ECOLOGICAL AND FUNCTIONAL CLUSTERING OF FORESTAL SPECIES IN THE SOUTH WESTERN AMAZONIA

A floresta amazonica e uma mistura de centenas de especies, com diferentes idades e taxas de 
crescimento, o seu conhecimento, tanto para pesquisadores quanto para as populacoes 
amazonicas, e um grande desafio. O objetivo deste estudo foi efetuar o agrupamento 
ecologico e funcional de especies presentes na floresta do Estado do Acre. Este trabalho foi 
desenvolvido a partir de dados de 95 parcelas permanentes, com area de um hectare cada (100 
x 100m), subdividida em subparcelas de 10 x 10 e instaladas no Projeto de Colonizacao (PC) 
Pedro Peixoto, Floresta Estadual do Antimary (FEA) e ST Manejo. Nestas sub-parcelas todos 
os individuos com diâmetro a altura do peito (DAP) maior ou igual a 10 cm foram medidos. O 
periodo de coleta foi de 1996 ate 2007, com medicoes em intervalos de tempo nao regulares. 
O processo de agrupamento ocorreu em tres estagios: (1) analise de Cluster para fazer o 
agrupamento das especies mais populosas. Para esse processo foram empregadas as variaveis 
Incremento Periodico Anual em diâmetro - IPADAP medio em Alta, Media e Baixa competicao 
e percentil 95% da distribuicao de frequencia cumulativa dos diâmetros pelo metodo 
hierarquico Ward; (2) analise Discriminante, para alocar as especies menos populosas aos 
grupos formados, utilizando-se as variaveis percentil 95% da distribuicao de frequencia 
cumulativa dos diâmetros e os incrementos periodicos medios anuais em diâmetro (IPADAP) e 
o metodo de Fisher; (3) estagio subjetivo, utilizado para alocar as especies com poucos 
individuos aos grupos formados. O metodo Ward utilizado na analise de Cluster e o metodo 
de Fisher usado no discriminante demonstraram-se eficazes na criacao e formacao dos grupos. 
A utilizacao destes metodos resultou na formacao de dez grupos de especies com 
crescimentos de alta similaridade entre individuos do mesmo grupo e baixa similaridade entre 
grupos. As variaveis: IPADAP para o povoamento e IPADAP em baixa, media e alta competicao 
e P95 da distribuicao de frequencia cumulativa dos diâmetros demonstraram-se variaveis uteis 
para a realizacao do agrupamento de especies. As variacoes nas taxas de crescimento relativas 
a media total dos dados foram reduzidas quando calculada para cada grupo de especies.


INTRODUCTION
It is estimated that there are 12,000 tree species in Amazonia with different ages and growth rates (LLERAS; LEITE, 2005), what elevates the comprehension difficulty of the forest dynamics.According to Azevedo (2006), the forest dynamics can be summarized in the comprehension on the behavior of the growth, recruiting and mortality rates, in natural conditions and under management.
Works have been shown that dry land forest do not have only a high species diversity, but it also presents a high percentage of rare species represented by a unique individual per hectare (OLIVEIRA et al., 2008).Azevedo et al (2008) verified that there is a low number of species that can be individually modeled and that the species of commercial interest are represented by few individuals.
All of these factors become the comprehension and modeling of the forest growth dynamics into a great challenge.So, what is supposed to be done in order to soften the difficulty in the modeling process of the forest dynamics, since characterizing forest dynamics processes is essential for the sustainable management of the natural forests (EISFELD; SANQUETA, 2000).
Species clustering facilitate the forest dynamics modeling process , and when it is based on species ecological characteristics and structurally similar forests, it will contribute to the definition of methodologies and applicable practices in the development of management plans (FERRAZ et al., 2004).Besides, the clustering of tree species can be useful to the elaboration of tropical forests growth and production simulation models capable to produce information to be applied in forest conservation, sustainable forest management, degraded areas rehabilitation and in studies aiming to find new alternatives to tropical forest management.
This study aimed to do an ecological and functional clustering of tree species present in the southwestern Amazon., seeking out to define: i. useful variables for the groups' formation, ii.diameter annual periodic increment and the most representative species of each formed group.Specifically, we test the hypothesis that the growth rates mean variance is reduced related to the total average will be reduced when it is calculated for each group of species.

