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Watterson Estimator
In population genetics, the Watterson estimator is a method for describing the genetic diversity in a population. It was developed by Margaret Wu and G. A. Watterson in the 1970s. It is estimated by counting the number of polymorphic sites. It is a measure of the "population mutation rate" (the product of the effective population size and the neutral mutation rate) from the observed nucleotide diversity of a population. \theta = 4N_e\mu, where N_e is the effective population size and \mu is the per-generation mutation rate of the population of interest ( ). The assumptions made are that there is a sample of n haploid individuals from the population of interest, that there are infinitely many sites capable of varying (so that mutations never overlay or reverse one another), and that n \ll N_e. Because the number of segregating sites counted will increase with the number of sequences looked at, the correction factor a_n is used. The estimate of \theta, often denoted as \widehat _w, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Genetics
Population genetics is a subfield of genetics that deals with genetic differences within and between populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and population structure. Population genetics was a vital ingredient in the emergence of the modern evolutionary synthesis. Its primary founders were Sewall Wright, J. B. S. Haldane and Ronald Fisher, who also laid the foundations for the related discipline of quantitative genetics. Traditionally a highly mathematical discipline, modern population genetics encompasses theoretical, laboratory, and field work. Population genetic models are used both for statistical inference from DNA sequence data and for proof/disproof of concept. What sets population genetics apart from newer, more phenotypic approaches to modelling evolution, such as evolutionary game theory and adaptive dynamics, is its emphasis on such genetic phenomena as dominance, epi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetic Diversity
Genetic diversity is the total number of genetic characteristics in the genetic makeup of a species, it ranges widely from the number of species to differences within species and can be attributed to the span of survival for a species. It is distinguished from ''genetic variability'', which describes the tendency of genetic characteristics to vary. Genetic diversity serves as a way for populations to adapt to changing environments. With more variation, it is more likely that some individuals in a population will possess variations of alleles that are suited for the environment. Those individuals are more likely to survive to produce offspring bearing that allele. The population will continue for more generations because of the success of these individuals. The academic field of population genetics includes several hypotheses and theories regarding genetic diversity. The neutral theory of evolution proposes that diversity is the result of the accumulation of neutral substitutions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Margaret Wu
Margaret Wu is an Australian statistician and psychometrician who specialises in educational measurement. She is an honorary professor at the University of Melbourne. Early life Wu studied statistics at the University of Melbourne and graduated in 1972. She worked at Monash University as a research assistant from 1973 to 1975, where she taught herself to program. She worked with Watterson on the Watterson estimator, a means to determine the genetic diversity of a population. Research and career Wu joined CSIRO as a technical officer in 1977. She earned a graduate diploma in computer studies from the Royal Melbourne Institute of Technology in 1985. Wu became a high school teacher at Ivanhoe Girls' Grammar School, teaching Chinese and mathematics. She was appointed as a senior research fellow in the Australian Council of Educational Research Development (ACER) in 1992, where she was deputy director of Programme for International Student Assessment (PISA). Working with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutation Rate
In genetics, the mutation rate is the frequency of new mutations in a single gene or organism over time. Mutation rates are not constant and are not limited to a single type of mutation; there are many different types of mutations. Mutation rates are given for specific classes of mutations. Point mutations are a class of mutations which are changes to a single base. Missense and Nonsense mutations are two subtypes of point mutations. The rate of these types of substitutions can be further subdivided into a mutation spectrum which describes the influence of the genetic context on the mutation rate. There are several natural units of time for each of these rates, with rates being characterized either as mutations per base pair per cell division, per gene per generation, or per genome per generation. The mutation rate of an organism is an evolved characteristic and is strongly influenced by the genetics of each organism, in addition to strong influence from the environment. The upper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haploid
