Mimosa scabrella Benth. planted for forest restoration in southern Brazil

Tropical trees planting resurgent in a global warming scenario, and this activity relies on information about forest species ecology and its different functional traits. we evaluated the initial performance of Mimosa scabrella using the Generalized Linear Models (GLM) technique to fit mathematical models for collar diameter growth x height, and for crown projection area x collar diameter in a forest restoration planting. The following variables were obtained in the first four years after planting: collar diameter (mm), total height (m), crown projection area (m2) and crown volume (m3). The models fitting was performed by GLM on Gamma, Normal and Poisson distribution, identity and logarithmical join function, and they were analyzed based on Akaike and Bayesian Information Criteria, standard deviation of the estimate and determination coefficient. M. scabrella showed an excelled performance on the 48 months of age, with average increment of 200.28 mm in collar diameter, 6.88 m in total height, 2.95 m2 in crown projection area and 83.41 m3 in crown volume. Its growth reduced only on periods of frost occurrence, but it restarted after these climatic events. The species growth, as well as its high survival rates and resprouting, allow its recommendation as a shady species of fast canopy fulfillment in forest restoration projects.


Introduction
Biodiversity conservation of forest ecosystems has been one of the main concerns of humanity in the last decades (Benayas et al., 2009). Tropical trees planting has arisen in a global warming scenario (Ripple et al., 2020), and this activity relies on information about forest species ecologic suitability in their different functional traits. The use of mathematical modeling is an important tool for monitoring the growth rate of tropical tree species, which is becoming increasingly important.
Mimosa scabrella Benth., popularly known in Brazil as "bracatinga", belongs to the Fabaceae family, Mimosoideae subfamily, and it is a native and endemic Brazilian species. It shows broad geographic distribution, occurring especially in southern Brazil, but also in parts of Minas Gerais, Rio de Janeiro and São Paulo states (Dutra & Morim, 2017). It is a pioneer species and occurs, mainly, on natural or anthropic openings of secondary formations in the Araucaria Forest, in high abundance, gradually replacing herb and shrub species of initial successional stages. Its distribution comprises altitudes from 300 to 1,800 m (Klein, 1981;Carvalho, 1994Carvalho, , 2002. This species stands out by its fast growth, reaching up to 20 m in height and 40 cm in dbh (Reitz, Klein & Reis, 1978;Fabrowski et al., 2005). It can reach its reproductive age at three years and live up to 30 years (Machado et al., 2006).
M. scabrella is perennial, low demanding in terms of physical and chemical soil conditions, and, due to is fast growth, is indicated for the reforestation of degraded areas (Carvalho, 1994). The species rusticity and light-demanding characteristics provides fast area coverage in a wide range of soils, such as riverbanks, forest edges and also degraded soils. Furthermore, characteristics as high increment rates, short-life and strong interaction with soil micro-organisms (nitrogen fixing bacteria and mycorrhizae), insects (mealy bugs, ants, bees, sawdust beetles) and vertebrates (birds and rodents) makes this species one of the main species indicated for facilitation in environment restoration programs (Reis & Kageyama, 2003).
Besides its application in restoration projects, M. scabrella is also known by its vast potential for wood supply for the construction industry, sticks for vegetables cultivation, lumber, wood panels, pulp, and also as a bee-keeping, fodder and ornamental plant (Machado et al., 2006). We assessed the initial growth of M. scabrella in the Iguazu River basin, Paraná state, Brazil, up to 4 years old in a forest restoration plantation, using Generalized Linear Models (GLM) to fit mathematical models.

