Artificial Intelligence (AI) Calculator for “Forest diversity and silvicultural index calculator”
Forest diversity and silvicultural indices quantify ecosystem complexity and guide sustainable forest management decisions.
This article explores key indices, formulas, tables, and real-world applications for precise forest diversity calculations.
- ¡Hola! ¿En qué cálculo, conversión o pregunta puedo ayudarte?
Example Numeric Prompts for Forest Diversity and Silvicultural Index Calculator
- Calculate Shannon Diversity Index for 5 species with abundances: 20, 15, 10, 5, 50.
- Compute Simpson’s Diversity Index for a forest plot with species counts: 30, 25, 20, 15, 10.
- Determine Stand Density Index given basal area 25 m²/ha and quadratic mean diameter 30 cm.
- Calculate Diversity Index and Silvicultural Index for mixed-species forest with species proportions: 0.4, 0.3, 0.2, 0.1.
Comprehensive Tables of Common Values for Forest Diversity and Silvicultural Indices
| Index | Description | Typical Range | Interpretation | Common Units |
|---|---|---|---|---|
| Shannon Diversity Index (H’) | Measures species diversity considering abundance and evenness | 0 to ~4.5 | Higher values indicate greater diversity and evenness | Dimensionless |
| Simpson’s Diversity Index (D) | Probability that two individuals belong to different species | 0 to 1 | Values near 1 indicate high diversity | Dimensionless |
| Stand Density Index (SDI) | Quantifies stand density relative to a reference tree size | 0 to 1000+ | Higher values indicate denser stands | Trees per hectare (scaled) |
| Basal Area (BA) | Cross-sectional area of tree stems per hectare | 5 to 50 m²/ha | Indicates stand stocking and productivity | m²/ha |
| Quadratic Mean Diameter (QMD) | Diameter of tree with average basal area | 10 to 50 cm | Used in density and volume calculations | cm |
| Species | Typical Abundance (%) | Common Habitat | Silvicultural Importance |
|---|---|---|---|
| Quercus robur (English Oak) | 15-30% | Temperate deciduous forests | High timber value, supports biodiversity |
| Pinus sylvestris (Scots Pine) | 20-40% | Boreal and temperate forests | Fast growth, important for reforestation |
| Fagus sylvatica (European Beech) | 10-25% | Temperate broadleaf forests | Shade tolerant, important for mixed stands |
| Picea abies (Norway Spruce) | 15-35% | Boreal forests | Valuable timber species, sensitive to drought |
| Betula pendula (Silver Birch) | 5-15% | Pioneer species in disturbed sites | Important for early succession and soil improvement |
Fundamental Formulas for Forest Diversity and Silvicultural Index Calculations
1. Shannon Diversity Index (H’)
The Shannon Diversity Index quantifies species diversity by combining species richness and evenness.
- H’: Shannon Diversity Index (dimensionless)
- pi: Proportion of individuals belonging to species i (ni / N)
- ni: Number of individuals of species i
- N: Total number of individuals of all species
Interpretation: Higher H’ values indicate greater species diversity and more even distribution.
2. Simpson’s Diversity Index (D)
Simpson’s Index measures the probability that two randomly selected individuals belong to different species.
- D: Simpson’s Diversity Index (dimensionless)
- pi: Proportion of individuals of species i
Interpretation: Values close to 1 indicate high diversity; values near 0 indicate low diversity.
3. Stand Density Index (SDI)
SDI standardizes stand density relative to a reference tree diameter, facilitating comparisons across stands.
- SDI: Stand Density Index (trees per hectare scaled)
- N: Number of trees per hectare
- Dq: Quadratic mean diameter of trees (cm)
- Dref: Reference diameter, commonly 25 cm
Interpretation: SDI values help determine if a stand is overstocked or understocked relative to species-specific maximum densities.
4. Basal Area (BA)
Basal area represents the cross-sectional area of tree stems per hectare, a key measure of stand stocking.
- BA: Basal area (m²/ha)
- D: Diameter at breast height (cm)
- N: Number of trees per hectare
Note: Diameter squared is in cm²; division by 10,000 converts cm² to m² per hectare.
5. Silvicultural Index (SI)
The Silvicultural Index is a composite metric integrating diversity and stand structure to guide management.
- SI: Silvicultural Index (dimensionless)
- H’: Shannon Diversity Index
- BA: Basal Area (m²/ha)
- SDI: Stand Density Index
Interpretation: Higher SI values indicate stands with balanced diversity and optimal density for silvicultural objectives.
