# Determining Statistically Robust Changes in Ungulate Browsing Pressure as a Basis for Adaptive Wildlife Management

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## Abstract

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## 1. Introduction

- (i)
- How can the variability of browsing impact and its change over time be predicted and tested for statistical significance?
- (ii)
- Can the sample size of the established regeneration inventory be reduced and still serve wildlife managers as a valuable information source?
- (iii)
- What is the minimum observable significant change with respect to browsing impact in the Bavarian Forest National Park in applying its current forest inventory method?

## 2. Methods

#### 2.1. Study Area

#### 2.2. Wildlife Management

#### 2.3. Inventory Method

^{−1}≥ 20 cm. It was ensured that the leading shoots of the observed seedlings are still within reach of the locally occurring herbivores. In the BFNP, the maximal possible browsing height (considering the snow conditions in winter) is set at 200 cm. Measurements only take place on regeneration areas that meet these criteria. There is no grid where, due to the aforementioned requirements, no regeneration information is available.

#### 2.4. Data Set

#### 2.5. Data Analysis

#### 2.5.1. Browsing Probability and Its Change

${\eta}_{ij}$ | = linear predictor for the browsing probability; |

${\beta}_{0}$ | = fixed intercept (the origin in our model); |

${u}_{i}$ | = cluster-specific (random) deviation from the fixed intercept; |

${\beta}_{0}+{u}_{i}$ | = random intercept for cluster (plot) i; |

${\beta}_{1}$ | = fixed slope parameter of covariate ${t}_{j}$ (year); |

${\u03f5}_{ij}$ | = error term; |

$P({y}_{ij}=1)$ | = browsing probability. |

#### 2.5.2. Sensitivity Analysis

#### 2.5.3. Simulation of Ungulate Browsing

#### 2.5.4. Computational Details

## 3. Results

#### 3.1. Browsing Probability Time Series

#### 3.2. Significance of Changes and Sample Sizes

#### 3.3. Simulation of Ungulate Browsing on Rowan

## 4. Discussion

#### 4.1. Evaluating Ungulate Browsing Impact (Question I)

#### 4.2. The Ideal Sample Size and Cost Efficiency (Question II and III)

#### 4.3. Inventory Design and Further Improvements

^{−1}. This sets the selection probability of individuals occurring in areas with low regeneration density to zero. Kuijper et al. [120] and Churski et al. [121] both observed that ungulate browsing is clustered on high density regeneration sites in forest gaps. Consequently, the ungulate impact on the total regeneration of the BFNP might be overestimated with the current regeneration site selection rule. At the same time, the seedling selection is limited to individuals above 20 cm. The browsing pressure and the shift of competitive conditions of selectively browsed species starts from a seedling’s germination [6,122,123,124,125]. Therefore, the BP estimates could be left truncated. Moreover, the variable transect size (which varies between 40–100 m) alters the selection probability of seedlings again. Furthermore, the inventory method excludes the edges of regeneration sites due to its 5 m wide buffer zone (compare [93]). Clustered browsing on the edge of regeneration sites with a high density, such as observed by Čermák et al. [126], cannot be captured. The selection probabilities of rare tree species are further increased by the inventory extension. Hence the selection probability of a seedling, which is already hard to grasp when using a distance sampling technique, is further modified by multiple additional constraints which have only minimal practical advantages. In addition, the inventory extension falsifies statements about the relative species composition by increasing the sample size of rare tree species. Therefore, we could not consider the selection probability for the purposes of the application of our evaluation tool, for estimating BPs or their change applied in the BFNP example.

#### 4.4. Opportunities for Future Research

#### 4.4.1. Which Tree Species Must Undergo a Browsing Change to Trigger an Intervention in the Wildlife Population?

- Act as an “early warning system” that reflects the influence of ungulate browsing of other tree species or, rather, a development of the ungulate densities in time;
- Be preferred by ungulates so that the indicator species sensitively indicates changes (large amplitude) rather than just indicating a change. Ideally, the species should be so sensitive that strong browsing quickly reduces its abundance;
- Be able to be monitored cost-efficiently; due to a high abundance and uniform distribution in the study area, an ideal browsing indicator species achieves a high estimation accuracy in data collection without great effort.

