Artificial Intelligence (AI) Calculator for “Tree competition index calculator”
Tree competition index calculators quantify the competitive pressure among trees in a forest stand. These indices help foresters assess growth potential, resource allocation, and stand dynamics.
This article covers key formulas, practical tables, and real-world examples to master tree competition index calculations effectively.
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Example User Inputs for Tree Competition Index Calculator
- Calculate competition index for a 30 cm DBH tree with 5 neighbors within 10 m radius.
- Determine Hegyi competition index for a 25 cm DBH tree surrounded by 3 trees of 20, 15, and 10 cm DBH.
- Compute basal area competition index for a stand with total basal area of 25 m²/ha and subject tree basal area of 0.5 m².
- Evaluate distance-dependent competition index for a 40 cm DBH tree with neighbors at distances 3 m, 5 m, and 7 m.
Comprehensive Tables of Common Values for Tree Competition Index Calculations
| Competition Index Type | Typical Range | Interpretation | Common Units |
|---|---|---|---|
| Hegyi Competition Index | 0 – 5 | Low to high competition pressure | Dimensionless |
| Basal Area of Larger Trees (BAL) | 0 – 30 m²/ha | Higher values indicate stronger competition | m²/ha |
| Distance-Dependent Index (e.g., Hegyi Distance) | 0 – 10 | Higher values mean closer and larger neighbors | Dimensionless |
| Crown Competition Factor (CCF) | 0 – 100% | Percentage of crown overlap or shading | % |
| Stand Density Index (SDI) | 0 – 5000 | Indicates stand stocking relative to maximum density | Trees/ha scaled |
| Variable | Typical Values | Description | Units |
|---|---|---|---|
| DBH (Diameter at Breast Height) | 5 – 100 | Tree diameter measured at 1.3 m above ground | cm |
| Distance to Neighbor Tree (dij) | 1 – 20 | Horizontal distance between subject and neighbor tree | m |
| Basal Area (BA) | 0.01 – 2.0 | Cross-sectional area of tree stem at breast height | m² |
| Number of Neighbors (N) | 1 – 20 | Count of trees considered around subject tree | Count |
Fundamental Formulas for Tree Competition Index Calculator
Tree competition indices quantify the influence of neighboring trees on a subject tree’s growth by integrating size and spatial relationships. Below are the most widely used formulas with detailed explanations.
1. Hegyi Competition Index (Distance-Dependent)
The Hegyi index is a classic distance-dependent competition index that sums the ratio of neighbor tree sizes to the subject tree size, weighted by the inverse of the distance between trees.
- CIi: Competition index for subject tree i
- Sj: Size measure of neighbor tree j (e.g., DBH, basal area)
- Si: Size measure of subject tree i
- dij: Distance between subject tree i and neighbor tree j (meters)
- N: Number of neighboring trees considered
Interpretation: Higher values indicate stronger competition due to larger neighbors closer to the subject tree.
2. Basal Area of Larger Trees (BAL)
BAL quantifies the total basal area of all trees larger than the subject tree within a specified area, reflecting competitive pressure from dominant neighbors.
- BALi: Basal area of larger trees around subject tree i (m²/ha)
- BAj: Basal area of neighbor tree j (m²/ha)
- M: Number of trees larger than subject tree i
Interpretation: Higher BAL values indicate greater competition from larger trees, often correlating with reduced growth rates.
3. Stand Density Index (SDI)
SDI standardizes stand density by adjusting for tree size, allowing comparison across stands with different tree sizes.
- N: Number of trees per hectare
- D: Quadratic mean diameter of trees (cm)
- 25.4 cm is the reference diameter (1 inch)
Interpretation: SDI values near maximum stocking levels indicate high competition and potential self-thinning.
4. Crown Competition Factor (CCF)
CCF estimates the proportion of site area occupied by tree crowns, indicating competition for light and space.
- Crown Area: Projected area of individual tree crowns (m²)
- Plot Area: Total area of the sample plot (m²)
Interpretation: Higher CCF values indicate denser canopy cover and increased competition for light.
Detailed Real-World Examples of Tree Competition Index Calculations
Example 1: Calculating Hegyi Competition Index for a Subject Tree
A subject tree has a DBH of 30 cm. It has 3 neighboring trees with DBHs of 25 cm, 20 cm, and 15 cm, located at distances of 4 m, 6 m, and 8 m respectively. Calculate the Hegyi competition index.
- Subject tree DBH (Si) = 30 cm
- Neighbor 1: S1 = 25 cm, di1 = 4 m
- Neighbor 2: S2 = 20 cm, di2 = 6 m
- Neighbor 3: S3 = 15 cm, di3 = 8 m
Step 1: Calculate each term (Sj / Si) / dij
- Neighbor 1: (25 / 30) / 4 = 0.8333 / 4 = 0.2083
- Neighbor 2: (20 / 30) / 6 = 0.6667 / 6 = 0.1111
- Neighbor 3: (15 / 30) / 8 = 0.5 / 8 = 0.0625
Step 2: Sum all terms to get CIi
CIi = 0.2083 + 0.1111 + 0.0625 = 0.3819
Interpretation: A Hegyi index of 0.38 suggests moderate competition pressure on the subject tree.
Example 2: Calculating Basal Area of Larger Trees (BAL)
Consider a forest plot where the subject tree has a DBH of 25 cm. The plot contains the following trees:
| Tree ID | DBH (cm) | Basal Area (m²) |
|---|---|---|
| 1 | 30 | 0.071 |
| 2 | 28 | 0.062 |
| 3 | 22 | 0.038 |
| 4 | 18 | 0.025 |
Step 1: Identify trees larger than subject tree (DBH > 25 cm): Trees 1 and 2.
Step 2: Sum their basal areas:
BAL = 0.071 + 0.062 = 0.133 m²
Interpretation: The subject tree experiences competition from neighbors with a combined basal area of 0.133 m², indicating moderate competitive pressure.
Additional Technical Details and Considerations
- Choice of Size Metric: DBH is most common, but basal area or crown dimensions can be used depending on study objectives.
- Distance Thresholds: Defining neighbor radius (e.g., 10 m) affects index sensitivity; larger radii capture more competition but increase data collection effort.
- Species-Specific Adjustments: Some indices incorporate species-specific growth rates or shade tolerance to refine competition estimates.
- Spatial Arrangement: Distance-independent indices ignore spatial data, while distance-dependent indices like Hegyi’s provide more precise competition modeling.
- Data Collection: Accurate measurement of DBH, distances, and crown dimensions is critical for reliable index calculation.
- Software Tools: Many forestry software packages and GIS tools support automated competition index calculations, improving efficiency and accuracy.
Authoritative Resources and Standards
- USDA Forest Service: Tree Competition Indices and Their Applications
- ScienceDirect: Review of Tree Competition Indices
- Northern Research Station: Forest Stand Dynamics and Competition
- FAO Forestry Paper: Forest Inventory and Competition Assessment
Mastering tree competition index calculations enables forest managers to optimize stand productivity and sustainability. This article provides the technical foundation and practical tools necessary for expert application.