Francis A. Roesch

Modelling diameter distributions of two-cohort forest stands with various proportions of dominant species: A two-component mixture model approach

In recent years finite-mixture models have been employed to approximate and model empirical diameter at breast height (DBH) distributions. We used two-component mixtures of either the Weibull distribution or the gamma distribution for describing the DBH distributions of mixed-species, two-cohort forest stands, to analyse the relationships between the DBH components, age cohorts and dominant species, and to assess the significance of differences between the mixture distributions and the kernel density estimates. The data consisted of plots from the Świętokrzyski National Park (Central Poland) and areas close to and including the North Carolina section of the Great Smoky Mountains National Park (USA; southern Appalachians). The fit of the mixture Weibull model to empirical DBH distributions had a precision similar to that of the mixture gamma model, slightly less accurate estimate was obtained with the kernel density estimator. Generally, in the two-cohort, two-storied, multi-species stands in the southern Appalachians, the two-component DBH structure was associated with age cohort and dominant species. The 1st DBH component of the mixture model was associated with the 1st dominant species sp1 occurred in young age cohort (e.g., sweetgum, eastern hemlock); and to a lesser degree, the 2nd DBH component was associated with the 2nd dominant species sp2 occurred in old age cohort (e.g., loblolly pine, red maple). In two-cohort, partly multilayered, stands in the Świętokrzyski National Park, the DBH structure was usually associated with only age cohorts (two dominant species often occurred in both young and old age cohorts). When empirical DBH distributions representing stands of complex structure are approximated using mixture models, the convergence of the estimation process is often significantly dependent on the starting strategies. Depending on the number of DBHs measured, three methods for choosing the initial values are recommended: min.k/max.k, 0.5/1.5/mean, and multistart. For large samples (number of DBHs measured ≥ 80) the multistage method is proposed--for the two-component mixture Weibull or gamma model select initial values using the min.k/max.k (for k=1,5,10) and 0.5/1.5/mean methods, run the numerical procedure for each method, and when no two solutions are the same, apply the multistart method also.

A primer for nonresponse in the US forest inventory and analysis program

Nonresponse caused by denied access and hazardous conditions are a concern for the USDA Forest Service, Forest Inventory and Analysis (FIA) program, whose mission is to quantify status and trends in forest resources across the USA. Any appreciable amount of nonresponse can cause bias in FIA’s estimates of population parameters. This paper will quantify the magnitude of nonresponse and describe the mechanisms that result in nonresponse, describe and qualitatively evaluate FIA’s assumptions regarding nonresponse, provide a recommendation concerning plot replacement strategies, and identify appropriate strategies to pursue that minimize bias. The nonresponse rates ranged from 0% to 21% and differed by land owner group; with denied access to private land the leading cause of nonresponse. Current FIA estimators assume that nonresponse occurs at random. Although in most cases this assumption appears tenable, a qualitative assessment indicates a few situations where the assumption is not tenable. In the short-term, we recommend that FIA use stratification schemes that make the missing at random assumption tenable. We recommend the examination of alternative estimation techniques that use appropriate weighting and auxiliary information to mitigate the effects of nonresponse. We recommend the replacement of nonresponse sample locations not be used.

Estimating forest conversion rates with annual forest inventory data.

The rate of land-use conversion from forest to nonforest or natural forest to forest plantation is of interest for forest certification purposes and also as part of the process of assessing forest sustainability. Conversion rates can be estimated from remeasured inventory plots in general, but the emphasis here is on annual inventory data. A new estimator is proposed based on analysis of plot-level variables that indicate when a change in forest condition occurs between inventory remeasurements. A weighted maximum likelihood estimator is derived that incorporates the binomial nature of the indicator variables, mapped plot conditions, and varying remeasurement periods. Example applications demonstrate the utility of the proposed methodology. This approach is broadly useful for estimating the annual rate of change from an initial condition to another condition from annual forest inventory data.