The lists of species obtained by purposive sampling by field ecologists can be used to improve the sample-based estimation of species richness. A new estimator is here proposed as a modification of the difference estimator in which the species inclusion probabilities are estimated by means of the species frequencies from incidence data. If the species list used to support the estimation is complete the estimator guesses the true richness without error. In the case of incomplete lists, the estimator provides values invariably greater than the number of species detected by the combination of sample-based and purposive surveys. An asymptotically conservative estimator of the mean squared error is also provided. A simulation study based on two artificial communities is carried out in order to check the obvious increase in accuracy and precision with respect to the widely applied estimators based on the sole sample information. Finally, the proposed estimator is adopted to estimate species richness in the Maremma Regional Park, Italy.

Forest attributes such as volume or basal area are concentrated at tree locations and are absent elsewhere. It is, therefore, more meaningful to consider the amount of forest attributes at a prefixed spatial grain, within regular plots of prefixed size centered at the points of the study area. In this way, the diversity of attributes within plots also can be considered and quantified by suitable indexes, giving rise to a diversity surface defined on the continuum of points constituting the area. We analyze the estimation of diversity surfaces when a sample of plots is selected by a probabilistic sampling scheme and diversity within nonsampled plots is estimated using an inverse distance weighting interpolator. We discuss the design-based asymptotic properties of the resulting maps when the survey area remains fixed and the number of sampled points increases. Because diversity surfaces share suitable mathematical properties, if the schemes adopted to select sample points ensure an even coverage of the study areas avoiding large portions of non-sampled zones, it can be proven that the estimated maps approach the true maps.

Non-detection of trees is an important issue when using single-scan TLS in forest inventories. A hybrid inference approach is adopted. Quoting from distance sampling, a detection function is assumed, so that the inclusion probability of each tree included within each plot can be determined. A simulation study is performed to compare the TLS-based estimators corrected and uncorrected for non-detection with the Horvitz–Thompson estimator based on conventional plot sampling, in which all the trees within plots are recorded. Results show that single-scan TLS provides more efficient estimators with respect to those provided by the conventional plot sampling in the case of low-density forests when no distance sampling correction is performed. In low-density forests, uncorrected estimators lead to a small bias (1%–6%), increasing with plot size. Therefore, care must be taken in enlarging the plot radius too much. The bias increases in forests with clustered spatial structures and in dense forests, where the bias levels (30%–50%) deteriorate the performance of uncorrected estimators. Even if the bias-corrected estimators prove to be effective in reducing the bias (below 15%), these reductions are not sufficient to outperform conventional plot sampling. Therefore, there is no convenience in using TLS-based estimation in high-density forests.

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