### Area of study

The present research was carried out in the conservation area of the Ternium Industrial Center of México, which has an area of 46 hectares and is located within the municipality of Pesquería, Nuevo León, in Northeastern Mexico (Fig. 1). It is located between latitude 25° 45’ N and longitude 99° 58’ W, at an average altitude of 306 masl, which belongs to the physiographic region of the North Gulf Coastal Plain [6]. The predominant climate is very dry and semi-warm (Bwhw), with an average annual temperature in the range from 20 to 21 °C. The types of soils present in the majority of cases are xerosol, castañozem, feozem, regosol and in the minority of cases are fluvisol, vertisol and rendzine. The average annual rainfall is 550 mm. The vegetation of the area corresponds to a mesquital with a history of cattle and hunting use and is currently disturbed [14].

### Analysis of the vegetation

In order to fulfill the objective, the “c” sub basin of the Pesquería River with in a low part of the San Juan River Basin (Rio Bravo, Rio Bravo) was selected, where the conservation area is located and where intermittent surface runoff occurs. Vegetation evaluation was carried out using three randomly distributed sampling sites. The dimensions of each site was 40 m × 40 m (1,600 m^{2}). A census was taken of all shrub and tree species with a basal diameter (d_{0.10}) ≥ 5 cm. The species of each individual was identified and recorded, taking the measurements of total height (h) and crown diameter (d_{crown}) in north-south and east-west directions. For the nomenclature of families, orders and species we followed the APG III [15], and the scientific names and families were corroborated in the database of Tropicos [16].

### Data analysis

#### Structure

In order to evaluate the horizontal structure of the species in the study community, we used the following structural variables: abundance, dominance, frequency, with which we calculated the Importance Value Index (IVI) which was calculated from the following mathematical equations [17, 18]:

$$ A{R}_i = \left(\raisebox{1ex}{${A}_i$}\!\left/ \!\raisebox{-1ex}{${\displaystyle \sum }{A}_i$}\right.\right)*100 $$

Where *AR*
_{
i
} is the relative abundance of species *i*, with respect to total abundance (*A*
_{
i
}); *Ni* is the number of individuals of species *i*, and *S* is the surface (ha).

To estimate the relative dominance we used:

$$ {D}_i = \raisebox{1ex}{$ A{b}_i$}\!\left/ \!\raisebox{-1ex}{$ S(ha)$}\right. $$

$$ D{R}_i = \left(\raisebox{1ex}{${D}_i$}\!\left/ \!\raisebox{-1ex}{${\displaystyle \sum }{D}_i$}\right.\right)*100 $$

Where *DR*
_{
i
} is the relative dominance of species *i*, with respect to total dominance (*D*
_{
i
}); *Ab*
_{
i
} is the crown area of species *i*, and *S* is the surface (ha).

$$ {F}_i = \raisebox{1ex}{${P}_i$}\!\left/ \!\raisebox{-1ex}{$ NS$}\right. $$

$$ F{R}_i = \left(\raisebox{1ex}{${F}_i$}\!\left/ \!\raisebox{-1ex}{${\displaystyle \sum }{F}_i$}\right.\right)*100 $$

Where *FR*
_{
i
} is the relative frequency of species *i* with respect to the total frequency (*F*
_{
i
}); *P*
_{
i
} is the frequency of species *i* at sampling sites, and *NS* is the total number of sampling sites. The Importance Value Index (*IVI*) is defined as:

$$ IVI = \frac{{\displaystyle {\sum}_n^{i=1}}\left( A{R}_i, D{R}_i, F{R}_i\right)}{3} $$

where *AR*
_{
i
} is the relative abundance; *DR*
_{
i
} is the relative dominance, and *FR*
_{
i
} is the relative frequency.

A graph of height classes was generated in order to evaluate the vertical structure of the community. The Vertical Distribution Index of Pretzsch [19] was calculated for three zones of height: zone I: 80–100% of the maximum height of the population, zone II: 50–80% of the maximum height of the population, zone III: 0–50% of the maximum height of the population [19]. In this study was the high strata (7.20 – 9.00 m), medium strata (4.50 – 7.19 m) and low strata (<4.50 m). The Vertical Distribution Index was calculated according to the following mathematical formula:

$$ A= - {\displaystyle \sum_{i=1}^S}{\displaystyle \sum_{j=1}^Z}{p}_{i j}*\ \ln \left({p}_{i j}\right) $$

Where *S* is the number of species present; *Z* is the number of height zones and *pij* is the proportion of species in each height zone:

where *nij* is the number of individuals of the same species (*i*) in the zone (*j*) and *N* is total number of individuals.

In order to compare the Pretzsch Index it is necessary to standardize it and this is undertaken by the value of *A*
_{
max
}, which is calculated in the following manner:

$$ Amax= In\left( S* Z\right) $$

Then the value of *A* can be standardized according to:

$$ Arel=\frac{A}{In\left( S* Z\right)}*100 $$

#### Diversity

To estimate species diversity, the Shannon Index [20] and the Margalef index [21], respectively, were estimated. The Shannon Index was estimated by using the following equation:

$$ {H}^{\prime }=-{\displaystyle \sum_{i=1}^S}{p}_i* \ln \left({p}_i\right) $$

where *S* is the number of species present, ln is natural logarithm and *pi* is the proportion of species. *P*
_{
i
}
*= n*
_{
i
}
*/N*, where *n*
_{
i
} is the number of individuals of species *i* and *N* is the total number of individuals. With the same meaning of the variables being common, the Margalef Diversity Index (*D*
_{
a
}) was estimated using the following equation:

$$ Da = \frac{\left( S-1\right)}{ \log N} $$

#### Species abundance curves

Species density was analyzed using species abundance curves. With these curves it is possible to make inferences about the state of the ecosystems, besides using for descriptions in the form of mathematical models.

In this study, the species abundance curves were fitted to known mathematical models. Currently, there are many models that are used to describe species diversity in a community. However, in this work only three of the best fit models are analyzed: the geometric model [22], the Poisson model of the logarithmic normal series [23], and the Neutral Model of Alonso and Mckane [24, 25].

For the selection of the best model, the Akaike Information Criterion (AIC) was used to compare the selected models, taking into account their fit and complexity. When comparing models using this method, the selection of the best model is based on the lowest value in the AIC. In addition, we used the delta AIC criterion (dAIC) which, when it has a value that is less than 2, indicates that the comparative models similarly explain the trend of the data, (that is, there are no differences between one and the other). To determine the goodness of fit of the models *χ*
^{2} was used, as recommended by Magurran [26].

#### Adjusting the models

The models were adjusted using the maximum likelihood method with software R version 3.1.2 [17], with the support of RStudio version 0.99 [27] and also running routines by Prado et al. [25].