A forest succession simulator, SILVA, has been developed for the mixed—conifer forest (seven major species) of the Sierra Nevada, California, to simulate the effects of fire on forest dynamics. SILVA is an extensive modification of a simulator for forests of the northeastern United States. The simulation includes the time development of the growth in tree diameter, tree height, and leaf—area index. Recruitment and mortality are modeled stochastically. Modifications include fire ecology, temporal seed—crop patterns, and seedling—survival factors unique to Sierra Nevada forests. The probability of mortality from fire is determined by the height of crown scorch (a function of fire intensity, diameter at breast height, and bark thickness). The model simulates the dynamic and structural responses of communities to many factors. For 500—yr simulations from an initial clear—cut condition, the time—averaged basal—area ratios of Pinus ponderosa to Abies concolor were 5.2:1 and 1:16 for elevations of 1524 m and 1829 m, respectively. At 1524 m, the ratio of P. ponderosa to A. concolor decreased 59% when fire suppression was introduced. Fire provides P. ponderosa with a strong competitive advantage. Its growth form and growth rate are significant factors in its ability to evade fire. Rank correlations of species were compared with data for stands of ponderosa pine and white fir. Correlations were significant at 1% and 10% levels, respectively.

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1 SummaryThe classical statistical method of confidence intervals is unsuitable for discovery sampling because it requires unnecessarily large sample sizes. We show that sample sizes can be dramatically reduced if we are willing to relax an extremely pessimistic assumption that underlies the method. We also treat the effect of measurement error on sample size. This summary section states the main results, and can be read as a standalone. The body of this report together with the appendices provide further technical details.Discovery sampling is a tool used in discovery auditing. In a discovery audit the auditors measure a random sample of items from an inventory to provide evidence that the whole inventory complies with a given set of criteria. Auditors expect the items in a sample to be free of compliance problems because they believe that the entire inventory has very few (if any) defects. As part of their work product, auditors are usually required to provide a confidence statement about the inventory such as: "We are 95% confident that less than 1% of the items in the inventory are defective." The standard statistical tool for making this kind of statement uses the classical method of confidence intervals. A confidence interval brackets the estimated number of defects in the inventory based on the number of defectives in the sample (usually zero in a discovery audit). The size of the sample is chosen so the tolerance level (maximum number of defectives) appears at the upper end of the confidence interval. If the interval would span the actual number of defects in (say) 95% of future audits, then it's called a "95% confidence interval." Discovery audits usually specify tight tolerances such as 1% or even 0.1%. Tight tolerances come with a steep price: large sample sizes. For example an auditor would need to sample nearly a quarter of a large inventory to achieve 95% confidence for a 1% tolerance. The reason classical confidence intervals require large samples stems from an implicit assumption which becomes evident once a Bayesian framework is adopted. The assumption becomes very pessimistic for tight tolerance audits. For example if a 1,000-item inventory is to be vetted to a 1% tolerance, use of classical confidence intervals implicitly assumes that there is a 98.9% chance the inventory is out of compliance before the auditors draw and measure the sample. In other words, the sample information must shift the odds from 99:1 against compliance to 20:1 for compliance-a factor of almost 2,000 change in the odds. It's no wonder that of confidence intervals require such large sample sizes, they must rebut an extremely pessimistic assumption. However by incorporating ancillary information about the inventory, expressed in terms of the prior 2 probability of compliance, we can dramatically reduce the required sample size. The figure below (based on a large inventory approximation) shows the cost of pessimism in terms of n, the sample size needed to achieve a 95% confidence for a tolerance of 1%. The method of confid...

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