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Revista mexicana de ciencias forestales

versión impresa ISSN 2007-1132

Rev. mex. de cienc. forestales vol.10 no.53 México may./jun. 2019

http://dx.doi.org/10.29298/rmcf.v10i53.406 

Articles

Spatial distribution of Pinus oocarpa Schiede ex Schltdl. through estimating Kernel density

José Germán Flores Garnica1 

Oscar Reyes Cárdenas2  * 

1Universidad Autónoma de San Luis Potosí. México.

2Centro de Investigación Regional Pacífico Centro, INIFAP. México.

Abstract

In the state of Chiapas, the species Pinus oocarpa is widely distributed throughout the Sierra Madre de Chiapas, specifically in the subprovinces of the central depression, the central highlands and the eastern mountains. In the present work the spatial distribution of this species was analyzed through Kernel density analysis, using information generated by the National Inventory of Forests and Soils of Mexico (INFyS), the proposed alternative process estimates the spatial distribution of this species through Kernel density analysis. For this reason, the presence of the species can allegedly be represented as a series of georeferenced events, which occur differentially along a given region, determining spatial variations in their density. To make the comparison between the different maps that present the distribution of P. oocarpa, a confusion matrix was defined for each one of the maps, which were based on a binary classification. The distribution defined through the Kernel density estimation confirms that P. oocarpa is located basically along the Sierra Madre of Chiapas and the Central High Plateau, generally agreeing with most of the illustrations of the geographical distribution of this species. The methodology proposed herein can be used in other regions where information from forest inventories (at national, state, region, or management level) is available, by limiting the definition of the distribution of the species of interest to the area covered by the sampling design.

Key words: Bandwidth; Kappa coefficient; interpolation; National Forest and Soil Inventory; confusion matrix; continuous surfaces

Introduction

The genus Pinus is represented by approximately 100 species in the world (Alba-López et al., 2003). Its natural distribution covers the Arctic and sub-Arctic regions of North America and Eurasia; its largest diversification center is located in the northern and central region of the American continent ―with approximately 70 taxa (Farjon et al., 1997; Price et al., 1998)―, in which Mexico houses the largest number of species in the world, naturally located in all the states of the country, except for Yucatán (Martínez, 1992). Nevertheless, the surfaces of pine forests in Mexico have dwindled, a situation that has called for the implementation of strategies for their restoration and promotion based mainly on the collection of seeds, and the production and planting of seedlings (Conafor, 2010). The success of these activities, however, depends upon the most accurate possible knowledge of the spatial distribution of the taxa of interest, as well as upon the estimation of the seed collection potential, the environmental conditions in which the species is located, and the best areas for its growth.

Important studies have been carried out on the ecogeography and biogeography of pine taxa (Vargas, 2008); however, greater geographical precision is required in order to determine their distribution. Especially, considering that this is determined not only by their adaptation to the environment of by their evolutionary history, but also by the impact of human activities in the last centuries. Therefore, it is necessary to locate the pine species in order to measure their present surface area; their environmental conditions must be characterized, and the areas with disturbances, potential areas for reforestation and promotion, and others, must be located, since no updated maps allowing to know the current and potential location of pine trees are available.

Specifically in the state of Chiapas, where the study documented herein was carried out, the physiographic regions where pines grow are, according to Mullerried (1957): the Central High Plateau (CHP), and the Sierra Madre of Chiapas (SMC) (Alba-López et al., 2003), which reportedly harbor approximately 12 pine species: P. ayacahuite Ehrenb. ex Schltdl., P. michoacana Martínez, P. hartwegi Lindl., P. maximinoi, P. montezumae Lamb., P. oocarpa Schiede ex Schltdl., P. patula Schiede ex Schltdl. & Cham., P. pseudostrobus Lindl., P. oocarpa var. ochoterenae Martínez, P. chiapensis (Martínez) Andresen, P. oaxacana Mirov. and P. teocote Schiede ex Schltdl. & Cham. (Breedlove, 1986; Perry, 1991; Martínez, 1992; Farjon et al., 1997; Conafor, 2011).

Specifically, P. oocarpa is distributed along the Sierra Madre of Chiapas, in the subprovinces of the Central Depression, the CHP and the eastern mountains (Gutiérrez et al., 2010), covering a wide range of altitudes, in an uneven orography with a long geological history; this allows for a huge variety of ecological conditions and, therefore, a large biological diversity (Breedlove, 1986; Ceballos et al., 1998). Nevertheless, there are few publications that illustrate the geographical distribution of this species (Figure 1), mainly at a national scale (Mirov, 1955; Sánchez and Huguet, 1959; Eguiluz-Piedra, 1985; Instituto Nacional de Investigaciones Forestales, 1974; FAO, 1977; Perry, 1991; Farjon et al., 1997; Howell and Mathiasen, 2004).

