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UniFrac
UniFrac is a distance metric used for comparing biological communities. It differs from dissimilarity measures such as Bray-Curtis dissimilarity in that it incorporates information on the relative relatedness of community members by incorporating phylogenetic distances between observed organisms in the computation. Both weighted (quantitative) and unweighted (qualitative) variants of UniFrac are widely used in microbial ecology, where the former accounts for abundance of observed organisms, while the latter only considers their presence or absence. The method was devised by Catherine Lozupone, when she was working with Rob Knight of the University of Colorado at Boulder in 2005. Research methods The distance is calculated between pairs of samples (each sample represents an organismal community). All taxa found in one or both samples are placed on a phylogenetic tree. A branch leading to taxa from both samples is marked as "shared" and branches leading to taxa which appears on ...
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Distance Metric
In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A metric may correspond to a metaphorical, rather than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hamming distance, which measures the number of characters that need to be changed to get from one string to another. Since they are very general, metric spaces are a tool used in many different branches of mathematics. Many types of mathematical objects have a natural notion of distance and ...
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Data Clustering
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of exploratory data analysis, and a common technique for statistical data analysis, used in many fields, including pattern recognition, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Cluster analysis itself is not one specific algorithm, but the general task to be solved. It can be achieved by various algorithms that differ significantly in their understanding of what constitutes a cluster and how to efficiently find them. Popular notions of clusters include groups with small distances between cluster members, dense areas of the data space, intervals or particular statistical distributions. Clustering can therefore be formulated as a multi-objective optimization problem. The ...
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Environmental Microbiology
A biophysical environment is a biotic and abiotic surrounding of an organism or population, and consequently includes the factors that have an influence in their survival, development, and evolution. A biophysical environment can vary in scale from microscopic to global in extent. It can also be subdivided according to its attributes. Examples include the marine environment, the atmospheric environment and the terrestrial environment. The number of biophysical environments is countless, given that each living organism has its own environment. The term ''environment'' can refer to a singular global environment in relation to humanity, or a local biophysical environment, e.g. the UK's Environment Agency. Life-environment interaction All life that has survived must have adapted to the conditions of its environment. Temperature, light, humidity, soil nutrients, etc., all influence the species within an environment. However, life in turn modifies, in various forms, its conditions. S ...
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Metagenomics Software
Metagenomics is the study of genetic material recovered directly from environmental or clinical samples by a method called sequencing. The broad field may also be referred to as environmental genomics, ecogenomics, community genomics or microbiomics. While traditional microbiology and microbial genome sequencing and genomics rely upon cultivated clonal cultures, early environmental gene sequencing cloned specific genes (often the 16S rRNA gene) to produce a profile of diversity in a natural sample. Such work revealed that the vast majority of microbial biodiversity had been missed by cultivation-based methods. Because of its ability to reveal the previously hidden diversity of microscopic life, metagenomics offers a powerful lens for viewing the microbial world that has the potential to revolutionize understanding of the entire living world. As the price of DNA sequencing continues to fall, metagenomics now allows microbial ecology to be investigated at a much greater scale ...
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Footnotes
A note is a string of text placed at the bottom of a page in a book or document or at the end of a chapter, volume, or the whole text. The note can provide an author's comments on the main text or citations of a reference work in support of the text. Footnotes are notes at the foot of the page while endnotes are collected under a separate heading at the end of a chapter, volume, or entire work. Unlike footnotes, endnotes have the advantage of not affecting the layout of the main text, but may cause inconvenience to readers who have to move back and forth between the main text and the endnotes. In some editions of the Bible, notes are placed in a narrow column in the middle of each page between two columns of biblical text. Numbering and symbols In English, a footnote or endnote is normally flagged by a superscripted number immediately following that portion of the text the note references, each such footnote being numbered sequentially. Occasionally, a number between brack ...
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Operational Taxonomic Unit
An Operational Taxonomic Unit (OTU) is an operational definition used to classify groups of closely related individuals. The term was originally introduced in 1963 by Robert R. Sokal and Peter H. A. Sneath in the context of numerical taxonomy, where an "Operational Taxonomic Unit" is simply the group of organisms currently being studied. In this sense, an OTU is a pragmatic definition to group individuals by similarity, equivalent to but not necessarily in line with classical Linnaean taxonomy or modern evolutionary taxonomy. Nowadays, however, the term "OTU" is commonly used in a different context and refers to clusters of (uncultivated or unknown) organisms, grouped by DNA sequence similarity of a specific taxonomic marker gene (originally coined as mOTU; molecular OTU). In other words, OTUs are pragmatic proxies for "species" (microbial or metazoan) at different taxonomic levels, in the absence of traditional systems of biological classification as are available for macroscopi ...
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Metagenomic
Metagenomics is the study of genetic material recovered directly from environmental or clinical samples by a method called sequencing. The broad field may also be referred to as environmental genomics, ecogenomics, community genomics or microbiomics. While traditional microbiology and microbial genome sequencing and genomics rely upon cultivated clonal cultures, early environmental gene sequencing cloned specific genes (often the 16S rRNA gene) to produce a profile of diversity in a natural sample. Such work revealed that the vast majority of microbial biodiversity had been missed by cultivation-based methods. Because of its ability to reveal the previously hidden diversity of microscopic life, metagenomics offers a powerful lens for viewing the microbial world that has the potential to revolutionize understanding of the entire living world. As the price of DNA sequencing continues to fall, metagenomics now allows microbial ecology to be investigated at a much greater scale ...
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Monte Carlo Simulation
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of risk in b ...
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Principal Co-ordinates Analysis
Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset. MDS is used to translate "information about the pairwise 'distances' among a set of n objects or individuals" into a configuration of n points mapped into an abstract Cartesian space. More technically, MDS refers to a set of related ordination techniques used in information visualization, in particular to display the information contained in a distance matrix. It is a form of non-linear dimensionality reduction. Given a distance matrix with the distances between each pair of objects in a set, and a chosen number of dimensions, ''N'', an MDS algorithm places each object into ''N''-dimensional space (a lower-dimensional representation) such that the between-object distances are preserved as well as possible. For ''N'' = 1, 2, and 3, the resulting points can be visualized on a scatter plot. Core theoretical contributions to MDS were made by James O. Ramsay of McG ...
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Community (ecology)
In ecology, a community is a group or association of populations of two or more different species occupying the same geographical area at the same time, also known as a biocoenosis, biotic community, biological community, ecological community, or life assemblage. The term community has a variety of uses. In its simplest form it refers to groups of organisms in a specific place or time, for example, "the fish community of Lake Ontario before industrialization". Community ecology or synecology is the study of the interactions between species in communities on many spatial and temporal scales, including the distribution, structure, abundance, demography, and interactions between coexisting populations. The primary focus of community ecology is on the interactions between populations as determined by specific genotypic and phenotypic characteristics. Community ecology also takes into account abiotic factors that influence species distributions or interactions (e.g. annual temperat ...
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Triangle Inequality
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side. This statement permits the inclusion of degenerate triangles, but some authors, especially those writing about elementary geometry, will exclude this possibility, thus leaving out the possibility of equality. If , , and are the lengths of the sides of the triangle, with no side being greater than , then the triangle inequality states that :z \leq x + y , with equality only in the degenerate case of a triangle with zero area. In Euclidean geometry and some other geometries, the triangle inequality is a theorem about distances, and it is written using vectors and vector lengths ( norms): :\, \mathbf x + \mathbf y\, \leq \, \mathbf x\, + \, \mathbf y\, , where the length of the third side has been replaced by the vector sum . When and are real numbers, they can be viewed as vectors in , and the trian ...
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