# Species Mixing Regulation with Respect to Forest Ecosystem Service Provision

^{*}

## Abstract

**:**

## 1. Introduction

- To propose a quantitative, growing space-based approach for regulation of mixture proportions in mixed stands;
- To demonstrate the efficiency of the approach by means of scenario simulations for a highly prominent tree species mixture in Central Europe;
- To assess the effect of mixture regulation on the provision of the wood production, diversity, and groundwater recharge ecosystem services.

## 2. Material and Methods

#### 2.1. Approach for the Regulation of Mixture Proportion

#### 2.1.1. Mean Diameter at Breast Height-Related Crown Projection Area (CPA)

^{2})) as dependent on the mean diameter at breast height (MDBH (cm)).

#### 2.1.2. Number of Trees for Full Stocking (FS)

#### 2.1.3. Necessary Growing Space Share (α)

^{2}) is the mean basal area of a tree and CPA (m

^{2}) is the corresponding crown projection area. The stand’s investment of growing space into basal-area (IS) describes the basal area a tree species in a stand has on one unit of its growing space (Equation (4)):

^{2}) is the basal area of one species on stand scale and A (m

^{2}) is the sum of the crown projection areas of one species on stand scale. We assume that the relation between the growing-space investments (Equations (3) and (4)) of the two species (1 and 2) is independent of whether we consider just two individual average trees or whole stands (Equation (5)):

_{2}and β

_{2}accordingly, we may write Equation (8) using relative shares of growing space and basal area instead of absolute ones. Hence, we obtain the relative growing space share (α) of one species, as dependent on its relative basal area share (Equation (11)):

#### 2.1.4. Species-Specific Stem Number (N) Guide Curves

#### 2.2. Example Calibration of the Species Mixing Regulation

#### 2.3. Simulation Study with Exemplary Calibrated Mixing Regulation

#### 2.3.1. Intention of the Simulation Study

#### 2.3.2. Forest Management Model Settings

_{100}development of beech and spruce assumed and calculated in Section 2.2. All simulation runs used the thinning kind of selective thinning and therefore the stand density was regulated according to the guide curves from the regulation approach of the study at hand and calibrated in Section 2.2.

#### 2.3.3. Calculation of the Ecosystem Services: Diversity, Productivity and Groundwater Recharge

_{total}(Equation (17)):

_{total}= GSS

_{spruce}GWR

_{spruce}+ GSS

_{beech}GWR

_{beech}

## 3. Results

#### 3.1. Exemplary Guide Curve Calibration

#### 3.1.1. Assumed Diameter and Top Height over Stand Age

_{100}to stand age is a basis for calibration of the presented regulation approach. We exemplarily assume values for beech and spruce (calculation in Section 2.2) to calibrate the approach for the simulation study.

_{100}in Figure 2 and thus reveal the exact difference between the assumed growth mean diameter at breast height and top height of spruce and beech. To sum up, we can say that the assumed growth potential of spruce regarding h

_{100}and MDBH is higher compared to beech.

#### 3.1.2. Diameter Related Crown Projection Area

^{2}at diameter at breast height of 10 cm, while the one of the remainder species is at only 5 m

^{2}. The crown projection area of European beech, starting from low values of diameter at breast height and throughout the whole diameter at breast height range, is markedly larger than that of Scots pine and Norway spruce. Up to a diameter at breast height of 50 cm, it also surpasses that of sessile oak. However, the slope of the crown projection area over diameter at breast height of beech decreases with diameter at breast height. Conversely, that of oak strongly increases. Thus, at a diameter at breast height of more than 50 cm, oak outruns the crown projection area of all other species. Pine, which like oak, is a light-demanding species, has a similar course of crown projection area over diameter at breast height as oak and approximates the values of beech at a diameter at breast height of 80 cm. Spruce has the lowest crown projection area over the whole range of diameter at breast height and one that constantly increases with diameter at breast height. To sum up, we can say that the species-specific relations between diameter and crown projection area are very different, even intersections are visible. Consequently, this relationship is of fundamental importance for the mixture regulation approach of this study.

#### 3.1.3. Exemplary Guide Curve Calculation

#### 3.2. Simulation Study Quantifying Ecosystem Services Provision Depending on Species Shares

## 4. Discussion

#### 4.1. The Approach Contributes to Develop Quantitative Guidelines for Mixed Species Forests

#### 4.2. Mixing Proportions Are Crucial for Managing the Ecosystem Services Provision

#### 4.3. Important Considerations within the Regulation Approach

#### 4.4. Weaknesses, Limitations, Further Development

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Stand Density Correction Factors

**Table A1.**Number of trees per ha (N) in mixed-species stands in relation to the neighboring monocultures calculated separately for five selected species assemblages (as resulting from evaluations in the context of [30] and kindly provided by the authors). Ratios mixed/mono above/below 1.00 indicate a superiority/inferiority of the species’ performance in mixed-species stands versus monocultures. Ratios in bold numbers indicate significant differences (p < 0.05) between mixed-species stands and monocultures.