Figure 1 History of the general location of the genus Pinus in Chiapas: a. Mirov, 1955; b. Eguiluz-Piedra, 1985; c. Instituto Nacional de Investigaciones Forestales, 1974; d. Howell y Mathiasen, 2004; e. Sánchez y Huguet, 1959; f. Perry, 1991; g. Farjon et al., 1997; h. FAO, 1978

On the other hand, certain works also include more localized maps of the P. oocarpa populations, in relation to seed collection (Sáenz-Romero et al., 2006) or to the presence of certain pests (Domínguez-Sánchez et al., 2008). Conventionally, the geographical distribution of P. oocarpa is represented by means of roughly outlined areas.

Within this context, the purpose of this work was to define the spatial distribution of P. oocarpa in the state of Chiapas, through Kernel density estimation, using information collected at the National Inventory of Forests and Soils (INFyS) for the 2004-2010 period (Conafor, 2011).

Materials and Methods

Description of Pinus oocarpa

Pinus oocarpa has the following synonyms: P. tecunumanii F. Schwerdtf. and P. oocarpoides Lindl. ex Loudon; in Chiapas, it is known as ocote, pino trompillo, pino alazán, and pino bola. This tree reaches a height of 30 to 35 m, with a normal diameter of up to 125 cm (Farjon et al., 1997). Its needles are straight and rigid, generally grouped in fascicles of five (rarely of 3 or 4), and measure 17 to 30 cm in length, and 0.8 to 1.4 mm in width. Its cones are solitary or occur in whorls of up to four, ovoid in shape when open and globular when closed; they are 3 to 10 cm long and 3 to 12 cm wide (Farjon et al., 1997). This species grows within an altitude range of 200 to 2 700 m, in sites with a minimum temperature of -1 °C and a maximum temperature of 40 °C; specifically in the state of Chiapas, it is found at an altitude between 401 and 2 401 masl; at a minimum, semi-cold temperature of 5 °C and a maximum, very warm temperature of 38 °C, in a warm or temperate climate with minimum annual precipitations of 600 mm and maximum annual precipitations of 3 500 mm (Gutiérrez et al., 2010). In the state, it grows on soils that are very rich in organic matter and nutrients, highly susceptible to erosion, with volcanic ashes, and with a high content of clay, formed from recent alluvial materials (Martínez, 1992). P. oocarpa is characterized by a rapid growth under semi-tropical conditions and is generally used for sawn wood and cellulose, but also as firewood.

Study area

The study area is located in the state of Chiapas, in southeastern Mexico, between the coordinates 14°31’37.41” and 17°59’26.6” N, and 90°22’8.20” and 94°9’11.64” W (Figure 2).

Simbología = Symbology; Límite estatal = State limit; Altitud = Altitude.

Figure 2 Location and altitude range of the state of Chiapas

INFyS clusters

The present study is based on data provided by the INFyS for the state of Chiapas, where 1 590 clusters were established (Figure 3); of these, 125 (8 %), located mainly in the SMC and the CHP, registered nine species of pines. The greatest diversity of genera is observed in 42 municipalities, notably in Comitán de Domínguez, La Concordia, and Ocosingo. Based on this information, the clusters where P. oocarpa are present were selected.

Figure 3 Clusters of the National Inventory of Forests and Soils in the state of Chiapas (Conafor, 2010). 

Kernel density estimation

It is assumed that the existence of a species can be represented as a series of georeferenced events occurring differentially along a particular region, which determines spatial variations in density (in this study, the number of clusters with a reported occurrence of P. oocarpa per unit of surface area) (Salvati and Ferrara, 2015).

