Bark Stripping Damage Caused by Red Deer (Cervus elaphus L.): Inventory Design Using Hansen–Hurwitz and Horvitz–Thompson Approach

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Abstract
This study investigates the use of adaptive cluster sampling (ACS) for estimating bark stripping damage in forests, employing the Hansen–Hurwitz (HH) and Horvitz–Thompson (HT) estimators. Through simulations, we analysed the total, summer, and new bark stripping damage with varying grid sizes and sample sizes in eight full-censused stands in Northern Styria/Austria. The results showed that the HT estimator consistently had lower standard errors (SEs) (variability of the sample mean from the true population mean) than the HH estimator. SEs decreased with increasing grid space for new and summer damages, but increased for total damage up to 35 m, then remained stable. Inclusion probabilities (IP) were highest for total damage. ACS showed precision gains, particularly for rare and clustered damages like new damage, but did not achieve the target SE of 10%. Adaptive sampling is most beneficial for monitoring rare and clustered events, though precision remains limited, especially for new damage. The study suggests ACS is suitable for rare damage types (e.g., summer and new bark stripping wounds) but requires further refinement to meet operational precision targets. Future work should focus on integrating adaptive designs with practical field methods, such as fixed-radius plots and refined damage criteria.

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