Different Modelling Approaches to Determine Suitable Areas for Conserving Egg-Cone Pine (Pinus oocarpa Schiede) Plus Trees in the Central Part of Mexico

Abstract

Various spatial modelling methods and tools have been used in ecology and biogeography. The application of these options serves a dual function: first, they offer information about the potential distribution of species to understand the richness and diversity of unassessed areas. Second, spatial modelling methods employ these predictions to select relevant sites to determine natural conservation areas. In this study, we compared three methods for modelling the spatial distribution of Egg-cone Pine (Pinus oocarpa Schiede), an important non-timber pine in Mexico. The final goal is to estimate suitable areas for the conservation and reproduction of superior individuals (plus trees) of P. oocarpa as a conservation strategy outside the known distribution since this species possesses a high ecological and economic value. The model used were a generalised linear model (GLM) as a parametric regression method, random forest (RF) as a machine-learning method, and the MaxEnt model, a standard procedure, implemented using the Kuenm R package. The results suggest that the models used performed well since the AUROC was between 0.95 and 0.98 in all cases. MaxEnt and random forest approaches provided more conservative predictions for the distribution of suitable areas of plus trees of P. oocarpa than the generalised linear model, but the random forest algorithm achieved the best performance. The results of the study allowed the determination of ex situ conservation areas for P. oocarpa plus trees outside of their known distribution.

1. Introduction

Forest species have a specific role within the terrestrial ecosystem. They provide goods and services for human communities, sequester carbon from the atmosphere, provide shelter and food to other species, and support biodiversity at different scales [1,2]. However, forests have faced challenges due to anthropogenic factors, and lately, climate change has been considered another factor that pressures the conservation of forest species [3]. The importance of forest conservation strategies takes relevance since they face the task of protecting ecological processes required for the protection of biodiversity over time [4] and, simultaneously, ensuring the provision of ecosystem services to people [5].

Mexico possesses 49 out of the 120 known species of pines [6]; however, most are restricted to specific habitats or suffer some pressure caused by anthropogenic or environmental conditions [7]. Pines in the Mexican territory are found as pure pine forests, pine–oak, and oak–pine forest communities, occurring at various elevations, climates, and exposures [8], representing the ecological biodiversity of the Mexican landscape. In addition to the anthropogenic pressure to which forest species are subject due to their value (economic and social, among others), extreme climatic factors (global warming) represent risk factors for the natural distribution of species [9]. Climate change will likely change species’ range, composition, and abundance in different plant communities [10]. Therefore, special attention should be given to those pine species that require consideration due to their economic, ecological, or social value and their conditions and requirements when defining conservation strategies.

The National Forestry Commission of Mexico states that Pinus oocarpa Schiede ex Schltdl. is arguably the most adaptable to extreme conditions [11], and it is considered a highly adaptative species [12] because of its altitudinal pattern of genetic differentiation of growth [13]. This species is the most resin-producing pine in Mexico [14], and yet, there are no research programmes to propose strategies to increase and make production more efficient. Forest genetic improvement strategies are crucial for enhancing and conserving resin forest species [12]. Genetic improvement should be understood as a long-term process that starts with the base population (e.g., natural stands) to subsequently generate the selection of individuals with superior morphological characteristics, propagation, and improvement of the selected population, where selection and genetic testing are essential [15,16].

In the last five years, a forest genetic improvement program with P. oocarpa began in Mexico to increase resin production based on the selection of “plus trees”. To identify suitable areas for conservation ex-situ of these “plus trees” as a function of the ecological and climatic requirements of the pine and the site’s characteristics, it became essential to examine suitable areas for establishing plantations of P. oocarpa plus trees as a prominent research area in Mexico, especially using different modelling approaches. This study proposes spatial modelling for determining Pinus oocarpa plus tree natural distribution and areas as a tool for defining conservation strategies [17]. We based our analysis on the advantages that ecological niche models combined with spatial modelling and analytical tools (i.e., GIS) offer for ecological and biogeography purposes.

Since conservation strategies must rely on a solid basis, it is essential to determine areas where P. oocarpa trees with superior characteristics (plus trees) are distributed based on spatial modelling and niche ecological models. To ensure the best outcome, we compared three popular niche ecological methods for determining the possible spatial distribution of superior individuals of P. oocarpa. The models used were the generalised linear model (GLM) in its logistic regression form, as a parametric regression method, random forest (RF) as machine-learning method, and the MaxEnt model, as standard procedure. The final goal is to determine suitable areas for the conservation and reproduction of individuals of P. oocarpa that are morphologically superior (selected population) compared to the rest of the population. Our study hypothesised that the models would perform well, but each would define a different area to conserve and reproduce P. oocarpa plus trees.

