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 pop ...

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 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, m ...

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 FRS(For) Honorary FRSE (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 alongsi ...

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 typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...

s have constant size, and their members can

mate Mate may refer to: Science * Mate, one of a pair of animals involved in: ** Mate choice, intersexual selection ** Mating * Multi-antimicrobial extrusion protein, or MATE, an efflux transporter family of proteins Person or title * Friendship ...

and

reproduce Reproduction (or procreation or breeding) is the biological process by which new individual organisms – "offspring" – are produced from their "parent" or parents. Reproduction is a fundamental feature of all known life; each individual org ...

with any other member. Another example is a Moran model, which has overlapping

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 gr ...

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 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 wo ...

that is very different from the census population size of the real population. For sexual

diploids 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, respective ...

, idealized populations will have genotype frequencies related to the allele frequencies according to Hardy-Weinberg equilibrium.

Hardy-Weinberg

In 1908, G. H. Hardy 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 Binomial may refer to: In mathematics *Binomial (polynomial), a polynomial with two terms * Binomial coefficient, numbers appearing in the expansions of powers of binomials *Binomial QMF, a perfect-reconstruction orthogonal wavelet decomposition ...

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 Joe Roman is a conservation biologist, academic, and author of the books ''Whale'' and '' Listed: Dispatches from America's Endangered Species Act''. His conservation research includes studies of the historical population size of whales, the ...

and Stephen R. Palumbi (2003). Using genetic diversity 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 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 wo ...

size of the females by two, assuming

sex ratio The sex ratio (or gender ratio) is usually defined as 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. Many species devia ...

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 There is evidence for interbreeding between archaic and modern humans during the Middle Paleolithic and early Upper Paleolithic. The interbreeding happened in several independent events that included Neanderthals and Denisovans, as well as sever ...

. 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 Stepping may refer to: * Walking, one of the main gaits of locomotion among legged animals Computing * Stepping level, an aspect of microprocessor version designation * Stepping (debugging), a method of debugging Dance * Chicago steppin ...

, 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 to perform

simulation A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of Conceptual model, models; the model represents the key characteristics or behaviors of the selected system or proc ...

s, including in silica ones, to hypothesize evolutionary outcomes. As an example
PopG
is a free

computer program A computer program is a sequence or set of instructions in a programming language for a computer to execute. Computer programs are one component of software, which also includes documentation and other intangible components. A computer program ...

that is capable of simulating simultaneous evolution of populations based on Fisher-Wright model. Idealised population model also, could be used in several simple simulations designed for education. So
Charles Darwin: Can you survive?
Simulation is designed to introduce general public to the concept of natural selection. Another example i

simulator (Requires an updated Java version), which is designed to visualize 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