An Estimation Procedure for the Joint Distribution of Spatial Direction and Thickness of Flat Bodies Using Vertical Sections. Part II: An application in soil micromorphology

In soil micromorphology fissures are considered in vertical sections. To get information about the properties of the soil the joint distribution of spatial direction and width of these fissures is of interest. The fissures are mathematically generalized to flat bodies which are defined as stationary weighted surface processes with the weight “thickness”. In a typical point of the surface process suitable, joint parametric distributions of direction and thickness are assumed. The parameters have to be estimated from measurements on vertical sections which are taken from the soil. On these sections only a visible thickness and a visible angle can be observed. The joint distribution of these variables can be expressed by the joint distribution of spatial direction and thickness with the same parameters and in this indirect way the parameters can be estimated. The paper describes how to randomize the vertical section and how to measure the visible variables on the sections. The Chi-Square method is proposed for the parameter estimation. Further it is discussed how to derive good starting values for the numerical procedure. All this is demonstrated in a simulation study using the Bingham-Mardia distribution for the direction and the lognormal distribution for the thickness including a way to correlate the mean thickness and the direction. Finally an application in soil micromorphology is demonstrated for one soil horizon.     

Estimation of Individual Growth Curves by Empirically Weighted Least Squares

The simultaneous estimation of individual growth curves and a mean growth curve is accomplished by weighted least squares. A polynomial curve is fitted for each individual and the polynomial parameters are linear functions of parameters corresponding to covariates. A simple, computationally efficient variance-covariance estimator is derived. The resultant estimate is used in the weighted least squares estimation. The results are compared to empirical Bayes estimation.     

Ordination of vegetation change in Guadalupe Mountains,New Mexico,USA

Vegetation change over a nine-year period was studied in Guadalupe Mountains, New Mexico. Permanent transects in desert shrub vegetation were sampled in 1972 and 1980. Emphasis was given to shrubs because of their importance to big game diets. Univariate paired t-tests and reciprocal averaging ordination were used to detect and display coordinated changes in species composition over time. Despite apparently less browsing pressure in desert shrub vegetation in 1980 there were few significant changes in species composition. In addition, preferred forage species showed reduced reproduction while species of intermediate and poor forage value dis-played increased reproduction during this time. These data do not support traditional rangeland succession theory which states that enhanced reproduction of preferred species should follow grazing or browsing pressure reduction.     

Effects of detrending and rescaling on correspondence analysis: solution stability and accuracy

Detrending and non-linear axis rescaling potentially improve the accuracy of gradient recovery in correspondence analyses but also reduce the stability or consistency of solutions. Variation among bootstrapped ordination solutions was compared across methods in analyses of both field and simulated data. Solution accuracy, measured with mean squared errors from Procrustes analysis, was compared using simulated data with known structure.Standard detrending-by-segments combined with non-linear rescaling entailed some cost in solution stability, but could improve the accuracy of solutions for long gradients. Without non-linear rescaling these solutions were usually less stable and less accurate. Although detrending-by-polynomials might be preferable on other grounds, it did not produce more accurate or stable solutions than detrending-by-segments.Abbreviations CA = correspondence analysis - DCA = detrended correspondence analysis - MSE = Procrustes mean squared error statistic - SD = standard deviation units of species turnover - SRV = scaled variance in species ranks     

Ecological optima and tolerances of Thelypteris limbosperma,Athyrium distentifolium,and Matteuccia struthiopteris along environmental gradients in Western Norway