Methodology
This study was carried out in an area of 7.2 ha at the Federal University of Technology -Parana, municipality of Dois Vizinhos, southern Brazil -25º41'44"S and 53º06'07"W. The area presents an average altitude of 500 m, and it is located in Araucaria Forest influenced by Seasonal Semideciduous Forest. The region in inserted in the third plateau of Paraná, with geological material from basaltic origin and soil characterized as Nitisol. The climate is described as Cfa subtropical (Alvares, Sentelhas & Stape, 2018), with occurrence of frosts at least each two years, absence of dry season and average of 22°C in the warmest month.
In December 2010, 70 native tree species were planted (3 x 2 m spacing), in four plots of 54 x 40 m ( Figure 1). In each plot, 18 seedlings of M. scabrella, from 30 to 60 cm high, were planted, totaling 72 plants. The seedlings were fertilized (5-20-10) into the holes, but also received 40 g of annual cover fertilization with urea, watered with hydrogel, and protected by cardboard mulching. Semesterly, weeds were controlled by mowing followed by glyphosate spraying. These silvicultural practices were done up to the third year. The data were collected biannually, measuring the following variables: survival (%), total height (h -m), collar diameter (cd -cm), crown projection area (ca -m²), crown height (ch -m) and crown volume (cv -m³). Two measurements of the crown diameter were obtained, perpendicularly, which were used to calculate the crown projection area through the ellipse formula: ca (m²) = dl.de.π/4, where ca is the crown projection area; dl and de are the crown diameters (m). The crown volume was estimated as an elliptical cylinder, multiplying the crown area by its length, as following: cv (m 3 ) = ca.ch, where cv is the crown volume, ca is the crown area (m²), and ch is the crown height (m). According to Terborch and Petren (1991), this method underestimates the real crown volume, but presents an estimate of branches and leaves quantity existing on the forest canopy (Montgomery & Chazdon, 2001).
To compare the species growth with temperatures and rainfall recorded during the observation window considered in this study, we used data from the meteorological station at the Federal University of Technology -Parana, Dois Vizinhos.
Regarding to the mathematical model fitting for the initial growth in collar diameter in terms of total height and crown projection area in terms of total height, the Generalized Linear Models (GLM) were applied. The GLM were tested in the three random fields, Normal, Gama and Poisson, using the identity (μ) and ln logarithmic (μ) join functions. The model was defined by the following formula: y = β0 + β1.xі + ԑ, where y represents the variable characteristics (collar diameter and crown area) xi the trees number, β0 and β1 are the estimated coefficients, and ԑ is the residual error. The fitting quality of the GLM models was assessed in terms of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), and the best model was the one with smaller value in both criteria (AIC and BIC). The models fitting was conducted on SAS V. 9.3. Statistical Software (SAS Institute Inc., 2004).