Thus, in order to map the spatial continuity of P. oocarpa, a density map was generated through Kernel density estimation (Fuenzalida et al., 2013). This helps generate continuous surface densities in clusters with data of the species of interest using calculations of local vicinity carried out under the structure of a grid (a net of cells), where the density value at a given point (or a particular cell) is estimated in relation to the number of points (cells) where P. oocarpa is present. Specifically, the Kernel density estimation is a non-parametric technique based on several functions ―quadratic function (Silverman, 1986), uniform function, Epanechnikov’s function, normal distribution, triangular function, quartic function, etc. (Turlach, 1999)―, in which the near points have a greater influence on the determination of the density, while the distant points have a lower weighting. This is in accordance with the first law of geography, which states that everything is related to everything else, but those things that are nearer one other are more closely interrelated than things that are far apart (Tobler, 1970). Thus, the Kernel density estimator is defined using Equation 1 (Amatulli et al., 2007):

f^x= 1nhdi-1nKx-Xih (1)

Where:

n = Number of observation points

h = Bandwidth

K = Core module (kernel)

x = Coordinate vector representing the location where the function is estimated

X = Coordinate vectors representing each observation point

d = Number of dimensions in space

The spatial distribution of P. oocarpa was modeled based on the above expression; its maximum search radius parameter (bandwidth) was a distance of 9 051 m, according to Silverman’s “golden rule” (1986).

Results validation

In order to compare between the different maps showing the distribution of P. oocarpa and the map resulting from the Kernel density model, a confusion matrix was determined for each of them; each matrix was based on the binary classification (YES = correct classification; NO = incorrect classification) of 221 systematically distributed points. For this purpose, the distribution of P. oocarpa determined by the distribution of likelihood resulting from the Kernel density estimation was assumed to be the actual distribution. The degree of agreement between the assigned classes was subsequently calculated by estimating the overall precision and the errors of omission and commission. However, since these statistics tend to overestimate the accuracy of the classification, the Kappa coefficient ―which represents the percentage in which a given classification is better than the one resulting from the application of a random classifier― was calculated, using the following expression (Congalton, 1991):

K^= Ni=1rxii- i=1rxi+ x+i x2 - i=1rxi+ x+i (2)

Where:

r = Number of rows in the matrix

xii = Number of observations in the element of row i and column i (the largest diagonal of the matrix)

xi+ = Total number of observations in the row

x+i = Total number of observations in the column

N = Total number of observations included in the matrix

Results and Discussion

Figure 4 illustrates the distribution of the 114 clusters of the INFyS where the presence of P. oocarpa in Chiapas was observed; these are distributed along the Sierra Madre of Chiapas, in the Central High Plateau and on the eastern mountains. The mensuration characteristics are summarized in Table 1.

Simbología = Symbology; Conglomerados = Clusters; Límite estatal = State limit; Altitud = Altitude.

Figure 4 INFyS clusters where Pinus oocarpa Schiede ex Schltdl. trees were identified in the state of Chiapas (Conafor, 2011). 

Table 1 Average dasometric parameters of the INFyS clusters where the presence of Pinus oocarpa Schiede ex Schltdl. was detected. 

Parameter Normal
Diameter
(cm)
Crown
Diameter
(m)
Total
Height
(m)
Stem
Height
(m)
Commercial
Height
(m)
Average 31.05 3.41 13.4 7.17 9.94
Maximum 85 8.69 33.69 22.73 30.44
Minimum 9.25 0.65 4.99 1.49 1

The result of the definition of the spatial variation of the density of clusters with P. oocarpa made it possible to measure and delimit its distribution (Figure 5). Likewise, we should take into account that the number of clusters that, based on the probabilities, can occur within a km2 circular area (Silverman, 1986), was determined through Kernel density estimation. Therefore, each cell contains the density value (cluster per km2) that corresponds to the original distribution of the clusters of the INFyS. Although it is possible to consider the density of P. oocarpa trees in each cluster can be considered, the present study did not do so; therefore, the work was based exclusively on the condition of the presence of the species.

Figure 5 Estimation of the spatial distribution of Pinus oocarpa Schiede ex Schltdl., based on the Kernel density estimation. 

The comparative analysis of the proposals concerning the geographical distribution of P. oocarpa takes into account the most recent cases (Figure 6). As for the qualitative analysis, it largely agrees with the results of the quantitative analysis shown in Table 2; in principle, the distribution proposed by the Instituto Nacional de Investigaciones Forestales (National Institute for Forest Research) (1974) had the greatest overall precision; it is followed by those of Farjon et al. (1997) and Eguiluz-Piedra (1985), with very similar overall precisions. On the other hand, the proposal by Perry (1991) evidences a geographical division between the distribution of the CHP and the SMC, which would imply a better approach to the actual distribution of P. oocarpa, compared to the distribution of Eguiluz-Piedra (1985).

