FUNCTIONAL DIVERSITY INFLUENCE IN FOREST WOOD STOCK : A STUDY OF THE BRAZILIAN SAVANNA

Research regarding biodiversity and ecosystem services has been demonstrating a positive correlation among the ecosystem processes, such as the carbon sink into plant biomass and the quantity of carbon in natural vegetation. Nonetheless, it is hard to understand the biodiversity measurements, because they involve gene, phenotypic, population, species, community and ecosystem diversity. The functional diversity refers to the species richness and variety, their characteristics and how that affects the functioning of an ecosystem. Primary productivity is a key factor that affects the functioning of a forest ecosystem. Thus, the aim of this paper was to evaluate the influence of functional diversity on the woody volume productivity (as a proxy for primary production) in the Brazilian savanna. We used six functional characteristics, and to verify the relation between forest production and functional diversity facets, we tested many models. Regarding wood volume, the best models were the exponential and logarithmic. None of the linear models showed significant regression parameters as there was no additive relationship among the multifaceted aspects of functional diversity and wood volume. We found a positive correlation between the functional diversity and primary productivity, which can be used to forecast the effects of diversity variation on ecosystem services.


INTRODUCTION
The Brazilian savanna or Cerrado is a woodland physiognomy with canopy cover of 10% to 60% made up of trees reaching up seven meters (EITEN, 1972).The vegetation is formed mostly by savanna-like vegetation and it occupies almost 70% of the biome area -around 2 million km² (SANO et al., 2010).Among the savanna formations, we have the cerrado sensu stricto occurring in well-drained area with deep soils and high altitude (OLIVEIRA-FILHO;RATTER, 2002).It is composed by a continuous herbaceous layer with discontinuous and occasional trees (OLIVEIRA-FILHO;RATTER, 2002).
Cerrado presents the highest biodiversity among the global savanna (MITTERMEIER et al., 2005) and is considered one of the biomes with the highest diversity of vascular plants in the world (MENDONÇA et al., 2008).However, the extant area of natural vegetation has been changed into areas of intensive arable crop -agriculture and pastures (SILVA et al., 2006).Human action in Cerrado had already deforested almost 1/3 of the original area (FELFILI et al., 2004), leaving 39.5% of preserved areas (SANO et al., 2010), as showed on the Figure 1.
Research on biodiversity and ecosystem services has been demonstrating a positive correlation among ecosystem processes, such as carbon sink and plant biomass, and the quantity of carbon in natural vegetation (HUSTON, 1997;TILMAN et al., 2001).Nonetheless, it is hard to understand the biodiversity measurements, because they involve gene, phenotypic, population, species, community and ecosystem diversity (MOUCHET et al., 2010).The classical biodiversity measurements (richness of species or biodiversity index, such as Shannon's and Simpson's) rely on (1) all species are the same or species importance is assessed by relative density; (2) all individuals are similar, independent of their dimension; and (3) the species density were correctly assessed (MAGURRAN, 2004).However, species are not equal when it comes to ecosystem function, making these assumptions invalid (MOUCHET et al., 2010).Diversity measurement incorporates information about the phylogenetic species relation (RICOTTA, 2005) or their functional characteristics (PETCHEY; GASTON, 2006) are better than the classical measurement (CIANCIARUSO;SILVA;et al., 2009).The functional diversity shows species values and range, their characteristics and how that affects the functioning of an ecosystem (TILMAN, 2001).Primary productivity is a key factor that affects the functioning of a forest ecosystem.Many ecologists use the biodiversity gradient, e.g.loss of species at plant communities to test the biodiversity influence in the ecosystem productivity (WANG et al., 2007).Understanding the process of ecosystem services is important to assess the effects of present and future changes on these services in their conservation (CARDINALE et al., 2012).
Functional diversity measures the difference among species based on functional characteristics of an ecosystem (CIANCIARUSO et al., 2009).Functional diversity measures diversity's functional traits that influence ecosystem processes regardless of organisms phylogeny (CIANCIARUSO et al., 2009).Tilman et al. (1997) and Hooper and Vitousek (1997) stated that ecosystems with a great diversity of functional characteristics have a better use of water, nutrients, solar light and high productivity.
Functional communities aspects or wood assemble could be included in the scope of forest management and restoration of degraded areas (KAGEYAMA; GANDARA, 2000).Approach based on functional features is a promising way to elucidate the diversity effects on productivity (ROSCHER et al., 2012), since the functional diversity explains the primary productivity better than the species richness (RUIZ-BENITO et al., 2014).A better understanding of how diversity and dominance affect ecosystems functioning would help to develop strategies of conservation and restoration of threatened or exploited ecosystems (CAVANAUGH et al., 2014).Thus, the aim of this paper was to evaluate the influence of functional diversity regarding volume productivity of woody assembly in a Brazilian Savanna area -cerrado sensu stricto -considering the hypothesis that functional diversity positively affects forest productivity.

