scholarly journals The shape of terrestrial abundance distributions

2015 ◽  
Vol 1 (8) ◽  
pp. e1500082 ◽  
Author(s):  
John Alroy
Keyword(s):  
Maximum Likelihood ◽  
Common Species ◽  
Two Dimensional ◽  
Niche Space ◽  
Numerous Species ◽  
Empirical Distributions ◽  
Terrestrial Mammals ◽  
Abundance Patterns ◽  
Leibler Divergence ◽  
Species Abundances

Ecologists widely accept that the distribution of abundances in most communities is fairly flat but heavily dominated by a few species. The reason for this is that species abundances are thought to follow certain theoretical distributions that predict such a pattern. However, previous studies have focused on either a few theoretical distributions or a few empirical distributions. I illustrate abundance patterns in 1055 samples of trees, bats, small terrestrial mammals, birds, lizards, frogs, ants, dung beetles, butterflies, and odonates. Five existing theoretical distributions make inaccurate predictions about the frequencies of the most common species and of the average species, and most of them fit the overall patterns poorly, according to the maximum likelihood–related Kullback-Leibler divergence statistic. Instead, the data support a low-dominance distribution here called the “double geometric.” Depending on the value of its two governing parameters, it may resemble either the geometric series distribution or the lognormal series distribution. However, unlike any other model, it assumes both that richness is finite and that species compete unequally for resources in a two-dimensional niche landscape, which implies that niche breadths are variable and that trait distributions are neither arrayed along a single dimension nor randomly associated. The hypothesis that niche space is multidimensional helps to explain how numerous species can coexist despite interacting strongly.

Large-sample confidence intervals of information-theoretic measures in linguistics

2020 ◽  
Vol 6 (1) ◽  
pp. 19-54
Author(s):  
Ryan Ka Yau Lai ◽  
Youngah Do
Keyword(s):  
Maximum Likelihood ◽  
Corpus Linguistics ◽  
Delta Method ◽  
Confidence Bounds ◽  
Likelihood Estimator ◽  
Information Theoretic ◽  
Leibler Divergence ◽  
Information Theoretic Measures ◽  
Data Points ◽  
Measure Of Uncertainty

This article explores a method of creating confidence bounds for information-theoretic measures in linguistics, such as entropy, Kullback-Leibler Divergence (KLD), and mutual information. We show that a useful measure of uncertainty can be derived from simple statistical principles, namely the asymptotic distribution of the maximum likelihood estimator (MLE) and the delta method. Three case studies from phonology and corpus linguistics are used to demonstrate how to apply it and examine its robustness against common violations of its assumptions in linguistics, such as insufficient sample size and non-independence of data points.

Connections Between Cultures: Using Empirical Distributions for Measuring Cultural Differences

2020 ◽  
pp. 002202212098237
Author(s):  
Wolfgang Messner
Keyword(s):  
Cultural Values ◽  
Cultural Differences ◽  
Distance Measures ◽  
Cultural Variation ◽  
Group Level ◽  
Psychological Phenomena ◽  
Empirical Distributions ◽  
Leibler Divergence ◽  
Country Differences ◽  
Cross Country

The past few decades have seen an explosion in the interest in cultural differences and their impact on many aspects of business management. A noticeable feature of most academic studies and practitioner approaches is the predominant use of national boundaries and group-level averages as delimiters and proxies for culture. However, this largely ignores the significance that intra-country differences and cross-country similarities can have for identifying psychological phenomena. This article argues for the importance of considering intra-cultural variation for establishing connections between two different cultures. It uses empirical distributions of cultural values that occur naturally within a country, thereby making intracultural differences interpretable and actionable. For measuring cross-country differences, the Gini/Weitzman overlapping index and the Kullback-Leibler divergence coefficient are used as difference measures between two distributions. The properties of these measures in comparison to traditional group-level mean-based distance measures are analyzed, and implications for cross-cultural and international business research are discussed.

scholarly journals A structure hierarchy for silicate minerals: sheet silicates

2018 ◽  
Vol 83 (1) ◽  
pp. 3-55 ◽  
Author(s):  
Frank C. Hawthorne ◽  
Yulia A. Uvarova ◽  
Elena Sokolova
Keyword(s):  
Double Layer ◽  
Structural Connectivity ◽  
Single Layer ◽  
Common Species ◽  
Two Dimensional ◽  
Structural Units ◽  
Coordination Polyhedra ◽  
Silicate Minerals ◽  
Sheet Silicates ◽  
Sheet Silicate