#### 4.4.2. From Which Browsing Probability or Threshold Does the Population of a Tree Species Decrease in the Long Run?

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BP | Browsing probability; |

BFNP | Bavarian Forest National Park; |

RLG | Rachel-Lusen region (in the Bavarian Forest National Park); |

FRG | Falkenstein-Rachel region (in the Bavarian Forest National Park); |

NP | National park; |

Obs. | Observation; |

PP | Percentage point. |

## Appendix A. Detailed Browsing Evaluation of the BFNP

#### Appendix A.1. Browsing Probability Time Series

#### Appendix A.1.1. Norway Spruce

**Figure A1.**Sample size development of the main tree species over time in the NP in (

**A**) total numbers (n) and (

**B**) relative frequency.

**Figure A2.**Sample size development of the main tree species over time in the FRG in (

**A**) total numbers (n) and (

**B**) relative frequency.

**Figure A3.**Sample size development of the main tree species over time in the RLG in (

**A**) total numbers (n) and (

**B**) relative frequency.

**Figure A4.**Time series and confidence intervals of the BP (

**A**) and the corresponding logarithmic change of the BP between two consecutive acquisition years (

**B**). The estimated logarithmic change of BP (black point inside the confidence intervals) is positive if BP increased compared to the previous year, and is negative if it decreased. If either the upper or the lower end of the confidence intervals completely crossed the zero on the x-axis, the change of the BP is not significant. The estimates are related to the data set of the entire NP.

**Figure A5.**Time series and confidence intervals of the BP (

**A**) and the corresponding logarithmic change of the BP between two consecutive acquisition years (

**B**). The estimated logarithmic change of BP (black point inside the confidence intervals) is positive if BP increased compared to the previous year, and is negative if it decreased. If either the upper or the lower end of the confidence intervals completely crossed the zero on the x-axis, the change of the BP is not significant. The estimates are related to the FRG data set.

**Figure A6.**Time series and confidence intervals of the BP (

**A**) and the corresponding logarithmic change of the BP between two consecutive acquisition years (

**B**). The estimated logarithmic change of BP (black point inside the confidence intervals) is positive if BP increased compared to the previous year, and is negative if it decreased. If either the upper or the lower end of the confidence intervals completely crossed the zero on the x-axis, the change of the BP is not significant. The estimates are related to the RLG data set.

**Table A1.**Summary statistics of all logistic mixed effect models for the respective tree species. Next to each categorical time step, logarithmic coefficients and the standard error (in parentheses) can be found.

Norway Spruce | European Beech | Rowan Berry | Silver Fir | Birch | Sycamore Maple | |
---|---|---|---|---|---|---|

2007 | −5.94 *** | −2.54 *** | −0.84 *** | −3.03 *** | −0.61 | $-0.63$ |

$\left(0.14\right)$ | $\left(0.10\right)$ | $\left(0.13\right)$ | $\left(0.21\right)$ | $\left(0.34\right)$ | $\left(0.38\right)$ | |

2008 | −4.73 *** | −2.81 *** | −1.87 *** | −2.74 *** | −1.52 *** | −1.84 *** |

$\left(0.09\right)$ | $\left(0.08\right)$ | $\left(0.11\right)$ | $\left(0.17\right)$ | $\left(0.45\right)$ | $\left(0.31\right)$ | |

2009 | −5.22 *** | −3.31 *** | −2.14 *** | −2.49 *** | −2.03 *** | −2.95 *** |

$\left(0.10\right)$ | $\left(0.09\right)$ | $\left(0.11\right)$ | $\left(0.15\right)$ | $\left(0.40\right)$ | $\left(0.40\right)$ | |

2010 | −4.75 *** | −2.95 *** | −1.71 *** | −2.23 *** | −1.87 *** | −1.54 *** |

$\left(0.09\right)$ | $\left(0.08\right)$ | $\left(0.08\right)$ | $\left(0.13\right)$ | $\left(0.28\right)$ | $\left(0.27\right)$ | |

