# Rating Potential Land Use Taking Ecosystem Service into Account—How to Manage Trade-Offs

*Standards*)

## Abstract

**:**

## 1. Introduction

#### Why Partial Ordering

## 2. Methodology

#### 2.1. Partial Ordering—The Basics

_{j}(x), j = 1, …, m, it can be compared to another object y, characterized by an identical set of indicators r

_{j}(y), if

_{i}(x) ≤ r

_{i}(y) for all i = 1, …, m

#### Concepts of Partial Ordering

- Max(MIS): the set of objects of the MIS, where no other object y can be found with y > x. This is the set of maximal objects of a partially ordered set (poset). If x is the only maximal object, it is called the “greatest” object;
- Min(MIS): the set of objects of the MIS, where no other object y can be found with y < x. This is the set of minimal objects of a poset. If x is the only minimal object, x is called the “least” object;
- Iso(MIS): the set of elements of the MIS that at the same time are elements of Max(MIS) and Min(MIS). Such objects are called isolated objects. Within the context of a MIS the data values leading to objects that are not compared to any other object. These elements may be of special interest;
- Chain: A subset of the MIS, where each object is mutually comparable with others;
- Antichain: A subset the MIS, where each object is mutually incomparable with others;
- Level: The subset of the MIS, where all objects have the same rank.

#### 2.2. The Hasse Diagram

#### The Orientation

#### 2.3. Average Ranking

#### 2.4. Sensitivity-Indicator Importance

#### 2.5. Indicators

#### 2.6. Data

#### 2.6.1. The Exemplary Case

#### 2.6.2. The Esgame

#### 2.7. Software

## 3. Results and Discussion

#### 3.1. An Exemplary Case

#### 3.2. The Esgame-Agriculture

^{2}, i.e., 100 hectar, which roughly corresponds to an average UK farm [38]. Each of the grid points are characterized by the 5 indicators crop_ag, agcarb, aghq, agwq and agrec (cf. Table 1). Quite a few of the grid points appear to be equivalent leaving 470 equivalent classes (cf. Section 2.2). Some of them are trivial classes, i.e., containing only one single grid point (called trivial equivalent classes), while other contain quite a few. Thus, the major non-trivial equivalent class contains all grid points where all indicator values equal zero. This class contains 274 objects. Further, 2 equivalent classes with 3 object and 8 with 2 objects, respectively, are present. The remaining 459 grid points are unique, i.e., trivial equivalent classes.

