Summary 1.In south-eastern Australia, browsing of commercial tree seedlings by mammalian herbivores in plantation forestry incurs a large economic cost to the industry, through its effect on tree survival, growth and form. In the absence of lethal methods to control herbivore populations, appropriate manipulation of vegetation through silvicultural management may reduce browsing but it relies on understanding the feeding responses of the herbivores to such changes. 2. We evaluated the extent to which vegetation patch characteristics affected browsing of pine Pinus radiata seedlings by generalist mammalian herbivores, including redbellied pademelons Thylogale billardierii , Bennett's wallaby Macropus rufogriseus rufogriseus and the common brushtail possum Trichosurus vulpecula . 3. In field trials, browsing of pine seedlings was greatest when they were located in patches of high quality, i.e. palatable short vegetation (grass), intermediate in high-quality tall vegetation ( Lomandra longifolia ) and least in low-quality tall vegetation (bracken and shrub). Patch structure also affected browsing: in low-quality patches pine seedlings were browsed more in short vegetation patches (12-24 cm shorter than the seedling) than in tall vegetation patches (at least as tall as the seedling). This difference was at least partly because herbivores took, on average, 2 weeks longer to locate seedlings in tall than in short vegetation. 4. In trials with captive red-bellied pademelons and brushtail possums, pine seedlings were browsed similarly in small short grass and soil patches. However, when these patches were large and spatially separated, they were browsed more in short grass than soil patches. Selection at the patch or individual plant level therefore depended on spatial scale and proximity of the patches. 5. Synthesis and applications . The influence of patch characteristics on browsing has the potential to be exploited for the management of browsing damage to commercially important tree seedlings in forestry plantations. Retention of relatively tall vegetation, particularly if it is unpalatable, in areas at risk of heavy browsing, for example by delaying the use of herbicide, may be a useful management strategy for reducing browsing. This needs to be weighed against the potential detrimental competitive effects of neighbouring vegetation on the seedlings.

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Even-aged, mixed species eucalypt regeneration with a wide range of initial stockings was established on a Tasmanian moist sclerophyll site by using a range of sowing rates. Stocking, growth and development were monitored on permanent measurement plots from the time of regeneration to age 16. Initial stocking data were combined with volume data from the age 13 and 16 measurements and used in conjunction with local expert knowledge on stand development to produce a preliminary model which predicts how initial stocking will affect the standing volume at any given age. This paper presents the model and outlines some other aspects of stand development for which the study, with its detailed information including the spatial location, species and size at repeated measurements of every tree on the plots, will provide a valuable data base.

Diameter distribution models based on probability density functions are integral to many forest growth and yield systems, where they are used to estimate product volumes within diameter classes. The three-parameter Weibull function with a constrained nonnegative lower bound is commonly used because of its flexibility and ease of fitting. This study compared Weibull and reverse Weibull functions with and without a lower bound constraint and left-hand truncation, across three large unthinned plantation cohorts in which 81% of plots had negatively skewed diameter distributions. Near-optimal lower bounds for the unconstrained Weibull function were negative for negatively skewed data, and the left-truncated Weibull using these bounds was 14.2% more accurate than the constrained Weibull, based on the Kolmogorov-Smirnov statistic. The truncated reverse Weibull fit dominant tree distributions 23.7% more accurately than the constrained Weibull, based on a mean absolute difference statistic. This work indicates that a blind spot may have developed in plantation growth modeling systems deploying constrained Weibull functions, and that left-truncation of unconstrained functions could substantially improve model accuracy for negatively skewed distributions.

Diameter distributions are invariably fitted with constrained zero or positive lower bounds to prevent negative diameters. Goodwin (2021) found that the bound for the 3-parameter Weibull could be negative for negatively skewed data, and that constraining it to zero reduced model accuracy. The loss of model accuracy due to a bound constraint is referred to here as constraint shock. This article shows that the 4-parameter Kumaraswamy and Johnson’s SB distributions can also have negative lower bounds and exhibit constraint shock. A 3-step parameter recovery method was used to fit these distributions to plots in unthinned mixed species eucalypt plantations and results were compared with the less flexible Weibull. Based on Kolmogorov-Smirnov statistics, mean and maximum constraint shock for the 4-parameter distributions were 19% and 62%, respectively, compared with 19% and 51% for the Weibull, which indicated that constraint shock was not affected by model flexibility. Constraint shock was largely avoided by truncating and normalizing distributions with negative bounds. This work introduces a paradigm shift in diameter distribution modelling and adds clarity to a field that has not previously recognized the existence of constraint shock. Study Implications: Constraint shock is the loss of accuracy incurred by constraining the negative lower bound of a distribution to a nonnegative value. For a plantation eucalypt dataset in which 83% of plot diameters were negatively skewed, maximum constraint shock was 62% for the Kumaraswamy and Johnson’s SB distributions, and 51% for the less flexible 3-parameter Weibull, based on Kolmogorov-Smirnov statistics. Using distribution expectations of kurtosis, skewness, maximum diameter, and minimum diameter—all independent of bound parameters—a tractable 3-step parameter recovery method is described for unconstrained, constrained, and truncated 3- and 4-parameter distributions. This work introduces a paradigm shift in the treatment of distribution bounds that will result in substantial model improvements for negatively skewed data.

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