population genetics Population genetics is a subfield of genetics that deals with genetic differences within and among populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as Adaptation (biology), adaptation, s ...

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 Sewall Green Wright ForMemRS HonFRSE (December 21, 1889March 3, 1988) was an American geneticist known for his influential work on evolutionary theory and also for his work on path analysis. He was a founder of population genetics alongside ...

and

Ronald Fisher Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic. For his work in statistics, he has been described as "a genius who a ...

(1922, 1930) and (1931). Wright-Fisher

population Population is a set of humans or other organisms in a given region or area. Governments conduct a census to quantify the resident population size within a given jurisdiction. The term is also applied to non-human animals, microorganisms, and pl ...

s have constant size, and their members can mate and reproduce with any other member. Another example is a Moran model, which has overlapping

generation A generation is all of the people born and living at about the same time, regarded collectively. It also is "the average period, generally considered to be about 20–⁠30 years, during which children are born and grow up, become adults, and b ...

s, 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 The effective population size (''N'e'') is the size of an idealised population that would experience the same rate of genetic drift as the real population. Idealised populations are those following simple one- locus models that comply with ass ...

that is very different from the census population size of the real population. For sexual diploids, idealized populations will have

genotype The genotype of an organism is its complete set of genetic material. Genotype can also be used to refer to the alleles or variants an individual carries in a particular gene or genetic location. The number of alleles an individual can have in a ...

frequencies related to the

allele An allele is a variant of the sequence of nucleotides at a particular location, or Locus (genetics), locus, on a DNA molecule. Alleles can differ at a single position through Single-nucleotide polymorphism, single nucleotide polymorphisms (SNP), ...

frequencies according to Hardy-Weinberg equilibrium.

Hardy-Weinberg

In 1908,

G. H. Hardy Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...

and Wilhelm Weinberg modeled an idealised population to demonstrate that in the absence of selection, migration, random genetic drift, allele frequencies stay constant over time, and that in the presence of random mating, genotype frequencies are related to allele frequencies according to a binomial square principle called the Hardy-Weinberg law.

Usage in population dynamics

A good example of usage idealised population model, in tracking natural population conditions, could be found in a research of Joe Roman and Stephen R. Palumbi (2003). Using

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 correlated to the span of survival for a species. It is d ...

data, they questioned: have populations of North Atlantic great whales recovered enough for commercial whaling? To calculate genetic diversity the authors multiply long term effective population size of the females by two, assuming

sex ratio A sex ratio is the ratio of males to females in a population. As explained by Fisher's principle, for evolutionary reasons this is typically about 1:1 in species which reproduce sexually. However, many species deviate from an even sex ratio, ei ...

1:1, and then multiply by mitochondrial genes substitution rate, per generation. Making several assumptions according to the sex ratio and number of juveniles, they were able to calculate that in contrast to historical records, modern whale populations are far from harvestable range.

Application to population history

Idealised population models could not only provide us with information about present populations conditions but are useful in revealing natural history and population dynamics in the past as well. Using an idealised population model, Anders Eriksson and Andrea Manica (2012) tested the hypothesis of the archaic human admixture with modern humans. The authors compare genome sequences of two human populations, Neanderthals and chimpanzee. Eriksson and Manica created a stepping stone model under which Africa and Eurasia are represented as a string of equal size populations. They concluded that under the stepping stone model, in which Europeans can exchange genetic information with Asians and not with Africans, similarities between Neanderthal genome and Eurasian could be explained by ancient populations structure.Eriksson, Anders, and Andrea Manica. "Effect of ancient population structure on the degree of polymorphism shared between modern human populations and ancient hominins." Proceedings of the National Academy of Sciences 109, no. 35 (2012): 13956-13960.

Computer simulations

Usage of models also allows the performance of

simulation A simulation is an imitative representation of a process or system that could exist in the real world. In this broad sense, simulation can often be used interchangeably with model. Sometimes a clear distinction between the two terms is made, in ...

s, including computerized ones, to hypothesize evolutionary outcomes:
PopG
is a free

computer program A computer program is a sequence or set of instructions in a programming language for a computer to Execution (computing), execute. It is one component of software, which also includes software documentation, documentation and other intangibl ...

that uses the Fisher–Wright model to simulate the simultaneous evolution of multiple populations and illustrate the results. *The University of Connecticut hosts a Java-base
genetic drift simulator
designed to illustrate the influence of genetic drift on natural populations.

References

*{{Cite journal , last1 = Hanage , first1 = W. P. , last2 = Spratt , first2 = B. G. , last3 = Turner , first3 = K. M. E. , last4 = Fraser , first4 = C. , title = Modelling bacterial speciation , doi = 10.1098/rstb.2006.1926 , journal = Philosophical Transactions of the Royal Society B: Biological Sciences , volume = 361 , issue = 1475 , pages = 2039–2044 , year = 2006 , pmid = 17062418, pmc = 1764933 Population genetics Statistical genetics