# Generation time

In population biology and demography, the generation time is the average time between two consecutive generations in the lineages of a population. In human populations, the generation time typically ranges from 22 to 33 years.[1] Historians sometimes use this to date events, by converting generations into years to obtain rough estimates of time.

## Definitions and corresponding formulas

The existing definitions of the generation time fall into two categories: those that treat the generation time as a renewal time of the population, and those that focus on the distance between individuals of one generation and the next. Below are the three most commonly used definitions:[2][3]

### The time it takes for the population to grow by a factor of its net reproductive rate

The net reproductive rate R0 is the number of offspring an individual is expected to produce during its lifetime (a net reproductive rate of 1 means that the population is at its demographic equilibrium). This definition envisions the generation time as a renewal time of the population. It justifies the very simple definition used in microbiology ("the time it takes for the population to double", or doubling time) since one can consider that during the exponential phase of bacterial growth mortality is very low and as a result a bacterium is expected to be replaced by two bacteria in the next generation (the mother cell and the daughter cell). If the population dynamic is exponential with a growth rate r (i.e. n(t) ~ α.ert, where n(t) is the size of the population at time t), then this measure of the generation time is given by:

${\displaystyle T={\frac {\log R_{0}}{r}}}$.

Indeed, ${\displaystyle \textstyle T}$ is such that n(t + T) = R0 n(t), i.e. erT = R0.

### The average difference in age between parent and offspring

This definition is a measure of the distance between generations rather than a renewal time of the population. Since many demographic models are female-based (that is, they only take females into account), this definition is often expressed as a mother-daughter distance (the "average age of mothers at birth of their daughters"). However, it is also possible to define a father-son distance (average age of fathers at the birth of their sons) or not to take sex into account at all in the definition. In age-structured population models, an expression is given by:[2][3]

${\displaystyle T=\int _{0}^{\infty }xe^{-rx}\ell (x)m(x)\,\mathrm {d} x}$,

where r is the growth rate of the population, (x) is the survivorship function (probability that an individual survives to age x) and m(x) the maternity function (or birth function, or age-specific fertility). For matrix population models, there is a general formula:[4]

${\displaystyle T={\frac {\lambda \mathbf {vw} }{\mathbf {vFw} }}={\frac {1}{\sum e_{\lambda }(f_{ij})}}}$,

where λ = er is the discrete-time growth rate of the population, F = (fij) is its fertility matrix, v its reproductive value (row-vector) and w its stable stage distribution (column-vector); the ${\displaystyle \textstyle e_{\lambda }(f_{ij})={\frac {f_{ij}}{\lambda }}{\frac {\partial \lambda }{\partial f_{ij}}}}$ are the elasticities of λ to the fertilities.

### The age at which members of a given cohort are expected to reproduce

This definition is very similar to the previous one but the population need not be at its stable age distribution. Moreover, it can be computed for different cohorts and thus provides more information about the generation time in the population. This measure is given by:[2][3]

${\displaystyle T={\frac {\int _{x=0}^{\infty }x\ell (x)m(x)\,\mathrm {d} x}{\int _{x=0}^{\infty }\ell (x)m(x)\,\mathrm {d} x}}}$.

Indeed, the numerator is the sum of the ages at which a member of the cohort reproduces, and the denominator is R0, the average number of offspring it produces.

## References

1. ^ OECD (12 May 2014). "OECD Family Database" (PDF). oecd.org. Retrieved 21 October 2015.
2. ^ a b c Coale, A.J. (1972). The Growth and Structure of Human Populations. Princeton University Press. pp. 18–19.
3. ^ a b c Charlesworth, B. (1994). Evolution in Age-structured Populations. Cambridge: University of Cambridge Press. pp. 28–30. ISBN 978-0-521-45967-9.
4. ^ Bienvenu, F.; Legendre, S. (2015). "A New Approach to the Generation Time in Matrix Population Models". The American Naturalist. 185 (6): 834–843. doi:10.1086/681104. PMID 25996867.
AirPort Time Capsule

The AirPort Time Capsule (originally named Time Capsule) is a wireless router sold by Apple Inc., featuring network-attached storage (NAS) and a residential gateway router, and is one of Apple's AirPort products. They are, essentially, versions of the AirPort Extreme with an internal hard drive. Apple describes it as a "Backup Appliance", designed to work in tandem with the Time Machine backup software utility introduced in Mac OS X 10.5.Introduced on January 15, 2008 and released on February 29, 2008, the device has been upgraded several times, matching upgrades in the Extreme series routers. The earliest versions supported 802.11n wireless and came with a 500 GB hard drive in the base model, while the latest model, introduced in 2013, features 802.11ac and a 3 TB hard drive. All models include three Gigabit Ethernet ports and a single USB port. The USB port can be used for external peripheral devices to be shared over the network, such as external hard drives or printers. The NAS functionality utilizes a built-in "server grade" hard drive. On April 26, 2018, Bloomberg announced that Apple's entire AirPort line had been discontinued without replacement.