MATERIAL AND METHODS
This study has been developed from data of 95 permanent plots installed in the Project of Colonization (PC) Pedro Peixoto, Antimary State Forest (FEA) and in the areas of the company ST Manejo.These plots are located in the states of Acre and Amazonas, Southwestern Amazonia.According to Köeppen classification, the weather is Am, corresponding to hot and humid with short period of dry season, with high temperatures, high and high levels of rain precipitation and high relative humidity of air.The forest typology that happens in the region corresponds to the open ombrophylous forest with palm trees, open ombrophylous forest with bamboo; dense forest; and alluvial forest.The measured plots have an area of one hectare each (100m x 100m) according to the guidelines of measurement and installation of permanent plots in Amazonia defined by SILVA et al. (2005).Each plot is divided by 100 sub-plots of 10 m x 10 m.In these subplots, all the individuals with diameter to the chest high -DAP e" 10 cm have been plated.
The annual improvements in diameter (IPA DAP ) for all the species in all the measurements intervals have been established for the competition levels, 'high', 'low', through using the independent diameter of the competition rate (C).The Competition Rate, C t , for the tree t, it is based on the location of each tree in the subsample: Where: z 1 , z 2 e z 3 = coefficients of relative importance for the competitions of the zones 1, 2 and 3, respectively; i, j and k = trees 'over-topping' in all the three zones; D = tree diameter.
The zone 1 is a square of 10 x 10 m contenting t trees and the zones 2 and 3 are defined as relative for the zone 1 (Picture 1).
The values used for the parameters z 1 , z 2 and z 3 , in the calculus of the absolute competition rate for each tree, were 9, 4 and 1, respectively.These values have been arbitrarily selected to represent the reduction in the concurrence with the distance increase among the trees.The difference between the species ecological clustering has been measured through the method of Ward through the standardized Euclidian distance.The following variables have been used: Annual improvement in diameter (IPA DAP ); IPA DAP in low competition; IPA DAP in medium competition; IPA DAP in high competition; Percentile 95% of the distribution of cumulative frequency of the diameters -DAP (P 95 ).

b) Discriminating Analysis -less populous species (20 < N < 50)
The species with at least 20 and less than 50 trees have been considered in order to do a discriminating analysis based on the percentile point 95% (P 95 ) and in the annual improvement in diameter (IPA DAP ), through the method of Fisher, in order to add to the groups formed in the Cluster.

c) Subject Method -(N < 20)
The species that present the number of individuals smaller than 20 have been added to the existing groups through subjective analysis, through the use of ecological characteristics such as: IPA DAP (found in other works), botanic classification and sociological position.
The hypothesis test for the equality between both population variances in a significance level of 5% has been used, in order to confirm the affirmation that the variations in the relative growth rates at the average would be reduced when calculated for each species group.NETO, E.L.V. et al.The study area has presented a diameter improvement of 0.36 cm/year.The species that represented bigger medium improvements were: Ceiba pubiflora (a.St.-hil.)k.Schum with 1.6 cm/year, Eschweilera parviflora (Aubl.)Miers with 1.4 cm/year and Swietenia macrophylla King with 1.4 cm/year.However, species like: Myrcia jabuticaba (Vell.)Baill.and Theobroma sp have presented an IPA DAP of 0.02cm/ year, the smallest diameter growth.

Hypothesis: H
Among the 604 species that were found in the study area, 142 (23.5%) had a unique measurement.
The relation between the Competition rate for each tree (Ct) and its respective diameter (D) has been described through the following nonlinear model.The model explains 72.12% of the total variation that happens in the Competition Rate (Ct), and it represents a standard mistake of the estimative of 37.25%.All the coefficients were significant at 1% of probability.
Most species, as expected, tends to present bigger growth in 'Low Competition' or it grows in a slower speed in 'High Competition'.In average terms, in 'High Competition', the species improve 0.21 cm/year while in 'Low Competition', the average improvement was 0.42 cm/year (Picture 2).
It has been checked that 50% of the species have P 95 bigger than 30 cm.The species Picramnia sp and Sterculia striata St. Hil.& Naudin have shown the smallest values of P 95 (10.2 cm), it means, that the species with individuals of smaller diameters.Thirteen species, or 2.1% of the total, have shown P 95 bigger than 100 cm.Among these species with big diameters are Bertholletia excelsa Bonpl.and Hymenaea courbaril L. with 128 and 124.8 cm respectively.

