Study area

The present research was carried out at the Metzabok Protected Natural Area (PNA), located in the northeast of the Selva Lacandona (17°08’ 36’’N and 91°34’42’’ W), in the Lacandona sub-community of Puerto Bello Metzabok, Ocosingo, Chiapas. This PNA has a surface area of 3 368 ha, at an altitude of 545 to 950 m (^{Conanp, 2006}). The climate is Af(m)w”(i)g, warm humid with rains throughout the year, a mean annual temperature of 24 °C and a mean annual precipitation of 3 160 mm (^{García, 2004}). The soil types are redzins, luvisols, gleysols, vertisols, cambisols and litosols (^{Sánchez-Gutiérrez et al., 2017}). According to the classification by ^{Miranda and Hernández-X (2014)}, the predominant vegetation is high evergreen tropical rain forest.

Altitude stratification and sampling

Five altitude strata were determined (AS1= < 600 masl, AS2= 600-700 masl, AS3= 700-800 masl, AS4= 800-900 masl, and AS5= > 900 masl) based on the generation of level curves at intervals of 100 m using the Global Mapper software, version 15. In each stratum, a 20 × 50 m (1 000 m²) sampling unit (SU) was installed, as shown in Figure 1; these sampling units were divided into ten 10 × 10 m (100 m²) sampling sub-units (SSU). In each SSU, all individuals of the stem class (reproductive trees) with normal diameter (DN) ≥ 2.5 cm were measured with diametric tape (Richter Messwerkzeuge, 283D/10M model) and located by their Cartesian coordinates (x, y) (^{Linzaga -Román et al., 2011}; ^{Dale and Fortin, 2014}); the lower left corner of the plane was taken with respect to the slope of each SU as the origin (0, 0), as suggested by ^{Ruiz-Aquino et al. (2015)}. Within Each SSU, a 5 × 5 m square was installed at random in order to register its saplings (young trees with a ND of < 2.5 cm and a height of > 1.5 m), and in each of these squares, two 2 × 2 m squares were established for the inspection of individuals classified as seedlings (with a height of < 1.5 m) (^{Zarco et al., 2010}).

Simbología = Simbology; Unidad de muestro = Sampling unit; Cuerpos de agua = Bodies of water; EA = AS

Figure 1 Location of the sampling units (SU) in each altitude stratum (AS) of the Metzabok Protected Natural Area, in the Selva Lacandona of Chiapas. 

The taxonomic identity of the individuals was determined with the support of the staff of the “ECOSCH-H” Herbarium of the Colegio de la Frontera Sur (Ecosur) (College of the Southern Border) in San Cristóbal de las Casas, Chiapas. The nomenclature was validated on the website Tropicos.org of the Missouri Botanical Garden (2008).

Spatial distribution analysis

Three height categories (lower, intermediate, higher) ―obtained from the inflection curves in the paper by ^{Sánchez-Gutiérrez et al. (2017)} ― were used for estimating the spatial distribution of the pole-sized trees. The spatial distribution pattern of the seedling and sapling development stages, as well as the height categories of the pole-sized trees, were determined using the Morisita-Horn index (^{Morisita, 1959}); when their value is equal to 1, the distribution is random; when it is > 1, it is clumped, and when it is < 1, it is uniform (^{Morisita, 1959}; ^{Zarco et al., 2010}; ^{Rivera-Fernández et al., 2012}). The Morisita-Horn index is defined in Equation (1):

Where:

Iδ = Spatial distribution index

q = Number of squares

ni = Number of individuals in the i ^th square

N = Total number of individuals in all the q squares

In order to obtain a more statistically robust and graphically representative index (^{Rozas and Camarero, 2005}; ^{Ledo et al., 2012}; ^{Dale and Fortin, 2014}), Ripley’s K(t) function was also calculated (^{Ripley, 1977}) for the spatial distribution of the height categories of the pole-sized trees, based on Equation (2):

Where:

n = Number of individuals of the sampling unit (SU-A)

(A( = Surface area of the SU-A (m²)

u _ij = Distance between the i^th and j ^th individual in the SU-A

t = Distance between two trees (m)

I _t (u) = 1 if u ( t and 0 u > t

W _ij = Proportion of the circumference of a circle with a center in SU-A (the summation of two the pairs of individuals ≤ t)

The variance was established by using the transformation of the square root of Ripley’s K(t), and the significance of the L(t) was determined based on Monte Carlo simulations (^{Besag, 1977}). The maximum and minimum limits of L(t) were defined with a confidence interval of 99 %:

Where:

K(t) = Ripley’s univariate function

π = 3.1416

t = Distance (m)

If the value of L(t) = 0, the spatial pattern with a t radium is random; L(t) > 0 indicates clumping and L(t) < 0 indicates a uniform pattern.

