Determining Statistically Robust Changes in Ungulate Browsing Pressure as a Basis for Adaptive Wildlife Management
Abstract
: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
2.4. Data Set
2.5. Data Analysis
2.5.1. Browsing Probability and Its Change
= linear predictor for the browsing probability; | |
= fixed intercept (the origin in our model); | |
= cluster-specific (random) deviation from the fixed intercept; | |
= random intercept for cluster (plot) i; | |
= fixed slope parameter of covariate (year); | |
= error term; | |
= 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
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
Norway Spruce | European Beech | Rowan Berry | Silver Fir | Birch | Sycamore Maple | |
---|---|---|---|---|---|---|
2007 | −5.94 *** | −2.54 *** | −0.84 *** | −3.03 *** | −0.61 | |
2008 | −4.73 *** | −2.81 *** | −1.87 *** | −2.74 *** | −1.52 *** | −1.84 *** |
2009 | −5.22 *** | −3.31 *** | −2.14 *** | −2.49 *** | −2.03 *** | −2.95 *** |
2010 | −4.75 *** | −2.95 *** | −1.71 *** | −2.23 *** | −1.87 *** | −1.54 *** |
2011 | −4.71 *** | −2.95 *** | −1.47 *** | −2.27 *** | −1.07 *** | −2.17 *** |
2012 | −5.31 *** | −2.88 *** | −1.70 *** | −2.92 *** | −3.57 *** | −2.49 *** |
2015 | −4.52 *** | −1.87 *** | −0.62 *** | −2.07 *** | −1.49 *** | −1.55 *** |
2018 | −5.08 *** | −2.58 *** | −0.67 *** | −1.68 *** | −0.90 *** | −1.08 ** |
AIC | 16,925.02 | 21,784.74 | ||||
BIC | 17,012.29 | 21,862.76 | ||||
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) |
Norway Spruce | European Beech | Rowan Berry | Silver Fir | Birch | Sycamore Maple | |
---|---|---|---|---|---|---|
2008–2007 | 1.208 *** | −0.27 * | −1.034 *** | −1.209 * | ||
2009–2008 | −0.49 *** | −0.503 *** | ||||
2010–2009 | 0.474 *** | 0.36 *** | 0.434 ** | 1.406 ** | ||
2011–2010 | ||||||
2012–2011 | −0.598 *** | −0.647 ** | −2.499 *** | |||
2015–2012 | 0.786 *** | 1.001 *** | 1.079 *** | 0.842 *** | 2.077 *** | |
2018–2015 | −0.557 *** | −0.708 *** | 0.395 * | |||
2018–2008 | −0.342 ** | 0.229 * | 1.203 *** | 1.056 *** | ||
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
Appendix A.2.2. Significant Changes of BP between 2015 and 2018
Appendix B. Figures
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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
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 StyleBödeker, 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