Description and location of the study area. The caldenal is a xeric forest dominated by N. caldenia and is the predominant tree formation of the caldenal district within the Espinal phytogeographic region (Fig. 1). Its structure is generally associated with other woody trees such as carob (Neltuma flexuosa DC), chañar (Geoffroea decorticans Burkart) and toro's shadow (Jodina rhombifolia Hook. et Arn. Reissek) which is accompanied by a shrub stratum where the following stand out: Schinus fasciculata (Griseb.), Celtis ehrenbergiana (Klotzsch) Liebm. and Condalia microphylla Cav. It has a dense herbaceous layer composed mainly of mixed perennial grasses (Anderson et al. 1970).
The region where the study was carried out is located in the southwest of the province of Córdoba, Argentina and is characterized as semiarid in transition to subhumid monsoon regime. The average annual temperature is 16.6°C and it has an average precipitation of 893 mm, although it presents great interannual variability (average climatological values 1981–2010 from the statistics of the National Meteorological Service).
Definition of the silvopastoral module. The study was carried out in the “Estancia Ralicó” establishment (34⁰54'25” S; 64⁰50'03” W) which has an area of 15,300 ha, of which 9,000 ha correspond to N. caldenia forest in different degrees of coverage and conservation (Fig. 1). Historically, the establishment was divided into pastures of approximately 600 hectares. Starting in 2016, a high instantaneous load rotational grazing system was implemented. To do this, a 600-hectare lot was divided into 30 20-hectare plots. The divisions were made using electric wire, searching for spaces within the mountain without opening fire-break streets. Grazing is carried out by introducing high loads, between 900 and 1,200 animals per plot, in periods of 3 to 4 days, once a year. The number of animals and the duration of time is adjusted depending on forage availability.
Forest inventory. To characterize the forest, a forest inventory was carried out following the guidelines of the First National Forest Inventory (SAyDS 2007). Circular plots of 500 m² were established, with a radius of 12.62 m. Diameter at Breast Height (DBH), which corresponds to the diameter at 1.3 m from the ground, and Total Height (H), which corresponds to the distance from the ground to the top of the tree, were measured by means of Suunto hypsometer. The specific composition at the stand level was evaluated by defining the relative values in number of feet (density) and basal area (BA). A marked dominance of N. caldenia (Utello et al. 2021) could be determined over the rest of the species where the average relative percentage of occupancy was greater than 90% of the basal area. The rest of the relative composition was distributed between N. flexuosa, G. décorticans, S. fasciculata and to a lesser extent by J. rhombifolia, which usually appears as dispersed individuals. Consequently, the modeling and analysis was approached from the main species (N. caldenia) as it was the one that would have the greatest impact on the forage resource and on the capture of C.
Measurement of herbaceous biomass. Once the different forest covers were established, from open forest (BA ≤ 5 m² ha− 1) to closed forest (BA ≥ 25 m² ha− 1), the availability of the herbaceous stratum was determined through completely randomized sampling under the conditions of: projection under glasses and between glasses. 24 repetitions were taken per condition (n = 96). Herbaceous biomass sampling was carried out prior to the entry of the animals and the collected material includes that accumulated between two grazing, according to the grazing system set out above. The sampling size for the herbaceous stratum was 0.25 m². In the laboratory, the species that make up the samples were identified and the percentages in terms of occupancy were determined. To obtain dry matter, the samples were placed in a forced air oven for 48 hours until constant weight.
Estimation of the load and emissions of the livestock component. Once the net aerial primary production for each tree density was determined, it was affected by an appropriate use factor (AUF = 50%), which represents the percentage of the annual forage production of a species that can be used without endangering the production, reproduction and longevity in the natural grassland (Holechek et al. 1989). Once the forage supply was obtained, it was compared with the nutritional demand of a herd of breeding cows of 400 kg live weight (LW). A daily allocation of forage in dry matter (% FDM) corresponding to 3% of the LW was proposed, this being a considerable value for the animal to present good reproductive performance (Rovira 1996). The animal load was determined by the ratio of forage supply and demand (Eq. 1).
