Introduction

Trees with special characteristics have been studied in most countries of the world. The interest in them is due to the fact that an important part of society considers them to be of great heritage, artistic, cultural, commercial, recreational and ecosystemic value (^{Gutiérrez, 2016}). From the importance and interest in their conservation, various experts in the field define different concepts for cataloguing them. Such is the case of veteran trees (^{Lonsdale, 2015}); champions (^{Ehrle, 2003}); heritage trees (^{Cortés and León, 2017}); significant trees (^{Sidney, 2013}), and monumental trees (^{Çağlar, 2014}; ^{Asan, 2017}), among others.

At present, there are countries such as Chile and Spain that propose the search for, and creation of legislative aspects as an instrument of protection for monumental or singular trees; other studies in the Iberian Peninsula are in charge of safeguarding genotypes of ancient olive trees in danger of extinction (^{Zapponi et al., 2017}; ^{Villota, 2018}). The concern for the preservation of special tree specimens arises because they represent a heritage, with scientific, artistic, cultural and commercial value, and also provide a service to the environment (^{Gutiérrez, 2016}).

Based on the documentary review, it is observed that the regulation of special trees in Mexico is limited, and therefore an adequate legislative regulation is required to promote their preservation.

There are several studies on the monumentality of special trees, one of which is that of ^{Asciuto et al. (2015)}, who carried out a survey using the Contingent Valuation Method among residents of households in Madonie Park (Sicily, Italy), to estimate the existence value of monumental trees on the nature trail called Piano Sempria-Piano Pomo, represented by a population of “Giant hollies” and seven other individual trees.

Some authors, such as ^{Meza (2015)}, mention that studies on urban vegetation and, particularly on trees in Mexico, are scarce, address very heterogeneous topics; the vast majority have been carried out for Mexico City, and a few, for the city of Monterrey. On the other hand, the location of long-lived trees is primordial and constitutes an additional element on which to base actions of protection, restoration of degraded ecosystems, as well as the formulation of ecotourism projects and conservation of biodiversity (^{Villanueva et al., 2010}).

Despite the contributions of the outstanding trees, they often face great survival challenges in the face of the imminent development of poorly planned urban projects, indiscriminate logging, lack of care and maintenance, vandalism and excessive tourism. Given the threats they face, it is important to highlight the care, conservation and protection of these trees as a natural and cultural heritage (^{Alanís and Ledezma, 2013}).

There are specimens that have a series of special attributes in Mexico, which have made them a matter of interest for conservation over time. Although there is little information on this subject, one of the documented efforts is that of ^{Vargas (1997)}, who made a compendium of historical and notable trees in Mexico, through a consultation collected with the participation of representative offices of the federal government. He thus obtained information regarding the presence of notable trees, which were classified into eight categories: notable tree, historical tree, notable and historical tree, undefined tree, notable grove, historical grove, notable and historical grove, and undefined grove. However, these are not described, nor are there criteria considered for their definition included.

The objectives of the present investigation were to analyze and qualify the monumentality of seven trees considered for their special characteristics; for this purpose, a set of criteria associated with a set of important weights were determined through the PROMETHEE II method.

Materials and Methods

The trees included in this work are just a sample of the many specimens that could be evaluated. There is an extensive list of them in the country, which will meet most of the criteria that define their monumentality (^{Verástegui, 2013}; ^{Meza, 2015}; ^{Hernández, 2019}). For research purposes, a set of trees that meet several of the following criteria were analyzed and agreed upon: a) Size of the tree, in which the height and circumference of the stem are considered; b) Conservation status, in which a value is assigned to the general status of conservation, based on the vigor, color and wilting of the foliage; c) Cultural significance, which is valued as a figure or natural element, linking the tree to history; d) Landscape significance, which refers to the landscape from the visual analysis that the tree offers to its surroundings; e) Rarity (scarcity) of the species, depending on the frequency of its occurrence in the environment.