Spatial correlation

The spatial correlation between height categories (lower-intermediate, lower-higher, and intermediate-higher) of the pole-sized tree species was analyzed using the L ₁₂ (t) bivariate function, derived from the K ₁₂ (t) function (^{Ripley, 1977}):

Where:

K ₁₂ (t) = Ripley’s bivariate function

π = 3.1416

t = Distance (m)

A L ₁₂ (t) value = 0 indicates that the two groups are spatially independent; L ₁₂ (t) > 0 refers to a positive association (attraction), and L ₁₂ (t) < 0 expressed a negative association (repulsion). The significance (p ≤ 0.01) of L ₁₂ (t) was determined with Monte Carlo simulations (^{Besag, 1977}; ^{Dale and Fortin, 2014}), and the maximum and minimum limits were defined with a 99 % confidence interval. Ripley’s univariate and bivariate patterns were generated with the Toolbox software (^{Fisher, 2000}).

Spatial distribution patterns of tree species

According to the Morisita-Horn index, the spatial distribution pattern of the tree species for pole-sized tree species in all five AS and for all three height categories (lower, intermediate and higher) had a clumped average behavior (Iδ=1.04) (Table 1), contrary to the proposed hypothesis. This finding is similar to that reported for the Selva Lacandona of Chiapas in the study by ^{Martínez-Ramos (2006)}, according to whom more than 60 % of the tree taxa were distributed in a clumped form.

It is worth noting that the general pattern recorded in the present study shows the differences when analyzed by AS. The lower height category exhibited a random and a clumped pattern at a lower and higher altitude, respectively (AS4 and 5) (Table 1). The cause of the clumped pattern is considered to be the clearings formed by natural disturbances: the fall or death of trees, pests and diseases (^{Brown et al., 2015}); these are colonized by pioneer species, whose regeneration depends on sunlight and seeds with a lower range of dispersion (^{Hubbell, 2001}).

However, the presence of both spatial patterns (random and clumped) in the present studio can also be the result of human activities that have modified the habitat and directly affected the survival, reproduction and establishment of the species, as proven by ^{Pavón-Hernández and Rico-Gray (2004)} for a transformed landscape in the state of Veracruz, Mexico.

The intermediate height category exhibited a random behavior (Iδ=1.0) along the altitude gradient, with the exception of AS2, which showed a clumped behavior (Iδ=1.3 (Table 1). The later pattern is due to the inclination of the slope (30 to 70°) revealed by the stratum, as well as to shallow soils that prevent the growth of the root system of the trees, as suggested by ^{John et al. (2007)} for various tropical taxa in the world.

Other studies (^{Blach‐Overgaard et al., 2010}) have shown that the cause of the clumped pattern in tropical rain forests is the fact that the rainy season is associated to strong winds, which promote the falling of trees, whereby microclimates are formed that favor repopulation in clusters. According to ^{Martínez-Ramos (2006)}, the clumped pattern is related to the topographic and edaphic characteristics; however, it has also been suggested that it can be due to deficient dispersion mechanisms of seeds and low seed depredation (^{Franklin and Rey, 2007}; ^{Hosaka et al., 2017}).

For the higher height category, the distribution of the species (Sebastiana longicuspis Standl, Pseudolmedia spuria (Sw.) Griseb, Manilkara zapota (L.) Royen and Pouteria reticulata (Engl.) Eyma) was uniform at a higher altitude and clumped at a lower altitude (Table 1). The clumped pattern in this category is considered to be caused by closeness to the community, as these are areas where the commoners extract timber for domestic use ―a situation that generates the formation of clearings which are taken up by a group of species (Dialium guianense (Aubl.) Sandwith, Heliocarpus appendiculatus Turcz. and Pseudolmedia oxiphyllaria Donn. Sm.) that need direct sunlight to grow and develop (^{Conanp, 2006}; ^{Rivera-Fernández et al., 2012}).

