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Effective Population Size
The effective population size (''N''''e'') is a number that, in some simplified scenarios, corresponds to the number of breeding individuals in the population. More generally, ''N''''e'' is the number of individuals that an idealised population would need to have in order for some specified quantity of interest (typically change of genetic diversity or inbreeding rates) to be the same as in the real population. Idealised populations are based on unrealistic but convenient simplifications such as random mating, simultaneous birth of each new generation, constant population size, and equal numbers of children per parent. For most quantities of interest and most real populations, the effective population size ''N''''e'' is usually smaller than the census population size ''N'' of a real population. The same population may have multiple effective population sizes, for different properties of interest, including for different genetic loci. The effective population size is most commonly ...
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Idealised Population
In population genetics an idealised population is one that can be described using a number of simplifying assumptions. Models of idealised populations are either used to make a general point, or they are fit to data on real populations for which the assumptions may not hold true. For example, coalescent theory is used to fit data to models of idealised populations. The most common idealized population in population genetics is described in the Wright-Fisher model after Sewall Wright and Ronald Fisher (1922, 1930) and (1931). Wright-Fisher populations have constant size, and their members can mate and reproduce with any other member. Another example is a Moran model, which has overlapping generations, rather than the non-overlapping generations of the Fisher-Wright model. The complexities of real populations can cause their behavior to match an idealised population with an effective population size that is very different from the census population size of the real population. For ...
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F-statistics
In population genetics, ''F''-statistics (also known as fixation indices) describe the statistically expected level of heterozygosity in a population; more specifically the expected degree of (usually) a reduction in heterozygosity when compared to Hardy–Weinberg expectation. ''F''-statistics can also be thought of as a measure of the correlation between genes drawn at different levels of a (hierarchically) subdivided population. This correlation is influenced by several evolutionary processes, such as genetic drift, founder effect, bottleneck, genetic hitchhiking, meiotic drive, mutation, gene flow, inbreeding, natural selection, or the Wahlund effect, but it was originally designed to measure the amount of allelic fixation owing to genetic drift. The concept of ''F''-statistics was developed during the 1920s by the American geneticist Sewall Wright, who was interested in inbreeding in cattle. However, because complete dominance causes the phenotypes of homozygote dominan ...
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Poisson Distribution
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson (; ). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume. For instance, a call center receives an average of 180 calls per hour, 24 hours a day. The calls are independent; receiving one does not change the probability of when the next one will arrive. The number of calls received during any minute has a Poisson probability distribution with mean 3: the most likely numbers are 2 and 3 but 1 and 4 are also likely and there is a small probability of it being as low as zero and a very small probability it could be 10. A ...
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Gamete
A gamete (; , ultimately ) is a haploid cell that fuses with another haploid cell during fertilization in organisms that reproduce sexually. Gametes are an organism's reproductive cells, also referred to as sex cells. In species that produce two morphologically distinct types of gametes, and in which each individual produces only one type, a female is any individual that produces the larger type of gamete—called an ovum— and a male produces the smaller type—called a sperm. Sperm cells or spermatozoa are small and motile due to the flagellum, a tail-shaped structure that allows the cell to propel and move. In contrast, each egg cell or ovum is relatively large and non-motile. In short a gamete is an egg cell (female gamete) or a sperm (male gamete). In animals, ova mature in the ovaries of females and sperm develop in the testes of males. During fertilization, a spermatozoon and ovum unite to form a new diploid organism. Gametes carry half the genetic information of ...
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Self-fertilisation
Autogamy, or self-fertilization, refers to the fusion of two gametes that come from one individual. Autogamy is predominantly observed in the form of self-pollination, a reproductive mechanism employed by many flowering plants. However, species of protists have also been observed using autogamy as a means of reproduction. Flowering plants engage in autogamy regularly, while the protists that engage in autogamy only do so in stressful environments. Occurrence Protists ''Paramecium aurelia'' '' Paramecium aurelia'' is the most commonly studied protozoan for autogamy. Similar to other unicellular organisms, ''Paramecium aurelia'' typically reproduce asexually via binary fission or sexually via cross-fertilization. However, studies have shown that when put under nutritional stress, ''Paramecium aurelia'' will undergo meiosis and subsequent fusion of gametic-like nuclei. This process, defined as hemixis, a chromosomal rearrangement process, takes place in a number of steps. First, t ...
