The suppression of forests throughout history in order to develop land for other uses has reduced the Atlantic Forest to fragments, threatening the biodiversity of the Brazilian biome [1] . Currently, there is only 12% of the original Atlantic Forest coverage, with less than half of on protected areas [2] . Most of the agricultural land of Brazil, as well as most of the country’s population, 125 million inhabitants, are located in this biome.

Governments and nongovernmental organizations (NGOs) have supported rural communities as a way to promote conservation and sustainability of tropical forests in Latin America and the world [3] . Their actions are often directed towards the use of non-timber forest products (NTFP). For instance, in Brazil the National Plan for the Promotion of Socio-biodiversity Products was implemented in 2009 [4] .

There is, however, scarce information on the production and sources of NTFP variation of commercial interest. Since NTFPs are considered an important component in tropical forest conservation strategies, this supposes a contradiction [5] .

The Juçara palm (Euterpe edulis Mart.) is one of the most important, abundant and valuable non-timber forest products exploited in the Atlantic Forest. The extraction of palm heart is its main use [1] . The collection of palm heart involves logging entities. This causes the death of the plant, since it has a single stipe and does not regrow [6] . Secretly exploited in sections of the Atlantic Rainforest, palm heart harvest has been the greatest threat to the species [7] .

The exploitation of fruits for pulp production is a recent option of economic use that generates low impact on the Euterpe edulis population [8] . The product is equivalent to the Amazonian açaí, produced by Euterpe oleracea Mart. It is widely consumed today, due to its nutritional and health perspectives, such as the high energy, mineral and anthocyanin levels [7] .

Juçara is one of the few tropical species with potential for commercial exploitation. It can be cultivated in native forests through sustainable management practices that guarantee the conservation of the remaining forest fragments [9] . The increasing interest in the management of the species for pulp production makes it necessary to further study the variation in fruit productivity and its causes [10] .

Some recent studies have evaluated Euterpe edulis fruit production, however, no methodologies are proposed for using field survey data to estimate yield [10] [11] . Neither are there variables that quantify the competition suffered by sampled entities in models constructed for Juçara fruit production assessment.

Studies on competition among tree entities have received great attention because of their strong effects on control in the structure and development of stands [12] . Competition between trees takes place when there is a scarcity of resources: production decreases below entity demand [13] .

In growth models and forest production, tree competition is an important quantitative variable [14] . However, as authors report, this is difficult to measure because their direct causes are not known. There are three categories for competition indices [14] : distance independent, which use variables at settlement level; distance dependent, which insert size and location of neighboring or competing trees with the object tree; and distance semi-independent, which are calculated by considering the neighboring trees in circular plots around the object tree.

This investigation aimed at constructing a probabilistic model to predict the production of Euterpe edulis bunches; using dendrometric variables and competition index.

The present study was carried out in fragments of the Semideciduous Seasonal Forest belonging to the Dênis Gonçalves Settlement Project (21˚34'30"S and 43˚12'33"W), located in Zona da Mata/Minas Gerais, in February and March 2016 (Figure 1). The study area is between 409 m and 928 m of altitude. Latosols is the predominant soil class [15] . The climate in the region is classified as Cwb (Köppen), its altitude as tropical, mesothermic, with hot summers and high precipitation (October to April), and cold and dry winters (May to September) [16] . The annual average temperature is 18.7˚C and annual rainfall of 1528 mm.

Fragments in the settlement are of secondary forest and total 1393.8 ha. They are kept in the Legal Reserve―areas in the interior of rural properties that are destined for conservation, described in the Brazilian Law [17] . These are previously planted with Coffea arabica L, and that have been destined to natural regeneration for more than 60 years (personal communication).

Areas were first identified in order to quantify and measure Euterpe edulis entities. Parcels of forest inventory were randomly allocated at these sites.

Twenty plots of 500 m² (10 × 50 m) were measured, totaling a sampling effort of one hectare.

All living and dead standing shrubs, with circumference at breast height (CBH) equal to or greater than 15.0 cm (DBH ≥ 4.8 cm), were sampled. Each entity’s scientific name, CBH value measured with tape measure, total height, and pheno-phase were recorded. Identification of the botanical material was carried out by consulting the literature, specialists or by comparisons with specimens present in the herbarium of University of Brasília, according to the classification system APG III [18] .

Distance-independent competition indices (IID) [19] were calculated calculated in order to assess each Euterpe edulis entity’s competition (Table 1).

DBH, total height (h) and I I D 1 were selected using Pearson correlation coefficients (Table 2) for the construction of the bunches production model for occurrence probability. As for the significance test alpha = 0.05, the p-value was lower than 2.2e−16 for all indices.

Sampled individuals were stratified by their diametrical distribution and vertical structure, in order understand the influence of dendrometric variables on the production of Juçara clusters. The definition of vertical strata followed the criteria described by [20] (Table 3). Strata were calculated by plot, including all sampled tree entities, of all species found.