Figure 6 Graphic comparison of the distribution of Pinus oocarpa Schiede ex Schltdl. in the state of Chiapas: A. Eguiluz-Piedra, 1985; B. Instituto Nacional de Investigaciones Forestales, 1974; C. Perry, 1991; D. Farjon et al., 1997

Table 2 Statistics resulting from the analysis of the confusion matrix when comparing the various maps of the distribution of Pinus oocarpa Schiede ex Schltdl. in Chiapas

Statistic 1 2 3 4
Overall precision 67.873 69.231 68.326 80.995
Kappa 35.695 38.354 36.837 62.065
Omission error 34.862 30.392 27.885 13.889
Commission error 31.731 34.259 35.345 22.500

1. Perry, 1991; 2. Eguiluz-Piedra, 1985; 3. Farjon et al., 1997; 4. Instituto Nacional de Investigaciones Forestales, 1974.

Nevertheless, the results of the corresponding confusion matrix showed that the proposal of Eguiluz-Piedra (1985) offers a greater overall precision. All of this is confirmed by the resulting values of the Kappa index.

According to the map of the location of P. oocarpa, this species is distributed mainly along the SMC and the CHP. The information contained in the clusters of the INFyS highlights the existence of trees with a normal diameter of almost 85 cm (at a height of 1.30 m), although these are rare. The average height of the trees was also observed to be low; i.e. most of the trees are at a youthful stage, or else, the species is located at places with low site quality, and as a result, the commercial height is also generally low.

The distribution determined through the Kernel density estimation has confirmed P. oocarpa to be located basically along the SMC and the CHP, as depicted in most of the illustrations of its geographical distribution. However, these clearly show a very approximate distribution, particularly in the maps that are previous to the 1990s (Mirov, 1955; Sánchez y Huguet, 1959; Eguiluz-Piedra, 1985), and a more accurate one in the versions of Farjon et al. (1997) and Perry (1991). Likewise, the distribution determined through the Kernel density estimation was found to agree with the exact location (sampling sites) of certain seed collection works (FAO, 1977) and studies on pests (Howell and Mathiasen, 2004).

However, certain sampling sites with P. oocarpa were located in unidentified areas at the INFyS, mainly to the southeast of the area between the SMC and the CHP, and at the center and north of the state, because these sites were sampled separately, without the purpose of defining the distribution of the species, and were not integrated into the density estimation.

From a qualitative perspective, and considering the actual distribution resulting from the Kernel density estimation, the geographical distribution of P. oocarpa cited by Eguiluz-Piedra (1985) agrees as to the area that covers the Sierra Madre of Chiapas (SMC), but differs in regard to a large part of the Central Plateau (CP). On the other hand, Perry’s proposal (1991) covers the distribution of P. oocarpa in the region of the CHP, although not in the region of the SMC, particularly in its central area. The distribution of Farjon et al. (1997) comprises the whole length of the SMC, but the species is absent from certain areas of its width. Finally, the proposal of the National Institute for Research on Forestry (1974) is the one that most agrees with the distribution determined in the present study through Kernel density estimation; however, it exhibits a slight spatial overestimation.

Conclusions

The data of the INFyS make it possible to determine a spatial distribution of P. oocarpa that generally agrees with certain areas considered in previous proposals. However, we observe certain differences, as the previous studies basically tend to overestimate the distribution surface area due to: a) a somewhat inaccurate delimitation of the boundaries of the distribution areas, or b) a reduction of the distribution area of P. oocarpa, due to overexploitation or change of soil use. On the other hand, new areas with the presence of P. oocarpa are defined.

There are few works on the spatial distribution of P. oocarpa, which is specifically depicted in maps; however, the information is very approximate across distribution areas whose boundaries are not geographically outlined. For this reason, the sample intensity involved in the field work of the INFyS in the state of Chiapas allows ensuring a more accurate determination of the spatial distribution of P. oocarpa, which is conditioned only to the correct identification of the species in the sampling clusters.

The use of strategies such as the Kernel density estimation makes it possible to profit from the information that is intensively collected from the INFyS to generate information that can be used to support restoration and promotion activities related to P. oocarpa in the state of Chiapas.

The proposed methodology can be used in other regions where (national, state, regional, management, etc.) forest inventories are available, by restricting its definition of the distribution of the species of interest to the area covered by the sampling design.

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Received: September 03, 2018; Accepted: February 20, 2019

Conflict of interests

The authors declare no conflict of interests.

Contribution by author

José Germán Flores Garnica: bibliographical research, modeling and analysis of the results and writing of the document; Oscar Reyes Cárdenas: bibliographical research, analysis of the results and writing of the document.

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