2. Materials and Methods

2.1. Study Area

The study area was located within temperate forested regions in the central part of Mexico, composed mainly of the genus Pinus [8,18] but including fir, cedar, junipers, and other types of vegetation associated with coniferous trees. Mexican coniferous temperate forests are located primarily on high altitudes over mountainous zones originated by volcanos [8,19] (Figure 1).

The natural distribution of the sampling sites of trees with superior characteristics (resin production) of Pinus oocarpa Schiede is extended to most of the country (15 out of 32 states) in a variety of agroclimatic conditions (

Table 1. Characteristics of the Pinus oocarpa reported in the literature *.

Height (m)	Diameter at Breast Height (cm)	Altitude (masl)	Temp (°C)	Precipitation (mm)
12–18	40–75	Min 1000 Max. 2400 Mean 1800	Min. 3 Max. 35 Mean 19	Min. 650 Max. 2600 Mean 1300

*: National Forestry Commission.

). Since the distribution of the species is too extensive, we focused our study on the central part of Mexico (Figure 1), specifically in the states of Mexico, Oaxaca, and Michoacan.

2.2. Data

2.2.1. Field Data

We conducted field surveys to collect data on the presence of P. oocarpa in the states of Oaxaca, Mexico, and Michoacán through visits to natural populations (Figure 1). We focused on resin-producing plus trees, which were labelled as optimal candidates for conservation/genetic purposes. A plus tree is a tree that is phenotypically outstanding in one or more traits of economic interest, in this case, for resin production. The objective of selecting plus trees is to use them as parents in breeding and production populations.

We recorded geographic coordinates (Datum WGS84), dasometric information (e.g., diameter at breast height, age, height), and other environmental variables at every location. Later, data on the presence of Pinus oocarpa trees were employed to model suitable areas for the distribution of the plus trees.

Since we only record presence data, we generated pseudo-absence observations assuming the same probability of occurrence of P. oocarpa [20]. Therefore, we use the “sdm” package [20] in the R software environment [21] to generate and use the “pseudo-absence” observations to compensate for the lack of “actual absence” data [22,23]. For analysis and modelling purposes, all data were divided for training (70%) and validation (30%) of the models.

2.2.2. Geographic Data

We used land cover and vegetation type maps at the national level at a scale of 1:250,000 (25-hectare minimum mapping unit geographic data) produced and published by the National Institute of Statistics and Geography of Mexico (INEGI, 2017). Using this layer (the sixth version of the land cover map), we isolated temperate forests where P. oocarpa is distributed and provided a spatial and temporal context for the analysis. Later, we create slope and aspect layers from a national digital elevation model (DEM) raster dataset with approximately 90 m pixel size for further analysis.

2.2.3. Climatic Layers

The climatic data layers used for modelling in this study were updated high-resolution (90 m pixel size) climatic surfaces for Mexico for the average monthly climate period 1910–2009 (https://rmets.onlinelibrary.wiley.com/doi/full/10.1002/joc.3848, accessed on 22 September of 2021). The layers correspond to monthly precipitation values, daily maximum and minimum temperature, and other bioclimatic variables derived from the monthly precipitation and temperature values [24] (

Table 2. Climatic and environmental variables used in this study.

Environmental Variables	Units	Variable Code
Annual mean temperature	°C	Bio1
Mean diurnal range (mean of monthly (max temp–min temp))	°C	Bio2
Isothermality (BIO2/BIO7) (multiply by 100)	°C	Bio3
Temperature seasonality (standard deviation multiplied by 100)	%	Bio4
Max temperature of the warmer month	°C	Bio5
Min temperature of the coldest month	°C	Bio6
Temperature annual range (Bio5-Bio6)	°C	Bio7
Mean temperature of wettest quarter	°C	Bio8
Mean temperature of driest quarter	°C	Bio9
Mean temperature of warmest quarter	°C	Bio10
Mean temperature of coldest quarter	°C	Bio11
Total precipitation	Mm	Bio12
Precipitation of the wettest season	mm	Bio13
Precipitation of the driest season	mm	Bio14
Precipitation seasonality (coefficient of variation)	%	Bio15
Precipitation of the wettest quarter	mm	Bio16
Precipitation of the driest quarter	mm	Bio17
Precipitation of warmer quarter	mm	Bio18
Precipitation of the coldest quarter	mm	Bio19
Altitude	masl	Altitude
Aspect	Degrees (°)	Aspect
Slope	Degrees (°)	Slope

).

