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Taylor's Law
Taylor's power law is an empirical law in ecology that relates the variance of the number of individuals of a species per unit area of habitat to the corresponding mean by a power law relationship. It is named after the ecologist who first proposed it in 1961, Lionel Roy Taylor (1924–2007). Taylor's original name for this relationship was the law of the mean. The name ''Taylor's law'' was coined by Southwood in 1966. Definition This law was originally defined for ecological systems, specifically to assess the spatial clustering of organisms. For a population count Y with mean \mu and variance \operatorname (Y), Taylor's law is written : \operatorname (Y) = a\mu^b, where ''a'' and ''b'' are both positive constants. Taylor proposed this relationship in 1961, suggesting that the exponent ''b'' be considered a species specific index of aggregation. This power law has subsequently been confirmed for many hundreds of species. Taylor's law has also been applied to assess the time d ...
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Ecology
Ecology () is the natural science of the relationships among living organisms and their Natural environment, environment. Ecology considers organisms at the individual, population, community (ecology), community, ecosystem, and biosphere levels. Ecology overlaps with the closely related sciences of biogeography, evolutionary biology, genetics, ethology, and natural history. Ecology is a branch of biology, and is the study of abundance (ecology), abundance, biomass (ecology), biomass, and distribution of organisms in the context of the environment. It encompasses life processes, interactions, and adaptations; movement of materials and energy through living communities; ecological succession, successional development of ecosystems; cooperation, competition, and predation within and between species; and patterns of biodiversity and its effect on ecosystem processes. Ecology has practical applications in fields such as conservation biology, wetland management, natural resource m ...
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Zooplankton
Zooplankton are the heterotrophic component of the planktonic community (the " zoo-" prefix comes from ), having to consume other organisms to thrive. Plankton are aquatic organisms that are unable to swim effectively against currents. Consequently, they drift or are carried along by currents in the ocean, or by currents in seas, lakes or rivers. Zooplankton can be contrasted with phytoplankton (cyanobacteria and microalgae), which are the plant-like component of the plankton community (the " phyto-" prefix comes from , although taxonomically ''not'' plants). Zooplankton are heterotrophic (other-feeding), whereas phytoplankton are autotrophic (self-feeding), often generating biological energy and macromolecules through chlorophyllic carbon fixation using sunlightin other words, zooplankton cannot manufacture their own food, while phytoplankton can. As a result, zooplankton must acquire nutrients by feeding on other organisms such as phytoplankton, which are generally smaller t ...
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Markov Process
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs ''now''." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). Markov processes are named in honor of the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes. They provide the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability distributions, and have found application in areas including Bayesian statistics, biology, chemistry, economics, finance, i ...
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Birth–death Process
The birth–death process (or birth-and-death process) is a special case of continuous-time Markov process where the state transitions are of only two types: "births", which increase the state variable by one and "deaths", which decrease the state by one. It was introduced by William Feller. The model's name comes from a common application, the use of such models to represent the current size of a population where the transitions are literal births and deaths. Birth–death processes have many applications in demography, queueing theory, performance engineering, epidemiology, biology and other areas. They may be used, for example, to study the evolution of bacteria, the number of people with a disease within a population, or the number of customers in line at the supermarket. Definition When a birth occurs, the process goes from state ''n'' to ''n'' + 1. When a death occurs, the process goes from state ''n'' to state ''n'' − 1. The process is speci ...
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Negative Binomial Distribution
In probability theory and statistics, the negative binomial distribution, also called a Pascal 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/constant/fixed number of successes r occur. For example, we can define rolling a 6 on some 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 (r=3). In such a case, the probability distribution of the number of failures that appear will be a negative binomial distribution. An alternative formulation is to model the number of total trials (instead of the number of failures). In fact, for a specified (non-random) number of successes , the number of failures is random because the number of total trials is random. For example, we could use the negative binomial distribution to model the number of days (random) a certain machin ...
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Fish
A fish (: fish or fishes) is an aquatic animal, aquatic, Anamniotes, anamniotic, gill-bearing vertebrate animal with swimming fish fin, fins and craniate, a hard skull, but lacking limb (anatomy), limbs with digit (anatomy), digits. Fish can be grouped into the more basal (phylogenetics), basal jawless fish and the more common jawed fish, the latter including all extant taxon, living cartilaginous fish, cartilaginous and bony fish, as well as the extinct placoderms and acanthodians. In a break to the long tradition of grouping all fish into a single Class (biology), class (Pisces), modern phylogenetics views fish as a paraphyletic group. Most fish are ectotherm, cold-blooded, their body temperature varying with the surrounding water, though some large nekton, active swimmers like white shark and tuna can hold a higher core temperature. Many fish can communication in aquatic animals#Acoustic, communicate acoustically with each other, such as during courtship displays. The stud ...