Variable | Species Combination | n | Species 1 Mixed/Mono (±SE) | Species 2 Mixed/Mono (±SE) | Total Stand Mixed/Mono (±SE) |
---|---|---|---|---|---|

Number of trees N (trees ha^{−1}) | |||||

spruce/pine | 7 | 1.78 (± 0.38) | 1.06 (± 0.12) | 1.44 (± 0.25) | |

spruce/larch | 10 | 2.72 (± 1.62) | 1.07 (± 0.20) | 1.57 (± 0.54) | |

spruce/beech | 52 | 0.90 (± 0.05) | 1.20 (± 0.06) | 1.03 (± 0.06) | |

pine/beech | 17 | 1.22 (± 0.10) | 1.59 (± 0.13) | 1.40 (± 0.09) | |

oak/beech | 24 | 1.23 (± 0.08) | 1.27 (± 0.13) | 1.25 (± 0.10) |

## Appendix B

#### Appendix B.1. Diameter-Related Crown Projection Area

^{2}to 431.7 m

^{2}and thus the magnitudes necessary for application purposes in this study are covered. The sample size for spruce and beech were highs.

Tree Species | Min | Median | Max | n | |
---|---|---|---|---|---|

spruce | cpa (m^{2}) | 0.22 | 11.80 | 251.95 | 9.997 |

dbh (cm) | 0.7 | 24.3 | 109.7 | ||

pine | cpa (m^{2}) | 0.26 | 10.05 | 151.36 | 4.520 |

dbh (cm) | 5.1 | 21.5 | 85.5 | ||

beech | cpa (m^{2}) | 0.29 | 26.04 | 431.70 | 10.348 |

dbh (cm) | 3.1 | 18.5 | 127.6 | ||

oak | cpa (m^{2}) | 0.20 | 19.39 | 348.03 | 3.937 |

dbh (cm) | 3.6 | 29.6 | 131.9 |

#### Appendix B.2. Diameter over Stand Age

Tree Species | Min | Median | Max | n | |
---|---|---|---|---|---|

beech | age (year) | 9 | 74.50 | 140 | 54,512 |

dbh (cm) | 7.0 | 23.3 | 46.5 | ||

spruce | age (year) | 9 | 74.50 | 140 | 122,743 |

dbh (cm) | 8.4 | 29.7 | 51.7 |

#### Appendix B.3. Top Height over Stand Age

Tree Species | Min | Median | Max | n | |
---|---|---|---|---|---|

beech | age (year) | 10 | 83.00 | 140 | 54,512 |

top height (m) | 3.1 | 26.4 | 46.1 | ||

spruce | age (year) | 9 | 60.00 | 140 | 122,743 |

top height (m) | 3.6 | 27.0 | 46.6 |

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**Figure 1.**Conceptual diagram of the approach for the regulation of mixture proportion and of the computation of tree number guide curves. To obtain the number of trees (N), we filled the necessary growing space share (α) required for the desired basal area share (β) until full stocking. The number of trees per hectare for full stocking (FS) results from the species-specific crown projection area (CPA) and a correction factor (CF) for suitability in mixed species stands. The necessary growing space share results from the desired basal area share and the stand age dependent diameter (MDBH) related crown projection area.

**Figure 2.**Assumed development of top height and mean diameter at breast height (MDBH) for the parametrization of the regulation approach within the exemplary simulation; parameters in Table 2 and Table 3 (more detailed database information, see Appendix B.2 and Appendix B.3).

**Figure 3.**Crown projection area (CPA) over diameter at breast height for sessile oak (cross), European beech (triangle), Scots pine (circle), Norway spruce (square), as expected with the fitted model after Equation (1), parameters in Table 4 (more detailed database information, see Appendix B.1).

**Figure 4.**Number of trees at full stocking per ha (FS) over stand age (t) based on Equation (2), given for Norway spruce (sp) and European beech (be); given in addition to over top height h

_{100}. Curves shown with a solid line refer to monospecific stands and therefore assume a mixture adjustment CF of 1.0 in Equation (2) (Section 2.1.2); curves shown with a dotted line assume that crowns overlap according to a mixture adjustment CF of 1.03 in Equation (2) (Section 2.1.2, Table 1). The mean diameter at breast height in Equation (2) was taken according to the stand age (Figure 2); crown projection parameters (c, d) from Table 4.

