Balancing Accuracy and Efficiency: Optimal Plot Design for Regeneration Sampling in Amazonian Secondary ForestsABSTRACT
Background Optimal sampling designs are crucial for accurate ecological and forestry assessments, particularly for regeneration studies in Amazonian secondary forests, which play an important role in biodiversity conservation and carbon sequestration. This study evaluated different sampling plot configurations for estimating regeneration diversity and structural attributes in a 30-year-old secondary forest in Belém, Brazil. Within a one-hectare permanent plot (100 × 100 m), all trees with a diameter at breast height (DBH) ≤ 10 cm were measured, identified, and geolocated, totaling 3,003 individuals. Trees were classified into two diameter classes: DBH < 5 cm and 5 cm ≤ DBH ≤ 10 cm. Resampling simulations using the bootstrap method subdivided the one-hectare plot into four sampling plot sizes (4 m², 25 m², 50 m², and 100 m²) with rectangular and square shapes. Simulations tested sample sizes ranging from four to (N − 1) units, with 1,000 iterations per configuration.
Results Accuracy and precision for diversity metrics (species richness and Shannon–Weaver index) and structural attributes (tree density, stem density, and basal area) were evaluated using Mean Absolute Error (MAE) and Relative Sampling Error (RSE). Results indicated that 4 m² sampling plots were the most suitable for estimating diversity metrics across both diameter classes, regardless of plot shape. For structural variables, square 4 m² plots performed best for trees with DBH < 5 cm, whereas rectangular 50 m² plots were optimal for trees with 5 cm ≤ DBH ≤ 10 cm. The influence of plot shape varied depending on the variable analyzed and the sampling plot size.
Conclusion Overall, sampling plots of 4 m² and 50 m² are recommended for efficient regeneration sampling in Amazonian secondary forests, as they provide better accuracy and precision for diversity and structural estimates across different diameter classes.
Keywords:
Forest inventory; sampling simulation; urban forest; forest degradation
Introduction
Secondary forests are critical ecosystems undergoing regeneration after severe natural or anthropogenic disturbances (Chokkalingam and De Jong, 2001). These disturbances often compromise essential ecosystem services, such as biodiversity conservation (Arasa-Gisbert et al., 2024) and carbon sequestration (Bullock and Woodcock, 2021; Pan et al., 2024). In the Amazon region, the transition from old-growth forests to less carbon-dense secondary forests, driven by deforestation and degradation (Smith et al., 2021), poses a significant challenge to the region’s role in mitigating climate change (Qin et al., 2021). Addressing these challenges requires an understanding of the ecological dynamics of forest regeneration and the development of strategies to optimize the restoration of ecosystem functions.
Forest restoration has emerged as a central approach to reestablishing the carbon storage capacity and biodiversity of secondary forests, thereby ensuring the long-term sustainability of ecosystem services (Bieng et al., 2021). Restoration success is measured against benchmarks derived from mature or older secondary forests, which serve as reference points to guide the recovery process (Shackelford et al., 2024; Chazdon et al., 2023). Attributes such as species composition, biodiversity indices, tree density, basal area, biomass, and abiotic conditions underpin restoration objectives (Giles et al., 2024).
Regeneration, defined as the recovery of richness, structure, and functional traits in disturbed forests, is a pivotal aspect of forest restoration (Hanbury-Brown; Ward; Kueppers, 2022). Small-diameter trees play a crucial role in regeneration, often relying on canopy gaps for growth, although some species can persist under shaded conditions (Swaine; Whitmore, 1988). Evaluating the diversity and structural characteristics of regenerating trees helps determine the resilience of secondary forests and provides insights into whether they can retain their ecological integrity (Brasil Neto et al., 2021; Zébazé et al., 2023). However, one of the challenges in assessing regeneration is optimizing inventory methods to strike a balance between precision and efficiency.
Forest inventories are indispensable tools for quantifying forest regeneration and growth. Their effectiveness depends on appropriate sampling plot configurations, specifically size and shape, which directly affect sampling accuracy and cost efficiency (Lister; Leites, 2021; Pinto et al., 2021). Recent advancements in methodologies, such as UAV-borne laser scanning highlighted by Sferlazza et al. (2022), show promise for refining sampling techniques and enabling enhanced monitoring of forest dynamics. This study demonstrates how technology-based approaches can complement traditional inventories, particularly in areas with complex topographies and dense canopies.