Results and Discussion
According to the meteorological data (Figure 2   Source: Authors. Carvalho (1982), studying the silvicultural performance of native forest species in a subtropical forest in South Brazil, proposed adequate levels of survival at 84 months of age, as follows: high (≥ 70%), regular (≥ 50% ≤ 69%) and low (≤ 49%).
Our survival rate for M. scabrella (89%), was classified as high, showing that the species was tolerant to possible biotic and abiotic stresses.
M. scabrella presented a prominent silvicultural performance at 48 months. The lowest mean values for total height, collar diameter, crown projection area and crown volume were observed at 12 and 36 months. The decrease on mean height increment at 36 months was probably a result of the frosts during the winter, but at 42 months, the species increased significantly its silvicultural performance on this variable ( Figure 4B). At the period of 36 months, frosts probably damaged the apical branches of some individuals, causing the decline on height ( Figure 4B). As the individuals lost their apical dominance, the vegetative growth reduced in terms of height leading to the development of more than one lateral resprout. It demonstrates that the species is not properly called resistant, but, in fact, it is resilient to frosts due to its resprouting potential. The release of new sprouts after frost modified the species silvicultural behavior, which began to shade a bigger area. This fact indicates that these resprouts can be beneficial since the capacity of cover and shade the soil is an extremely important characteristic and it must be considered when choosing native tree species that promote forest succession (Wishnie et al., 2007).
At 48 months of age, the highest values in all variables were noticed, suggesting that, after 36 months of age, trees of M. scabrella can be considered as already recruited, even with low increment on height, crown projection area and crown volume provoked by the intense frosts. The mean individual crown volume was 83.44 m³ ( Figure 4D). The mean crown projection area observed in this period was 23.01 m² ( Figure 4C), three times bigger than the planting spacing, which was 6 m², indicating a high efficiency on invasive grasses control, and an important feature for catalyzing the establishment of new species on the understory (Elliott, Blakesley, Hardwick, 2013, Chazdon, 2015. The crown projection area and volume increased gradually over time ( Figure 4B and 4D). However, the boxplots at 36 months showed a reduction on growth caused probably by the climate, which resulted in a median lower than the other periods. The physiological damage caused by the cold, from May to September, probably reduced the vegetative growth. Where: GLM = Generalized Linear Model; JF = join function; μ = identity; s = standard deviation; BIC = Bayesian Information Criterion; AIC = Akaike Information Criterion. Source: Authors.
The allometric relation between collar diameter and height was discontinuous on different ages. Changes on growth pattern might be linked to frost occurrence, which reduced the development and resulted on death of the apical sprouts in some M. scabrella individuals, inducing lateral sprouting. These results agree with the hypothesis that individuals of the same species may present different allometric relation over their guilds (Guerin & Mendonça, 2009).
It is possible to affirm that on 6 months of age M. scabrella focused on height growth. A continuous growth was observed from 12 months on, and it decreased at 36 months when there was a balance between height and collar diameter ( Figure 3A and 3B). It probably indicates that this species tends to invest more in height growth than diameter. According to its allometric behavior, it can be noted that M. scabrella focus on height growth on the first years.
The investment on diameter is possibly related to the trunk capacity of sustaining the plant structure, resisting to its own mass and to the windthrow (Fontes, 1999, Sterck & Bongers, 1998, which is intensified in opened degraded areas, edges and forest corridors (Santos et al., 2012). Thus, the collar diameter increase is directly associated with tree size since a tall tree with large crown has a significant mass as well, which requires a large diameter to stand its structure. This means that the increase in diameter in a plant occurs as it grows (Guerin & Mendonça, 2009) demanding more support (Sterck &Borges, Research, Society andDevelopment, v. 10, n. 3, e33710312629, 2021 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v10i3.12629 8 1998). However, when the individuals reach a bigger size, the height proportion for a certain circumference tends to stabilize, so growth becomes continuous in both dimensions (Fontes, 1999).
The fitting criteria used to select the best fitting on different ages between crown projection area and total height are displayed on Table 2. Height could describe most of the crown area variation over time, but, again, the fitting criteria showed large variation due to the data heterogeneity. M. scabrella showed higher development in height at 12 months with lower investment rates in crown area. There was a constant increase in crown area investment on the following months, and it reached the asymptote at 30 months. After that, crown area reduced, keeping the allometric relation between crown area and height on constant levels of growth.
The species had a larger rise on height up to 30 months of age compared to the other months. This behavior could be typical of the species since it attempts to assure itself on the canopy during vegetation development (Fontes, 1999) or could be associated to ecological factors that have influenced the growth strategy change (Portela & Santos, 2003). After its growth in height, this species starts to invest on crown area growth due to more light availability from less tree density, allowing the existence of lower live branches (Siqueira, 2006) and horizontal occupation (Costa et al., 2012). On the other hand, the canopy structuring increased crowns competition for light, favoring upper branches (Siqueira, 2006), and requiring a growth strategy on height. Another hypothesis is related to the development level of some individuals, which would already have crowns as mature individuals, so the increase in crown area in the following years would be smaller. Santos et al. (2012) stated that different behavior presented by species in forests can be explained by their regeneration guilds and the strategies adopted to obtain the necessary resources for their development. Siqueira (2006) affirmed that the fitting to different allometric models by tree individuals for each environment suggests that ecological factors can play a restrictive role on species allometry. Therefore, the registered variations on allometry might be a result of the species specificity that can be driven by natural seasonal or sporadic events, requiring prompt reactions to outline a strategy.
This is a consensus decision in populations that have the same role in the ecosystem and occupy the same ecological niche.

Conclusion
M. scabrella showed an excellent performance for reforestation, reducing its growth only when severe frosts occurred in the region and recovering it after such events. The species growth at 48 months of age, as well as its survival rate and resprouting, makes this species suitable for restoration projects, specially in South Brazil, as a shady species with fast canopy recovering ability.