Ploidy () is the number of complete sets of chromosomes in a cell, and hence the number of possible alleles for autosomal and pseudoautosomal genes. Sets of chromosomes refer to the number of maternal and paternal chromosome copies, respectively, in each homologous chromosome pair, which chromosomes naturally exist as. Somatic cells, tissues, and individual organisms can be described according to the number of sets of chromosomes present (the "ploidy level"): monoploid (1 set), diploid (2 sets), triploid (3 sets), tetraploid (4 sets), pentaploid (5 sets), hexaploid (6 sets), heptaploid or septaploid (7 sets), etc. The generic term polyploid is often used to describe cells with three or more chromosome sets. Virtually all sexually reproducing organisms are made up of somatic cells that are diploid or greater, but ploidy level may vary widely between different organisms, between different tissues within the same organism, and at different stages in an organism's life cycle. Half ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single-nucleotide Polymorphism
In genetics, a single-nucleotide polymorphism (SNP ; plural SNPs ) is a germline substitution of a single nucleotide at a specific position in the genome. Although certain definitions require the substitution to be present in a sufficiently large fraction of the population (e.g. 1% or more), many publications do not apply such a frequency threshold. For example, at a specific base position in the human genome, the G nucleotide may appear in most individuals, but in a minority of individuals, the position is occupied by an A. This means that there is a SNP at this specific position, and the two possible nucleotide variations – G or A – are said to be the alleles for this specific position. SNPs pinpoint differences in our susceptibility to a wide range of diseases, for example age-related macular degeneration (a common SNP in the CFH gene is associated with increased risk of the disease) or nonalcoholic fatty liver disease (a SNP in the PNPLA3 gene is associated with inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Number
In mathematics, the -th harmonic number is the sum of the reciprocals of the first natural numbers: H_n= 1+\frac+\frac+\cdots+\frac =\sum_^n \frac. Starting from , the sequence of harmonic numbers begins: 1, \frac, \frac, \frac, \frac, \dots Harmonic numbers are related to the harmonic mean in that the -th harmonic number is also times the reciprocal of the harmonic mean of the first positive integers. Harmonic numbers have been studied since antiquity and are important in various branches of number theory. They are sometimes loosely termed harmonic series, are closely related to the Riemann zeta function, and appear in the expressions of various special functions. The harmonic numbers roughly approximate the natural logarithm function and thus the associated harmonic series grows without limit, albeit slowly. In 1737, Leonhard Euler used the divergence of the harmonic series to provide a new proof of the infinity of prime numbers. His work was extended into the comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coalescent Theory
Coalescent theory is a model of how alleles sampled from a population may have originated from a common ancestor. In the simplest case, coalescent theory assumes no recombination, no natural selection, and no gene flow or population structure, meaning that each variant is equally likely to have been passed from one generation to the next. The model looks backward in time, merging alleles into a single ancestral copy according to a random process in coalescence events. Under this model, the expected time between successive coalescence events increases almost exponentially back in time (with wide variance). Variance in the model comes from both the random passing of alleles from one generation to the next, and the random occurrence of mutations in these alleles. The mathematical theory of the coalescent was developed independently by several groups in the early 1980s as a natural extension of classical population genetics theory and models, but can be primarily attributed to John K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bias Of An Estimator
In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called ''unbiased''. In statistics, "bias" is an property of an estimator. Bias is a distinct concept from consistency: consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased; see bias versus consistency for more. All else being equal, an unbiased estimator is preferable to a biased estimator, although in practice, biased estimators (with generally small bias) are frequently used. When a biased estimator is used, bounds of the bias are calculated. A biased estimator may be used for various reasons: because an unbiased estimator does not exist without further assumptions about a population; because an estimator is difficult to compute (as in unbiased estimation of standard deviation); because a biased estimato ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \sigma^2, s^2, \operatorname(X), V(X), or \mathbb(X). An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Growth
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth). If the constant of proportionality is negative, then the quantity decreases over time, and is said to be undergoing exponential decay instead. In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay since the function values form a geometric progression. The formula for exponential growth of a variable at the growth rate , as time goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is x_t = x_0(1+r)^t where is the value of at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