2.3. Description of the Models Used

2.3.1. Generalised Linear Model (GLM): Logistic Regression

GLMs are mathematical extensions of linear models that do not force data into unnatural scales, allowing for non-linearity and non-constant variance structures in the data [25,26]. GLM consists of three components. First is the random component, the response variable, and probability distribution. Second is the systematic component, which represents the model’s predictors (X variables). The third is the link function, which links the random and systematic components. GLMs are considered parametric models because a probability distribution is specified for the response variable and, therefore, for the error terms from the model [27]. One significant application of GLMs in biology is to model binary response variables (e.g., presence/absence, alive/dead) in logistic regression, where the predictors can be either continuous and/or categorical. Logistic regression was selected for modelling the possible spatial distribution of the P. oocarpa plus trees.

In logistic regression, when the response variable is binary (i.e., categorical with two levels, zero or one), we model (x), the probability that Y equals one for a given value of X. The usual model we fit such data with is the logistic regression model, a nonlinear model with a sigmoidal shape. The change in the probability that Y equals one for a given change in X is most significant for values of X near the middle of its range rather than for values at the extremes. The error terms from the logistic model are not normally distributed; because the response variable is binary, the error terms have a binomial distribution. Then, the logistic regression model is $Y=E\left(Y\right)+\epsilon$, and $E\left(Y\right)=\pi$ is expressed as [28,29]:

$$E\left(Y\right)=\pi =\frac{\exp \left(X^{\prime }\beta \right)}{1+\exp \left(X^{\prime }\beta \right)}$$

where $E\left(Y\right)$ is the response variable taking only values of 1 and 0 with probabilities $\pi$ and 1 − $\pi$, respectively.

2.3.2. Random Forest

The random forest algorithm is a machine learning method that can be defined as an ensemble of multiple decision trees at training time. This modelling method uses bagging (bootstrap aggregation) to combine many trees. Bagging involves taking many bootstrap samples from the training data, fitting a tree to each sample, and making an average prediction over all fitted trees [30]. In this study, we used the random forest method’s occurrence probabilities for P. oocarpa [31].

We implemented the random forest method by following the typical steps [32]: (i) the samples are bootstrapped from the original dataset to generate multiple sets (ntree) of training data; (ii) unpruned regression trees are created with the bootstrapped samples, and in each node of the tree, a subset of variables is selected randomly to define the split (mtry), and the best split is chosen; and (iii) predictions are made by averaging the predictions of the ntree regression trees. The random forest method was implemented inside the R environment using the random forest package [33].

2.3.3. MaxEnt

Maximum entropy ecological niche modelling (MaxEnt) [34] predicts species occurrences by applying a machine learning technique called maximum entropy modelling. From a set of environmental datasets and georeferenced points, the model estimates a probability distribution where each grid cell has the expected suitability of conditions for the species of interest. This study implemented the MaxEnt model employing the Kuenm package [35] in the R statistical software environment [21]. Kuenm is an R package for the detailed development of ecological niche models using MaxEnt. In essence, Kuenm automates essential calibration and evaluation steps using the Maxent modelling algorithm, systematises model calibration, creates final models and their transfers and evaluations, and assesses extrapolation risks.

2.3.4. Model’s Validation

We calculated all models’ sensitivity, specificity, and concordance indices as measures of goodness of fit. These metrics were calculated on the validation sample separated for validation purposes and independent from the training set. Later, we estimated the overall accuracy metric from the confusion matrix of each model. Additionally, we used all models’ calculated receiver operating characteristic (ROC) curves and the true skill statistic (TSS) for comparison purposes. Next, these two metrics were used to evaluate model performance according to previous studies [36,37,38]. It is worth noting that TSS has become popular due to its simplicity (sensitivity + specificity − 1) but robust and intuitive measure of the performance of species distribution models [38].

2.4. Identifying Areas for Conservation Purposes (Ex Situ) of the Species

After evaluation, we applied the models to prepare maps of suitable areas for P. oocarpa. First, we classified the different probability categories from each model to obtain a binary map (suitable, not suitable) based on the premise that all pixels with values above 0.56 were reclassified as suitable and pixels below 0.56 as non-suitable for the establishment of the species (

Table 3. Parameters to classify land suitability of Pinus oocarpa trees.

Probability of Occurrence	Category	New Pixel Value
0.0 to 0.1	Non-suitable	0
0.12 to 0.25	Non-suitable	0
0.26 to 0.40	Non-suitable	0
0.40 to 0.55	Non-suitable	0
0.56 to 1	Suitable	1

).

