The experiment was carried out in the Experimental Field of Moju, belonging to Embrapa Eastern Amazon and located at Km 30 of the PA 150 highway, municipality of Moju, Pará state, Brazil, between the latitudes 2°07'30"S and 2°12'06"S and longitudes 48°46'57"W and 48°48'30"W. The region's climate is Ami (warm and humid), according to the Köppen classification (Alvares et al., 2013). Annual rainfall varies from 2,000 to 3,000 mm, irregularly distributed and the average relative humidity is 85%, with monthly average temperatures from 21 °C to 33 °C. The relief is plain, with slopes of 3% where Distrofic Yellow Latosols are the most common soils in the area, in different textures there are also Red-Yellow Podzols, Gley low humid, and Plintossols. The original vegetation of the study area is Ombrophilous Dense Forest (IBGE, 2012).

The experiment about the influence of logging gaps on the dynamics of Theobroma subincanum was established in 1998, one year after the conserved forest had been harvested under techniques of reduced impact logging (RIL) in 1997. Nine logging gaps opened by tree felling due to RIL were selected, where a minimum distance of 150 m between them was kept as a buffer zone to avoid possible influences on each other. Gap's areas were calculated by the ellipse formula, and varied from 231 to 748 m². In addition, logging gaps were divided in three size classes: small (200 - 400 m²), medium (401 - 600 m²), and large gaps (>600 m²). Three logging gaps were selected in each size class.

Four 10 m x 50 m strips starting from the logging gap's border towards the forest were established around every logging gap. Each one of the four strips was directed to the cardinal points North, South, East, and West. In addition, all strips were divided in five 10 m x 10 m permanent plots (Fig. 1).

After installing the permanent plots, individuals of T. subincanum with DBH ≥ 5 cm were identified and measured during the years 1998, 1999, 2000, 2001, 2007, and 2010, totaling six measurements in 12 years of monitoring (Table 1).

Density (seedlings m^-2) of T. subincanum, with the 10 x 10 m² plot as the sampling unit, was calculated in relation to the distances from the gap's border into the forest. Individuals of T. subincanum were divided in six diameter classes from DBH ≥ 5 cm with intervals of 5 cm. The six diameter classes were: 5.0 – 9.9 cm (1), 10.0 – 14.9 cm (2), 15.0 – 19.9 cm (3), 20.0 – 24.9 cm (4), 25.0 – 29.9 cm (5), and ≥ 30.0 cm (6). For comparisons, this distribution was done twice: in 1998 and 2010 (one year and 12 years after logging).

The diameter growth was calculated by the difference between diameters measured only in the alive trees along all five monitoring periods (1998-1999, 1998-2000, 1998-2001, 1998-2007, and 1998-2010), according to the formula (DBH_final – DBH_initial)/T_(time). From this measure, the Periodic Annual Increment in diameter (PAIdbh) was calculated.

The analysis of variance (ANOVA) was done through a Generalized Linear Model (GLM) for gap's size (small, medium, and large), distance in relation to the gap's border (plots far away 10, 20, 30, 40, and 50 m from the gap's border), and the time of experiment monitoring (12 years) on the dependent variable (PAIdbh). The data were analyzed through repeated measures ANOVA and, in case of significant differences among treatments, the post-hoc Tukey test was applied to compare means. All statistical analyses were run with the software R version 3.6.1 (R Development Core Team, 2019), at p < 0.05 of significance.

Seedling density in relation to the distance of the gap's border decreased up to 30 m from the gap's border, regardless the year after logging. The number of individuals per plot reduced from 7.00 at 10 m to 3.00 at 30 m from the gap's border. Density increased again at 40 m and 50 m after logging (Fig. 2).

In the first measurement after RIL (1998), the seedling density of Theobroma subincanum with DBH ≥ 5 cm, regardless the treatment, was 15.00 seedlings ha^-1 and in the last, 12 years after RIL (2010), was 17.78 seedlings ha^-1 (Fig. 3). Although varying among diameter classes, the diameter distribution of T. subincanum maintained an increasing shape in the two first classes (5.0-9.9 and 10.0-14.9) and a decreasing shape in the third class forwards (15.0 cm) during the entire monitoring period (Fig. 3). The largest changes in the distribution of individuals were observed in the first class (decrease) and in the third and fourth class (increase).

There was a significant difference in the Periodic Annual Increment in diameter (PAIdbh) of T. subincanum in relation to the distance of the individual to the gap's border (p = 0.001). The shorter is distance of the individual from the gap's border the higher is its PAIdbh (Fig. 4). There was a significant difference in the two first years after RIL among all plot distances in relation to the gap's border (10, 20, 30, 40, and 50 m). The 10 m distance presented higher increment (0.75 cm year^-1, F_4,63 = 4.97, p = 0.002) in the two first years. The year following RIL also influenced positively the seedlings growth (p = 0.001). PAIdbh was significantly higher in the first year after the application of RIL and decreased significantly from the second year after logging. From nine years after logging onwards, growth stagnated where no more differences in PAIdbh were observed in both plots distance from the gaps' border and time (p = 0.161). At the end of 12 years of monitoring, the seedlings had an average increase of 1.82 cm in diameter, which represented an average PAIdbh of 0.15 cm year^-1.

