OverdispersionIn statistics, overdispersion is the presence of greater variability (statistical dispersion) in a data set than would be expected based on a given statistical model. A common task in applied statistics is choosing a parametric model to fit a given set of empirical observations. This necessitates an assessment of the fit of the chosen model. It is usually possible to choose the model parameters in such a way that the theoretical population mean of the model is approximately equal to the sample mean.
Tritrophic interactions in plant defenseTritrophic interactions in plant defense against herbivory describe the ecological impacts of three trophic levels on each other: the plant, the herbivore, and its natural enemies. They may also be called multitrophic interactions when further trophic levels, such as soil microbes, endophytes, or hyperparasitoids (higher-order predators) are considered. Tritrophic interactions join pollination and seed dispersal as vital biological functions which plants perform via cooperation with animals.
Poisson regressionIn statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. A Poisson regression model is sometimes known as a log-linear model, especially when used to model contingency tables.
PlantPlants are eukaryotes, predominantly photosynthetic, that form the kingdom Plantae. Many are multicellular. Historically, the plant kingdom encompassed all living things that were not animals, and included algae and fungi. All current definitions exclude the fungi and some of the algae. By one definition, plants form the clade Viridiplantae (Latin for "green plants") which consists of the green algae and the embryophytes or land plants. The latter include hornworts, liverworts, mosses, lycophytes, ferns, conifers and other gymnosperms, and flowering plants.
Plant defense against herbivoryPlant defense against herbivory or host-plant resistance (HPR) is a range of adaptations evolved by plants which improve their survival and reproduction by reducing the impact of herbivores. Plants can sense being touched, and they can use several strategies to defend against damage caused by herbivores. Many plants produce secondary metabolites, known as allelochemicals, that influence the behavior, growth, or survival of herbivores. These chemical defenses can act as repellents or toxins to herbivores or reduce plant digestibility.
Quasi-likelihoodIn statistics, quasi-likelihood methods are used to estimate parameters in a statistical model when exact likelihood methods, for example maximum likelihood estimation, are computationally infeasible. Due to the wrong likelihood being used, quasi-likelihood estimators lose asymptotic efficiency compared to, e.g., maximum likelihood estimators. Under broadly applicable conditions, quasi-likelihood estimators are consistent and asymptotically normal. The asymptotic covariance matrix can be obtained using the so-called sandwich estimator.
HerbivoreA herbivore is an animal anatomically and physiologically adapted to eating plant material, for example foliage or marine algae, for the main component of its diet. As a result of their plant diet, herbivorous animals typically have mouthparts adapted to rasping or grinding. Horses and other herbivores have wide flat teeth that are adapted to grinding grass, tree bark, and other tough plant material. A large percentage of herbivores have mutualistic gut flora that help them digest plant matter, which is more difficult to digest than animal prey.
Beta-binomial distributionIn probability theory and statistics, the beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers arising when the probability of success in each of a fixed or known number of Bernoulli trials is either unknown or random. The beta-binomial distribution is the binomial distribution in which the probability of success at each of n trials is not fixed but randomly drawn from a beta distribution.
Medicinal plantsMedicinal plants, also called medicinal herbs, have been discovered and used in traditional medicine practices since prehistoric times. Plants synthesize hundreds of chemical compounds for various functions, including defense and protection against insects, fungi, diseases, and herbivorous mammals. The earliest historical records of herbs are found from the Sumerian civilization, where hundreds of medicinal plants including opium are listed on clay tablets, c. 3000 BC. The Ebers Papyrus from ancient Egypt, c.
Count dataIn statistics, count data is a statistical data type describing countable quantities, data which can take only the counting numbers, non-negative integer values {0, 1, 2, 3, ...}, and where these integers arise from counting rather than ranking. The statistical treatment of count data is distinct from that of binary data, in which the observations can take only two values, usually represented by 0 and 1, and from ordinal data, which may also consist of integers but where the individual values fall on an arbitrary scale and only the relative ranking is important.
Negative binomial distributionIn probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of successes (denoted ) occurs. For example, we can define rolling a 6 on a dice as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success ().
Multivariate statisticsMultivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied.
Dirichlet negative multinomial distributionIn probability theory and statistics, the Dirichlet negative multinomial distribution is a multivariate distribution on the non-negative integers. It is a multivariate extension of the beta negative binomial distribution. It is also a generalization of the negative multinomial distribution (NM(k, p)) allowing for heterogeneity or overdispersion to the probability vector. It is used in quantitative marketing research to flexibly model the number of household transactions across multiple brands.
ArthropodArthropods (ˈɑːrθrəpɒd, (gen. ποδός)) are invertebrate animals in the phylum Arthropoda. They possess an exoskeleton with a cuticle made of chitin, often mineralised with calcium carbonate, a segmented body, and paired jointed appendages. In order to keep growing, they must go through stages of moulting, a process by which they shed their exoskeleton to reveal a new one. They are an extremely diverse group, with up to 10 million species. Haemolymph is the analogue of blood for arthropods.
HypothesisA hypothesis (: hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous observations that cannot satisfactorily be explained with the available scientific theories. Even though the words "hypothesis" and "theory" are often used interchangeably, a scientific hypothesis is not the same as a scientific theory.
Multivariate normal distributionIn probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.
Standard ModelThe Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks.
Physics beyond the Standard ModelPhysics beyond the Standard Model (BSM) refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the inability to explain the fundamental parameters of the standard model, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy. Another problem lies within the mathematical framework of the Standard Model itself: the Standard Model is inconsistent with that of general relativity, and one or both theories break down under certain conditions, such as spacetime singularities like the Big Bang and black hole event horizons.
Case studyA case study is an in-depth, detailed examination of a particular case (or cases) within a real-world context. For example, case studies in medicine may focus on an individual patient or ailment; case studies in business might cover a particular firm's strategy or a broader market; similarly, case studies in politics can range from a narrow happening over time like the operations of a specific political campaign, to an enormous undertaking like, world war, or more often the policy analysis of real-world problems affecting multiple stakeholders.
Dirichlet-multinomial distributionIn probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector , and an observation drawn from a multinomial distribution with probability vector p and number of trials n.