Here we assumed that the three models used in this study estimate probability of occurrence of P. oocarpa plus trees. Once we produced binary maps (0′s and 1′s), we used the vegetation and land cover map provided by INEGI to isolate the categories “grasslands”, “secondary vegetation of temperate forests”, “no visible vegetation”, and “Agriculture” and used them as potential zones for the establishment of conservation areas of the species outside of natural pine forests. All the analysis and spatial processes were made inside the software Arc View^® version 10.8 environment.

3. Results

After the field campaign, we identified and selected 285 individuals of P. oocarpa that demonstrated superior characteristics compared to the rest of the population. It is worth noting that the biggest tree was in the state of Michoacan (36.7 m height and 130 cm of diameter at breast height); according to

Table 4. Characteristics of the Pinus oocarpa trees used in the study.

Location	Mean Height (SD)	Mean Diameter at Breast Height (SD)	Age (SD)	Observations of Presence
Mexico State	19.05 (4.98)	44.68 (12.11)	71 (20)	100
Michoacan	21.19 (5.47)	59.76 (15.75)	62 (20)	99
Oaxaca	19.86 (4.96)	47.04 (10.33)	63 (23)	86

SD: standard deviation.

, Michoacan possesses the trees with the best dimensions, followed by Oaxaca and Mexico State.

The spatial distribution of the P. oocarpa plus trees was characterised by their preference for high altitudes in the Trans-Mexican Volcanic Belt (above 1400 masl) for Mexico State and Michoacan and moderate slopes (10 to 40%). However, for Oaxaca’s case, the distribution range varies from 860 to 1390 masl and steep slopes (25 to 90%) (Figure 2).

3.1. Generalised Linear Model (GLM) and Logistic Regression Modelling

The generalised linear model family selected logistic regression to predict the potential distribution of P. oocarpa. Logistic regression presumes the probability distribution as the response variable; therefore, the error terms from the fitted model are effectively explained by the chosen random component [39]. Here the best model fitted used climatic variables related to precipitation (bio12, bio13, bio17, bio19, bio14), temperature (bio02 and bio04), and topography (slope) (Table 4).

The model predicted a probability of occurrence where values close to 1 represent areas where the species has better chances of being present or established. The area with a probability higher than 56%, as was stated before, was classified as suitable for the development of plus trees of P. oocarpa. Those areas were located at high elevations and well distributed across the study area (Figure 3).

3.2. Random Forests

We used a bagging procedure for averaging the outputs of different CARTs (classification and regression trees) for the random forest modelling process. Bagging stands for “bootstrap aggregation”. An essential feature of random forests is the out-of-bag samples, which means that the prediction/fit for a specific data point is only derived from averaging trees that did not include this data point during tree growing [31]. Thus, the output of random forests is essentially cross-validated. Random forests estimate variable importance by a permutation procedure, which measures for each variable the drop in mean accuracy when this variable is permutated. For our case, the variable importance can be seen in Figure 3; Bio04, Bio05, Bio13, and Bio16 were the most important for modelling (Figure 4).

The procedure used for the random forest model was a regression, using a total of 250 trees, and was able to explain 92.5% of the variability with a mean of squared residuals of 0.018. The final regression tree (Figure 5).

Finally, we applied the regression model to predict the spatial distribution of P. oocarpa plus trees and created a raster file using the function “writeRaster” within “R” software. Later the raster was exported to ArcGIS, and we classified all pixels above 0.56 (56% of probability) as suitable areas for the development of the trees (Figure 6).

3.3. MaxEnt

A total of 434 candidate models were analysed, with parameters reflecting all combinations of 14 regularisation multiplier settings (variables), 31 feature class combinations, and one distinct set of environmental variables. Model performance was evaluated based on statistical significance (partial ROC), omission rates (OR), and the Akaike information criterion corrected for small sample sizes (AICc) (

Table 5. Parameters for modelling potential distribution using the GML approach.

Model	Estimates	Standard Error	p Value
$\begin{array}{ll}\widehat{{\pi }^{\prime }}=lo{g}_e\frac{\widehat{\pi }}{1-\widehat{\pi }}& ={\beta }_0+{\beta }_1\left(bio12\right)+{\beta }_2\left(bio13\right)+{\beta }_3\left(bio17\right)\\ & +{\beta }_4\left(slope\right)+{\beta }_5\left(Bio02\right)+{\beta }_6\left(bio04\right)\\ & +{\beta }_7\left(bio19\right)+{\beta }_8\left(bio14\right)\end{array}$	2.6049 0.0435 −0.1623 −0.3899 −0.2800 −0.6139 0.0138 0.0980	3.5611 0.0050 0.0195 0.0926 0.0640 0.2743 0.0110 0.02747	0.4644 <0.0001 <0.0001 <0.0001 <0.0001 0.025 0.2077 <0.0001

).

