Book•
Circular statistics in biology
01 Jan 1981-
About: The article was published on 1981-01-01 and is currently open access. It has received 4608 citations till now.
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TL;DR: The development, current features, and some directions for future development of the AMBER package of computer programs are described, embodying a number of the powerful tools of modern computational chemistry-molecular dynamics and free energy calculations.
Abstract: We describe the development, current features, and some directions for future development of the AMBER package of computer programs. This package has evolved from a program that was constructed to do Assisted Model Building and Energy Refinement to a group of programs embodying a number of the powerful tools of modern computational chemistry-molecular dynamics and free energy calculations.
2,953 citations
TL;DR: The CircStat toolbox for MATLAB is implemented which provides methods for the descriptive and inferential statistical analysis of directional data and analyzes a dataset from neurophysiology to demonstrate the capabilities of the Circstat toolbox.
Abstract: Directional data is ubiquitious in science. Due to its circular nature such data cannot be analyzed with commonly used statistical techniques. Despite the rapid development of specialized methods for directional statistics over the last fifty years, there is only little software available that makes such methods easy to use for practioners. Most importantly, one of the most commonly used programming languages in biosciences, MATLAB, is currently not supporting directional statistics. To remedy this situation, we have implemented the CircStat toolbox for MATLAB which provides methods for the descriptive and inferential statistical analysis of directional data. We cover the statistical background of the available methods and describe how to apply them to data. Finally, we analyze a dataset from neurophysiology to demonstrate the capabilities of the CircStat toolbox.
2,557 citations
Cites background or methods from "Circular statistics in biology"
...Despite the fact that circular statistics is still in very active development, several monographs and textbook lay out a standard repertoire of circular statistics methods (e.g., Batschelet 1981; Fisher 1995; Zar 1999; Jammalamadaka and Sengupta 2001)....
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...Rao’s spacing test Rao’s spacing test for circular uniformity is an additional alternative to the Rayleigh test (Batschelet 1981)....
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TL;DR: It is revealed that the larger the group the smaller the proportion of informed individuals needed to guide the group, and that only a very small proportion ofinformed individuals is required to achieve great accuracy.
Abstract: For animals that forage or travel in groups, making movement decisions often depends on social interactions among group members. However, in many cases, few individuals have pertinent information, such as knowledge about the location of a food source, or of a migration route. Using a simple model we show how information can be transferred within groups both without signalling and when group members do not know which individuals, if any, have information. We reveal that the larger the group the smaller the proportion of informed individuals needed to guide the group, and that only a very small proportion of informed individuals is required to achieve great accuracy. We also demonstrate how groups can make consensus decisions, even though informed individuals do not know whether they are in a majority or minority, how the quality of their information compares with that of others, or even whether there are any other informed individuals. Our model provides new insights into the mechanisms of effective leadership and decision-making in biological systems.
2,463 citations
Book•
29 Oct 1993TL;DR: This book presents a meta-modelling framework for analysing two or more samples of unimodal data from von Mises distributions, and some modern Statistical Techniques for Testing and Estimation used in this study.
Abstract: Preface 1. The purpose of the book 2. Survey of contents 3. How to use the book 4. Notation, terminology and conventions 5. Acknowledgements Part I. Introduction: Part II. Descriptive Methods: 2.1. Introduction 2.2. Data display 2.3. Simple summary quantities 2.4. Modifications for axial data Part III. Models: 3.1. Introduction 3.2. Notation trigonometric moments 3.3. Probability distributions on the circle Part IV. Analysis of a Single Sample of Data: 4.1. Introduction 4.2. Exploratory analysis 4.3. Testing a sample of unit vectors for uniformity 4.4. Nonparametric methods for unimodal data 4.5. Statistical analysis of a random sample of unit vectors from a von Mises distribution 4.6. Statistical analysis of a random sample of unit vectors from a multimodal distribution 4.7. Other topics Part V. Analysis of Two or More Samples, and of Other Experimental Layouts: 5.1. Introduction 5.2. Exploratory analysis 5.3. Nonparametric methods for analysing two or more samples of unimodal data 5.4. Analysis of two or more samples from von Mises distributions 5.5. Analysis of data from more complicated experimental designs Part VI. Correlation and Regression: 6.1. Introduction 6.2. Linear-circular association and circular-linear association 6.3. Circular-circular association 6.4. Regression models for a circular response variable Part VII. Analysis of Data with Temporal or Spatial Structure: 7.1. Introduction 7.2. Analysis of temporal data 7.3. Spatial analysis Part VIII. Some Modern Statistical Techniques for Testing and Estimation: 8.1. Introduction 8.2. Bootstrap methods for confidence intervals and hypothesis tests: general description 8.3. Bootstrap methods for circular data: confidence regions for the mean direction 8.4. Bootstrap methods for circular data: hypothesis tests for mean directions 8.5. Randomisation, or permutation, tests Appendix A. Tables Appendix B. Data sets References Index.
2,323 citations
TL;DR: The ellipses are unbiased with respect to sample size, and their estimation via Bayesian inference allows robust comparison to be made among data sets comprising different sample sizes, which opens up more avenues for direct comparison of isotopic niches across communities.
Abstract: 1. The use of stable isotope data to infer characteristics of community structure and niche width of community members has become increasingly common. Although these developments have provided ecologists with new perspectives, their full impact has been hampered by an inability to statistically compare individual communities using descriptive metrics. 2. We solve these issues by reformulating the metrics in a Bayesian framework. This reformulation takes account of uncertainty in the sampled data and naturally incorporates error arising from the sampling process, propagating it through to the derived metrics. 3. Furthermore, we develop novel multivariate ellipse-based metrics as an alternative to the currently employed Convex Hull methods when applied to single community members. We show that unlike Convex Hulls, the ellipses are unbiased with respect to sample size, and their estimation via Bayesian inference allows robust comparison to be made among data sets comprising different sample sizes. 4. These new metrics, which we call SIBER (Stable Isotope Bayesian Ellipses in R), open up more avenues for direct comparison of isotopic niches across communities. The computational code to calculate the new metrics is implemented in the free-to-download package Stable Isotope Analysis for the R statistical environment.
2,226 citations
Cites background or methods from "Circular statistics in biology"
...The standard ellipse on the other hand contains c. 40% of the data regardless of sample size (Batschelet 1981)....
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...Central to the proposed new method is the standard ellipse, which is to bivariate data as SD is to univariate data (Batschelet 1981)....
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...As an alternative we suggest using metrics based on standard ellipses (Batschelet 1981), comparable to SD in univariate cases, to draw inference on isotopic niche width instead of convex hulls and other extreme value metrics....
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