Seedling growth stages and environmental conditions further influence the dynamics of tree regeneration. Harris et al. (2022) emphasize the importance of subdividing seedlings into height classes to better predict sapling recruitment, as taller seedlings are more likely to contribute to forest recovery. Incorporating this approach into regeneration assessments improves the accuracy of forecasting stand development trajectories. Additionally, permanent plots are essential for monitoring tree communities, allowing the capture of ecological and structural changes that can inform restoration strategies (Phillips, 2023). The relationship between seedling diversity and regeneration is also assessed using rarefaction and extrapolation techniques (Chiu, 2023). These statistical methods enhance the reliability of regeneration estimates and ensure adequate representation of tree species, even in highly diverse ecosystems like the Amazon. Integrating such advanced analytical tools into inventory designs can bridge gaps in understanding regeneration dynamics.
This study seeks to address the critical question: What are the optimal plot configurations for assessing regeneration diversity and structural variables in tropical secondary forests? Comparing optimal plot size and shape, and drawing on prior literature and recent advancements, the research hypothesizes that larger plot sizes minimize sampling errors and that square-shaped plots yield more consistent estimates of diversity and density. By focusing on regeneration processes and inventory optimization, the findings aim to inform evidence-based practices for restoring secondary forests and enhancing their contributions to mitigating global climate change.
Material and Methods
Study Area
The study area corresponds to a secondary urban forest that has undergone natural regeneration for approximately six decades following experimental land use and subsequent abandonment (Terezo, 2014; Guzmán, 2022). Although exhibiting structural and compositional attributes typical of mid- to late-successional forests, the site remains subject to low-to-moderate anthropogenic disturbance due to its urban context. The forest located near the Institute of Agricultural Sciences (ICA) at the Federal Rural University of Amazonia (UFRA) in Belém, Pará, Brazil. The central point of the experimental area is situated at coordinates 1°27’24”S and 48°26’15”W. This forest represents a tropical humid ecosystem with an average annual temperature of 27°C and rainfall of approximately 2,834 mm, classified as Af by the Köppen-Geiger system. The predominant soil type is a concretionary laterite alisol with low base saturation (Santos et al., 1983). The experimental area has been planned for a permanent plot establishment since 2017 and has been remeasured annually to monitor forest dynamics and regeneration.
Installation of the Experimental Area
An aerial georeferenced image produced by a drone in 2017 was used for inventory planning. The high-resolution image, with spatial resolution at the centimeter scale typical of UAV surveys, projected in UTM coordinates, facilitated the delineation and analysis of the study area. The site was selected for its lack of flooding during rainy periods and its well-established natural regeneration. A permanent plot measuring 1-hectare (100 m x 100 m) was installed using a Ruide R2 Total Station to accurately define the external boundaries and internal subdivisions. The permanent plot was subdivided into 4 blocks (50 m x 50 m), each containing 25 subplots (10 m x 10 m), for a total of 100 subplots. Topographic stakes were placed at each vertex to ensure durability and ease of relocation for future assessments. Subplot divisions were performed manually through geometric triangulation, using two 50 m measuring tapes simultaneously to position each vertex based on fixed distances to adjacent and perpendicular reference points, ensuring accurate 10 × 10 m subplot layout despite challenging field conditions.
Data Collection
The inclusion criterion for the forest inventory was trees less than 1.3 m in height and with a diameter at breast height (DBH) ≤ 10 cm, classified as natural regeneration to distinguish these juvenile individuals from the mature population. Data collection was organized by grouping subplots into strips, with each strip consisting of five subplots (10 m x 50 m). Measurements followed a systematic path along these strips. In each subplot, we measured all stems meeting the inclusion criteria, and the subsequent analysis divided this data into the number of trees per hectare (D) and the number of stems per hectare (Ds), as some individuals had more than one stem.
A digital caliper was used for stems with a diameter at breast height (DBH) ≤ 5 cm, and a measuring tape was used for stems with a DBH > 5 cm. Measurements included quantitative variables (DBH, XY coordinates, basal area) and qualitative variables (health condition, crown illumination, stem classification). Each individual was marked with red oil-based paint at the measurement height for future remeasuring, and identification numbers were assigned using plastic tags. Botanical identification was primarily conducted in the field with the help of a parabotanist, and the trees not identified by this method were collected and dried for subsequent identification using field guides and other specialized literature.
Georeferencing and Sampling Simulations
All field data were digitized and subsequently organized into a geospatial database. Cartesian coordinates for each tree were adjusted to match their true positions within the plot. Georeferencing utilized “control points” placed at the plot vertices, ensuring spatial accuracy for further analysis. The geospatial database facilitated the visualization and manipulation of tree distribution and characteristics across the study area. For the regeneration sampling, we divided the database into two groups: trees with DBH < 5 cm and trees with 5 cm ≤ DBH ≤ 10 cm, to identify the best plot configuration for each diameter class. Resampling simulations using the bootstrap method were conducted with a fixed-area random sampling design, dividing the 1 ha plot into four smaller plot sizes (4 m², 25 m², 50 m², and 100 m²), with square and rectangular plot shapes, resulting in eight different plot configurations. We selected these sampling plot sizes to optimize the 1-ha permanent plot area and because they had already been used in previous studies. Simulations tested sample sizes from four to (N - 1) units, with 1,000 iterations per configuration, and not discarding zero-plots, plots without trees, from the simulated samples. Simulations were performed using R, and statistical metrics, including mean, variance, mean absolute error (MAE), and relative sampling error (RSE), were calculated. The acceptable sampling error was 10%, a technical standard widely used in tropical forest inventories and frequently required in environmental licensing processes in the Amazon.