AbstractThe structure hierarchy hypothesis states that structures may be ordered hierarchically according to the polymerisation of coordination polyhedra of higher bond-valence. A hierarchical structural classification is developed for sheet-silicate minerals based on the connectedness of the two-dimensional polymerisations of (TO4) tetrahedra, where T = Si4+ plus As5+, Al3+, Fe3+, B3+, Be2+, Zn2+ and Mg2+. Two-dimensional nets and oikodoméic operations are used to generate the silicate (sensu lato) structural units of single-layer, double-layer and higher-layer sheet-silicate minerals, and the interstitial complexes (cation identity, coordination number and ligancy, and the types and amounts of interstitial (H2O) groups) are recorded. Key aspects of the silicate structural unit include: (1) the type of plane net on which the sheet (or parent sheet) is based; (2) the u (up) and d (down) directions of the constituent tetrahedra relative to the plane of the sheet; (3) the planar or folded nature of the sheet; (4) the layer multiplicity of the sheet (single, double or higher); and (5) the details of the oikodoméic operations for multiple-layer sheets. Simple 3-connected plane nets (such as 63, 4.82 and 4.6.12) have the stoichiometry (T2O5)n (Si:O = 1:2.5) and are the basis of most of the common rock-forming sheet-silicate minerals as well as many less-common species. Oikodoméic operations, e.g. insertion of 2- or 4-connected vertices into 3-connected plane nets, formation of double-layer sheet-structures by (topological) reflection or rotation operations, affect the connectedness of the resulting sheets and lead to both positive and negative deviations from Si:O = 1:2.5 stoichiometry. Following description of the structural units in all sheet-silicate minerals, the minerals are arranged into decreasing Si:O ratio from 3.0 to 2.0, an arrangement that reflects their increasing structural connectivity. Considering the silicate component of minerals, the range of composition of the sheet silicates completely overlaps the compositional ranges of framework silicates and most of the chain-ribbon-tube silicates.

scholarly journals A Fixed-radius Point Count Method for Nonbreeding and Breeding Season Use

The Auk ◽  
1986 ◽  
Vol 103 (3) ◽  
pp. 593-602 ◽  
Author(s):  
Richard L. Hutto ◽  
Sandra M. Pletschet ◽  
Paul Hendricks
Keyword(s):  
Bird Species ◽  
Common Species ◽  
Bird Abundance ◽  
Point Count ◽  
Bird Density ◽  
Count Method ◽  
Species Abundances ◽  
Fixed Radius ◽  
Point Count Method ◽  
A Site

Abstract We provide a detailed description of a fixed-radius point count method that carries fewer assumptions than most of the currently popular methods of estimating bird density and that can be used during both the nonbreeding and breeding seasons. The method results in three indices of bird abundance, any of which can be used to test for differences in community composition among sites, or for differences in the abundance of a given bird species among sites. These indices are (1) the mean number of detections within 25 m of the observer, (2) the frequency of detections within 25 m of the observer, and (3) the frequency of detections regardless of distance from the observer. The overall ranking of species abundances from a site is similar among the three indices, but discrepancies occur with either rare species that are highly detectable at great distances or common species that are repulsed by, or inconspicuous when near, the observer. We argue that differences in the behavior among species will preclude an accurate ranking of species by abundance through use of this or any other counting method in current use.

Error-weighted maximum likelihood (EWML): a new statistically based method to cluster quantitative micropaleontological data

1993 ◽  
Vol 67 (3) ◽  
pp. 475-486 ◽  
Author(s):  
Evan Fishbein ◽  
R. Timothy Patterson
Keyword(s):  
Maximum Likelihood ◽  
Rare Species ◽  
Degrees Of Freedom ◽  
Statistical Hypothesis ◽  
Data Set ◽  
Clustering Techniques ◽  
Iterative Processing ◽  
Clustering Model ◽  
Species Abundances ◽  
Computer Based

The advent of readily available computer-based clustering packages has created some controversy in the micropaleontological community concerning the use and interpretation of computer-based biofacies discrimination. This is because dramatically different results can be obtained depending on methodology. The analysis of various clustering techniques reveals that, in most instances, no statistical hypothesis is contained in the clustering model and no basis exists for accepting one biofacies partitioning over another. Furthermore, most techniques do not consider standard error in species abundances and generate results that are not statistically relevant. When many rare species are present, statistically insignificant differences in rare species can accumulate and overshadow the significant differences in the major species, leading to biofacies containing members having little in common.A statistically based “error-weighted maximum likelihood” (EWML) clustering method is described that determines biofacies by assuming that samples from a common biofacies are normally distributed. Species variability is weighted to be inversely proportional to measurement uncertainty. The method has been applied to samples collected from the Fraser River Delta marsh and shows that five distinct biofacies can be resolved in the data. Similar results were obtained from readily available packages when the data set was preprocessed to reduce the number of degrees of freedom. Based on the sample results from the new algorithm, and on tests using a representative micropaleontological data set, a more conventional iterative processing method is recommended. This method, although not statistical in nature, produces similar results to EWML (not commercially available yet) with readily available analysis packages. Finally, some of the more common clustering techniques are discussed and strategies for their proper utilization are recommended.

scholarly journals Deconvolution of Two-Dimensional NMR Spectra by Fast Maximum Likelihood Reconstruction: Application to Quantitative Metabolomics

2011 ◽  
Vol 83 (12) ◽  
pp. 4871-4880 ◽  
Author(s):  
Roger A. Chylla ◽  
Kaifeng Hu ◽  
James J. Ellinger ◽  
John L. Markley
Keyword(s):  
Maximum Likelihood ◽  
Nmr Spectra ◽  
Two Dimensional ◽  
Quantitative Metabolomics
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