a) Cluster Analysis (most populous species -N > 50 individuals)
One hundred sixty (166) species have been through this stage of the clustering process.They are species with high representativeness and have 89.17% of the present individuals in the area (Table 1).The 34,242 trees from these species have presented 36,803 growth measures.
The Cluster Analysis has identified the natural division in the forest, classifying -in the same group -species with similar growth and ecological characteristics, as for example, Bertholletia excelsa Bonpl.and Dipteryx odorata (Aublet) Willd, clustering 6, denominated as emerging and climax that are present in the forest superior dossal.Ecological and functional clustering of forestal...
The clustering process demands that the user decides on how many groups can exist in advance.The choice of the number of groups is subjective, but it must look for equilibrium between having more data per group and, more groups that represent the variation in the forest.With visual representations, using the characteristic variables values, it is possible to provide subjective judgment on the clustering utility.This is easy with 2 variables, however, no subjective judgment was undertaken.Consequently, the total of groups has been defined based on the previous studies of Phillips et al. (2001Phillips et al. ( , 2002)), so allowing comparisons with other works that had used the same quantity.

b) Discriminating Analysis -less populous species (20 < N < 50)
The least populous species have been allocated in 10 groups created by the Cluster Analysis.79 species that were used in the discriminating analysis -this corresponds to 2,477 individuals and 4,074 growth measures.

c) Subjective Method -(N < 20)
The 362 remaining non grouped species have been added to groups that were created based on the average and standard deviation of the IPA DAP .However, 117 species that did not have growth measures have been allocated in a manual way, based on the ecological characteristics available in the literature.
In the ten clustering formation, 40,877 growth measures, 38,401 individuals and 604 species have been found.The Table 2 presents the main characteristics of each group.Group 8, named 'Fast Growth Pioneers', has presented the bigger improvement, average 0.97 cm/ year, over the growth average of the study area, 0.36 cm/year.Among these representative species, we have: Cecropia palmata Willd and Pourouma bicolor Mart, popularly known as 'imbaúba, imbaubarana'.Species that normally are the first to appear in an area that has suffered a kind of disorder.
In a general way, the other groups are formed by intermediate species that are classified as species of inferior, medium and superior canopy, with fast or slow growth.
The Table 3 presents the results of the tests of population variance equality with each group of specie.
Based on the values of probability associated to the test F, one can say that the situations, to the level of 5% of significance, refuse the hypothesis of nullity, it means, the general variance of the IPA DAP is bigger than the IPA DAP variance in each group.