2011 | −4.71 *** | −2.95 *** | −1.47 *** | −2.27 *** | −1.07 *** | −2.17 *** |

$\left(0.10\right)$ | $\left(0.09\right)$ | $\left(0.10\right)$ | $\left(0.15\right)$ | $\left(0.29\right)$ | $\left(0.39\right)$ | |

2012 | −5.31 *** | −2.88 *** | −1.70 *** | −2.92 *** | −3.57 *** | −2.49 *** |

$\left(0.12\right)$ | $\left(0.09\right)$ | $\left(0.10\right)$ | $\left(0.17\right)$ | $\left(0.45\right)$ | $\left(0.37\right)$ | |

2015 | −4.52 *** | −1.87 *** | −0.62 *** | −2.07 *** | −1.49 *** | −1.55 *** |

$\left(0.10\right)$ | $\left(0.08\right)$ | $\left(0.09\right)$ | $\left(0.14\right)$ | $\left(0.29\right)$ | $\left(0.32\right)$ | |

2018 | −5.08 *** | −2.58 *** | −0.67 *** | −1.68 *** | −0.90 *** | −1.08 ** |

$\left(0.12\right)$ | $\left(0.09\right)$ | $\left(0.09\right)$ | $\left(0.13\right)$ | $\left(0.23\right)$ | $\left(0.36\right)$ | |

AIC | 16,925.02 | 21,784.74 | $8843.43$ | $4960.29$ | $981.75$ | $725.74$ |

BIC | 17,012.29 | 21,862.76 | $8907.84$ | $5023.52$ | $1026.91$ | $768.45$ |

Log Likelihood | −8453.51 | −10,883.37 | −4412.72 | −2471.14 | −481.87 | −353.87 |

Num. obs. | 120,164 | 42,979 | 9474 | 8313 | 1117 | 850 |

Num. groups: PlotID | 412 | 343 | 370 | 254 | 132 | 76 |

Var: PlotID (Intercept) | $1.70$ | $1.05$ | $0.69$ | $1.35$ | $1.11$ | $0.68$ |

**Table A2.**Summary statistics of the multiple comparisons of means between year levels for the respective tree species. Next to each categorical time step, logarithmic coefficients and the standard error (in parentheses) can be found.

Norway Spruce | European Beech | Rowan Berry | Silver Fir | Birch | Sycamore Maple | |
---|---|---|---|---|---|---|

2008–2007 | 1.208 *** | −0.27 * | −1.034 *** | $0.296$ | $-0.907$ | −1.209 * |

$\left(0.13\right)$ | $\left(0.09\right)$ | $\left(0.15\right)$ | $\left(0.24\right)$ | $\left(0.53\right)$ | $\left(0.43\right)$ | |

2009–2008 | −0.49 *** | −0.503 *** | $-0.271$ | $0.244$ | $-0.516$ | $-1.11$ |

$\left(0.08\right)$ | $\left(0.08\right)$ | $\left(0.13\right)$ | $\left(0.18\right)$ | $\left(0.57\right)$ | $\left(0.46\right)$ | |

2010–2009 | 0.474 *** | 0.36 *** | 0.434 ** | $0.265$ | $0.166$ | 1.406 ** |

$\left(0.08\right)$ | $\left(0.08\right)$ | $\left(0.12\right)$ | $\left(0.15\right)$ | $\left(0.45\right)$ | $\left(0.44\right)$ | |

2011–2010 | $0.042$ | $0.0004$ | $-1.71$ | $-0.042$ | $0.796$ | $-0.623$ |

$\left(0.09\right)$ | $\left(0.08\right)$ | $\left(0.11\right)$ | $\left(0.14\right)$ | $\left(0.36\right)$ | $\left(0.42\right)$ | |