#### Indicator Importance

#### 3.3. The Esgame-Ranching

## 4. Conclusions and Outlook

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Xiangzheng, D.; Zhihui, L.; Gibson, J. A review on trade-off analysis of ecosystem services for sustainable land-use management. J. Geogr. Sci.
**2016**, 26, 953–968. [Google Scholar] [CrossRef][Green Version] - Munda, G. Social Multi-Criteria Evaluation for a Sustainable Economy; Springer: Berlin/Heidelberg, Germany, 2008; Available online: https://www.springer.com/la/book/9783540737025 (accessed on 19 August 2021).
- Lee, H.; Lautenbach, S. A quantitative review of relationships between ecosystem services. Ecol. Indic.
**2016**, 66, 340–351. [Google Scholar] [CrossRef] - Kaim, A.; Cord, A.; Volk, M. Optimal Land Use?—A Review on Optimization Techniques Used in Multi-Criteria Decision Analysis. International Congress on Environmental Modelling and Software. 2016. Available online: https://scholarsarchive.byu.edu/iemssconference/2016/Stream-B/37 (accessed on 19 August 2021).
- Hallouin, T.; Bruen, M.; Kelly-Quinn, M.; Christie, M.; Bullock, C.; Kelly, F.; Feeley, H.B. Multi-Criteria Decision Analysis and Ecosystem Services: Knowledge Gaps and Challenges for Policy and Decision-Making Conference. In Proceedings of the 8th International Congress on Environmental Modelling and Software (iEMSs 2016)—International Environmental Modelling and Software Society, Toulouse, France, 10–14 July 2016. [Google Scholar]
- Saarikoski, H.; Barton, D.N.; Mustajoki, J.; Keune, H.; Gomez-Baggethun, E. Multi-Criteria Decision Analysis (MCDA) in Ecosystem Service Valuation. 2017. Available online: http://www.opennessproject.eu/sites/default/files/SP_MCDA.pdf (accessed on 19 August 2021).
- Vogdrup-Schmidt, M.; Strange, N.; Olsen, S.B.; Thorsen, B.J. Trade-off analysis of ecosystem service provision in nature networks. Ecosyst. Serv.
**2017**, 23, 165–173. [Google Scholar] [CrossRef] - Saarikoski, H.; Mustajoki, J.; Hjerppe, T.; Aapala, K. Participatory multi-criteria decision analysis in valuing peatland ecosystem services—Trade-offs related to peat extraction vs. pristine peatlands in Southern Finland. Ecol. Econ.
**2019**, 162, 17–28. [Google Scholar] [CrossRef] - Annoni, P.; Bruggemann, R.; Carlsen, L. A multidimensional view on poverty in the European Union by partial order theory. J. Appl. Stat.
**2015**, 42, 535–554. [Google Scholar] [CrossRef] - Bruggemann, R.; Patil, G.P. Ranking and Prioritization for Multi-indicator Systems—Introduction to Partial Order Applications; Springer: New York, NY, USA, 2011; Available online: https//www.springer.com/gp/book/9781441984760 (accessed on 19 August 2021).
- Bruggemann, R.; Voigt, K. Basic Principles of Hasse Diagram Technique in Chemistry. Comb. Chem. High Throughput. Screen
**2008**, 11, 756–769. [Google Scholar] [CrossRef] [PubMed] - Carlsen, L. Happiness as a sustainability factor. The World Happiness Index. A Posetic Based Data Analysis. Sustain. Sci.
**2018**, 13, 549–571. [Google Scholar] [CrossRef] - Carlsen, L.; Bruggemann, R. Partial order methodology a valuable tool in chemometrics. J. Chemometr.
**2013**, 28, 226–234. [Google Scholar] [CrossRef] - Carlsen, L.; Bruggemann, R. The ”Failed State Index” Offers More than Just a Simple Ranking. Soc. Indic. Res.
**2014**, 115, 525–530. [Google Scholar] [CrossRef] - Carlsen, L.; Bruggemann, R. Environmental perception in 33 European countries an analysis based on partial order. Environ. Dev. Sustain.
**2018**, 22, 1873–1896. [Google Scholar] [CrossRef] - Carlsen, L.; Bruggemann, R. The 17 United Nations’ sustainable development goals: A status by 2020. Int. J. Sust. Develop. World Ecol.
**2021**, 1–11. [Google Scholar] [CrossRef] - Newlin, J.; Patil, G.P. Application of partial order to stream channel assessment at bridge infrastructure for mitigation management. Environ. Ecol. Stat.
**2010**, 17, 437–454. [Google Scholar] [CrossRef] - Zou, Z.; Zeng, F.; Wang, K.; Zeng, Z.; Tang, H.; Zhang, H. Evaluation and Tradeoff Analysis of Ecosystem Service for Typical Land-Use Patterns in the Karst Region of Southwest China. Forests
**2020**, 11, 451. [Google Scholar] [CrossRef][Green Version] - Lacayo, M. Esgame. 2019. Available online: https://github.com/mlacayoemery/esgame (accessed on 19 August 2021).
- Esgame. Tradeoff: Agriculture edition. 2021. Available online: http://esgame.unige.ch/ (accessed on 19 August 2021).