Characterization and location of the study area
This study was carried out in a cerrado sensu stricto area located at Fazenda Água Limpa (FAL) at coordinates 15º56' -15º59' S and 47º55' -47º58' W (has 4,390.0ha) in Brazilian Federal District (BFD), 20 km Southern of Brasília, Brazil.The soil on the study area was a yellowish Oxisol, poor in plant nutrients and high in aluminium saturation (BARBOSA et al., 2009).
The average altitude in FAL is 1,100 m and according to the Köppen classification, the climate is Aw, characterized by two defined seasons, a warmer and rainy season that occurs from October to April, and cold and dry season from May to September, with average temperatures around 22,1°C and average annual rainfall around 1,500 mm (ALVARES et al., 2014).

Sampling of vegetation
The species composition and their abundances were analyzed following the survey conducted by Borges (2009).In this site we implemented ten random plots measuring 20 x 50 m (1,000 m²) and all woody stems equal or greater than 5 cm of diameter at 0.30 m from ground level were measured in each plot (FELFILI et al., 2005).During the sampling, tree heights and diameters were measured.Plants were identified at species level according to AGP III (CHASE; REVEAL, 2009) using data available in the Missouri Botanic Garden (MOBOT), International Plant Names Index (IPNI) and Flora do Brazil.
Primary production on plots was assessed by wood volume (m³).The volume of each individual was calculated based on the equation described by (REZENDE et al., 2006) for the woody vegetation in cerrado sensu stricto: V = 1.09 × 10 -4 × D 2 × 4.51 × 10 -4 × D 2 × H V= Volume (m³); H= height (m); D= diameter (cm) Functional diversity was determined by selecting species with high abundance and that represented 80% of the whole study community abundance (PAKEMAN;QUESTED, 2007).We used six functional traits: crown dimension, leaf area, wood density and bark density (Table 1).We randomized ten individuals for each evaluated species and, from this we evaluated their functional traits.Crown dimension was determined by mean in two perpendicular measurements, where the first measurement was on larger radius of the crown.Regarding the specific basic wood density and bark we used data from a study performed by Vale et al. (2002) at the same place of sampling.
To measure leaf traits of functional diversity (leaf size, leaves' dry mass content and specific leaf area) we took ten adult leaves from each tree without any sign of diseases or attacked by herbivore (PÉREZ-HARGUINDEGUY et al., 2013).Quantification of dry leaf mass was made by the average of dry weight after 24 hours in an oven at 105°C.Dry weight was divided by leaf mass saturated in water for five hours (PÉREZ-HARGUINDEGUY et al., 2013).To measure length and leaf area we digitalized five leaves.Using the digital image we calculated the length following the primary vein and the specific leaf area was taken by dividing the leaf area and leaf dry mass mater content (PÉREZ-HARGUINDEGUY et al., 2013).EBImage in the R software Project was used for the task (PAU et al., 2010).
The functional diversity was measured by three multifaceted aspects (divergence, evenness and dispersion) through functional divergence index, functional evenness (VILLÉGER et al., 2008) and functional dispersion (LALIBERTÉ; LEGENDRE, 2010).We calculated each aspect by using the software R through the package FD (LALIBERTÉ; LEGENDRE, 2010).
Functional divergence measures divergence on the distribution of functional abundance of species in the convex volume (MOUCHET et al., 2010).This divergence was measured through the Fdiv index (Functional Divergence), which quantifies how the specie diverges in the functional space (MOUCHET et al., 2010).The functional evenness is the regularity of the distribution of abundance in niche space, which links all the other species in the traits multidimensional space given by Feve index (Functional Evenness) (VILLÉGER et al., 2008;MOUCHET et al., 2010).The functional dispersion (Fdis) is the average distance of individual species to the centre of mass of all species in the community on a multidimensional space (LALIBERTÉ; LEGENDRE, 2010).Those were calculated using the multivariate dispersion (ANDERSON, 2006).