Data Analysis
Five key variables were analyzed: the number of trees per hectare (D), the number of stems per hectare (Ds), basal area (G), richness, and the Shannon-Weaver index. Estimates were extrapolated for a 1-hectare scale. Statistical analyses were conducted to evaluate the accuracy and precision of various sampling designs, with the aim of optimizing efficiency while ensuring compliance with technical and ecological standards. The results were organized by creating graphs comparing the MAE and RSE with the sampled area to assess their impact on precision and accuracy. This allowed us to determine which plot required less sampling intensity to achieve the lowest MAE and an RSE of 10%, the standard in forestry practices for the Amazon. The diversity variables were compared with the sampled area for the same purpose.
Results
The total count of individual stems measured in the 1 ha plot was 4,406, of which 3,647 had DBH < 5 cm and 759 had 5 cm ≤ DBH ≤ 10 cm, while the basal area of the plot was equal to 4.51 m² ha−1 for all stems. These stems belong to 3,003 trees in total, distributed across 40 botanical families, 67 genera, and 87 species. (Table 1).
The species richness was 83 for trees with DBH < 5 cm and 55 for trees with 5 cm ≤ DBH ≤ 10 cm. In both classes, species richness increased linearly with sampled area, with little variation in estimates across the sampling plot sizes and shapes tested. Regardless of the sampling plot configuration, a sampled area of 0.87 to 0.95 ha for DBH < 5 cm, and 0.85 to 0.95 ha for 5 cm ≤ DBH ≤ 10 cm, was necessary to obtain the parametric value of richness. (Figure 1; Figure 2).
The Shannon–Weaver index was 3.21 nats/ind. for trees with DBH < 5 cm and 3.16 for trees with 5 cm ≤ DBH ≤ 10 cm. For trees with DBH < 5 cm, rectangular or square 4 m² plots required 0.66 ha of sampled area to obtain the parametric value; rectangular or square 100 m² plots required around 0.85–0.86 ha. For trees with 5 cm ≤ DBH ≤ 10 cm, rectangular or square 4 m² plots required 0.70–0.71 ha, while rectangular or square 100 m² plots required around 0.88–0.90 ha.
The D of the 1 ha plot totaled 2,389 trees with DBH < 5 cm, and MAE analysis showed that the 4 m² sampling plot yielded the best results. For the 5 cm ≤ DBH ≤ 10 cm diameter class, D was equal to 614 trees, and the 4 m² sampling plot also had the best results, although sampled area had greater influence on accuracy than in the smaller diameter class. (Figure 3; Figure 4).
The Ds for trees with DBH < 5 cm were 3,647 stems; the smaller sampling plots were the most precise, with the 4 m² sampling plot being the most accurate. In this case, plot shape influenced the results, with a square plot yielding better accuracy for all plot sizes. For trees with 5 cm ≤ DBH ≤ 10 cm, the Ds was 759 stems, and greater accuracy was obtained by the rectangular 50 m² sampling plot.
G for the DBH < 5 cm diameter class was 1.6077 m², and the smaller sampling plots performed better, with the square 4 m² sampling plot being the best. For the 5 cm ≤ DBH ≤ 10 cm diameter class, G was equal to 2.9074 m², and the best overall results were obtained with the rectangular 50 m² sampling plot. Relative sampling error results are presented in Figure 5 and Figure 6.
Ecological variables of trees with DBH < 5 cm in a one-hectare sampled area. A – richness; B – Shannon–Weaver index. The graphs are on a logarithmic scale to facilitate visualization, and the horizontal dashed black line indicates the parametric value of each variable.
Ecological variables of trees with 5 cm ≤ DBH ≤ 10 cm in a one-hectare sampled area. A – richness; B – Shannon–Weaver index. The graphs are on a logarithmic scale to facilitate visualization, and the horizontal dashed black line indicates the parametric value of each variable.
Mean Absolute Error (MAE) of the structural variables of the DBH < 5 cm diameter class in the 1 ha plot in relation to the sampled area. A – Tree density, B – Stem density, and C – Basal area. MAE – Mean Absolute Error, D – Tree density, Ds – Stem density, G – Basal area. The graphs are on a logarithmic scale to facilitate visualization.