- Tosato, M.L.; Marchini, S.; Passerini, L.; Pino, A.; Eriksson, L.; Lindgren, F.; Hellberg, S.; Jonsson, J.; Sjöström, N.; Skagerberg, B.; et al. QSARs based on statistical design and their use for identifying chemicals for further biological testing. Environ. Toxicol. Chem.
**1990**, 9, 265–277. [Google Scholar] [CrossRef] - Bock, H.H. Automatische Klassifikation; Vandenhoeck&Ruprecht: Göttingen, Germany, 1974. [Google Scholar]
- Bock, H.H. Clusteranalyse mit unscharfen Partitionen. In Bd 6 Klassifikation und Erkenntnis III—Numerische Klassifikation; Studien zur Klassifikation; Bock, H.H., Ed.; Gesellschaft für Klassifikation: Frankfurt, Germany, 1979; pp. 137–163. [Google Scholar]
- Mucha, H.-J.; Bartel, H.-G.; Dolata, J. Techniques of Rearrangements in Binary Trees (Dendrograms) and Applications. Match. Commun. Math. Comput. Chem.
**2005**, 54, 561–582. Available online: https://match.pmf.kg.ac.rs/electronic_versions/Match54/n3/match54n3_561-582.pdf (accessed on 10 May 2021). - Bruggemann, R.; Carlsen, L. Partial Order in Environmental Sciences and Chemistry; Bruggemann, R., Carlsen, L., Eds.; Springer: Berlin/Heidelberg, Germany, 2006. [Google Scholar]
- Bruggemann, R.; Carlsen, L.; Wittmann, J. Multi-Indicator Systems and Modelling in Partial Order; Bruggemann, R., Carlsen, L., Wittmann, J., Eds.; Springer: New York, NY, USA, 2014. [Google Scholar]
- Fattore, M.; Bruggemann, R. Partial Order Concepts in Applied Science; Fattore, M., Bruggemann, R., Eds.; Springer: Cham, Switzerland, 2017. [Google Scholar]
- Bruggemann, R.; Carlsen, L.; Beycan, T.; Suter, C.; Maggino, M. Measuring and Understanding Complex Phenomena. Indicators and Their Analysis in Different Scientific Fields; Springer: Cham, Switzerland, 2021. [Google Scholar]
- Bubley, R.; Dyer, M. Faster random generation of linear extensions. Discr. Math.
**1999**, 201, 81–88. [Google Scholar] [CrossRef][Green Version] - Bruggemann, R.; Münzer, B. A Graph-Theoretical Tool for Priority Setting of Chemicals. Chemosphere
**1993**, 27, 1729–1736. [Google Scholar] [CrossRef] - Bruggemann, R.; Voigt, K. An Evaluation of Online Databases by Methods of Lattice Theory. Chemosphere
**1995**, 31, 3585–3594. [Google Scholar] [CrossRef] - Bruggemann, R.; Carlsen, L. An improved estimation of averaged ranks of partial orders. MATCH Commun. Math. Comput. Chem.
**2011**, 65, 383–414. Available online: http://match.pmf.kg.ac.rs/electronic_versions/Match65/n2/match65n2_383-414.pdf (accessed on 19 August 2021). - Bruggemann, R.; Annoni, P. Average heights in partially ordered sets. MATCH Commun. Math. Comput. Chem.
**2014**, 71, 117–142. Available online: http://match.pmf.kg.ac.rs/electronic_versions/Match71/n1/match71n1_117-142.pdf (accessed on 19 August 2021). - Bruggemann, R.; Sørensen, P.B.; Lerche, D.; Carlsen, L. Estimation of Averaged Ranks by a Local Partial Order Model. J. Chem. Inf. Comp. Sci.
**2004**, 44, 618–625. [Google Scholar] [CrossRef] [PubMed] - De Loof, K.; De Meyer, H.; De Baets, B. Exploiting the Lattice of Ideals Representation of a Poset. Fundam. Inform.
**2006**, 71, 309–321. [Google Scholar] - De Loof, K.; Rademaker, M.; Bruggemann, R.; De Meyer, H.; Restrepo, G.; De Baets, B. Order Theoretical Tools to Support Risk Assessment of Chemicals. MATCH. Commun. Math. Comput. Chem.
**2012**, 67, 213–230. Available online: https://match.pmf.kg.ac.rs/electronic_versions/Match67/n1/match67n1_213-230.pdf (accessed on 15 May 2021). - Bruggemann, R.; Halfon, E.; Welzl, G.; Voigt, K.; Steinberg, C.E.W. Applying the Concept of Partially Ordered Sets on the Ranking of Near-Shore Sediments by a Battery of Tests. J. Chem. Inf. Comp. Sci.
**2001**, 41, 918–925. [Google Scholar] [CrossRef] [PubMed] - Dodds, S. What Size is the Average Farm? 2019. Available online: https://www.macintyrehudson.co.uk/ (accessed on 19 August 2021).

