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A histogram is an approximate representation of the distribution of numerical data. It was first introduced by Karl Pearson. To construct a histogram, the first step is to "bin" the range of values—that is, divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins (intervals) must be adjacent and are often of equal size.
Statistics is a field of inquiry that studies the collection, analysis, interpretation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities; it is also used and misused for making informed decisions in all areas of business and government.
Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions. Nonparametric statistics is based on either being distribution-free or having a specified distribution but with the distribution's parameters unspecified. Nonparametric statistics includes both descriptive statistics and statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are violated.
In probability and statistics, density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. The unobservable density function is thought of as the density according to which a large population is distributed; the data are usually thought of as a random sample from that population.
Biological dispersal refers to both the movement of individuals from their birth site to their breeding site, as well as the movement from one breeding site to another . Dispersal is also used to describe the movement of propagules such as seeds and spores. Technically, dispersal is defined as any movement that has the potential to lead to gene flow. The act of dispersal involves three phases: departure, transfer, settlement and there are different fitness costs and benefits associated with each of these phases. Through simply moving from one habitat patch to another, the dispersal of an individual has consequences not only for individual fitness, but also for population dynamics, population genetics, and species distribution. Understanding dispersal and the consequences both for evolutionary strategies at a species level, and for processes at an ecosystem level, requires understanding on the type of dispersal, the dispersal range of a given species, and the dispersal mechanisms involved.
Mark and recapture is a method commonly used in ecology to estimate an animal population's size where it is impractical to count every individual. A portion of the population is captured, marked, and released. Later, another portion will be captured and the number of marked individuals within the sample is counted. Since the number of marked individuals within the second sample should be proportional to the number of marked individuals in the whole population, an estimate of the total population size can be obtained by dividing the number of marked individuals by the proportion of marked individuals in the second sample. The method is most useful when it is not practical to count all the individuals in the population. Other names for this method, or closely related methods, include capture-recapture, capture-mark-recapture, mark-recapture, sight-resight, mark-release-recapture, multiple systems estimation, band recovery, the Petersen method, and the Lincoln method.
In statistics, kernel density estimation (KDE) is a non-parametric way to estimate the probability density function of a random variable. Kernel density estimation is a fundamental data smoothing problem where inferences about the population are made, based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy.
The following is a glossary of terms used in the mathematical sciences statistics and probability.
Spatial ecology studies the ultimate distributional or spatial unit occupied by a species. In a particular habitat shared by several species, each of the species is usually confined to its own microhabitat or spatial niche because two species in the same general territory cannot usually occupy the same ecological niche for any significant length of time.
Local convex hull (LoCoH) is a method for estimating size of the home range of an animal or a group of animals, and for constructing a utilization distribution. The latter is a probability distribution that represents the probabilities of finding an animal within a given area of its home range at any point in time; or, more generally, at points in time for which the utilization distribution has been constructed. In particular, different utilization distributions can be constructed from data pertaining to particular periods of a diurnal or seasonal cycle.
In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution. In many applications it is the right tail of the distribution that is of interest, but a distribution may have a heavy left tail, or both tails may be heavy.
In ecology, local abundance is the relative representation of a species in a particular ecosystem. It is usually measured as the number of individuals found per sample. The ratio of abundance of one species to one or multiple other species living in an ecosystem is referred to as relative species abundances. Both indicators are relevant for computing biodiversity.
The term kernel is used in statistical analysis to refer to a window function. The term "kernel" has several distinct meanings in different branches of statistics.
In statistics, Kernel regression is a non-parametric technique to estimate the conditional expectation of a random variable. The objective is to find a non-linear relation between a pair of random variables X and Y.
A home range is the area in which an animal lives and moves on a periodic basis. It is related to the concept of an animal's territory which is the area that is actively defended. The concept of a home range was introduced by W. H. Burt in 1943. He drew maps showing where the animal had been observed at different times. An associated concept is the utilization distribution which examines where the animal is likely to be at any given time. Data for mapping a home range used to be gathered by careful observation, but nowadays, the animal is fitted with a transmission collar or similar GPS device.
Mean shift is a non-parametric feature-space analysis technique for locating the maxima of a density function, a so-called mode-seeking algorithm. Application domains include cluster analysis in computer vision and image processing.
Predator satiation is an anti-predator adaptation in which prey briefly occur at high population densities, reducing the probability of an individual organism being eaten. When predators are flooded with potential prey, they can consume only a certain amount, so by occurring at high densities prey benefit from a safety in numbers effect. This strategy has evolved in a diverse range of prey, including notably many species of plants, insects, and fish. Predator satiation can be considered a type of refuge from predators.
In ecology, a priority effect is the impact that a particular species can have on community development due to prior arrival at a site.
Kernel density estimation is a nonparametric technique for density estimation i.e., estimation of probability density functions, which is one of the fundamental questions in statistics. It can be viewed as a generalisation of histogram density estimation with improved statistical properties. Apart from histograms, other types of density estimators include parametric, spline, wavelet and Fourier series. Kernel density estimators were first introduced in the scientific literature for univariate data in the 1950s and 1960s and subsequently have been widely adopted. It was soon recognised that analogous estimators for multivariate data would be an important addition to multivariate statistics. Based on research carried out in the 1990s and 2000s, multivariate kernel density estimation has reached a level of maturity comparable to its univariate counterparts.
Reid's Paradox of Rapid Plant Migration or Reid's Paradox, describes the observation from the paleoecological record that plant ranges shifted northward, after the last glacial maximum, at a faster rate than the seed dispersal rates commonly occur. Rare long-distance seed dispersal events have been hypothesized to explain these fast migration rates, but the dispersal vector(s) are still unknown. The plant species' geographic range expansion rates are compared to the actualistic rates of seed dispersal using mathematical models, and are graphically visualized using dispersal kernels. These observations made in the paleontological record, which inspired Reid's Paradox, are from fossilized remains of plant parts, including needles, leaves, pollen, and seeds, that can be used to identify past shifts in plant species' ranges.
References
- ↑ Anderson, D. John (February 1982). "The Home Range: A New Nonparametric Estimation Technique". Ecology. 63 (1): 103–112. doi:10.2307/1937036. ISSN 0012-9658. JSTOR 1937036.
- ↑ Worton, B. J. (February 1989). "Kernel Methods for Estimating the Utilization Distribution in Home-Range Studies". Ecology. 70 (1): 164–168. doi:10.2307/1938423. ISSN 0012-9658. JSTOR 1938423.
- ↑ Lichti, Nathanael I.; Swihart, Robert K. (February 2011). "Estimating utilization distributions with kernel versus local convex hull methods". The Journal of Wildlife Management. 75 (2): 413–422. doi:10.1002/jwmg.48. ISSN 0022-541X.
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