The distribution and abundance of Thelypteris limbosperma, Athyrium distentifolium, and Matteuccia struthiopteris are modelled statistically in relation to 14 environmental variables along the major climatic, topographic, and edaphic gradients in western Norway. The data are from 624 stands from which measurements or estimates of mean January and mean July temperatures, humidity, altitude, aspect, and slope are available. From 182 of these stands eight soil variables have also been measured. The species responses are quantified by two numerical methods: Gaussian logit regression and weighted averaging (WA) regression. The estimated WA optima suggest that A. distentifolium has an ecological preference for low July and January temperatures, high altitudes, and soils of low-medium pH and base content. The species shows statistically significant Gaussian responses with summer temperature, humidity (= Martonnes humidity index), altitude, slope, aspect, pH, cation exchange capacity, and base saturation with optima of 8.7 °C, 188.9, 1220 m, 28°, 29°, 4.8, 13.77 mEq 100 g dry soil^-1, and 13.4%, respectively. These suggest that the occurrence and relative abundance of A. distentifolium are well predicted by summer temperature, topography, and soil pH and base status. T. limbosperma has WA optima that suggest that it favours moderately high winter and summer temperatures, high humidity, medium altitude, and soils of low pH and base content. It has significant Gaussian responses to summer temperature (optimum =12.6 °C), winter temperature (-1.8 °C), humidity (179.2), altitude (459.5 m), slope (22.5°), and Na (0.7 mg 100 g dry soil^-1). These suggest that climatic factors, altitude, and slope are significant predictors for its occurrence and abundance. M. struthiopteris has high WA optima for summer temperature, pH, Ca, Mg, K, Na, cation exchange capacity (CEC), and base saturation, and a low optima for humidity and winter temperature. Of these, summer temperature (16.0 °C), Ca (63.1 mg 100 g dry soil^-1), Mg (41.0 mg 100 g dry soil^-1), K (23.6 mg 100 g dry soil^-1), Na (5.0 mg 100 g dry soil^-1), CEC (60.7 mEq 100 g dry soil^-1), and base saturation (56.3%) have significant Gaussian logit responses, as do aspect (150.2°) and loss-on-ignition (9.4%). These results suggest that the occurrence and relative abundance of M. struthiopteris are well predicted by high soil base cations, a generally southern aspect, low organic content in the soil, and high July temperatures.     

Recent palaeolimnology of three shallow Danish lakes

Recent eutrophication histories of three shallow lakes (mean depths <3 m) were studied using palaeolimnological methods. Freeze-cores were dated using ²¹⁰Pb, ¹³⁷Cs, ¹³⁴Cs and ²⁴¹Am. Resultant chronologies were problematical at two sites (Væng Sø and Vesterborg Sø) due to sediment-water interface mixing, indicated by uniform ¹³⁷Cs profiles over the surface 20–30 cm. Sediments at Langesø and Vesterborg Sø have a high carbonate content, which together with the high mixing rate have resulted in diatom dissolution below 30 cm at Vesterborg Sø. Diatom stratigraphy indicates relatively small biological changes at both Væng Sø and Langesø both lakes have been eutrophic for at least the last 150–200 years. Væng Sø is dominated by planktonic diatoms together with high percentages of benthic Fragilaria spp., and Langesø by planktonic diatoms, especially Cyclostephanos dubius and Stephanodiscus parvus.Epilimnetic phosphorus concentrations were inferred using weighted averaging; at Væng Sø the diatom-inferred TP (DI-TP) concentrations were close to observed values in the early 1980s, but failed to record the post-biomanipulation decrease to 55 g l^-1 after 1988, presumably due to the smoothing of the sediment record by resuspension and mixing. At Langesø two increases in DI-TP suggest a two-phase enrichment of the lake, initial eutrophication 1880, and hypertrophy after 1950. The recent DI-TP values are lower than the annual observed values, and reasons for this are discussed. Despite problems associated with sediment mixing, the sediment records of these shallow systems can still be used for monitoring and for environmental reconstructions.     

Pattern analysis in Belgian limestone grasslands

Pattern analyses were made in several limestone grasslands of Belgium. Vegetation has been sampled in continuous transects. Monospecific patterns are defined by means of two non-parametric indices; multivariate analysis (reciprocal averaging) completed the analysis. The following kinds of pattern are described and explained: random, aggregate, clump, gap, stationary density variation, non-stationary density variation, gradient and many complex patterns. The multivariate analysis leads to a careful phytosociological study of the transects and to the definition of floristically homogeneous regions. Some particular points of pattern analysis, the problem of vegetation sampling and some perspectives are discussed.     

Book reviews

Editing of community data matrices is complementary to analyzing data by multivariate techniques of classification and ordination in the overall task of data analysis. A computer program, DATAEDIT, is described that can perform numerous editing functions, including data transformation, deletion of certain species or samples, deletion of rare species, deletion of outliers, separation of disjunet sample groups, reordering of the species or samples of a data matrix, and the formation of composite samples or of sample subsets. DATAEDIT can use the information in a nonhierarchical or hierarchical classification, and includes its own internal routine for reciprocal averaging ordination.We appreciate valuable suggestions from the late Robert H. Whittaker, and from Philip Dixon, David Hieks, Laura Huenneke, Linda Olsvig-whittaker, and Mark Wilson. Mark O. Hill kindly supplied a fast subroutine for reciprocal averaging.