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Dioecious
Dioecy (; ; adj. dioecious , ) is a characteristic of a species, meaning that it has distinct individual organisms (unisexual) that produce male or female gametes, either directly (in animals) or indirectly (in seed plants). Dioecious reproduction is biparental reproduction. Dioecy has costs, since only about half the population directly produces offspring. It is one method for excluding self-fertilization and promoting allogamy (outcrossing), and thus tends to reduce the expression of recessive deleterious mutations present in a population. Plants have several other methods of preventing self-fertilization including, for example, dichogamy, herkogamy, and self-incompatibility. Dioecy is a dimorphic sexual system, alongside gynodioecy and androdioecy. In zoology In zoology, dioecious species may be opposed to hermaphroditic species, meaning that an individual is either male or female, in which case the synonym gonochory is more often used. Most animal species are dioeci ...
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Population Bottleneck
A population bottleneck or genetic bottleneck is a sharp reduction in the size of a population due to environmental events such as famines, earthquakes, floods, fires, disease, and droughts; or human activities such as specicide, widespread violence or intentional culling, and human population planning. Such events can reduce the variation in the gene pool of a population; thereafter, a smaller population, with a smaller genetic diversity, remains to pass on genes to future generations of offspring through sexual reproduction. Genetic diversity remains lower, increasing only when gene flow from another population occurs or very slowly increasing with time as random mutations occur. This results in a reduction in the robustness of the population and in its ability to adapt to and survive selecting environmental changes, such as climate change or a shift in available resources. Alternatively, if survivors of the bottleneck are the individuals with the greatest genetic fitness, the ...
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Arithmetic Mean
In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the '' mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results of an experiment or an observational study, or frequently a set of results from a survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics, because it helps distinguish it from other means, such as the geometric mean and the harmonic mean. In addition to mathematics and statistics, the arithmetic mean is used frequently in many diverse fields such as economics, anthropology and history, and it is used in almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population. While the arithmetic mean is often used to report central tendencies, it is not a robust statistic, meaning that it is great ...
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Harmonic Mean
In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired. The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. As a simple example, the harmonic mean of 1, 4, and 4 is : \left(\frac\right)^ = \frac = \frac = 2\,. Definition The harmonic mean ''H'' of the positive real numbers x_1, x_2, \ldots, x_n is defined to be :H = \frac = \frac = \left(\frac\right)^. The third formula in the above equation expresses the harmonic mean as the reciprocal of the arithmetic mean of the reciprocals. From the following formula: :H = \frac. it is more apparent that the harmonic mean is related to the arithmetic and geometric means. It is the reciprocal dual of the arithmetic mean for positive inputs: :1/H(1/x_1 \ldots 1/x_n) = A(x_1 \ldots x_n) The harmonic mean is a Schur-conca ...
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Generation
A generation refers to all of the people born and living at about the same time, regarded collectively. It can also be described as, "the average period, generally considered to be about 20–⁠30 years, during which children are born and grow up, become adults, and begin to have children." In kinship terminology, it is a structural term designating the parent-child relationship. It is known as biogenesis, reproduction, or procreation in the biological sciences. ''Generation'' is also often used synonymously with ''cohort'' in social science; under this formulation it means "people within a delineated population who experience the same significant events within a given period of time". Generations in this sense of birth cohort, also known as "social generations", are widely used in popular culture, and have been the basis for sociological analysis. Serious analysis of generations began in the nineteenth century, emerging from an increasing awareness of the possibility of ...
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Conditional Variance
In probability theory and statistics, a conditional variance is the variance of a random variable given the value(s) of one or more other variables. Particularly in econometrics, the conditional variance is also known as the scedastic function or skedastic function. Conditional variances are important parts of autoregressive conditional heteroskedasticity (ARCH) models. Definition The conditional variance of a random variable ''Y'' given another random variable ''X'' is :\operatorname(Y, X) = \operatorname\Big(\big(Y - \operatorname(Y\mid X)\big)^\mid X\Big). The conditional variance tells us how much variance is left if we use \operatorname(Y\mid X) to "predict" ''Y''. Here, as usual, \operatorname(Y\mid X) stands for the conditional expectation of ''Y'' given ''X'', which we may recall, is a random variable itself (a function of ''X'', determined up to probability one). As a result, \operatorname(Y, X) itself is a random variable (and is a function of ''X''). Explanation, r ...
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Idealized Population
In population genetics an idealised population is one that can be described using a number of simplifying assumptions. Models of idealised populations are either used to make a general point, or they are fit to data on real populations for which the assumptions may not hold true. For example, coalescent theory is used to fit data to models of idealised populations. The most common idealized population in population genetics is described in the Wright-Fisher model after Sewall Wright and Ronald Fisher (1922, 1930) and (1931). Wright-Fisher populations have constant size, and their members can mate and reproduce with any other member. Another example is a Moran model, which has overlapping generations, rather than the non-overlapping generations of the Fisher-Wright model. The complexities of real populations can cause their behavior to match an idealised population with an effective population size that is very different from the census population size of the real population. Fo ...
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