|
The effective population size (Ne) is defined as "the number of breeding individuals in an idealized population that would show the same amount of dispersion of allele frequencies under random genetic drift or the same amount of inbreeding as the population under consideration" (Sewall Wright). It is a basic parameter in many models in population genetics. The effective population size is usually smaller than the absolute population size (N). The concept of effective population size was first derived by the American geneticist Sewall Wright, who wrote two landmark papers on it (Wright 1931, 1938) See also small population size. Allele frequency is a term of population genetics that is used in characterizing the genetic diversity of a species population, or equivalently the richness of its gene pool. ...
Genetic drift is a mechanism of evolution that acts in concert with natural selection to change the characteristics of species over time. ...
Inbreeding is breeding between close relatives. ...
Sewall Green Wright (December 21, 1889 - March 3, 1988) was one of the primary founders of population genetics which led to the modern evolutionary synthesis. ...
Population genetics is the study of the distribution of and change in allele frequencies under the influence of the five evolutionary forces: natural selection, genetic drift, mutation, migration and nonrandom mating. ...
In population genetics and population ecology, population size (usually denoted N) is the number of individual organisms in a population. ...
Genetics (from the Greek genno γεννώ= give birth) is the science of genes, heredity, and the variation of organisms. ...
Sewall Green Wright (December 21, 1889 - March 3, 1988) was one of the primary founders of population genetics which led to the modern evolutionary synthesis. ...
Species with a small population size are subject to a higher chance of extinction because their small population size makes them more vulnerable to genetic drift, resulting in stochastic variation in their gene pool, their demography and their environment. ...
Definitions Effective populaiton size may be defined in two ways, variance effective size and inbreeding effective size. These are closely linked, and derived from F-statistics. In statistics and probability, the F-distribution is a continuous probability distribution. ...
Variance effective size In an idealized population, the variance in allele frequency (p) is given by: Allele frequency is a term of population genetics that is used in characterizing the genetic diversity of a species population, or equivalently the richness of its gene pool. ...
then this gives:
Inbreeding effective size Alternatively, the effective population size may be defined by how much the inbreeding coefficient changes from one generation to the next, and then define Ne by the same amount of inbreeding there would be in the idealized population. is usually taken to be 0, because it is its size relative to that is important, meaning that the above equation simplifies to:
Examples
Variations in population size Population size varies over time. Suppose there are t non-overlapping generations, then effective population size is given by the harmonic mean of the population sizes: Generation is the act of producing offspring, or procreation. ...
In mathematics, the harmonic mean is one of several methods of calculating an average. ...
For example, say the population size was N = 10, 100, 50, 80, 20, 500 for six generations (t = 6). Then the effective population size is the harmonic mean of these, giving: -
Note this is less than the arithmetic mean of the population size, which in this example is 126.7 In mathematics and statistics, the arithmetic mean of a set of numbers is the sum of all the members of the set divided by the number of items in the set. ...
Of particular concern is the effect of a population bottleneck. A population bottleneck (or genetic bottleneck) is an evolutionary event in which a significant percentage of a population or species is killed or otherwise prevented from reproducing, and the population is reduced by 50% or more, often by several orders of magnitude. ...
Dioeciousness If a population is dioecious, i.e. there is no self-fertlisation then In biology, Dioecious is an adjective which indicates the exisistence of separate sexes in a species of organisms. ...
or more generally, where D represents dioeciousness and may take the value 0 (for not dioecious) or 1 for dioecious.
When N is large; Ne approximately equals N, so this is usually trivial and often ignored:
Non-Fisherian 1:1 sex-ratios When the sex ratio of a population varies from the Fisherian 1:1 ratio, effective population size is given by: Sex ratio is the ratio of males to females in a population. ...
Sir Ronald Fisher Sir Ronald Aylmer Fisher, FRS (February 17, 1890 – July 29, 1962) was an evolutionary biologist, geneticist and statistician. ...
Where Nm is the number of males and Nf the number of females. For example, with 80 males and 20 females (and thus an absolute population size of 100): -
Again, this results in Ne being less than N.
Unequal contributions to the next generation If population size is to remain constant, each individual must contribute on average two gametes to the next generation. An idealized population assumes that this follows a Poisson distribution so that the variance of the number of gametes contributed, k is equal to the mean number contributed, i.e. 2: Gametes (in Greek: γαμέτες) —also known as sex cells, germ cells, or spores—are the specialized cells that come together during fertilization (conception) in organisms that reproduce sexually. ...
In probability theory and statistics, the Poisson distribution is a discrete probability distribution (discovered by Siméon-Denis Poisson (1781–1840) and published, together with his probability theory, in 1838 in his work Recherches sur la probabilité des jugements en matières criminelles et matière civile [Research on the...
In probability theory and statistics, the variance of a random variable is a measure of its statistical dispersion, indicating how far from the expected value its values typically are. ...
In statistics, mean has two related meanings: the average in ordinary English, which is more correctly called the arithmetic mean, to distinguish it from geometric mean or harmonic mean. ...
However, in natural populations the variance is larger than this, i.e. The effective population size is then given by: Note that if the variance of k is less than 2, Ne is less than N. Heritable variation in fecundity, usually pushes Ne lower. For the scientific journal Heredity see Heredity (journal) Heredity (the adjective is hereditary) is the transfer of characters from parent to offspring, either through their genes or through the social institution called inheritance (for example, a title of nobility is passed from individual to individual according to relevant customs and...
Fecundity is the potential reproductive capacity of an organism or population, measured by the number of gametes (e. ...
Overlapping generations and age-structured populations If generations overlap (i.e. they are not discrete) then: - Ne = TNa
where T is the mean time to reproduction and Na is the number of individuals born per year that survive to adulthood.
Measurement in wild
-
References - Wright, S. (1931). Evolution in Mendelian populations. Genetics 16:97-159 Offsite pdf file
- Wright, S. (1938). Size of population and breeding structure in relation to evolution. Science 87:430-431
Genetics is a monthly scientific journal publishing investigations bearing on heredity and variation. ...
Science is the journal of the American Association for the Advancement of Science. ...
External links | 
Feeds |
Contact