The selected trees are located in different cities of the country and the description that follows is based, mainly, on the works of the Instituto Nacional de Ecología y Cambio Climático (National Institute of Ecology and Climate Change) ^{(INECC) (2007)} and ^{Vargas (1997)}.

Tule tree: scientific name, Taxodium mucronatum Ten. It is located in the atrium of the Santa María de la Asunción church, in Santa María del Tule, Oaxaca (Figure 1). Its diameter at breast height (DBH) exceeds 14.36 m, and its height is 35.40 m. Among its relevant aspects, it is considered to be one of the trees with the largest trunk in the world and one of the oldest (aged more than 2 000 years). In 2003, the United Nations Educational, Scientific and Cultural Organization (UNESCO) declared it a World Cultural Heritage Site, and the Secretaría de Medio Ambiente y Recursos Naturales (Ministry of the Environment and Natural Resources) (Semarnat) recognized it is “The Most Remarkable Tree in the state of Oaxaca”.

Prepared by the authors. Source: ^{Conabio (2011)}.

Figure 1 Tule tree and its location. 

El Sabino: scientific name, Taxodium Mucronatum Ten. It is located in Zimapán, Hidalgo, at El Sabino Park (Figure 2). Its DBH is 4.6 m, and its height is 25 m. In 1993, El Sabino was recognized by the National Institute of Ecology as the only Remarkable Tree in the state. It was used, according to different versions, for executing criminals during the time of the Mexican Revolution.

Prepared by the authors. Source: ^{Conabio (2011)}.

Figure 2 El Sabino tree and its location. 

El Ahuehuete: scientific name, Taxodium mucronatum Ten., located in Victoria de Durango, at El Guadiana Park (Figure 3). Its DBH is 5.50 m, and its height is 9.10 m. It is the longest living ahuehuete in the Guadiana Park, with an approximate age of 200 years (^{Árboles Monumentales, 2013}).

Prepared by the authors. Source: ^{Conabio (2011)}.

Figure 3 El Ahuehuete and its location. 

La Higuera (The Fig Tree): scientific name, Ficus aurea Nutt., located in La antigua Veracruz, Mexico (Figure 4). A relevant aspect, among others, is that it is located in the house that was owned by Hernán Cortés.

Prepared by the authors. Source: ^{Conabio (2011)}.

Figure 4 La Higuera and its location. 

The Baobab of the Mexico City freeway: scientific name, Adansonia digitate L., located on Bulevar Manuel Ávila Camacho, Mexico City (Figure 5). This tree was placed by Architect Víctor Lama, who decided to establish it in the windows of a ninth floor, in the frame of a very busy urban avenue. It was transplanted into a two-meter diameter pot for its survival, the interior of which contains more than a ton of soil. In order to meet the hydration needs of the Baobab, the pot has a mechanism, brought from Europe, which operates a watering system by means of a photocell.

Prepared by the authors. Source: ^{Conabio (2011)}.

Figure 5 The Baobab and its location. 

6. Ginkgo: scientific name, Ginkgo biloba L., is located at La Bombilla Park, Álvaro Obregón City Hall, Mexico City (Figure 6), with a DBH of 0.44 and a height of 18 m. It is believed that it was introduced by Engineer Miguel Ángel de Quevedo, the father of forest engineering in Mexico, who during a conference in the port of Veracruz mentioned that: “…in modern societies, forest conservation must be considered a necessary and obligatory function of the State.” (^{Boyer, 2007}).

Prepared by the authors. Source: ^{Conabio (2011)}.

Figure 6 Gingko and its location. 

7. El Árbol de los Acuerdos (Agreements Tree): scientific name, Fraxinus udhei (Wenz.) Lingelsh. This tree is located at the Universidad Autónoma Chapingo (Autonomous University of Chapingo) (Figure 7), with a DBH of 2.9 m and a height of 50 m. Under the shade of this tree, General Manuel González, who was the President of the Mexico, made some agreements. Later, it became the meeting place for the student community of the Escuela Nacional de Agricultura (National School of Agriculture), later he Universidad Autónima Chapingo (Autonomous University of Chapingo), for making agreements.