Amoebophyra

Amoebophyra (or Amoebophrya) is a genus of dinoflagellates.Amoebophyra is a syndinian parasite that infects free-living dinoflagellates that are attributed to a

single species by using several host-specific parasites.

It acts as "biological control agents for red tides and in defining species of Amoebophrya." Researchers have found a correlation between a large amount of host specify and the impact host parasites may have on other organisms. Due to the host specificity found in each strain of Amoebophrya's physical makeup, further studies need to be tested to determine if the Amoebophrya can act as a control against harmful algal blooms.

Athrotaxis selaginoides

Athrotaxis selaginoides is a species of Athrotaxis, endemic to Tasmania in Australia, where it grows at 400–1,120 m altitude. In its habitat in the mountains, snow in winter is very usual. It is often called King Billy Pine or King William Pine (believed to be in reference to the Tasmanian aborigine William Lanne), although it is not a true pine.It is an evergreen coniferous tree growing to 20–30 m tall, with a trunk up to 1.5 m diameter. The leaves are claw-like, 7–18 mm long and 3–4 mm broad, arranged spirally on the shoots. The seed cones are globose, 15–30 mm diameter, with 20–30 spirally-arranged scales; they are mature about six months after pollination. The pollen cones are 4–5 mm long.The main cause of past decline has been fire, with about one third of its habitat burnt in the twentieth century. Like the other two Athrotaxis species, A. selaginoides is sensitive to fire. Another cause of past decline has been logging. The overall decline is estimated to be about 40% over the last 200 years. This is within the three generation time limit where one generation is estimated to be at least 100 years. Although 84% of forests are now in protected areas, fires still are a potential hazard. Tasmanian government policy precludes logging of this species in and outside these protected areas.Away from its native range, it is occasionally cultivated as an ornamental tree in northwestern Europe. It succeeds in Scotland where it receives the necessary rainfalls for its good growth and produces fertile seeds there.

Carpe diem

Carpe diem is a Latin aphorism, usually translated "seize the day", taken from book 1 of the Roman poet Horace's work Odes (23 BC).

Chronometry

Chronometry (from Greek χρόνος chronos, "time" and μέτρον metron, "measure") is the science of the measurement of time, or timekeeping. Chronometry applies to electronic devices, while horology refers to mechanical devices.

It should not to be confused with chronology, the science of locating events in time, which often relies upon it.

Clostridium perfringens

Clostridium perfringens (formerly known as C. welchii, or Bacillus welchii) is a Gram-positive, rod-shaped, anaerobic, spore-forming pathogenic bacterium of the genus Clostridium. C. perfringens is ever-present in nature and can be found as a normal component of decaying vegetation, marine sediment, the intestinal tract of humans and other vertebrates, insects, and soil. It has the shortest reported generation time of any organism at 6.3 minutes in thioglycolate medium.C. perfringens is one of the most common causes of food poisoning in the United States, alongside norovirus, Salmonella, Campylobacter, and Staphylococcus aureus. However, it can sometimes be ingested and cause no harm.Infections due to C. perfringens show evidence of tissue necrosis, bacteremia, emphysematous cholecystitis, and gas gangrene, which is also known as clostridial myonecrosis. The toxin involved in gas gangrene is known as α-toxin, which inserts into the plasma membrane of cells, producing gaps in the membrane that disrupt normal cellular function. C. perfringens can participate in polymicrobial anaerobic infections. It is commonly encountered in infections as a component of the normal flora. In this case, its role in disease is minor.

The action of C. perfringens on dead bodies is known to mortuary workers as tissue gas. It causes extremely accelerated decomposition, and cannot be stopped by normal embalming measures. These bacteria are resistant to the presence of formaldehyde in normal concentrations.