The distribution model generated by MaxEnt for P. oocarpa was different concerning the scope of the prediction area; however, the model generated AUC values close to 1, which is supported by a fastness statistic. AUC values of 0.5 and close to 1 indicate that the generated model is better than the prediction.

Table 6. General statistics of models that met distinct criteria.

Criteria	Number of Models
All candidate models	434
Statistically significant models	434
Models meeting omission rate criteria	108
Models meeting AICc criteria	8
Statistically significant models meeting omission rate criteria	108
Statistically significant models meeting AICc criteria	8
Statistically significant models meeting omission rate and AICc criteria	1

summarises the performance statistics of applying the MaxEnt model using the Kuenm package to estimate the potential spatial distribution of plus trees of P. oocarpa.

Table 7. Performance statistics for the best models selected.

Model	Mean AUC Ratio	Partial ROC	Omission Rate at 5%	AICc	W_AICc	Parameters
Pinus oocarpa	1.94	0	0.049	7394.212	0.947	24

shows the performance of the best model selected.

Figure 7 shows the position of the selected models in the distribution of all candidate models in terms of statistical significance, omission rates, and AICc values.

The MaxEnt model assigns the increase in gain to the environmental variables that are occupied, converts values to percentages, and creates a test to estimate the most critical variables in the model (jackknife), by using the Kuenm package. According to the results, the temperature was the most crucial factor in determining suitable areas for the species. Temperature seasonality, minimum temperature of the coldest month, mean temperature of the driest quarter, and precipitation of the wettest quarter accounted for more than 80% of the contribution of the predictive model (

Table 8. Top predictors and their percentage contribution reported from the Maxent model for Pinus oocarpa.

Predictor Variable	Contribution (%)
Temperature seasonality (Bio 4)	20.50
Min temperature of the coldest month (Bio 6)	18.16
Mean temperature of the driest quarter (Bio09)	15.44
Precipitation of wettest quarter (Bio16)	13.21
Precipitation seasonality (Bio 15)	8.38
Precipitation of the wettest season (Bio 13)	5.60

). It is worth noting that four variables related to temperature comprised about 70% of the contributions.

The potential spatial distribution generated for plus trees of P. oocarpa is shown in Figure 8, where the higher probabilities of the presence of the pine are in well-conservated forest areas and elevations over 2000 m above sea level (Figure 8).

3.4. Validation of the Models

In this work, the AUC value was taken as a primary measure of model performance since this metric provides a reliable and fast way to assess the performance of the distribution models [40]. The total potential distribution generated with the different approaches used in this work for plus trees of P. oocarpa indicates reliable modelling since the AUC was very high for all cases: 0.93, 0.99, and 0.97, for logistic regression, random forests, and MaxEnt, respectively (Figure 9).

As can be seen in Figure 9, the best performance was achieved using the random forest modelling approach. According to previous studies, random forests have been evidenced to be a machine learning algorithm that outperforms other methods [36,41,42].

Table 9. Validation metrics used for comparison purposes.

Model	AUC	TSS	Accuracy
Logistic	0.93	0.67	0.83
Random forest	0.99	0.93	0.96
MaxEnt	0.97	0.76	0.81

shows the performance of the models; it is worth noting that although accuracy was adequate in all cases, the random forest modelling demonstrated higher values for AUC, TSS, and accuracy.

3.5. Identifying Areas for Conservation Purposes (Ex Situ) of the Species

The land cover map distributed by INEGI has around 72 categories representing the types of vegetation present in the country. We performed discrimination of all the categories listed to focus on those potentially eligible for the establishment of conservation areas ex situ (plantations) of P. oocarpa plus trees. The categories “grasslands”, “secondary vegetation from temperate forests”, and “Agriculture” from the land cover map were selected as a target for this purpose (

Table 10. Land suitability for the establishment of plus trees of P. oocarpa.

	Suitable Area (ha)
Land Use	Logistic	Random Forest	Max Ent
Agriculture	85,497.93	25,446.15	8689.68
Grasslands	139,452.8	29,205.36	12,729.15
No vegetation	220.32	150.66	0
Secondary vegetation	576,968.7	104,869.89	39,681.9
Total	802,139.8	159,672.06	61,100.73

).

After evaluation, we applied the models to prepare maps of suitable areas for P. oocarpa, considering the above land categories. In all cases, according to the validation metrics used, the models demonstrated good agreement regarding accuracy; however, it is worth noting that the models estimated different amounts of a suitable surface for each one of the land use categories used. The spatial distribution of the suitable areas for the development of plus trees of P. oocarpa is shown in Figure 10.