Prepared by the authors. Source: ^{Conabio (2011)}.

Figure 7 Árbol de los Acuerdos (Agreements Tree) and its location. 

The PROMETHEE method is one of several methods utilized to make Preference Ranking Organization Method for Enriched Evaluation (^{Brans and Vincke, 1985}). It is one of the methods that use outranking relationships decisions about problems related to a set of alternatives rated according to a group of criteria.

This English acronym comes from the name between each pair of alternatives, based on the scores they record for each criterion or attribute. The PROMETHEE I method can provide a partial ranking of the decision alternatives, while PROMETHEE II produces a complete ranking of all the alternatives (^{Athawale and Chakraborty, 2010}).

The literature records a very wide range of applications of the PROMETHEE method in different research fields. For example, the selection of airport locations (^{Palczewski and Salabun, 2019}); the classification of districts by flood risk (^{Wendpanga, 2019}); the evaluation of regeneration processes (^{Bottero et al., 2018}); comparison of alternatives in hydraulic structures (^{Brankovic et al., 2018}); the selection of best students (^{Fadlina et al., 2017}); the competence analysis and classification of industrial companies (^{Veza et al., 2015}); the selection of industrial equipment (^{Yilmaz and Dağdeviren, 2011}), among many others.

The structure of the information used in PROMETHEE, as in any multi-criteria problem, generally consists of a matrix (Table 1) where 𝐴={ 𝑎 1 , 𝑎 2 , …, 𝑎 𝑛 } is the set of alternatives, trees in our case; 𝐶= 𝑐 1 , 𝑐 2 , …, 𝑐 𝑚 is the set of criteria, which in this problem are assumed to be maximized; and 𝑐 𝑖 ( 𝑎 𝑗 ) is the evaluation of the alternat/ive 𝑎 𝑗 based on the criterion 𝑐 𝑖 . It was assume that 𝑐 𝑖 ( 𝑎 𝑗 ) is a numerical value.

In the present research, the PROMETHEE II method was applied by developing the following steps (^{Ishizaka and Nemery, 2013}):

Estimation of the degrees of preference, denoted by Pijc in each criterion c for each arranged pair of trees ij. Decisions on degrees of preference can be enriched by Preference functions; ^{Brans and De Smet (2016)} propose six to express them. This study utilizes the function known as usual ENT#091;Figure 3, and Equation (1); in which the values of the thresholds of indifference and preference are equal to zero. This means that, in the face of the slightest positive difference in ciai-ci(aj) the degree of preference is strong, equal to 1.; if the difference is negative or zero, the degree of preference is zero or indifferent.

Figure 8 Usual preference function. 

Calculation of the positive, negative and unicriteria net flows. The positive flow indicates how a tree is preferred over all trees based on a particular criterion. Its estimation results from the following formula:

Negative unicriteria flows measure how the other alternatives (trees) are preferred with respect to a particular alternative, this is given by:

Net flows consider the positive and negative aspects of an alternative. They are obtained by subtracting the negative flow from the positive one. They represent the balance between the strength and weakness of an alternative, and their value is always between -1 and 1.

Estimation of the overall positive, negative and net flows, which consider all the criteria simultaneously. They are represented as:

Where:

πij = The “Global Preference Grades”: This value represents the overall preference grades, taking into account the unicriteria preference grades and the weights (wj) associated to every criterion, that is:

The Global Net Flow is the difference between the Global Positive Flow and the Global Negative Flow.

For the analysis of the monumentality and the application of the method, data were collected from the seven trees selected with the participation of 15 experts (Table 2), whose average assessments were assumed to be consensus values.