In relation to gap size, seedlings placed around small, medium, and large logging gaps did not present significant differences in PAIdbh (p= 0.308). Growth was higher during the three first years for all gap sizes (Fig. 5a). Seedlings around medium size gaps had higher PAIdbh in the two first years, however this was not statistically significant. Regarding cardinal points, there was no significant differences in PAIdbh (p= 0.503) in relation to each direction. Growth was highest in the first year after logging in all cardinal directions and started decreasing in response to canopy closing (Fig. 5b).

Seedling density of Theobroma subincanum had no relation with distances from the gap's border. The density of individuals reduced in the first 30 m and, from the distance of 40 m it increased again. This result shows that the distance from the gap's border had influence on T. subincanum growth (Fig. 4), but not on its density (Fig. 2).

The density of individuals of T. subincanum did not have any significant change during 12 years of monitoring (Fig. 3). A stable density indicates that recruitment and mortality rate were constant over time. Hence, the influence of logging gaps on T. subincanum was restricted to trees' growth and not to population dynamics, at least when considered individuals ≥ 5 cm in DBH. This is an indication that the species takes indirect advantage of canopy gaps caused by the fall of harvested trees.

The diameter distribution of T. subincanum in different periods showed the presence of seedlings in all classes, one and 12 years after logging, with no steep alteration along time. One year after logging, the number of individuals in the two first diameter classes (5.0-9.9 and 10.0-14.9) remained stable, distributed in a decreasing pattern from the third class forwards (15.0-19.9). Twelve years after logging, the number of individuals in class 5.0-9.9 diminished as a consequence of mortality and switch of individuals to upper diameter classes (Fig. 3). This distribution pattern is proper of shade-tolerant species. Although shade-tolerant species grow in conditions of close canopy and understory, they benefit from direct or indirect sunlight coming from canopy gaps, as well as direct light flecks that cross canopy and attain the soil (Jardim, 2015). Individuals of T. subincanum were distributed according to a reverse “J” shape, the most common distribution pattern of native tropical forests. This curve indicates a population dynamic balance of a shade-tolerant species, where most of the individuals are concentrated in smaller diameter classes.

In all analyzed plots, T. subincanum obtained higher growth in the first year of monitoring, which is related to higher availability of sun radiation reaching the forest floor. However, the longer is the plot distance from the border the lower is PAIdbh. According to Jardim (2015), shade-tolerant species benefit from the solar radiation coming from logging gaps, as well as small flecks of direct solar radiation coming from logging gaps or forest canopy. In studies carried out in the Tapajós National Forest, Eastern Amazon, Schwartz et al. (2012) observed that individuals of shade-tolerant species under total illumination obtained better growth rates than those under partial or with no illumination. Shade-tolerant species are sensible to low quantities of light, as even those plots far 40 and 50 m away from the gaps' border, two years after RIL, still presented statistical differences from each other. The difference in growth between the 40 and 50 m plots only disappeared in the third year after RIL (Fig. 4).

Theobroma subincanum stabilized its growth in diameter nine years after logging. According to Dionisio et al. (2017, 2018) growth, mortality, and recruitment rates in managed forests under RIL in the Eastern Amazon stabilize between seven and eleven years after logging.

The lack of difference in PAIdbh of T. subincanum when compared to gap size shows that small gaps, even when opened by branches fall, are sufficient to speed up growth of shade-tolerant species. Although the literature shows influence of gap size on species richness and growth, T. subincanum did not respond to this variable. This can be a pattern of responses of shade-tolerant species to light (Schwartz et al., 2012). While pioneer species demand high amounts of light to grow, shade-tolerant species need minimum amounts of light to develop. Any small increase in light is enough to trigger positive growth responses from shade-tolerant species. Large gaps promote higher germination and growth of individuals belonging to pioneer and light-demanding species and promote growth of shade-tolerant species. On the other hand, small and medium size gaps have low influence on germination and growth of pioneer and light-demanding species, but still promote growth of shade-tolerant species (Brokaw, 1985; Kobe et al., 1995).

Like gap size, the plots direction following cardinal points also did not interfere on T. subincanum growth. The dissimilar light availability in different cardinal points around the logging gap due to sunlight movements was not sufficient to promote different responses in growth of T. subincanum. Light incidence had great effect on T. subincanum growth, but not in relation to cardinal points around the gap. The location of a given individual inside a canopy gap can reflect on its growth, where there are differences in sunlight incidence in function of daytime (Denslow, 1980; Barton, 1984; Jardim, 2015), but not inside the forest immediately around the gap. Despite the fact that individuals of T. subincanum grew better in a light gradient, they did not respond to their location in cardinal points.