Common year

A common year is a calendar year with 365 days, as distinguished from a leap year, which has 366. More generally, a common year is one without intercalation. The Gregorian calendar, (like the earlier Julian calendar), employs both common years and leap years to keep the calendar aligned with the tropical year, which does not contain an exact number of days.

The common year of 365 days has 52 weeks and one day, hence a common year always begins and ends on the same day of the week (for example, January 1 and December 31 fell on a Sunday in 2017) and the year following a common year will start on the subsequent day of the week. In common years, February has four weeks, so March will begin on the same day of the week. November will also begin on this day.

In the Gregorian calendar, 303 of every 400 years are common years. By comparison, in the Julian calendar, 300 out of every 400 years are common years, and in the Revised Julian calendar (used by Greece) 682 out of every 900 years are common years.

HD2IOA

HD2IOA is the callsign of a time signal radio station operated by the Navy of Ecuador. The station is located at Guayaquil, Ecuador and transmits in the HF band on 3.81 and 7.6 MHz.The transmission is in AM mode with only the lower sideband (part of the time H3E and the rest H2B/H2D) and consists of 780 Hz tone pulses repeated every ten seconds and voice announcements in Spanish.

While sometimes this station is described as defunct, reception reports of this station on 3.81 MHz appear regularly at the Utility DX Forum.

Intercalation (timekeeping)

Intercalation or embolism in timekeeping is the insertion of a leap day, week, or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendars may require intercalations of both days and months.

Litecoin

Litecoin (LTC or Ł) is a peer-to-peer cryptocurrency and open-source software project released under the MIT/X11 license. Creation and transfer of coins is based on an open source cryptographic protocol and is not managed by any central authority. Litecoin was an early bitcoin spinoff or altcoin, starting in October 2011. In technical details, litecoin is nearly identical to Bitcoin.

Medicago

Medicago is a genus of flowering plants, commonly known as medick or burclover, in the legume (Fabaceae) family. It contains at least 87 species and is distributed mainly around the Mediterranean basin. The best-known member of the genus is alfalfa (M. sativa), an important forage crop, and the genus name is based on the Latin name for that plant, medica, from Greek: μηδική (πόα) Median (grass). Most members of the genus are low, creeping herbs, resembling clover, but with burs (hence the common name). However, alfalfa grows to a height of 1 meter, and tree medick (M. arborea) is a shrub. Members of the genus are known to produce bioactive compounds such as medicarpin (a flavonoid) and medicagenic acid (a triterpenoid saponin). Chromosome numbers in Medicago range from 2n = 14 to 48.The species Medicago truncatula is a model legume due to its relatively small stature, small genome (450–500 Mbp), short generation time (about 3 months), and ability to reproduce both by outcrossing and selfing.

Comprehensive descriptions of the genus are Lesinš and Lesinš 1979 and Small and Jomphe 1989. Major collections are SARDI (Australia), USDA-GRIN (United States), ICARDA (Syria), and INRA (France).

Medicago truncatula

Medicago truncatula, the barrelclover, strong-spined medick, barrel medic, or barrel medick, is a small annual legume native to the Mediterranean region that is used in genomic research. It is a low-growing, clover-like plant 10–60 centimetres (3.9–23.6 in) tall with trifoliate leaves. Each leaflet is rounded, 1–2 centimetres (0.39–0.79 in) long, often with a dark spot in the center. The flowers are yellow, produced singly or in a small inflorescence of two to five together; the fruit is a small, spiny pod.

This species is studied as a model organism for legume biology because it has a small diploid genome, is self-fertile, has a rapid generation time and prolific seed production, is amenable to genetic transformation, and its genome has been sequenced.It forms symbioses with nitrogen-fixing rhizobia (Sinorhizobium meliloti and Sinorhizobium medicae) and arbuscular mycorrhizal fungi including Rhizophagus irregularis (previously known as Glomus intraradices). The model plant Arabidopsis thaliana does not form either symbiosis, making M. truncatula an important tool for studying these processes.

It is also an important forage crop species in Australia.

Minute

The minute is a unit of time or angle. As a unit of time, the minute is most of times equal to ​1⁄60 (the first sexagesimal fraction) of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a negative leap second, which would result in a 59-second minute, but this has never happened in more than 40 years under this system). As a unit of angle, the minute of arc is equal to ​1⁄60 of a degree, or 60 seconds (of arc). Although not an SI unit for either time or angle, the minute is accepted for use with SI units for both. The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. 5′, for angle measurement. The prime is also sometimes used informally to denote minutes of time.

