Environmental and Ecological Statistics 

About: Environmental and Ecological Statistics is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Sampling (statistics) & Population. It has an ISSN identifier of 1352-8505. Over the lifetime, 861 publications have been published receiving 23763 citations.

Measuring Biological Diversity

Abstract: The diversity of a set of species refers to the joint dissimilarity of the species in the set. This paper discusses the measurement of diversity from the set of pairwise distances between the species in the set. A measure called the effective number of species is developed from a non-parametric probability inequality and is shown to have a simple interpretation in terms of comparing linear experiments.

Nonparametric estimation of Shannon’s index of diversity when there are unseen species in sample

Abstract: A biological community usually has a large number of species with relatively small abundances. When a random sample of individuals is selected and each individual is classified according to species identity, some rare species may not be discovered. This paper is concerned with the estimation of Shannon’s index of diversity when the number of species and the species abundances are unknown. The traditional estimator that ignores the missing species underestimates when there is a non-negligible number of unseen species. We provide a different approach based on unequal probability sampling theory because species have different probabilities of being discovered in the sample. No parametric forms are assumed for the species abundances. The proposed estimation procedure combines the Horvitz–Thompson (1952) adjustment for missing species and the concept of sample coverage, which is used to properly estimate the relative abundances of species discovered in the sample. Simulation results show that the proposed estimator works well under various abundance models even when a relatively large fraction of the species is missing. Three real data sets, two from biology and the other one from numismatics, are given for illustration.

Matching species traits to environmental variables: a new three-table ordination method

Abstract: This paper addresses the question of studying the joint structure of three data tablesR,L andQ. In our motivating ecological example, the central tableL is a sites-by-species table that contains the number of organisms of a set of species that occurs at a set of sites. At the margins ofL are the sites-by-environment data tableR and the species-by-trait data table Q. For relating the biological traits of organisms to the characteristics of the environment in which they live, we propose a statistical technique calledRLQ analysis (R-mode linked toQ-mode), which consists in the general singular value decomposition of the triplet (R t D I LD J Q,D q ,D p ) whereD I ,D J ,D q ,D p are diagonal weight matrices, which are chosen in relation to the type of data that is being analyzed (quantitative, qualitative, etc.). In the special case where the central table is analysed by correspondence analysis,RLQ maximizes the covariance between linear combinations of columns ofR andQ. An example in bird ecology illustrates the potential of this method for community ecologists.

Nonparametric spatial covariance functions: Estimation and testing

Abstract: Spatial autocorrelation techniques are commonly used to describe genetic and ecological patterns. To improve statistical inference about spatial covariance, we propose a continuous nonparametric estimator of the covariance function in place of the spatial correlogram. The spline correlogram is an adaptation of a recent development in spatial statistics and is a generalization of the commonly used correlogram. We propose a bootstrap algorithm to erect a confidence envelope around the entire covariance function. The meaning of this envelope is discussed. Not all functions that can be drawn inside the envelope are candidate covariance functions, as they may not be positive semidefinite. However, covariance functions that do not fit, are not supported by the data. A direct estimate of the L0 spatial correlation length with associated confidence interval is offered and its interpretation is discussed. The spline correlogram is found to have high precision when applied to synthetic data. For illustration, the method is applied to electrophoretic data of an alpine grass (Poa alpina).

A process-convolution approach to modelling temperatures in the North Atlantic Ocean

Abstract: This paper develops a process-convolution approach for space-time modelling. With this approach, a dependent process is constructed by convolving a simple, perhaps independent, process. Since the convolution kernel may evolve over space and time, this approach lends itself to specifying models with non-stationary dependence structure. The model is motivated by an application from oceanography: estimation of the mean temperature field in the North Atlantic Ocean as a function of spatial location and time. The large amount of this data poses some difficulties; hence computational considerations weigh heavily in some modelling aspects. A Bayesian approach is taken here which relies on Markov chain Monte Carlo for exploring the posterior distribution.