Permanent sample plots for natural tropical forests: A rationale with special emphasis on Central Africa

Permanent sample plots (PSP), where trees are individually and permanently marked, have received increased interest in Central Africa as a tool to monitor vegetation changes. Although techniques for mounting PSP in tropical forests are well known, their planning still deserves attention. This study aims at defining a rationale for determining the size and number of replicates for setting up PSP in mixed tropical forests. It considers PSP as a sampling plan to estimate a target quantity with its associated margin of error. The target quantity considered here is the stock recovery rate, which is a key parameter for forest management in Central Africa. It is computed separately for each commercial species. The number of trees to monitor for each species defines the margin of error on the stock recovery rate. The size and number of replicated plots is obtained as the solution of an optimization problem that consists in minimizing the margin of error for every species while ensuring that the mounting cost remains below a given threshold. This rationale was applied using the data from the M’Baïki experimental site in the Central African Republic. It showed that the stock recovery rate is a highly variable quantity, and that the typical cost that forest managers are prone to devote to PSP leads to high margins of error. It also showed that the size and number of replicated plots is related to the spatial pattern of trees: clustered or spatially heterogeneous patterns favor many small plots, whereas regular or spatially homogeneous patterns favor few large plots.  

A Variance Estimator for Constrained Estimates of Change in Relative Categorical Frequencies

Consistent estimators of change and state becomes an issue when sample data come from a mix of permanent and temporary observation units. A joint maximum likelihood estimator of state and change creates estimates of state that depend on antecedent viz. posterior survey results and may differ from estimates of state derived from a single-date analysis of the sample data. A constrained estimator of change in relative categorical frequencies that eliminates this potential inconsistency is proposed and a model based estimator of their sampling variance is developed. The performance of the constrained estimator is quantified against six criteria and a joint maximum likelihood estimator in simulated sampling from 15 populations with three combinations of permanent and temporary samples, four to six categorical class attributes, and constant size between sampling dates. Bias of the constrained estimators was negligible but larger than for joint maximum likelihood estimators. Mean absolute deviations and variances of constrained estimators were generally at par with the joint estimators. Constrained estimators of root mean square errors and achieved coverage of nominal confidence intervals of constrained estimators were occasionally better. A generalized variance function for the constrained estimates of change is provided as a computational shortcut.  

Joint versus separate estimation of state and change in category frequencies from repeat stratified two-phase sampling with a fallible classifier

Joint maximum likelihood estimates (JML) of category frequencies and change from repeat stratified two-phase samplingsurveys with a fallible classifier are often seriously biased andhave large root mean square errors when they are obtained for small populations (<5000) with three or more categories and amoderate to small phase II sample size (<1000). JML estimates of state also depend on antecedent or posterior data, a recipe for inconsistency. In these situations, a separate maximum likelihood estimation (SML) of category frequenciesat each survey date appears preferable. SML estimates of net change are obtained as the difference in states. SML standard errors of change are obtained via an estimate of the temporal correlation and variances of state. A bivariate binarylogistic model of change provided the estimate of temporal correlation. SML generally outperformed JMLsignificantly in terms of bias and root mean square errors in eight case studies.