Gary W. Fowler

BIAS, PRECISION, AND ACCURACY OF FOUR MEASURES OF SPECIES RICHNESS

Species richness is a widely used surrogate for the more complex concept of biological diversity. Because species richness is often central to ecological study and the establishment of conservation priorities, the biases and merits of richness measurements demand evaluation. The jackknife and bootstrap estimators can be used to compensate for the underestimation associated with simple richness estimation (or the sum of species counted in a sample). Using data from five forest communities, we analyzed the simple measure of richness, the first- and second-order jackknife, and the bootstrap estimators with simulation and resampling methods to examine the effects of sample size on estimator performance. Performance parameters examined were systematic under- or overestimation (bias), ability to estimate consistently (precision), and ability to estimate true species richness (accuracy). For small sample sizes in all studied communities (less than ∼25% of the total community), the least biased estimator was the ...

Estimating diameter at breast height and basal diameter of trees from stump measurements in Nepal's lower temperate broad-leaved forests.

Multiple linear regression models for predicting diameter at breast height (DBH) and basal diameter (BD) of trees from stump measurements are presented. These models were developed for the lower temperate broad-leaved forests of Nepals central middle hills. In addition to general prediction models based on all trees in the sample, specific models for this forest type are presented for small (< 35 cm DBH) and large (⩾ 35 cm DBH) trees, and for two dominant taxa, Schima wallichii and the genus Castanopsis. The models were derived from a total of 1304 diameter observations measured on 163 trees in two forests. Diameters were measured on each tree at eight different stem heights (3.0 to 180.0 cm above the ground level), which included BD and DBH (measured at 30.0 and 130.0 cm above the ground level, respectively). In addition, two general simple linear regression models are presented to predict DBH from BD, and vice versa. Cross-validation results indicate good predictive ability, and reliability and validity of the models. Seventeen commonly occurring tree species and ten families were represented in the sample. These models are recommended for general use in the lower temperate broad-leaved forests of the central Himalayas, particularly in those forests dominated by the Schima-Castanopsis association.

Calculating shape descriptors from Fourier analysis: shape analysis of Asterionella (Heterokontophyta, Bacillariophyceae)

Abstract In our study, shape descriptors were calculated for specimens from the diatom genus Asterionella, using the method of arc lengths and tangent angles in Fourier analysis. Asterionella species are character-poor, populations being distinguished mostly by subtle shape differences. Fourier analysis has been used in the past as an aid in taxonomy for many organisms. Fourier coefficients are least-squares estimators of best-fit planar closed curves that provide a quantitative measure of shape and can be useful shape descriptors in character-poor organisms. We determined the relation between number of x,y coordinates and the number of Fourier coefficients used in shape analysis for Asterionella. In a worked example, using a single extracted specimen outline, the method of calculating Fourier coefficients is demonstrated; coefficients were calculated for 100, 140, and 200 coordinates, in order to determine how many coordinates are necessary for effective shape analysis. Then, for each in a size range of Asterionella specimens, Fourier coefficients were calculated, using the same number of coordinates for each. Reconstructed outlines were compared graphically with the original. Statistical measures of average difference, variance, standard deviation, and coefficient of variation were calculated between xs, ys and Euclidean distance for the original and reconstructed outlines. From this, using 100 x,y coordinates, the number of Fourier coefficients necessary to give the best-fit outline over a size range from 30 to 95 μm is 22. Although we used Asterionella as an example, the method may be applied to any diatom valve outline.

Prediction models for estimating total heights of trees from diameter at breast height measurements in Nepal's lower temperate broad-leaved forests

Abstract Multiple linear regression models are presented for predicting total heights of trees from diameter at breast height (dbh) measurements in Nepals lower temperate broad-leaved forests. In addition to a general prediction model based on all trees in the sample, specific models are presented for three classes of anthropogenic disturbance levels (light, moderate, and heavy), and for two dominant taxa, Schima wallichii and the genus Castanopsis. The models were derived from dbh and total heights measured on 2361 trees encountered on 170 survey plots across five forests ranging from relatively light to heavy levels of anthropogenic disturbance. Fifty-six tree species and 32 families were represented in the sample. Cross-validation results indicate good predictive ability, and reliability and validity of the models. Predictive ability and reliability and validity of the models were better for forests with lower levels of anthropogenic disturbance. These models are recommended for general use in Nepals lower temperate broad-leaved forests, particularly in forests dominated by the Schima-Castanopsis association, which generally tend to be under heavy cutting and lopping pressure from subsistence farmers.