Detailed Real-World Examples of Forest Diversity and Silvicultural Index Calculations
Example 1: Calculating Shannon and Simpson Diversity Indices for a Mixed Forest Plot
A forest plot contains five species with the following individual counts:
- Species A: 20 individuals
- Species B: 15 individuals
- Species C: 10 individuals
- Species D: 5 individuals
- Species E: 50 individuals
Step 1: Calculate total individuals (N)
N = 20 + 15 + 10 + 5 + 50 = 100
Step 2: Calculate proportions (pi)
- pA = 20 / 100 = 0.20
- pB = 15 / 100 = 0.15
- pC = 10 / 100 = 0.10
- pD = 5 / 100 = 0.05
- pE = 50 / 100 = 0.50
Step 3: Calculate Shannon Diversity Index (H’)
H’ = – [ (0.20 × ln 0.20) + (0.15 × ln 0.15) + (0.10 × ln 0.10) + (0.05 × ln 0.05) + (0.50 × ln 0.50) ]
Calculations:
- 0.20 × ln(0.20) = 0.20 × (-1.6094) = -0.3219
- 0.15 × ln(0.15) = 0.15 × (-1.8971) = -0.2846
- 0.10 × ln(0.10) = 0.10 × (-2.3026) = -0.2303
- 0.05 × ln(0.05) = 0.05 × (-2.9957) = -0.1498
- 0.50 × ln(0.50) = 0.50 × (-0.6931) = -0.3466
Sum = -0.3219 – 0.2846 – 0.2303 – 0.1498 – 0.3466 = -1.3332
H’ = – (-1.3332) = 1.3332
Step 4: Calculate Simpson’s Diversity Index (D)
D = 1 – [ (0.20)2 + (0.15)2 + (0.10)2 + (0.05)2 + (0.50)2 ]
Calculations:
- 0.20² = 0.04
- 0.15² = 0.0225
- 0.10² = 0.01
- 0.05² = 0.0025
- 0.50² = 0.25
Sum = 0.04 + 0.0225 + 0.01 + 0.0025 + 0.25 = 0.325
D = 1 – 0.325 = 0.675
Interpretation: The Shannon index of 1.33 and Simpson index of 0.675 indicate moderate species diversity with some dominance by Species E.
Example 2: Calculating Stand Density Index and Silvicultural Index for a Managed Forest Stand
A forest stand has the following characteristics:
- Number of trees per hectare (N): 400
- Quadratic mean diameter (Dq): 30 cm
- Basal area (BA): 25 m²/ha
- Shannon Diversity Index (H’): 1.5 (calculated from species data)
- Reference diameter (Dref): 25 cm (standard for SDI)
Step 1: Calculate Stand Density Index (SDI)
SDI = N × (Dq / Dref)1.605
Calculate the ratio:
30 / 25 = 1.2
Raise to power 1.605:
1.21.605 ≈ 1.324
Calculate SDI:
SDI = 400 × 1.324 = 529.6
Step 2: Calculate Silvicultural Index (SI)
SI = (H’ × BA) / SDI
SI = (1.5 × 25) / 529.6 = 37.5 / 529.6 ≈ 0.0708
Interpretation: The SDI of 530 indicates a moderately dense stand, while the SI of 0.071 suggests balanced diversity and stocking suitable for sustainable management.
Additional Technical Insights on Forest Diversity and Silvicultural Indices
- Species Richness vs. Evenness: Diversity indices like Shannon’s incorporate both the number of species (richness) and their relative abundances (evenness), providing a nuanced view of ecosystem complexity.
- Reference Diameter Selection: The choice of Dref in SDI calculations is species- and region-specific; 25 cm is common for temperate conifers but may vary.
- Basal Area Measurement: Accurate BA requires precise DBH measurements and plot sampling techniques, often using prism or angle gauge methods.
- Silvicultural Index Applications: SI can be adapted to include other variables such as tree height, volume, or site index for more comprehensive stand assessments.
- Remote Sensing Integration: Modern forest inventory increasingly uses LiDAR and multispectral data to estimate diversity and structural indices at landscape scales.
Authoritative Resources and Standards for Forest Diversity and Silvicultural Calculations
- USDA Forest Service: Forest Inventory and Analysis National Program – Guidelines on forest measurement and diversity indices.
- International Union of Forest Research Organizations (IUFRO) – Research on silvicultural practices and forest diversity.
- Forest Stand Density Management Diagrams – Technical manual for SDI and stand density management.
- USDA NRCS Soil and Water Conservation Handbook – Contextual information on forest ecosystem diversity and management.
By mastering these indices and their calculations, forestry professionals can optimize silvicultural treatments, enhance biodiversity conservation, and improve forest productivity sustainably.