Mycobacterium bovis

Mycobacterium bovis (M. bovis) is a slow-growing (16- to 20-hour generation time) aerobic bacterium and the causative agent of tuberculosis in cattle (known as bovine TB). It is related to Mycobacterium tuberculosis, the bacterium which causes tuberculosis in humans. M. bovis can jump the species barrier and cause tuberculosis in humans and other mammals.

Mycobacterium canetti

Mycobacterium canettii, a novel pathogenic taxon of the Mycobacterium tuberculosis complex (MTBC), was first reported in 1969 by the French microbiologist Georges Canetti, for whom the organism has been named. It formed smooth and shiny colonies, which is highly exceptional for the MTBC. It was described in detail in 1997 on the isolation of a new strain from a 2-year-old Somali patient with lymphadenitis. It did not differ from Mycobacterium tuberculosis in the biochemical tests and in its 16S rRNA sequence. It had shorter generation time than clinical isolates of M. tuberculosis and presented a unique, characteristic phenolic glycolipid and lipo-oligosaccharide. In 1998, Pfyffer described abdominal lymphatic TB in a 56-year-old Swiss man with HIV infection who lived in Kenya. Tuberculosis caused by M. canettii appears to be an emerging disease in the Horn of Africa. A history of a stay to the region should induce the clinician to consider this organism promptly even if the clinical features of TB caused by M. canettii are not specific. The natural reservoir, host range, and mode of transmission of the organism are still unknown.

Nuclear chain reaction

A nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, this leading to the possibility of a self-propagating series of these reactions. The specific nuclear reaction may be the fission of heavy isotopes (e.g., uranium-235, 235U). The nuclear chain reaction releases several million times more energy per reaction than any chemical reaction.

Predator satiation

Predator satiation (less commonly called predator saturation) is an antipredator 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.As available food increases, a predator has more chances of survival, growth, and reproduction. However, as food supply begins to overwhelm the predator's ability to consume and process it, consumption levels off. This pattern is evident in the functional response of type II. There are also limits to population growth (numerical response), dependent on the generation time of the predator species.

This phenomenon is particularly conspicuous when it takes the form of masting, the production of large numbers of seeds by a population of plants.

Some periodical cicada (Magicicada) species erupt in large numbers from their larval stage at intervals in years that are prime numbers, 13 or 17. At high-density sites, research finds that the number eaten by birds does not increase with the number of cicada individuals and the risk of predation for each individual decreases.In contrast to predator satiation, a different pattern is seen in response to mutualistic consumers, which benefit an organism by feeding from it (such as frugivores, which disperse seeds). For example, a vine's berries may ripen at different times, ensuring frugivores are not swamped with food and so resulting in a larger proportion of its seeds being dispersed.

Voltinism

Voltinism is a term used in biology to indicate the number of broods or generations of an organism in a year. The term is most often applied to insects, and is particularly in use in sericulture, where silkworm varieties vary in their voltinism.

Univoltine – (adjective) referring to organisms having one brood or generation per year

Bivoltine – (adjective) referring to organisms having two broods or generations per year

Multivoltine – (adjective) referring to organisms having more than two broods or generations per year

Semivoltine – (adjective) referring to organisms whose generation time is more than one year

Western clawed frog

The western clawed frog (Xenopus tropicalis) is a species of frog in the family Pipidae, also known as tropical clawed frog. It is the only species in the genus Xenopus to have a diploid genome. Its genome has been sequenced, making it a significant model organism for genetics that complements the related species Xenopus laevis (the African clawed frog), a widely used vertebrate model for developmental biology. X. tropicalis also has a number of advantages over X. laevis in research, such as a much shorter generation time (<5 months), smaller size (4–6 cm (1.6–2.4 in) body length), and a larger number of eggs per spawn.It is found in Benin, Burkina Faso, Cameroon, Ivory Coast, Equatorial Guinea, Gambia, Ghana, Guinea, Guinea-Bissau, Liberia, Nigeria, Senegal, Sierra Leone, Togo, and possibly Mali. Its natural habitats are subtropical or tropical moist lowland forests, moist savanna, rivers, intermittent rivers, swamps, freshwater lakes, intermittent freshwater lakes, freshwater marshes, intermittent freshwater marshes, rural gardens, heavily degraded former forests, water storage areas, ponds, aquaculture ponds, and canals and ditches.

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