**Figure 2.**Hasse diagram visualizing the partial ordering of the seven monoculture pattens (cf. Zou et al. [18]).

Indicator | Notation | Explanation |
---|---|---|

Production | crop_ag/past_ps | Agriculture/Ranching |

Ecosystem service | agcarb/pscarb | Carbon storage (Agriculture/Ranching) |

Ecosystem service | aghq/pshq | Habitat Quality (Agriculture/Ranching) |

Ecosystem service | agwq/pswq | Water Quality (Agriculture/Ranching) |

Ecosystem service | agrec/psrec | Hunting and Foraging (Agriculture/Ranching) |

RES | Provisioning | Regulating | Supporting | Cultural |
---|---|---|---|---|

Corn | 0.021 | 0.052 | 0.154 | 0.252 |

Marigold | 0.052 | 0.23 | 0.141 | 0.504 |

Orange | 0.025 | 0.587 | 0.473 | 0.607 |

Pear | 0.144 | 0.576 | 0.586 | 0.607 |

Peach | 0.038 | 0.881 | 0.846 | 0.607 |

Apple | 0.169 | 0.872 | 0.811 | 0.814 |

Pomegranate | 0.955 | 0.508 | 0.678 | 0.814 |

**Table 3.**Tabular version of the Hasse diagram corresponding to the agriculture grid. The naming of the single grid point corresponds to their location (cf. Figure 1).

Level | No of Grid Points | Grid Point (Equivalent Classes) |
---|---|---|

12 | 31 | A1 C23 H20 I10 I11 I12 J10 J11 J17 K27 L8 L13 L27 M7 M9 M13 M26 N17 N21 N26 N27 S24 S26 S27 T17 T23 T24 T26 T27 U24 Y15 |

11 | 55 | A21 B22 B23 D12 D15 E10 E11 E22 F10 F11 F22 G21 I17 I19 J20 J21 K7 K10 K20 K26 L7 L9 L12 L26 M10 M11 M20 M27 N18 N22 O17 O23 P14 P26 Q14 Q15 Q24 R2 R3 R15 R28 U8 U9 U17 V3 V7 W4 W6 X15 X22 Y9 Y10 Y14 Y16 Y18 |

10 | 70 | D16 E12 E15 F12 F23 G22 H14 H19 I13 I18 J18 J22 J23 K6 K8 K11 K19 L4 L5 L6 L19 L20 M2 M6 M8 M12 M18 N2 N7 N16 N20 O2 O3 O6 O7 O9 O18 O22 O24 P6 P15 P23 P24 Q2 Q28 R14 R27 S12 S14 S17 S28 T12 T14 T18 U14 U16 U18 U21 U22 U23 V4 V22 W22 X9 X10 X16 X17 Y19 Z10 Z14 |