4. Discussion

Numerous spatial modelling methods and tools have been developed recently, although they have mainly been used in ecology and biogeography for conservation purposes, predicting future impacts and determining suitable areas for species [42,43]. The use of these alternatives serves a dual function: firstly, they provide insights into the distribution potential of species to understand the richness and diversity of areas with little or no information. Secondly, they use these predictions to select sites of interest for determining biological conservation areas or establishing species where they do not naturally occur [17,44]. Spatial modelling to determine the natural and suitable ranges of the forest species of interest has been used to define strategies for conservation, planning, and management of the species in the face of climate change. For this purpose, spatial modelling and mainly ecological niche models, together with other analytical tools (e.g., geographic information systems, GIS), have been used to assess species’ climatic requirements and to model their distribution under current and future conditions [40,41,45].

In this study, we used the advantages of the ecological niche models combined with geographic tools to define areas suitable for establishing P. oocarpa plus trees according to their natural and potential distribution. The evaluation of suitable areas for plantation establishment remains a prominent area of research in Mexico, especially using different spatial modelling approaches, such as logistic regression, decision trees, multi-criteria analysis, and artificial intelligence algorithms. Using these tools is critical in identifying impacts on resin pine trees, considered species with a high adaptive capacity [8]; however, these species’ growth tolerance and survival intervals have not been described in the necessary detail. Therefore, it is considered essential to estimate suitable areas for ex-situ conservation based on the species ecological requirements and the site’s characteristics. These factors, mainly climatic, condition the growth and resin production [46], so it is important to determine them and use them in the planning processes to establish plantations.

Conservation strategies for species of interest include collecting, storing, and conservating germplasm in botanical gardens, germplasm banks, and plant tissue culture laboratories in Mexico [46]. P. oocarpa may have a high adaptive capacity. It is crucial to determine the tolerance intervals of the populations for good growth and survival rate. Therefore, it is essential to generate the potential zoning, a function of the species ecological requirements and the site’s characteristics, factors that condition the trees, and their production levels [47,48]. The delimitation of areas by productive potential allows for the efficient use of resources [49,50].

4.1. Implications and Conservation Strategies

Although it is considered that widely distributed species such as P. oocarpa may have a high adaptive capacity, it is essential to determine the environmental tolerance intervals of the populations for good growth and survival rate. For example, P. oocarpa seedlings from populations originating at lower altitudes tend to grow larger than seedlings originating from populations at higher altitudes [51]. Therefore, it is essential to generate the potential zoning, a function of the species ecological requirements and the site’s characteristics, factors that condition the trees, and their production levels [47,48]. The delimitation of areas by productive potential allows for the efficient use of resources [49,50].

Our results suggest that the best conditions for the optimal development of P. oocarpa are related to temperature seasonality (Bio04) and precipitation of the wettest season (Bio13), the first variable in all models and the former in two. Similarly, the growth of P. oocarpa seedlings in Michoacán, Mexico was related to the annual humidity index, annual temperature, precipitation, summer humidity index, and degree days of the source populations [51]. This highlights the importance of defining areas for the conservation and reproduction of plus trees of P. oocarpa through the modelling of potential distribution in this study. Likewise, shared garden and field trials are necessary for a second phase to define the geographical limits to establish conservation and reproduction plantations without sacrificing adaptation [13,51,52,53].

It is also important to highlight that the potential distribution modelled agrees with the ecological and climatic requirements of the species since P. oocarpa grows at altitudes between 700 and 2000 m above sea level, with regular dry seasons and severe drought (total rainfall of 500 mm) [11,12,47]. Since we are focused on plus trees, the ecological and climatic requirements were narrowed, as the results demonstrated, and the potential distribution was set in regions where this species grows naturally, where there are six months with an average rainfall of less than 50 mm. Additionally, all suitable areas are where the species grow naturally and are in eroded soils derived from ancient volcanic material and containing a large amount of quartz. It has been stated that the optimum temperature for the growth of this species is between 13 and 23 °C [47]. However, it can withstand certain minimum temperatures of 0 °C and maximum temperatures of 45 °C, and P. oocarpa can withstand sporadic frosts. Precipitation in the pine habitat is around 1300 mm per year, with a minimum of 500 and 2600 mm per year [14,54].