Data processing
To verify the relation between forest productivity (volume) and functional diversity (divergence, evenness and dispersion), we tested many models, combining independent variables (functional diversity) and response variable (forest productivity).Thus, we adjusted the regression for each forest productivity variable (excluding death of individuals) and analysed the relation between forest productivity and functional diversity of woody assembly, identifying which aspect of functional diversity relates better to the productivity (Table 2).

Table 2:
Model to assess the volume related to functional diversity parameters.V: Wood Volume (m³), FDiv: Functional divergence; FEve: Functional evenness and FDis: Functional dispersion.
We evaluated the quantity of adjusts by: significance of the parameters, F value, residual graphic distribution and adjusted coefficient of determination (R 2 Adj ).We adjusted the models by using the R project software.

RESULTS
We measured 1,694 trees distributed in 27 families and 56 species (Table 3), and the 42 most abundant species were used to calculate functional diversity.Considering the 56 species identified, 46 was among the hundred most common of cerrado sensu stricto (BRIDGEWATER et al., 2004;RATTER et al., 2006).The species-richest botanic families were Fabaceae (12 species), Vochysiaceace (5 species) e Malpighiaceae (4 species) Fifteen families were represented by a single species.The species with the greatest number of individuals were Roupala montana (127), Ouratea hexasperma (120), Miconia leucocarpa (113), Caryocar brasiliense (110), Eremanthus glomerulatus (109) e Qualea grandiflora (91).Only five species were represented by a single individual.The species with high wood volume were C. brasiliense, Q. grandiflora, D. miscolobium, and unidentified dead trees.The studied area showed a total wood volume of 14.667 m³/ha with a sampling error of 1.099 m³.ha -1 with a minimum of 1.2374 m³.ha -1 and maximum value of 1.8754 m³.ha -1 per plot (Table 4) Among the tested models, only three of them showed significant regressions (Table 5).Only model V4 presented all parameters significant (p < 0.05).This model differed from the model V3 by the absence of the FDiv facet.The remaining regressions were not significant.Thus, we evaluated a positive relationship between functional diversity and volume (FEve, FDdiv and FDis).But this relationship was logarithmic, ie from a certain functional diversity value onwards, there was a smaller wood volume increase in the community.When it comes to logarithms of the dependent variables (model V7 and V8) or independent, we have obtained significant parameters.The FDiv facet was not a significant parameter in any model.That is, the functional dispersion was not significant for determining the volume.The residual plot for volume (Figure 2) illustrates the models that presented special dependence of residues for the models V1, V5, V6 and V7.Thus, due to the quality of fit, those models were not good to assess the volume.Among the models that present significant regression, the V4 model showed the best results in the relationship observed versus estimated volume (Figure 3).

