as their corresponding standard deviations: (

**g**) GLM; (

**h**) GAM; (

**i**) RF; (

**j**) SVM; (

**k**) ANN; and (

**l**) ensemble model. Note: X-axis represents velocity (m/s), ranging from 0 to 1, and Y-axis represents depth (m) ranging from 0 to 1.2.

**Figure 5.**Scatter plots between observed and simulated fish abundance: (

**a**) GLM; (

**b**) GAM; (

**c**) RF; (d) SVM; (

**e**) ANN and (

**f**) the ensemble model. Note: X-axis represents observed count ranging from 0 to 5, and Y-axis represents simulated count ranging from 0 to 5.

#### 3.3. Spatial Heterogeneity of Flow Conditions and of HSI

**Figure 6.**Density distribution of information entropy of HSI (1000 runs) obtained using (

**a**) GLM; (

**b**) GAM; (

**c**) RF; (

**d**) SVM; (

**e**) ANN; and (

**f**) the ensemble models. Note: X-axis represents entropy, and Y-axis represents density.

**Table 2.**Descriptive statistics for information entropy of habitat suitability in six models in 1000 realizations.

Model | Mean | Standard Deviation | Median | Min | Max | Range | Skew | Kurtosis |
---|---|---|---|---|---|---|---|---|

GLM | 0.74 | 0.09 | 0.76 | 0.18 | 0.89 | 0.71 | –1.67 | 3.68 |

GAM | 0.60 | 0.23 | 0.69 | 0.03 | 0.89 | 0.85 | –1.05 | –0.06 |

RF | 0.63 | 0.05 | 0.63 | 0.45 | 0.80 | 0.35 | –0.08 | 0.03 |

SVM | 0.67 | 0.06 | 0.67 | 0.46 | 0.84 | 0.38 | –0.22 | –0.36 |

ANN | 0.59 | 0.12 | 0.60 | 0.29 | 0.86 | 0.57 | –0.21 | –0.46 |

Ensemble | 0.64 | 0.10 | 0.66 | 0.04 | 0.83 | 0.79 | –1.03 | 1.93 |

#### 3.4. Variability in Maps of HSI and WUA

^{2}(17.28), 68.06 m

^{2}(32.44), 101.05 m

^{2}(13.57), 106.32 m

^{2}(15.70), 106.61 m

^{2}(16.03) and 99.68 m

^{2}(20.40), respectively. The result of Kruskal–Wallis test showed significant differences between WUA obtained using six SDMs (p-value < 0.001). In addition, the multiple comparison test indicated that all of the WUA derived from six models are significantly different from one another, except for those derived from RF and ensemble model, and between SVM and ANN.

Model | GLM | GAM | RF | SVM | ANN | Ensemble |
---|---|---|---|---|---|---|

GLM | – | 0.85 | 0.88 | 0.70 | 0.91 | 0.93 |

GAM | – | – | 0.87 | 0.83 | 0.87 | 0.96 |

RF | – | – | – | 0.84 | 0.91 | 0.96 |

SVM | – | – | – | – | 0.77 | 0.87 |

ANN | – | – | – | – | – | 0.96 |

Ensemble | – | – | – | – | – | – |

## 4. Discussion

#### 4.1. Usefulness of River 2D in Simulating Flow Conditions

#### 4.2. SDM-Determined Suitability of Habitat with Respect to Spatial Heterogeneity

**Figure 8.**Maps of current velocity (

**a**–

**c**) and water depth (

**d**–

**f**) when the quantity of flow is 0.5, 0.26 and 0.12 m

^{3}/s.

#### 4.3. Variability in HSI That Originates from Various Sources of Uncertainty

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Lin, Y.-P.; Lin, W.-C.; Wu, W.-Y.
Uncertainty in Various Habitat Suitability Models and Its Impact on Habitat Suitability Estimates for Fish. *Water* **2015**, *7*, 4088-4107.
https://doi.org/10.3390/w7084088

**AMA Style**

Lin Y-P, Lin W-C, Wu W-Y.
Uncertainty in Various Habitat Suitability Models and Its Impact on Habitat Suitability Estimates for Fish. *Water*. 2015; 7(8):4088-4107.
https://doi.org/10.3390/w7084088

**Chicago/Turabian Style**

Lin, Yu-Pin, Wei-Chih Lin, and Wei-Yao Wu.
2015. "Uncertainty in Various Habitat Suitability Models and Its Impact on Habitat Suitability Estimates for Fish" *Water* 7, no. 8: 4088-4107.
https://doi.org/10.3390/w7084088