Most of the specimens were known to the experts; however, the assessments were supported by the display of recent photographs of the trees of interest. In rating the performance of the trees based on the various criteria, the experts expressed their assessments using a five-term linguistic scale, which was subsequently converted into a numerical one as follows: Very good, 4; Good, 3; Fair, 2; Bad, 1, and Very bad, 0. The weighting of the criteria was estimated with the distribution of 100 points among them, according to the importance given to each criterion. Estimates for the application of the PROMETHEE II method were made using the Smart Picker Pro-version 4.1.0^© software (^{Smart Picker, 2019}).

Results

The assessments expressed by the experts for each tree in each criterion are shown in Table 3. On a first inspection of the data, as is usually the case with multi-criteria problems, it can be seen that none of the trees have the best scores for all the criteria considered. The weights assigned to each criterion were as follows: Size = 0.3; State of Conservation = 0.15; Cultural Significance = 0.3; Landscape Significance = 0.15, and Rarity = 0.1.

The calculation of the degree of preference of one over the others ( 𝑃 𝑖𝑗 𝑐 ), as well as the degree of preference of the others in relation to each particular tree ( 𝑃 𝑗𝑖 𝑐 )) (Table 4). The estimate of the overall net flow defined the individual position of the specimens evaluated (Table 5).

Discussion

The results show that only two trees exhibit positive values in the Net Global Flow (Tule Tree, Agreements Tree). This indicates that, considering the set of criteria that determine the monumentality, they are the most preferred in comparison with the rest of the trees.

Based on the above, we observe that the best evaluated, and consequently the most monumental tree, based on the Net Global Flow (0.758, Table 5), was the Tule Tree. In its rating, two criteria had the best performance, expressed in the value of their net flows unicriteria corresponding to Cultural Significance and Landscape Significance. However, the influence of the first was greater because of the weight of the criterion (0.3); while, the influence of the second was lower because of its lower weight (0.15). The contributions of both criteria to the monumentality of the Tule Tree are expressed in the colors green and brown, respectively (Figure 4). The influence of the criterion Size had a unicriterial net value of 0.833 (Table 3), which, multiplied by its assigned weight of importance (0.3), was 0.25, in orange (Figure 4). In this case, the contribution of all the criteria was positive.

Figure 4 Trees with the best rating in monumentality. 

Figure 4 shows only the three trees with the best rating in monumentality. The second tree with the highest monumentality rating was the Agreements Tree, whose highest criterion was Size (0.25). Likewise, negative contributions are observed in the criteria: Conservation Status (-0.05) and Rarity (-0.1), which means that in both criteria, the average sum of the preferences of the rest of the trees, with respect to the Agreements Tree, was higher. Even though this tree occupies the second place, its monumentality value (0.30) is very distant from that of the Tule Tree (Figure 4).

La Higuera recorded a negative monumentality value, very close to zero, although it is in third position. This is explained by the negative contribution of two criteria: Size (-0.15), and Rarity (-0.067).

The rest of the trees had negative Global Net Flow which indicates very low degrees of preference in the paired comparisons made by the experts, between the different trees for each of the criteria, which resulted in negative monumentality values.

There are very few documented examples of the evaluation of special trees, and what applies is the weighted sum of the assessments in the alternatives. One such study is that of ^{Villota (2016)} conducted in the historical territory of Álava, Spain, in which a list was generated and ordered from the highest to the lowest importance of uniqueness of the trees evaluated. It is important to note that there is no study in the literature on the evaluation of trees using the PROMETHEE method, which demonstrates the importance of this study.

Conclusions

The monumentality of the trees studied is well suited to the application of multi-criteria analysis methods in general, and the PROMETHEE II method in particular.

Within the framework of the research, the two trees with the greatest monumentality are the Tule Tree and the Agreements Tree. For the Tule Tree, all its characteristics are evaluated positively, but it is most prominent in Cultural Significance, Landscape Significance, and Size. On the other hand, the Agreements Tree is also rated outstanding based on its Size and Cultural Significance.

The order from most to least monumentality thus obtained can be useful for defining management and conservation priorities, as well as for budget allocation within the context of a policy of support for the maintenance and preservation of monumental trees and of trees with characteristics of monumentality in the various cities of the country.