Taylor's Law
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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 ...
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Ecology
Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overlaps with the closely related sciences of biogeography, evolutionary biology, genetics, ethology, and natural history. Ecology is a branch of biology, and it is not synonymous with environmentalism. Among other things, ecology is the study of: * The abundance, biomass, and distribution of organisms in the context of the environment * Life processes, antifragility, interactions, and adaptations * The movement of materials and energy through living communities * The successional development of ecosystems * Cooperation, competition, and predation within and between species * Patterns of biodiversity and its effect on ecosystem processes Ecology has practical applications in conservation biology, wetland management, natural resource managemen ...
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Zooplankton
Zooplankton are the animal component of the planktonic community ("zoo" comes from the Greek word for ''animal''). Plankton are aquatic organisms that are unable to swim effectively against currents, and consequently drift or are carried along by currents in the ocean, or by currents in seas, lakes or rivers. Zooplankton can be contrasted with phytoplankton, which are the plant component of the plankton community ("phyto" comes from the Greek word for ''plant''). Zooplankton are heterotrophic (other-feeding), whereas phytoplankton are autotrophic (self-feeding). This means zooplankton cannot manufacture their own food but must eat other plants or animals instead — in particular they eat phytoplankton. Zooplankton are generally larger than phytoplankton, most are microscopic, but some (such as jellyfish) are macroscopic and can be seen with the naked eye. Many protozoans (single-celled protists that prey on other microscopic life) are zooplankton, including zooflagellates, fo ...
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Markov Process
A Markov chain or Markov process is a stochastic model 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). It is named after the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes, such as studying cruise control systems in motor vehicles, queues or lines of customers arriving at an airport, currency exchange rates and animal population dynamics. Markov processes are the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability distr ...
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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. 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. 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 specified by birth rates \_ and death rates \_. Recu ...
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Negative Binomial Distribution
In 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 r) occurs. For example, we can define rolling a 6 on a die 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 (r), the number of failures (n - r) are random because the total trials (n) are random. For example, we could use the negative binomial distribution to model the number of days n (random) a certain machine works (specified by r) ...
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Fish
Fish are aquatic, craniate, gill-bearing animals that lack limbs with digits. Included in this definition are the living hagfish, lampreys, and cartilaginous and bony fish as well as various extinct related groups. Approximately 95% of living fish species are ray-finned fish, belonging to the class Actinopterygii, with around 99% of those being teleosts. The earliest organisms that can be classified as fish were soft-bodied chordates that first appeared during the Cambrian period. Although they lacked a true spine, they possessed notochords which allowed them to be more agile than their invertebrate counterparts. Fish would continue to evolve through the Paleozoic era, diversifying into a wide variety of forms. Many fish of the Paleozoic developed external armor that protected them from predators. The first fish with jaws appeared in the Silurian period, after which many (such as sharks) became formidable marine predators rather than just the prey of arthropods. Mos ...
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Sheep
Sheep or domestic sheep (''Ovis aries'') are domesticated, ruminant mammals 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 shearing. In Commonw ...
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Tick
Ticks (order Ixodida) are parasitic arachnids that are part of the mite superorder Parasitiformes. Adult ticks are approximately 3 to 5 mm in length depending on age, sex, species, and "fullness". 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 from the Cretaceous period, around 100 million years old. 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 cephalothorax and abdomen are completely fused. In addit ...
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Leaf
A leaf ( : leaves) is any of the principal appendages of a vascular plant stem, usually borne laterally aboveground and specialized for photosynthesis. Leaves are collectively called foliage, as in "autumn foliage", while the leaves, stem, flower, and fruit collectively form the shoot system. In most leaves, the primary photosynthetic 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. Most leaves are flattened and have distinct upper (adaxial) and lower ( abaxial) surfaces that differ in color, hairiness, the number of stomata (pores that intake and output gases), the amount and structure of epicuticular wax and other features. Leaves are mostly green in color due to the presence of a compound called chlorophyll that is essential for photosynthesis as it absorbs light ...
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Mite
Mites are small arachnids (eight-legged arthropods). Mites span two large orders of arachnids, the Acariformes and the Parasitiformes, which were historically grouped together in the subclass Acari, but genetic analysis does not show clear evidence of a close relationship. 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 again 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 The mites are not a defined taxon, but is used for two disti ...
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Plant
Plants are predominantly photosynthetic eukaryotes of the kingdom Plantae. Historically, the plant kingdom encompassed all living things that were not animals, and included algae and fungi; however, all current definitions of Plantae exclude the fungi and some algae, as well as the prokaryotes (the archaea and bacteria). By one definition, plants form the clade Viridiplantae (Latin name for "green plants") which is sister of the Glaucophyta, and consists of the green algae and Embryophyta (land plants). The latter includes the flowering plants, conifers and other gymnosperms, ferns and their allies, hornworts, liverworts, and mosses. Most plants are multicellular organisms. Green plants obtain most of their energy from sunlight via photosynthesis by primary chloroplasts that are derived from endosymbiosis with cyanobacteria. Their chloroplasts contain chlorophylls a and b, which gives them their green color. Some plants are parasitic or mycotrophic and have lost the ...
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Insect
Insects (from Latin ') are pancrustacean hexapod invertebrates of the class Insecta. They are the largest group within the arthropod phylum. Insects have a chitinous exoskeleton, a three-part body ( head, thorax and abdomen), three pairs of jointed legs, compound eyes and one pair of antennae. Their blood is not totally contained in vessels; some circulates in an open cavity known as the haemocoel. Insects are the most diverse group of animals; they include more than a million described species and represent more than half of all known living organisms. The total number of extant species is estimated at between six and ten million; In: potentially over 90% of the animal life forms on Earth are insects. Insects may be found in nearly all environments, although only a small number of species reside in the oceans, which are dominated by another arthropod group, crustaceans, which recent research has indicated insects are nested within. Nearly all insects hatch from eggs. ...
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