# How Important Are Resistance, Dispersal Ability, Population Density and Mortality in Temporally Dynamic Simulations of Population Connectivity? A Case Study of Tigers in Southeast Asia

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, including parts of Thailand, Cambodia, and a small section of southern Lao PDR. The area contains a heterogeneous mix of topography, forest, and anthropogenic land cover. Forest cover configuration in this area varies considerably, from small, relatively isolated patches to large contiguous forest blocks. Much of this forest cover occurs within protected areas, with most land use outside protected areas dominated by agriculture, villages and urban areas.

#### 2.2. Landscape Connectivity Simulations

#### 2.2.1. Resistance Surfaces

#### 2.2.2. Population Source Points

#### 2.2.3. Dispersal Ability

#### 2.2.4. Population Density and Growth

^{2}or 1/100 km

^{2}), reflecting potential differences in simulated territory spacing and carrying capacity of tigers in the study area. These resampled kernel layers were rescaled between 0 and 1, which was then subtracted by a uniform random raster (0–1). This difference raster produced a probabilistic layer for the generation of new source points at both densities for the next timestep, proportional to predicted dispersal density.

#### 2.2.5. Mortality

#### 2.3. Evaluation of Simulated Scenarios

## 3. Results

#### 3.1. Population Trajectory and Colonization

#### 3.2. Analysis of Variance

#### 3.3. Multivariate Interactions

#### 3.4. Multivariate Trajectory Analysis

^{2}), with substantially lesser effects for different resistance surfaces. Figure 5 shows one view of this three-dimensional space at timestep 6 and readers are encouraged to view the full 3D dynamic visualizations in Supplementary Materials 3.

#### 3.5. Analysis of Effect Size and Interactions among Factors Using Mantel Tests

## 4. Discussion

#### 4.1. Implications for Tiger Management and Conservation

#### 4.2. Limitations

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Study area for connectivity analysis. Protected areas were generated from UNEP-WCMC and IUCN [35]; a full listing of names can be found in Supplementary Materials 1. Forest cover was generated from 2018 SERVIR–Mekong Regional Land Cover Monitoring System (RLCMS; [36]) reclassed into dense forest (including Forest, Evergreen Forest, Flooded Forest, and Mixed Forest), and Shrubland/Grassland/Other Forest (including Shrubland, Grassland, Wetlands and Orchard/Plantation). Major roads were derived from OpenStreetMap [37]. The eastern section (TCL-24) of the Dong Phayayen-Khao Yai forest complex (2–5) acts as the source site for our simulations.

**Figure 2.**Diagram depicting methods workflow, including development of highway crossing resistance scenarios (SCEN), resistance transformation (RES), adjusting dispersal ability (KERN), adjusting population density (DENS), and developing and applying mortality functions (MORT). Ash et al. [41]; Reddy et al. [34].

**Figure 3.**Sample maps demonstrating divergence in cumulative resistance kernels and populations between combinations of mortality function (MORT—R1, R2, E1, E2, and M0) and dispersal ability (KERN—125 kcu, 250 kcu, and 375 kcu) at timestep 6, holding highway mitigation scenario (SCEN—S3), territory spacing (DENS—7.5 km), and resistance transformation (RES—r10) constant. Values reflect the expected cumulative density of dispersing individuals from each source point. Additional maps and timestep animations can be found in Supplementary Materials 3, Tables S1–S6.

**Figure 4.**Surface plots showing variation in predicted (

**a**) population size (N), (

**b**) kernel extent, and (

**c**) sum of kernel value for the 15 combinations of dispersal ability (KERN—3 levels) and mortality risk (MORT—5 levels) for resistance transformation 1.0 (RES—r10) and maximum density 1/7.5 km

^{2}(DENS—7.5 km) at timestep 9. The figure shows a strong interaction between dispersal ability and mortality risk, with the predicted values of all three variables remaining low for all scenarios involving elevated mortality risk, across all dispersal abilities, while all three variables increase linearly with dispersal ability when there is no differential mortality risk across the landscape. Animations of these and other plots can be viewed in Supplementary Materials 3, Tables S7–S12.

**Figure 5.**Three orthogonal views of the three-dimensional trajectory of scenarios in a space defined by kernel extent, sum kernel value, and population size, at timestep 6 across density (DENS) and resistance transformations (RES). Sphere color indicates different combinations of dispersal ability (KERN) and mortality risk (MORT). The figure shows that scenarios with low mortality risk (M0; red spheres) in which population density is high have much greater predicted kernel extent, kernel sum, and higher simulated population size (extreme values extending outside axis limits). Animations of these and other plots can be viewed in Supplementary Materials 3, Tables S13–S18.

**Figure 6.**Mantel correlations between response variables (

**a**) Kernel Extent, (

**b**) Population Size, (

**c**) Kernel Sum, and (

**d**) multivariate distance between these response variables and divergence among scenarios over timesteps. Timestep is depicted on the x-axis with Mantel correlation on the y-axis. The highest correlating factors are labeled: MORT—mortality model matrix with all mortality scenarios coded 1 and non-mortality 0; MORT2—mortality model matrix with scenarios coded ordinally from highest to lowest degree of mortality risk; KERN—dispersal distance varying with kernel bandwidth; KERN-MORT2—model matrix combining KERN and MORT2 by addition; KERN-RES—model matrix combining KERN and resistance model matrices by addition; KERN-SCEN—model matrix combining KERN and highway mitigation model matrices by addition; and KERN-MORT2-RES—model matrix combining KERN, MORT2 and RES model matrices by addition.