**Figure 5.**Conversion between growing space share (α) and basal area share (β) in a mixed stand of European beech (be) and Norway spruce (sp). Each line presents one stand age (t): triangle = 20 years, square = 60 years, circle = 100 years. α was calculated as α

_{1}from Equation (11) and as dependent on the basal area share given as β

_{1}in Equation 11. The diameter at breast height in Equation (2) was taken according to the stand age (Figure 2); parameters c

_{1}and c

_{2}in Equation (11) were taken from Table 4.

**Figure 6.**Guide curves of tree number per ha over age calculated with Equation (13) for Norway spruce (sp) and European beech (be) and each of three different basal area shares (β

_{species}= 20%, 50% and 80%); The diameter at breast height was taken according to the stand age (Figure 2); parameters c

_{1}and c

_{2}in Equation (13) were taken from Table 3.

**Figure 7.**Influence of basal area composition on water availability, diversity and productivity based on simulation runs within a mixed stand of European beech and Norway spruce (Section 2.3); each column refers to exactly one run; that run presumed a relation of beech vs. spruce basal area as given by the column header; dotted line—beech, dashed line—spruce, horizontal line—average, solid line—total stand.

**Table 1.**Correction factors for species combinations of four tree species (values resulting from evaluations in the context of [30], see Appendix A). European beech, Norway spruce, Scots pine and sessile oak.

Species Combination | Correction Factor (CF) |
---|---|

spruce/pine | 1.44 |

spruce/beech | 1.03 |

pine/beech | 1.40 |

oak/beech | 1.25 |

**Table 2.**Estimates of the MDBH functions for European beech, Norway spruce (Equation (14); Section 2.2; more detailed database information, see Appendix B.2).

Tree Species | v | p | n | ||
---|---|---|---|---|---|

Estimate | Std. Error | Estimate | Std. Error | ||

Beech | 0.04223 | 0.07 | 0.73227 | 0.02 | 54,512 |

Spruce | 0.4462 | 0.04 | 0.6904 | 0.01 | 122,743 |

**Table 3.**Estimates of the h

_{100}-functions for European beech, Norway spruce (Equation (15); Section 2.2; more detailed database information, see Appendix B.3).

Tree Species | w | u | k | n | |||
---|---|---|---|---|---|---|---|

Estimate | Std. Error | Estimate | Std. Error | Estimate | Std. Error | ||

Beech | 40.72 | 0.46 | 0.01916 | 0.00 | 0.9808 | 0.03 | 54,512 |

Spruce | 40.45 | 0.20 | 0.03106 | 0.00 | 1.2549 | 0.03 | 122,743 |

**Table 4.**Estimates of the crown projection area functions for European beech, Norway spruce, Scots pine and sessile oak (Equation (1); Section 2.1.1; more detailed database information, see Appendix B.1).

Tree Species | ln(c) | d | |||
---|---|---|---|---|---|

Estimate | Std. Error | Estimate | Std. Error | n | |

Beech | 0.712 | 0.03 | 0.85 | 0.01 | 10,348 |

Spruce | −0.8921 | 0.03 | 1.06 | 0.01 | 9997 |

Pine | −2.21 | 0.05 | 1.48 | 0.02 | 4520 |

Oak | −2.66 | 0.05 | 1.70 | 0.01 | 3937 |

Desired Beech Basal Area Share (%) | Average of Simulated Beech Basal Area Share (%) | Average of Simulated Beech Growing Space Share (%) |
---|---|---|

0 | 0 | 0 |

20 | 23 | 52 |

50 | 52 | 79 |

80 | 82 | 94 |

100 | 100 | 100 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Schwaiger, F.; Poschenrieder, W.; Biber, P.; Pretzsch, H. Species Mixing Regulation with Respect to Forest Ecosystem Service Provision. *Forests* **2018**, *9*, 632.
https://doi.org/10.3390/f9100632

**AMA Style**

Schwaiger F, Poschenrieder W, Biber P, Pretzsch H. Species Mixing Regulation with Respect to Forest Ecosystem Service Provision. *Forests*. 2018; 9(10):632.
https://doi.org/10.3390/f9100632

**Chicago/Turabian Style**

Schwaiger, Fabian, Werner Poschenrieder, Peter Biber, and Hans Pretzsch. 2018. "Species Mixing Regulation with Respect to Forest Ecosystem Service Provision" *Forests* 9, no. 10: 632.
https://doi.org/10.3390/f9100632