\(\text{Animal load= }\frac{\text{Forage supply (Kg DM Ha}\text{-1}\text{) × AUF (50 %)}}{\text{LW (kg) × % FDM × Rotation length (1 year)}}\text{ }\) [1]
The load values based on tree density allowed estimating GHG emissions generated by livestock using what was proposed by Nieto et al. (2014) who evaluated GHG emissions from enteric fermentation and manure management for different categories of cattle with conditions similar to the study site; the result is that cattle breeding generates an average of emissions of 1,427 kg eq-CO2 animal− 1 year− 1. In addition, the emissions generated by the lactating cow category were considered, which reaches the maximum pollution levels of 2,407 kg eq-CO2 animal− 1 year− 1 in the region's breeding systems based on natural grasslands.
Obtaining a diameter distribution model. To establish the diameter distribution model of the woody component under study, the guidelines proposed in the model, or De Liocourt's Law (Madrigal 1994), were followed:
\({N}_{i}={{N}_{max}(1+a)}^{({D}_{max}-{D}_{i})/d}\) [2]
Where, Ni: Number of feet of class i; Di: Average diameter of class i; Nmax: Number of feet of maximum diameter class; Dmax: Average diameter of the maximum diameter class; d: Interval of diameter classes; and a: model constant.
The exponential model can also be formulated with the expression [3]:
\(Ni=k.{e}^{-q*Di}\) [3]
Where k and q are constants, with q = 1/d * ln (1 + a). The exponential function [3] was transformed into a linear function by applying logarithms [4]:
\(\text{ln}y=\text{ln}k-q* \text{ln}e Di\) [4]
And then expressed as:
\(Z={\beta }_{0} + {\beta }_{1}*{X}_{i}\) [5]
Where, Z is the number of feet for a basal area value (BA), the maximum diameter (Dmax) and the De Liocourt quotient “q”. The term Xi replaces Di.
This transformed function allowed us to establish relationships that made it possible to calculate the coefficient \({\beta }_{1}\)for a chosen value of “q” and \({\beta }_{0}\) for a certain basal area (Araujo 2014).
The quotient between the number of individuals of consecutive diameter classes is equal to the constant “q”, therefore, it can be expressed as:
\(\frac{\text{N}\text{i}}{\text{N}\text{i}+1}=\frac{{e}^{(\beta 0+\beta 1*Xi)}}{{e}^{(\beta 0+\beta 1*Xi+1)}}=q\) [6]
Multiplying the terms of the equation, we obtain:
\({q*e}^{(\beta 0+\beta 1*Xi+1)}={e}^{(\beta 0+\beta 1*Xi)}\) [7]
Applying logarithms and simplifying:
\(\text{ln}q+\left(\beta 0+\beta 1*Xi+1\right)\text{ln}e=\left(\beta 0+\beta 1*Xi\right)\text{ln}e\) [8]
\(\text{ln}q=\beta 0+ \beta 1*Xi-\beta 0-\beta 1*Xi+1\) [9]
\(\text{ln}q=\beta 1*Xi-\beta 1*Xi+1\) [10]
\(\text{ln}q=\beta 1(Xi-Xi+1)\) [11]
Solving the term β1:
\({\beta }1=\frac{\text{L}\text{n} \text{q}}{\text{X}\text{i}-\text{X}\text{i}+1}\) [12]
With this expression, the new value of β1 was calculated for a certain value of “q”. In the same way, the basal area (BA), expressed in m2 ha− 1, is defined by:
\(\text{B}\text{A}=\frac{\pi *D₁²}{40.000}*f₁+\frac{\pi *D₂²}{40.000}*f₂+\dots \frac{\pi *Dn²}{40.000}*fn\) [13]
In which D₁²…, Dn² represent the smallest and largest diameter of the distribution and f₁..., fn are the respective frequencies.
