Using Plot Correlation Structure to Compare Species Accumulation Curves Derived from Nested and Non-nested Sampling Schemes

An approach for computing the correlations of species richness values obtained from nested and non-nested sampling schemes is described. The correlations obtained are used to construct species accumulation curves for the Carolina Vegetation Survey data set using the log Arrhenius, Gleason, and Arrhenius models. These models are then used to predict the richness at the 400 m2 scale, a value outside the range of the data. To compare nested and non-nested sampling schemes using the different models the MSE, bias, and variance of the different estimators of predicted species richness were calculated. These quantities were then used to make aggregated comparisons (comparing the overall distributions of the estimator properties ignoring the plot from which they claim) and pairwise comparisons (comparing the results of the different sampling schemes on the same plot for all plots). Comparisons were made both with (GLS) and without (OLS) including the plot correlation structure in the fitting of the models and the results of the two estimation methods contrasted. The aggregated approach provided a clear MSE ranking of the models. The Arrhenius model is superior to the log Arrhenius model which is superior to the Gleason model. This same ranking was obtained for both nested and non-nested samples. The estimator based on the Gleason model is negatively biased, often extremely so, but highly precise. The estimator based on the log Arrhenius model is the least precise of the three and is positively biased. The Arrhenius model is also positively biased but typically less so than the log Arrhenius model. GLS estimation greatly improved the estimates obtained from the log Arrhenius model. A paired difference approach was used to compare the sampling schemes. Results varied depending on the model used. Non-nested samples yield estimates that typically are more biased (positively) and have larger MSE than do nested samples when using the log Arrhenius model, although much of the difference in MSE and some of the difference in bias is removed by using GLS estimation. With the Gleason model non-nested samples yield better estimates than do nested samples as measured by all three criteria: MSE, bias, and variance. But the Gleason model with either sampling scheme yields extremely biased estimates a fact that is not improved by switching to GLS estimation. When using the Arrhenius model nested and non-nested samples are indistinguishable with respect to MSE and variance. It is the case that estimates from nested samples tend to be less biased than those from non-nested samples with the difference between them increasing monotonically with the value being estimated.