DISCUSSION
The study area has presented a diameter improvement of 0.36 cm/year.This result is lower than the ones that were found by Junior et al. (2007) who found a diameter improvement of 0.40 cm/year in plots of 10 ha and by Vieira (2003) who, while measuring individuals with diameter over 10 cm, found a diameter improvement of 0.39 cm/year.Both results mentioned before have been obtained in study areas in Acre/Brazil.However, this result is higher than the one found by Vieira (2003) in the regions of Manaus (Amazonas) and Santarem (Para) that had a diameter improvement average rate of 0.31 and 0.17 cm/year respectively.According to this author, in Santarem, the forest is classified as dry land dense ombrophylous.This indicates that this difference in the average rate of the diameter improvement can be related to the fact that the comparison is being done among regions with different forest typologies.
However, the result found by Colpini et al. (2008) were similar to the ones found in this sturdy.They measured 69 permanent plots installed in Marcelandia (Mato Grosso) from 2001 to 2007 and found a diameter improvement of 0.34 cm/year.According to BRASIL (1981), this study area in Marcelandia is an ecological tension area in the region of contact ombrophylous forest/seasonal forest, with predominance of the formation named semideciduous forest.NETO, E.L.V. et al.
Once all the clustering stages are done (Cluster Analysis, Discriminating Analysis and subjective Method) you can observe a summary of the main characteristics of each group in the table 2. The group 8 (named Fast Growth Pioneers) is highlighted and it shows the bigger average improvement, average of 0.97 cm/year, bigger than the average of growth of the study area, 0.36 cm/year.Among the representative species of this group, we have: Cecropia palmata and bicolor Pourouma -species that are normally the first ones to appear in the area that had suffered any kind of disorder.According to Laurance et al. (1998), the first bodies to colonize the habitat receive the name of pioneers.They are species that need bigger quantities of light and they compete for the soil resources.
Group 7, named Emerging -Climax, is composed by species from this type.Here they are: Bertholletia excelsa Bonpl., Ceiba pentandra (L.) Gaertn., Dipteryx odorata, Copaifera multijuga.These species present a fast growth and the biggest DAPs.Budowski (1966) says that the biggest diameters are found in the late secondary species and climax, what the P 95 of 107.5 cm confirms -bigger than all.
When Lira (2011)   G is the number of the group, P 95 is the percentile 95% of the diameter (cm) accumulated distribution, IPA is the annual improvement in diameter (cm/year -1 ), Nt is the number of trees, Ns is the number of species in each group, sIPA are standard deviations.(MACIEL et al., 2003) and this can explain an IPA DAP of 0.74 cm/year for this group.

Group
Group 1, named Slow Growth, Medium Canopy, has an IPA DAP of 0.25 cm/year, a low growth if it is compared to the average of the area growth.This slow growth is explained due to the fact of this group show a bigger quantity of individuals per specie, as it can be observed in Table 2, and this considerably raises the competition among individuals with similar necessities.It is composed by species such as Theobroma microcarpum Mart, Pseudolmedia laevis (Ruiz & Pav.) J.F. Macbr and Pouteria sp, which are the most abundant in the area.According to Klein (1983), the lower canopy is one of the densest stratums of the forest composed by a great quantity of species that are composed by individuals that live in 'High Competition'.
Group 5, introduced in the Table 2 as Very Slow Growth, Lower Canopy, shows the smallest IPA DAP , 0.13 cm/year.The smallest average improvement found by Azevedo (2006) e Lira (2011) in his clustering was 0.09 cm/year, slow growth, understory.

CONCLUSION
Based on the obtained results, it is possible to conclude that: The Ward method used in the Cluster analysis and the Fisher method used in the discriminating have been efficient in the creation of the groups' formation; The variables general IPA DAP , in low IPA DAP , in medium IPA DAP , in high Competition IPA DAP and P 95 of the distribution of the cumulative frequency of the diameters were useful variables for the species clustering formation; The clustering has allowed a better ecological and functional knowledge of the species that have similarity in the average annual improvement and in the Percentile 95% of the distribution of the diameters cumulative frequency -DAP; The variations in the growth rates related to the data total average have been conducted when calculated for each species group.
The competition rate has been calculated based on the following way: C = C t -C t The predicted competition rate C t is the result of the adjustment of the relation between C t e D, according to the equation below:Where:C t =Predicted value of the competition rate, C t ; D = Tree diameter; b 0 , b 1 and b 2 = parameters.Values of C over 40.0 were classified as being 'High Competition' and values under -40.0 were classified as being 'Low Competition'.The values of this interval (-40 < C < 40) were defined as 'Medium Competition'.The process for species clustering has involved trees stages: a) Cluster Analysis (most populous species -N > 50 individuals)

Table 1 -
Population level by species in the study area.Tabela 1 -Nível populacional por espécies na área de estudo.
did the ecological and functional clustering for the Western Amazonia also noticed the Pioneers and the Climax in the groups' formation.Group 10, classified as Late Secondary presents a high P 95

Table 2 -
Description of the ten groups resulting from the clustering process.Tabela 2 -Descrição dos dez grupos resultantes do processo de agrupamento.

Table 3 -
F values and probability of hypothesis test at 5 % significance level.Tabela 3 -Valores de F e de Probabilidade do teste de hipótese ao nível de 5% de significância.Ecological and functional clustering of forestal...