In Mexico, conservation strategies for species of interest are varied, including Protected Natural Areas (ANPs), ecological planning, Management Units for the Conservation of Wildlife (UMAs), payment for environmental services, and community forest management [N], as well as the collection, storage, and conservation of germplasm in botanical gardens, germplasm banks, and plant tissue culture laboratories in Mexico [55]. The P. oocarpa plus trees sampled in this study are not located in ANPs. The plus trees in Oaxaca are more than 60 km from the Lagunas de Chacahua National Park, with a difference of more than 500 m in elevation. The plus trees in the State of Mexico are 5.7 km from an ANP (Forest Protection Zone, the constitutive lands of the basins of the Valle de Bravo, Malacatepec, Tilostoc, and Temascaltepec rivers), but with a difference of 300 m in elevation. Meanwhile, the trees in Michoacán are more than 10 km from the Zicuirán-Infiernillo Biosphere Reserve, with more than 800 m of altitude difference. Due to the above, these trees’ in situ conservation strategy in PNAs is not an alternative.

Although in situ conservation is essential to renew genetic diversity and face future environmental changes, ex situ conservation is operationally convenient for short-term results [56]. Regarding the ex situ conservation of plus trees of P. oocarpa in PNA, of the 159,672.06 ha estimated with the RandomForest model as surface suitable for conservation, only 15.08 ha is located within the “Sierra de Huautla Biosphere Reserve”, 73.8 ha in the “Forest Protection Zone the constitutive lands of the basins of the Valle de Bravo, Malacatepec, Tilostoc and Temascaltepec rivers”, and 1251 ha in the “Zicuirán-Infiernillo Biosphere Reserve”. The preceding shows that only 0.84% of the area located within a PNA is suitable for conservation for plus trees of P. oocarpa; compare to sites that can be established plantations exclusively dedicated to ex situ conservation. This shows that the PNA network in Mexico does not adequately protect Pinus [57] species, so in situ and ex situ conservation activities must be proposed for each species [9].

Among the viable alternatives for the in situ conservation of P. oocarpa plus trees is the establishment of Management Units for the Conservation of Wildlife (UMAs), in which owners can make sustainable use of the habitat by harvesting seeds and, at the same time, work on the conservation of the species [17,55]. It is suggested that the main ex situ conservation strategy be the establishment of conservation plantations in the areas determined in this study. However, to mitigate the future effect of global climate change, conservation and production plantations, with plus tree germplasm of P. oocarpa, should be established at altitudes higher than their natural origin, up to 150 m [51].

Another ex situ conservation strategy is establishing plantations for resin production with plus tree germplasm of P. oocarpa in the suitable areas determined in this study. These production plantations must be linked to a genetic improvement program [15,16]. A forest genetic improvement program begins with the selection of the base population (natural stands) to obtain the selected population (plus trees). It continues with the propagation and breeding populations to generate the first improved generation, where genetic tests play a fundamental role [15,16]. The selected population comprises plus trees located in natural stands in the study area of this work; the care and maintenance of these trees are a viable in situ conservation strategy through UMAs. The population of propagation and crossing is constituted by the seed orchards, the product of the recurrent additional selection; in this case, three seed thefts were established with plus tree seeds in suitable areas determined in this study. These seed orchards constitute an essential in situ conservation strategy for P. oocarpa plus resin trees. Genetic tests such as progeny tests, which should be established in sites where it is required to test the performance of P. oocarpa plus trees, will constitute an ex situ conservation strategy [16].

For P. oocarpa, there is an altitudinal pattern of genetic growth differentiation [51], a significant linear relationship between latitude and longitude of populations with survival and frost tolerance [52], genetic groups correlated with geography, two centres of diversity [58], and interfamily variation in growth [13]. The preceding demonstrates the importance of conducting detailed studies to conserve P. oocarpa plus trees. Among the actions that will contribute to the conservation of P. oocarpa plus trees is the study of the reproductive potential (seed production and germination), the quality of plants, the chemical quality of resin, and the study of genetic diversity. Several of the above studies are underway to improve and conserve plus resin trees in Mexico. Although some natural populations of P. oocarpa are high [13,59], it is necessary to evaluate the genetic diversity of selected trees to generate guidelines for conservation and genetic improvement [16]. Superior phenotypes should be evaluated using progeny testing in the areas determined in this study to estimate genetic variation, genetic gain, heritability, and genetic correlations between various traits, which will allow the identification of genotypically superior families [15,16,53]. To evaluate these genetic parameters related to resin production, trees need to grow to a diameter sufficient to allow resin production.