The sapling and seedling development stages profiled a clumped pattern, except for the last AS5 (> 900 masl), in which a random behavior was observed (Table 1). The clearings allow entry of the sunlight, which affects the incorporation and growth of undergrowth plants (^{Martínez-Ramos, 2006}), as in the case of saplings and seedlings. Therefore, any alteration of the characteristics of the canopy has an impact on germination, growth rate, survival and the distribution of the plants (^{Brienen and Zuidema, 2006}; ^{Yili et al., 2013}), given the specific dominant conditions within the clearing that promote the clustering of the species.

^{Martínez-Ramos (2006)} cites that the clumped pattern is greater in small individuals (with a ND of 1 to 5 cm) than in larger individuals (ND ≥ 10 cm), which have a random distribution. Actually, in the random pattern, individuals are totally independent from the position of any other individual in the population; this behavior occurs only in certain species of temperate forests (^{Hernández et al., 2018}), but it is very common in tree individuals of tropical rain forests (^{Franklin and Rey, 2007}; ^{Yili et al., 2013}).

The results of this study suggest a certain tendency with altitude gradients and indicate that, at the Metzabok PNA, there is a climate variation by gradient that modifies the structure and the makeup of the rain forest; this agrees with other studies on tree structure, composition and diversity performed in the same study area (^{Martínez-Ramos, 2006}; ^{Sánchez-Gutiérrez et al., 2017}). While in Costa Rica, ^{Cruz (2010)} found that, at altitudes between 400 and 900 m, there is no influence of the altitude gradient on the spatial distribution pattern; he also explains that this may be due to the fact that the altitude interval is relatively small, and therefore, the climate conditions do not vary between strata. Consequently, it has been suggested that studies on the vegetation by altitude gradients should be carried out in large geographical expanses (^{Fossa, 2004}).

Spatial distribution of tree species with Ripley’s K(t) function

According to Ripley’s univariate K(t) function, the spatial distribution of the three height categories of pole-sized trees exhibited a significant pattern (p ≤ 0.01) ―clumped, random or uniform― at different distances, which implies that the suggested hypothesis is accepted (Figure 2). This is a similar result to that obtained with the Morisita-Horn index for pole-sized trees (Table 1).

Distancia = Distance; Inferior = Lower; Intermedia = Intermediate; Superior = Higher.

Figure 2 L(t) univariate distribution values for the three height categories of pole-sized trees in five altitude strata (AS) of the Metzabok Protected Natural Area in the Selva Lacandona of Chiapas. 

In general, the lower height category had a clumped pattern, with variation at different distances and altitude strata (Figure 2). AS1 and 4 have a clumped distribution at distances of 1 to 6 m, and a uniform distribution at distances of more than 7 m; AS2 had a random behavior, and the distribution of AS3 was uniform at distances of 1 to 2 m, and a clumped distribution at distances of 3 to 10 m (Figure 2). AS5 had a clumped distribution at all the distances.

The variation in the distribution patterns in the different AS is related to the clearings generated by the intermediate and higher categories, since, having been affected by some disturbance (such as the falling of branches or of the whole tree, tree fellings or death due to pests and diseases), these surfaces are repopulated by species that demand light and which change their initial (clumped) pattern into a random pattern through death processes (^{Franklin and Rey, 2007}; ^{Barreto-Silva et al., 2014}). Within the study area, the clearings are colonized by R. guatemalensis (S. Watson) Bartlett, which coincides with the results obtained by ^{Zarco et al. (2010)} in rain forests of Tabasco, according to whom this species grows and is prevalent in the lower stratum of rain forests where disturbs occur.

The intermediate height category had a mostly random distribution, although at shorter distances the trees adopt a uniform pattern, with the exception of AS2, which as a clumped distribution at distances of 2 to 10 m (Figure 2). The random distribution in this category is due mainly to the timber extraction that took place in the study area during the 1970s (^{Conanp, 2006}), which promoted the mortality of a heterogeneous group of species in space. On the other hand, clumped patterns may be a response to the environmental variability between strata and are ecologically common in large individuals (^{Dixon, 2013}).