2012–2011 | −0.598 *** | $0.078$ | $-1.47$ | −0.647 ** | −2.499 *** | $-0.324$ |

$\left(0.11\right)$ | $\left(0.08\right)$ | $\left(0.11\right)$ | $\left(0.18\right)$ | $\left(0.49\right)$ | $\left(0.48\right)$ | |

2015–2012 | 0.786 *** | 1.001 *** | 1.079 *** | 0.842 *** | 2.077 *** | $0.942$ |

$\left(0.11\right)$ | $\left(0.07\right)$ | $\left(0.11\right)$ | $\left(0.17\right)$ | $\left(0.48\right)$ | $\left(0.43\right)$ | |

2018–2015 | −0.557 *** | −0.708 *** | $-0.044$ | 0.395 * | $0.593$ | $0.466$ |

$\left(0.11\right)$ | $\left(0.07\right)$ | $\left(0.10\right)$ | $\left(0.13\right)$ | $\left(0.30\right)$ | $\left(0.43\right)$ | |

2018–2008 | −0.342 ** | 0.229 * | 1.203 *** | 1.056 *** | $0.616$ | $0.757$ |

$\left(0.1\right)$ | $\left(0.07\right)$ | $\left(0.12\right)$ | $\left(0.17\right)$ | $\left(0.48\right)$ | $\left(0.44\right)$ |

#### Appendix A.1.2. European Beech

#### Appendix A.1.3. Rowan Berry

#### Appendix A.1.4. Silver Fir

#### Appendix A.1.5. Birch

#### Appendix A.1.6. Sycamore Maple

#### Appendix A.2. Significance of Changes and Sample Sizes

#### Appendix A.2.1. Significant Changes of BP between 2012 and 2015

**Figure A7.**The results of the sensitivity analysis for the BP change of all tree species for which its change was as significant between 2012 and 2015. On the x-axis, the sample size and the estimates of the confidence intervals (dashed) of the logarithmic BP change on the y-axis.

#### Appendix A.2.2. Significant Changes of BP between 2015 and 2018

**Figure A8.**The results of the sensitivity analysis for the BP change of all tree species for which its change was tested as significant between 2015 and 2018. The sample size is on the x-axis and the estimates of the confidence intervals (dashed) of the logarithmic BP change is on the y-axis.

## Appendix B. Figures

**Figure A9.**Overview of the administrative organization of the study area (Bavarian Forest National Park); RLG = Rachel-Lusen-Region (light blue); FRG = Falkenstein-Rachel-Region (light green); systematic distributed plots of the regeneration inventory. The few plots which fall out of that grid near the NP’s borders are not incorporated in our analysis.

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**Figure 2.**Time series and confidence intervals of the BP (

**A**) and the corresponding logarithmic change of the BP between two consecutive acquisition years (

**B**). The estimated logarithmic change of BP (black point inside the confidence intervals) is positive if BP increased compared to the previous year and the change is negative if it decreased. If either the upper or the lower end of the confidence intervals completely crossed the zero on the x-axis, the change of the BP is not significant. The estimates are related to the data set of the entire NP.

**Figure 3.**Minimum required sample sizes to achieve a significant BP change based on the data from 2015 to 2018 for rowan; fitted by exponential functions with coefficient of determination (R

^{2}).

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Bödeker, K.; Ammer, C.; Knoke, T.; Heurich, M.
Determining Statistically Robust Changes in Ungulate Browsing Pressure as a Basis for Adaptive Wildlife Management. *Forests* **2021**, *12*, 1030.
https://doi.org/10.3390/f12081030

**AMA Style**

Bödeker K, Ammer C, Knoke T, Heurich M.
Determining Statistically Robust Changes in Ungulate Browsing Pressure as a Basis for Adaptive Wildlife Management. *Forests*. 2021; 12(8):1030.
https://doi.org/10.3390/f12081030

**Chicago/Turabian Style**

Bödeker, Kai, Christian Ammer, Thomas Knoke, and Marco Heurich.
2021. "Determining Statistically Robust Changes in Ungulate Browsing Pressure as a Basis for Adaptive Wildlife Management" *Forests* 12, no. 8: 1030.
https://doi.org/10.3390/f12081030