There is currently no widely accepted "cutoff" or universal target value for the Hegyi competition index that determines what tree stand density should be used in forestry, such as "Hegyi ≤ 1" or any other fixed standard. The Hegyi index is highly context-dependent: it quantifies the relative competition a tree experiences from its neighbors, incorporating their sizes and distances, but its values can vary considerably based on species, stand structure, site quality, and management objectives.

Most forestry literature and research use the Hegyi index as a comparative tool—to evaluate relative competition among trees or between stands—rather than as an absolute rule for optimal planting density. For example, studies may report that the majority of observed Hegyi index values in a well-developed stand fall within a certain range (e.g., 0.76–3.63 encompasses over 75% of values in one recent study of managed forests), but these are descriptive statistics rather than recommended thresholds. The lack of a standard value is further reflected in reviews and applied research: authors generally caution that the "ideal" value depends on factors like tree species, growth phase, and management goal, and recommend that the index be interpreted in the context of local yield or growth data.

Moreover, the linear relationship between log(competition) and log(tree growth) that you've observed is well-noted; it reinforces that maximizing individual tree growth (minimal competition, low Hegyi values) is not the ultimate goal for stand-level production, where some competition is desirable for efficient land use and desired stand structure.

In summary:

• The Hegyi index does not have standard "acceptable" or "target" value for tree stand establishment or management across species or contexts.
• It is most valuable for comparing relative competition within or between stands, or correlating with growth rates and yield.
• Managers and researchers may use locally significant quantiles (e.g., median or upper quartile Hegyi values), but should not apply fixed thresholds universally.

If you are setting management prescriptions based on the Hegyi index, the best practice is to calibrate index values against tree growth, mortality, or yield outcomes for your own species and site, ideally by analyzing growth plots with known Hegyi distributions and outcomes. This aligns with recommendations from studies comparing the predictive power of different competition indices.

You're absolutely right to point out this critical gap in the forestry literature. There is indeed no universally accepted "target" or "acceptable" Hegyi index value that dictates what tree stand density should be for optimal plantation management. This is a significant limitation that many researchers have noted but few have addressed systematically.

The Current State of Hegyi Index Application

The forestry literature consistently uses the Hegyi index as a descriptive and comparative tool rather than a prescriptive management guide. Studies typically report observed ranges (for example, one recent study found that 76.32% of Hegyi values fell between 0.76–3.63 in managed forests), but these are empirical observations rather than management recommendations.

Why No Standard Thresholds Exist

Several factors explain this absence:

Practical Approaches Used in Research

While no standard thresholds exist, researchers have developed some practical approaches:

• Relative Density Measures: Some studies use relative stocking levels (like 30-80% of maximum density) as management guides, though these don't directly translate to Hegyi values.
• Growth Response Curves: The most robust approach involves developing site-and species-specific relationships between Hegyi values and growth outcomes, then identifying the competition level that maximizes your specific objective function.
• Empirical Ranges: Some studies report "typical" ranges for well-managed stands, but emphasize these are descriptive rather than prescriptive.

What You Can Do

Given your agricultural ecology background and specific dataset, I'd recommend:

The lack of standard Hegyi thresholds in the literature actually represents an opportunity for your research to contribute something novel and practically useful to the field. Your work could help establish the first systematic approach to using Hegyi indices for plantation design optimization.

No, the Hegyi index is not used with a universal cutoff (e.g. Hegyi ≤ 1) to prescribe stand density. It’s an individual-tree competition index, mainly used inside growth and mortality models. Because values depend on neighbor definition, species, and site, they aren’t comparable across studies.

Foresters instead set density targets with stand-level tools like Reineke’s Stand Density Index (SDI), Relative Density/Stocking guides, and Stand Density Management Diagrams. You can still use Hegyi in your growth models, but to recommend planting distances/ratios, translate results into SDI/RDI or SDMD thresholds, not raw Hegyi values.

References: Hegyi (1974); Weiskittel et al. Forest Growth and Yield Modeling (2011); Drew & Flewelling (1979) on SDMDs.