DISCUSSION
We found a positive correlation between primary productivity (wood volume) and functional diversity.So, the ecosystem service evaluated in this work, wood volume stock, is affected by functional diversity and their aspects.Also, in a small scale, our data supports the hypothesis that environments with greater functional diversity show higher biomass/wood stock (TILMAN et al., 2001).The positive correlation showed that the volume variation was directly proportional to the functional diversity and its facets.In addition, it increases the evidence that different species groups are important for different processes of ecosystems and biodiversity, especially when ecosystem variety processes are considered (GAMFELDT et al., 2013).Forests with greater functional diversity may present not only greater biomass but also gains in other ecosystem services.
The use of functional diversity as a variable in management planning and recovery of degraded areas could be an important factor to increase the resilience and ecosystem services recovery.To maintain the resilience, a higher functional diversity and functional similarity between dominant species and the less abundant species are important.Thus, in case of perturbation and/or changes in abundance, the least abundant species could replace the dominant and keep the environment resilience (WALKER et al., 1999).
In our study, plots with greater functional diversity showed higher biomass wood stocks.That stock tends to be higher because of a niche complementation, in other words, species that occupy different niches do not compete against each other for the same resource, being rather complementary (DÍAZ; CABIDO, 2001;CAVANAUGH et al., 2014).Niche complementarily works as a guide for productivity and other ecosystem processes and it is more implicit, especially under conditions with relatively limiting resources when species need to differentiate their resource use strategies to be able to coexist (LOHBECK et al., 2015).When key resources are unlimited, dominant species (those more effectively using resources) can determine the biomass productivity (PAQUETTE; MESSIER, 2011).Other studies show this positive correlation between biomass/wood stock and functional diversity (TILMAN et al., 1996;LOREAU et al., 2001;CARDINALE et al., 2007;ZENG et al., 2012;CONTI;DÍAZ, 2013;ROSCHER et al., 2013;RUIZ-BENITO et al., 2014).Nonetheless, Freitas et al. (2012) have not identified significant relationship between the two variables when they were evaluating the effects of functional diversity on decomposition rate of woody assembly in cerrado sensu stricto.However, it is important to evaluate the effects of functional diversity in small scale, once that they can reveal more details about the mechanism of subjacent biologic stand (WIENS, 1989).
Functional diversity and its facets were able to explain up to 49% of the volume variation within the assembly.The functional diversity seems to explain the variation in productivity better than the climatic effects (CAVANAUGH et al., 2014;RUIZ-BENITO et al., 2014), and the effects of soil structure influence the production capacity of volume and biomass (COLE, 1986;RUIZ-BENITO et al., 2014).We can infer that functional diversity can explain the variation of primary productivity better in homogeneous environments in terms of soil and climate.
Primary productivity presents a near asymptote model, which is well adjusted to the logarithmic models.As soil characteristics may limit biomass production, so, it is expected that the present maximum wood volume inventory limit is due to environmental carrying capacity (MCKENDRY, 2002).This explains that the significant adjustments for the studied wood volume and functional diversity facets parameters were those with logarithms models.This corroborates the literature that suggests that logarithmic models are the most appropriate way to associate functional diversity and forest stock (TILMAN et al., 2001).
The models that best explained the variation of primary productivity within the assembly were not linear.Therefore, the facets of the functional diversity are not additive, i.e. complementary.Both aspects are important to clarify the changes on forest stock.In addition to these aspects alone, their interaction was also an important parameter in the explanation of wood volume variation within the assembly.The combination of functional community characteristics and aspects of functional diversity lead to a better evaluation of assembly stock variation than an individual analysis of each functional aspect (ROSCHER et al., 2013).
As we demonstrated in our study, functional diversity was positively related to biomass.Our hypothesis is true, that there is a positive relationship between functional diversity and wood volume on ecosystem services.Therefore, we can use those variables to forecast the effects of functional diversity loss on plant assemblages and communities, and on ecosystem services.With the relationship between functional diversity and ecosystem services better defined, we can quantitatively predict how much functional diversity can influence an ecosystem service.Thus, when applied those theories in the recovery of degraded areas, for example, we can predict what and how much each service will be recovered.

Figure 2 .
Figure 2. Graphic distribution of residuals on models for wood volume in the study areas of Cerrado sensu stricto, Brasília, Brazil.

Figure 3 .
Figure 3. Wood volume observed versus estimated for models tested in areas of Cerrado sensu stricto, Brasília, Brazil.

Table 1 .
Functional traits used to calculate the functional diversity of woody species in areas of Cerrado sensu stricto, Brasília, Brazil.

Table 3 .
List of woody species with individuals' number (IN) and wood volume (V) in areas of Cerrado sensu stricto, Brasília, Brazil.

Table 5 .
Models adjusting to quantify wood volume in areas of Cerrado sensu stricto, Brasília, Brazil.β i : Model parameters; p-value: level of significance ANOVA of the regression; S: standard error; R²adj: adjusted coefficient of determination.*: significant parameter with 95% probability.