In the higher height category, AS1 and 2 exhibited a clumped pattern at distances of less than 8 m (Figure 2), due both to the natural death of certain old trees and to the selective extraction of precious woods such as mahogany (Swietenia macrophylla King) and cedar (Cedrela odorata L.). In fact, in the years 1975 and 1984, the exploitation of 55 000 m³ and 20 000 m³ of common tropical species in the Selva Lacandona was authorized (^{Vásquez-Sánchez et al., 1992}), and the timber exploitation by the population of certain areas of the PNA for purposes of building homes is ongoing (^{Conanp, 2006}); these populations leave clusters of the species M. zapota, P. reticulata, Manilkara chicle (Pittier) Gilly and Brosimun alicastrum Sw standing because their wood is hard and dense, and therefore difficult to handle, which renders them less valuable.

This agrees with the findings of ^{Franklin and Rey (2007)} and of ^{Dale and Fortin (2014)}, according to whom the logical evolution of the spatial pattern with the increasing age of the individuals is caused by the accumulated effect of the disturbances, competition and attack by pathogens. Therefore, a random pattern can change into a clumped or uniform pattern, according to the environmental and anthropic characteristics of the habitat.

Although a uniform behavior is rare in natural assemblies, it may be found in stable environments with minimal disturbances (^{Antos and Parish, 2002}). Indeed, the model proposed by ^{Janzen (1970)} states that the consequence of the mortality of trees is a uniform distribution of the surviving adult individuals, as was corroborated by ^{Lan et al. (2009)} in the tropical rain forests of China, where they observed that these tend to follow a uniform distribution in environments with multiple species.

The extremely variable spatial pattern registered in AS3, 4 and 5 (Figure 2) may be due to the difficulty to access these strata, as there are no records of timber exploitation, and it is possible to find Calophyllum brasiliense Cambess., Terminalia amazonia (J.F. Gmel.) Exell, Guatteria anomala R.E. Fr., M. chicle and M. zapota individuals with a diameter of up to 190 cm and heights above 50 m. Certain authors (^{Rozas and Camarero, 2005}; ^{Linzaga-Román et al., 2011}) propose that such a variable behavior in the distribution pattern is accounted for by the topographic factors of the site. Thus, it may be suggested that the distribution of species at the Metzabok PNA can be associated to the environmental heterogeneity induced by the relief and by the disturbances produced in each site, as suggested by Montáñez et al. (2010) and ^{Barreto-Silva et al. (2014)} for certain tropical rain forests of Colombia.

Spatial correlation patterns

According to the spatial correlation of Ripley’s K ₁₂ (t) function, the bivariates of the AS2, 3 and 5 of the lower-intermediate height category indicated spatial repulsion in distances of less than 2 m and attraction of between 3 and 10 m (Figure 3). The repulsion at a small scale between the two categories would be a consequence of the density-dependent mortality of the seedlings located beneath the crowns of the intermediate and higher height categories; therefore, species of the lower height categories (Myriocarpa longipes Liebm. and Piper psilorhachis C. DC.) colonize the available spaces, except under the crown of taxa of the higher categories, such as C. brasiliense, T. amazonia and G. anomala (^{Lan et al., 2009}).

Distancia = Distance; EA = AS; Inferior-Intermedia = Lower-intermediate; Inferior-Superior = Lower-higher; Intermedia- Superior = Intermediate-higher.

Figure 3 Matrix of the ratio of the bivariate L ₁₂ (t) distribution to the three height categories of the pole-sized tree species in five altitude strata (AS) of the Metzabok Protected Natural Area in the Selva Lacandona of Chiapas. 

This behavior can also be caused by depredation processes, as it is more likely that the predators will eliminate those individuals that are closest to the seed tree (^{Hosaka et al., 2017}); this would explain the existence of repulsion between the lower-higher category at near distances, and of attraction in the intermediate-higher, as the distance to the parent tree increases (^{Rozas and Camarero, 2005}; ^{Barreto-Silva et al., 2014}).

This contrasts with the AS1 and 4, in which the correlation pattern was independent, as it was the same that was observed for all the strata of the lower-higher category. In the intermediate-superior category (Haematoxylum campechianum L. and Hauya elegans DC. vs. D. guianense and Pouteria durlandii (Standl.) Baehni, respectively), negative associations (repulsion) occur at different distances; this was more noticeable in the AS4 (Figure 3). This type of behavior is perhaps a response to the high mortality of seeds and lower individuals close to the higher trees. Diseases and depredation are concentrated in the vicinity of the parent trees, which causes density-dependent mortality, as there is a higher probability of survival and seed-producing adults (^{Janzen, 1970}; ^{Franklin and Rey, 2007}; ^{Hosaka et al., 2017}).