To establish seed orchards, one must start with selecting individuals in natural stands, which may imply low genetic diversity; however, this depends on population size and other factors such as the number of parents in the orchard, seed orchard design, fecundity, and pollen contamination. Although seeds from seed orchards are used in large regions, very few studies have compared the genetic diversity in the orchard concerning the genetic diversity of the regions where they are planted [60]. Genetic variability between altitudinal gradients and between different natural populations of P. oocarpa has been assessed utilising isoenzymes [59], DNA markers [61], and quantitative morphological data [51]. However, there are no known studies on the genetic variability in high-quality seed orchards.

4.2. Model Selection and Implications

Ecological niche modelling as a set of analytical tools has been used in many different applications, including conservation strategies [17], climate change impacts [62], and forest insect outbreaks [63], among other applications in ecology and biogeography [64]. In the last couple of years, ecological niche modelling based on machine learning tools has gained popularity in determining forest species’ land suitability or potential spatial distribution [44,65,66]. Machine learning algorithms are relatively more flexible and accurate and require less time than traditional methods. In the last couple of years, machine learning methods have been proven to be more adequate for noisy or sparse data than many well-known methods [32].

Although computational improvements and programming efficiency facilitate the use of machine learning algorithms in ecological niche modelling, methods such as MaxEnt are still in use due to their simplicity of application and the flexibility of adaptation to several situations [22,23,24]. One good example is the Kuenm R package [38], which uses R and MaxEnt to enable detailed model calibration and selection, final model creation, and extrapolation risk analysis. In this study, the Kuenm R package results demonstrated promising results (AUC = 0.97, TSS = 0.76 and accuracy = 0.81) compared to those obtained using random forests (AUC = 0.99, TSS = 0.93 and accuracy = 0.96). In both cases, model selection, calibration, and validation are easy to follow, allowing the user to choose one method.

One significant advantage of using ML, e.g., random forests, is that there is no limitation on the number of predictor variables used compared to the traditional approaches. More traditional approaches, such as general linear and occupancy, depend on technical expertise to meet statistical assumptions and produce unbiased output [31,67], which makes machine learning methods even more attractive to use. Another advantage of the random forest model is its strength in efficiently recognising data patterns, lack of assumptions related to the properties of the data, user-friendly parameters, and ability to address the interactions between predictive variables [30] flexibly. Additionally, random forests modelling has been recognised to be solid for training with small sample sizes [32]. We confirmed the advantages and better performance of machine learning methods, such as random forest, over traditional methods as demonstrated by our results according to the comparison metrics used in this study.

4.3. Final Considerations

In this study, we determined the primary potential distribution and determined areas of possible interest to establish plus trees of P. oocarpa. It is essential to highlight that the spatial distribution and number of observations collected and retrieved from the diverse databases were essential factors in the performance of all models and the ability to predict the spatial distribution of the pine accurately. Although it was not part of this study, it would be worth performing an analysis by region, including other crucial variables such as distance to roads or population density, as they are considered factors in the vulnerability of Mexican forests [59]. It is important to highlight that land cover change affects suitable species distribution areas.

In this paper, we reported three methods for modelling the spatial distribution of modelling P. oocarpa, an important non-timber pine in Mexico. According to the results, we could estimate suitable areas for the conservation and reproduction of superior individuals (plus trees) of P. oocarpa as a conservation strategy outside the known distribution since this species possesses a high ecological and economic value. We had a limited number of observations from the field due to the specificity of the study and the morphological characteristics of the trees we were looking for; however, we considered the dataset to be enough and that it fulfilled the study’s objectives.

Although species distribution models (e.g., MaxEnt algorithm) can fit with limited presence-only data [64], random forests was considered a better option as it presented the best performance according to the metrics used compared to MaxEnt and logistic regression [16,65]. Still, some issues need to be considered before selecting the appropriate modelling method: the clarification of the niche concept, sampled data, parametrisation strategies, model selection, predictor contribution, and evaluation strategies [66]. That being said, our results demonstrated good agreement with the performance of all models according to the validation process.

Finally, we would like to highlight that the novelty of the work we presented in this paper is significant to forest planners and decision-makers because it provides evidence of the use of spatial modelling to define conservation areas for specific target species. The authors’ consideration for future research endeavours concerns the addition of the impacts of climate change on species distribution modelling to deliver more complete and accurate results for the operation of conservation plans and the genetic improvement programmes for Pinus oocarpa.

5. Conclusions

The models presented good performance; each estimated varied surfaces for the conservation and reproduction of P. oocarpa plus trees.

The random forest model performed better, providing a more conservative prediction. This study’s definition of suitable areas for conservation and reproduction contributes to defining ex situ conservation strategies for P. oocarpa plus trees.

Our findings agreed with previous reports that machine learning algorithms have superior performance compared to traditional ecological niche and spatial distribution modelling methods.