9 | 64 | A18 A20 A22 B18 B19 C22 E13 E16 F13 G10 H12 H17 H18 H21 J16 J19 K9 K13 K16 K22 K23 K24 L3 L10 L11 L25 M17 M19 N10 N12 N13 N14 O27 P5 P25 Q13 Q23 R4 R16 R24 S2 S3 S11 S13 S23 T8 T11 T15 T16 T21 T22 U7 U15 V6 V14 V23 W3 W12 X11 X12 Y11 Y17 Y21 Z9 |

8 | 57 | D20 D22 D23 E14 E23 G19 G20 H11 H13 I20 J12 K17 K21 K25 L2 M14 M21 N3 N4 N15 N23 O5 O10 O14 O16 O26 P2 P7 P27 Q11 Q12 Q16 Q25 R10 R23 S9 S10 S16 S25 T3 T6 T13 T19 U4 U10 V1 V11 V12 V13 W2 W8 W13 X14 Y12 Y20 AA10 AA14 |

7 | 64 | A17 A19 B17 B20 G12 G16 G17 H10 J13 K12 K15 K18 L16 L17 L18 L21 M3 M4 M25 N8 N9 N11 N19 N24 O4 O13 O25 P3 P4 P8 P9 P10 P12 P13 P16 P28 Q3 Q5 Q7 Q10 R5 R22 R26 S15 T1 T9 U1 U12 U13 U19 V5 V9 V10 V21 W7 W9 W11 W14 W17 X13 Y13 Z13 AA11 AA13 |

6 | 56 | B21 C17 D19 E18 E20 F17 F19 G11 G15 G18 I16 L22 L24 M16 M22 M24 N6 N25 O8 O11 O20 O21 P11 P22 Q4 Q6 Q9 Q17 Q18 Q22 R6 R7 R11 R17 R18 S4 S5 S6 S22 T2 T5 T7 T25 U3 U6 U11 V2 V15 V18 V19 W10 W15 X18 X21 Z11 AA12 |

5 | 35 | C18 C20 D17 D18 E17 E19 F18 F21 G14 H16 I14 L14 M23 O12 O19 Q8 Q21 Q27 R13 R19 R21 S7 S8 S18 S19 T4 T10 U2 V8 V16 V17 W16 W19 X19 X20 |

4 | 23 | C19 C21 D21 E21 F16 F20 G13 H15 K14 L15 L23 M5 M15 P17 Q19 Q20 Q26 R9 R12 R20 U5 W18 W20 |

3 | 10 | F14 I15 J14 J15 N5 P18 P19 P21 R8 W21 |

2 | 4 | S20 S21 T20 V20 |

1 | 1 | U20 |

**Table 4.**Indicator values of the top ranked grid point based on an average ranking (I11) and an aggregation process (M13).

Grid Point | crop_ag | agcarb | aghq | agwq | agrec | SUM |
---|---|---|---|---|---|---|

I11 | 1050 | −100 | −150 | −50 | −75 | 675 |

M13 | 1500 | −200 | −300 | −150 | −100 | 750 |

**Table 5.**Indicator values of the top ranked grid point based on an average ranking (L13) and an aggregation process (Q23).

Grid Point | past_ps | pscarb | pshq | pswq | psrec |
---|---|---|---|---|---|

L13 | 800 | −100 | −125 | −25 | 0 |

Q23 | 950 | −100 | −125 | −50 | −25 |

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Carlsen, L. Rating Potential Land Use Taking Ecosystem Service into Account—How to Manage Trade-Offs. *Standards* **2021**, *1*, 79-89.
https://doi.org/10.3390/standards1020008

**AMA Style**

Carlsen L. Rating Potential Land Use Taking Ecosystem Service into Account—How to Manage Trade-Offs. *Standards*. 2021; 1(2):79-89.
https://doi.org/10.3390/standards1020008

**Chicago/Turabian Style**

Carlsen, Lars. 2021. "Rating Potential Land Use Taking Ecosystem Service into Account—How to Manage Trade-Offs" *Standards* 1, no. 2: 79-89.
https://doi.org/10.3390/standards1020008