**Figure 7.**Mantel correlations between response variables (

**a**) Kernel Extent, (

**b**) Population Size, (

**c**) Kernel Sum, and (

**d**) multivariate distance between these response variables and displacement of scenarios from initial value over timesteps. Timestep is depicted on the x-axis with Mantel correlation on the y-axis. The highest correlating factors are labeled: MORT—mortality model matrix with all mortality scenarios coded 1 and non-mortality 0; MORT2—mortality model matrix with scenarios coded ordinally from highest to lowest degree of mortality risk; KERN—dispersal distance varying with kernel bandwidth; KERN-MORT2—model matrix combining KERN and MORT2 by addition; KERN-RES—model matrix combining KERN and resistance model matrices by addition; MORT2-SCEN—model matrix combining MORT2 and highway mitigation model matrices by addition and KERN-MORT2-RES—model matrix combining KERN, MORT2 and RES model matrices by addition.

**Figure 8.**Plot of Mantel correlation of the best model for (

**a**) divergence and (

**b**) displacement over timesteps for each of the response variables: es—kernel extent, ns—population size, ks—kernel sum, and nsesks—multivariate combination of kernel extent, population size, and kernel sum. In both cases, population size had the strongest correlation with the best scenario model matrix over nearly all timesteps, only equaled by kernel extent in timestep 5.

**Table 1.**Summary of simulation results within factor groups by parameter at timestep 9 out of 2700 simulations. Results are summarized by (

**a**) simulated population (N) at timestep 9 and (

**b**) number of simulations in which source points were generated in Khao Yai National Park (NP), Cambodia, or Laos at timestep 9 (e.g., successful colonization). This reflects a summary of all simulation results specific to each factor group—resistance surface (highway mitigation scenario (SCEN) and resistance transformation, (RES)), dispersal ability (KERN), population density (DENS), and mortality function (MORT)—amalgamating all other factors and parameters. A detailed breakdown of simulation results can be found in Supplementary Materials 2; Tables S1 and S2.

Factor | Parameter | (a) | (b) | |||||
---|---|---|---|---|---|---|---|---|

N > 30 | N = 30 | N = 1 to 30 | N = 0 | Khao Yai NP | Cambodia | Laos | ||

SCEN | S1 | 233 | 7 | 500 | 160 | 455 | 79 | 16 |

S2 | 238 | 11 | 508 | 143 | 498 | 76 | 9 | |

S3 | 235 | 11 | 499 | 155 | 472 | 88 | 13 | |

DENS | 10 km | 268 | 18 | 812 | 252 | 641 | 99 | 18 |

7.5 km | 438 | 11 | 695 | 206 | 784 | 144 | 20 | |

MORT | M0 | 507 | 5 | 28 | - | 474 | 235 | 38 |

E1 | 4 | 3 | 363 | 170 | 169 | 1 | - | |

E2 | 21 | 5 | 393 | 121 | 220 | 1 | - | |

R1 | - | - | 373 | 167 | 124 | - | - | |

R2 | 174 | 16 | 350 | - | 438 | 6 | - | |

RES | r07 | 243 | 17 | 555 | 85 | 438 | 64 | - |

r10 | 240 | 5 | 508 | 147 | 473 | 69 | 1 | |

r15 | 223 | 7 | 444 | 226 | 514 | 110 | 37 | |

KERN | 125 kcu | 264 | 17 | 608 | 11 | 371 | 12 | - |

250 kcu | 256 | 10 | 525 | 109 | 609 | 92 | - | |

375 kcu | 186 | 2 | 374 | 338 | 445 | 139 | 38 | |

All | 706 | 29 | 1507 | 458 | 1425 | 243 | 38 |

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## Share and Cite

**MDPI and ACS Style**

Ash, E.; Cushman, S.A.; Macdonald, D.W.; Redford, T.; Kaszta, Ż.
How Important Are Resistance, Dispersal Ability, Population Density and Mortality in Temporally Dynamic Simulations of Population Connectivity? A Case Study of Tigers in Southeast Asia. *Land* **2020**, *9*, 415.
https://doi.org/10.3390/land9110415

**AMA Style**

Ash E, Cushman SA, Macdonald DW, Redford T, Kaszta Ż.
How Important Are Resistance, Dispersal Ability, Population Density and Mortality in Temporally Dynamic Simulations of Population Connectivity? A Case Study of Tigers in Southeast Asia. *Land*. 2020; 9(11):415.
https://doi.org/10.3390/land9110415

**Chicago/Turabian Style**

Ash, Eric, Samuel A. Cushman, David W. Macdonald, Tim Redford, and Żaneta Kaszta.
2020. "How Important Are Resistance, Dispersal Ability, Population Density and Mortality in Temporally Dynamic Simulations of Population Connectivity? A Case Study of Tigers in Southeast Asia" *Land* 9, no. 11: 415.
https://doi.org/10.3390/land9110415