Solving the term (π / 40.000), the common factor eβ0 and replacing the frequencies f by their value [e(β0 + β1 Xi)] we obtained:
\(\text{B}\text{A}=\frac{\pi }{40.000}*{[e}^{\beta 0}(D₁²*{e}^{\left(\beta 1*D₁\right)}+D₂²*{e}^{\left(\beta 1*D₂\right)}+\dots D{n}^{2}*{e}^{\left(\beta 1*Dn\right)})]\) [13]
Where:
\({e}^{\beta 0}=\frac{BA\text{*}40.000}{\pi *(D₁²*{e}^{\left(\beta 1*{D}^{1}\right)}+D₂²*{e}^{\left(\beta 1*{D}^{2}\right)}+\dots +D{n}^{2}*{e}^{\left(\beta 1*Dn\right)})}\) [14]
Finally, applying natural logarithm, we arrived at the expression that relates the coefficient β0 to the basal area BA:
\({\beta }0=Ln*\left[\frac{BA*40.000}{\pi *\left(\varSigma D{i}^{2}*{e}^{\left(\beta 1*Di\right)}\right)}\right]\) [15]
The basis of the method is the determination of proportional parts of BA for the different classes, which are then used to calculate a correct basal area, distributing the desired level of BA in the respective classes. Then, the chosen basal area is transformed into the number of trees to construct the diameter distribution. To define the balanced distribution, a value of q = 1.46 was selected, used for the construction of the balance curve, which was obtained from previous adjustments in forests with good coverage status. The BA was raised from 5 m² ha− 1, starting at 1 to 25 m² ha− 1, this was related to the BA values in which the forage biomass was evaluated. A maximum diameter for management of 50 cm was used, established from the fact that, under the thinning harvesting regime, the last class is cut, reaching a minimum cutting diameter of 45 cm. When individuals reach that diameter, it guarantees good development, capable of producing abundant seeds and good sawmill performance. Furthermore, as stated by Bogino and Villalba (2008), around that diameter the current annual increment is equal to the average annual increment, establishing the optimal moment of use from a biological point of view.
Forest growth projection. Growth modeling was carried out through a diameter class model, using as a basis the initial equilibrium diameter distribution obtained in the previous section. Assuming the proposal of Silva (1989), the fraction of trees that moves annually throughout the entire class interval, due to diametral growth, can be estimated by a growth index (GI), calculated by Equation [16]:
\(GI=Ci*P/a\) [16]
Where, GI: Growth index. Ci: Current increments in class diameter. P: Number of years in the period considered. a: Amplitude of the diameter class.
The current increments (Ci) for the year considered were obtained from a total of 19 dendrometers distributed in the trees of each diameter class in 7 permanent sampling plots at different tree densities (16, 20, 21, 23, 32, 36 and 42 m2 ha− 1 of BA). Knowing the average annual stock in number of individuals per diameter class and the GI, it is possible to calculate the number of years necessary for all the feet of one class to pass to the next and project its diameter distribution.
Determination of total and stem biomass. To estimate biomass and its distribution by class, the allometric functions developed by Risio et al. (2013) [Equation 17]:
\(W=\left(\beta *{BA}^{2}\right) + {\lambda }*h\) [17]
Where: W: is the weight of dry biomass (kg) of the different fractions of the tree; BA: basal area; h: tree height; β and λ: estimated model parameters (total biomass: β: 0.000366 and λ: 7.558194; stem biomass: β: 0.000093 and λ: 1.0858).
Height determination was carried out using equation [18], adjusted by Utello et al. (2019):
\(h=\frac{\text{10,94}}{1+\text{1,73}\times {e}^{-\text{3,69}*DBH}}\) [18]
Where, h: total height of the tree (m). DBH: Diameter at Breast Height (m).
Statistical analysis. The herbaceous biomass data were analyzed by analysis of variance (ANOVA) and Fisher's LSD test for the comparison of means, using the Infostat statistical software (Di Rienzo 2018). The same software was used for regression analyzes where it uses the least squares method in linear models and the Nelder-Mead simplex algorithm method for non-linear ones (Nelder and Mead 1965). The selection of the models was carried out by comparing the coefficient of determination (R2), the mean square of the error, the level of significance of the parameters, and the values of the Akaike information criterion and the information criterion Bayesian.