Mean Absolute Error (MAE) of the structural variables of the 5 cm ≤ DBH ≤ 10 cm diameter class in the 1 ha plot in relation to the sampled area. A – Tree density, B – Stem density, and C – Basal area. MAE – Mean Absolute Error, D – Tree density, Ds – Stem density, G – Basal area. The graphs are on a logarithmic scale to facilitate visualization.
Relative Sampling Error (RSE) of the structural variables of the DBH < 5 cm diameter class in the 1 ha plot in relation to the sampled area. A – Tree density, B – Stem density, and C – Basal area. RSE – Relative Sampling Error, D – Tree density, Ds – Stem density, G – Basal area. The graphs are plotted on a logarithmic scale to facilitate visualization, and the horizontal black dashed line indicates a relative standard error (RSE) of 10%.
Relative Sampling Error (RSE) of the structural variables of the 5 cm ≤ DBH ≤ 10 cm diameter class in the 1 ha plot in relation to the sampled area. A – Tree density, B – Stem density, and C – Basal area. RSE – Relative Sampling Error, D – Tree density, Ds – Stem density, G – Basal area. The graphs are plotted on a logarithmic scale to facilitate visualization, and the horizontal black dashed line indicates a relative standard error (RSE) of 10%.
Structural variables of the trees (DBH ≤ 10 cm) measured in the 1 ha plot of Amazon secondary forest situated in Belém, State of Pará, Brazil.
D – Tree density, DS – Stem density, G – Basal area (m² ha−1), NI – Not identified.
Discussion
Overall, the diameter distribution for natural regeneration followed a negative exponential curve, indicative of uneven-aged native forests, and the basal area of 4.51 m² ha−1 closely aligns with estimates reported for sites under regeneration in ombrophilous dense forest. These findings corroborate established patterns of regeneration dynamics under light and environmental constraints.
When considering regeneration diversity, a single smaller plot will produce a less accurate estimate than a single larger plot; however, all plot sizes and shapes can accurately estimate diversity variables with the appropriate sampled area. In this case, the decision regarding the ideal sampling plot size and shape is based on time and cost constraints, as well as operational practicalities.
For structural variables, the square 4 m² sampling plot achieved the best accuracy when sampling the DBH < 5 cm diameter class. The rectangular 50 m² sampling plot yielded the best results for the Ds and G variables for the 5 cm ≤ DBH ≤ 10 cm diameter class, while for D, the best results were obtained with the 4 m² sampling plot, independent of shape.
The discrepancy between MAE and RSE results shows the difference between accuracy and precision in forest sampling. Sampling with smaller plots achieved a precision of 10%, covering a significantly smaller area compared to larger plots. However, due to the strong bias in sampling D, Ds, and G, the accuracy of the estimates varied depending on the diameter class and plot size used. (Table 2).
Our findings showed that, for ecological variables such as richness and the Shannon–Weaver index, the 4 m² sampling plot was the most effective, regardless of plot shape or diameter class. It is important to note that 218 trees were not identified and therore were not included in the ecological variables analysis. This limitation likely rlects challenges in identifying juvenile trees and seedlings in the Amazon.
Conclusion
Sampling simulations highlighted the efficiency of square plots of 4 m² and rectangular plots with 50 m², particularly when several sampling units were used. These results validate the applicability of fixed-area sampling and demonstrate the value of integrating spatial tools, such as GIS, for inventory optimization.
This study confirms that random sampling, combined with advanced geospatial technologies and sound statistical methodologies, can yield high-accuracy forest inventory data. Contrary to the initial hypothesis, the largest sampling plot was not the most effective under all sampling conditions. The influence of plot shape on accuracy depended on multiple factors, making it impossible to recommend a single plot shape for all scenarios.
This paper is a product of Vitor Mateus de Carvalho Morais’s Master’s thesis in forest science. The authors are grateful to the Graduate Program in Forest Sciences from the Federal Rural University of Amazon (UFRA) for the opportunity to conduct this study. We also thank the Laboratory of Mensuration and Forest Resource Management (LabFor) for their support in preparing this manuscript. This work is part of the research project “Dynamics of Urban Forests and Their Effect on the Planning of Anthropized Ecosystems in Belém and Surrounding Regions”.
Authorship Contribution
Project Idea: FE; RGMN
Funding: FE; RGMN
Database: RGMN; FE
Processing: BBB; VMCM
Analysis: BBB; VMCM; RGMN
Writing: VMCM
Review: BBB; DVS; FE; RGMN
Data Availability
The datasets analyzed during the current study are available from the corresponding author upon reasonable request.
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Scientific Editor:
Rafaella Carvalho Mayrinck