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Sheep
Sheep (: sheep) or domestic sheep (''Ovis aries'') are a domesticated, ruminant mammal typically kept as livestock. Although the term ''sheep'' can apply to other species in the genus '' Ovis'', in everyday usage it almost always refers to domesticated sheep. Like all ruminants, sheep are members of the order Artiodactyla, the even-toed ungulates. Numbering a little over one billion, domestic sheep are also the most numerous species of sheep. An adult female is referred to as a ''ewe'' ( ), an intact male as a ''ram'', occasionally a ''tup'', a castrated male as a ''wether'', and a young sheep as a ''lamb''. Sheep are most likely descended from the wild mouflon of Europe and Asia, with Iran being a geographic envelope of the domestication center. One of the earliest animals to be domesticated for agricultural purposes, sheep are raised for fleeces, meat ( lamb, hogget or mutton), and milk. A sheep's wool is the most widely used animal fiber, and is usually harvested by ...
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Tick
Ticks are parasitic arachnids of the order Ixodida. They are part of the mite superorder Parasitiformes. Adult ticks are approximately 3 to 5 mm in length depending on age, sex, and species, but can become larger when engorged. Ticks are external parasites, living by feeding on the blood of mammals, birds, and sometimes reptiles and amphibians. The timing of the origin of ticks is uncertain, though the oldest known tick fossils are around 100 million years old, and come from the Cretaceous period. Ticks are widely distributed around the world, especially in warm, humid climates. Ticks belong to two major families: the Ixodidae, or hard ticks, and the Argasidae, or soft ticks. '' Nuttalliella'', a genus of tick from southern Africa, is the only member of the family Nuttalliellidae, and represents the most primitive living lineage of ticks. Adults have ovoid/pear-shaped bodies (idiosomas) which become engorged with blood when they feed, and eight legs. Their cephalotho ...
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Leaf
A leaf (: leaves) is a principal appendage of the plant stem, stem of a vascular plant, usually borne laterally above ground and specialized for photosynthesis. Leaves are collectively called foliage, as in "autumn foliage", while the leaves, stem, flower, and fruit collectively form the Shoot (botany), shoot system. In most leaves, the primary Photosynthesis, photosynthetic Tissue (biology), tissue is the palisade mesophyll and is located on the upper side of the blade or lamina of the leaf, but in some species, including the mature foliage of ''Eucalyptus'', palisade mesophyll is present on both sides and the leaves are said to be isobilateral. The leaf is an integral part of the stem system, and most leaves are flattened and have distinct upper (Glossary of botanical terms#adaxial, adaxial) and lower (Glossary of botanical terms#abaxial, abaxial) surfaces that differ in color, Trichome, hairiness, the number of stomata (pores that intake and output gases), the amount and ...
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Mite
Mites are small arachnids (eight-legged arthropods) of two large orders, the Acariformes and the Parasitiformes, which were historically grouped together in the subclass Acari. However, most recent genetic analyses do not recover the two as each other's closest relative within Arachnida, rendering the group invalid as a clade. Most mites are tiny, less than in length, and have a simple, unsegmented body plan. The small size of most species makes them easily overlooked; some species live in water, many live in soil as decomposers, others live on plants, sometimes creating galls, while others are Predation, predators or Parasitism, parasites. This last type includes the commercially destructive ''Varroa'' parasite of honey bees, as well as scabies mites of humans. Most species are harmless to humans, but a few are associated with allergies or may transmit diseases. The scientific discipline devoted to the study of mites is called acarology. Evolution and taxonomy Mites are not ...
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Plant
Plants are the eukaryotes that form the Kingdom (biology), kingdom Plantae; they are predominantly Photosynthesis, photosynthetic. This means that they obtain their energy from sunlight, using chloroplasts derived from endosymbiosis with cyanobacteria to produce sugars from carbon dioxide and water, using the green pigment chlorophyll. Exceptions are parasitic plants that have lost the genes for chlorophyll and photosynthesis, and obtain their energy from other plants or fungi. Most plants are multicellular organism, multicellular, except for some green algae. Historically, as in Aristotle's biology, the plant kingdom encompassed all living things that were not animals, and included algae and fungi. Definitions have narrowed since then; current definitions exclude fungi and some of the algae. By the definition used in this article, plants form the clade Viridiplantae (green plants), which consists of the green algae and the embryophytes or land plants (hornworts, liverworts ...
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Insect
Insects (from Latin ') are Hexapoda, hexapod invertebrates of the class (biology), class Insecta. They are the largest group within the arthropod phylum. Insects have a chitinous exoskeleton, a three-part body (Insect morphology#Head, head, Thorax (insect anatomy), thorax and abdomen (insect anatomy), abdomen), three pairs of jointed Arthropod leg, legs, compound eyes, and a pair of antenna (biology), antennae. Insects are the most diverse group of animals, with more than a million described species; they represent more than half of all animal species. The insect nervous system consists of a insect brain, brain and a ventral nerve cord. Most insects reproduce Oviparous, by laying eggs. Insects Respiratory system of insects, breathe air through a system of Spiracle (arthropods), paired openings along their sides, connected to Trachea#Invertebrates, small tubes that take air directly to the tissues. The blood therefore does not carry oxygen; it is only partly contained in ves ...
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