# Idealised population

In population genetics an idealised population is one that can be described using a number of simplifying assumptions. Idealised population models are widely used in population genetics for calculating migration rates, drift effects, mutation rates and effects, divergence and selection. Coalescent theory, also widely applies idealised population principals.[1] In biology idealized population often referred to a population in Hardy-Weinberg equilibrium.[2] Fisher-Wright population after R.A. Fisher and Sewall Wright, is a population whose members can mate and reproduce with any other member of the other gender, has a sex ratio of 1 and no overlapping generations. Another example is a Moran model, which has overlapping generations. Deviation from the idealised population results in the effective population size being different from the census population size.

## History

The first idealised population model was created in 1908 y. by G. H. Hardy and Wilhelm Weinberg. Hardy was a British mathematician and Weinberg was a German physician. Both of them published binomial square principle at the same year, independently. However, only Hardy got an initial credit for his work. Weinberg’s paper was published in German. This work was not easily available for British and American geneticists. When it was finally recognized, years later, it was already displaced by other population genetics models. Now, the binomial square principle is called the Hardy-Weinberg law.[3] From that time, idealised population models are one of the main tools in population genetics.

## Usage in Population Dynamics

If an idealised population is consistent with Hardy-Weinberg principals and maintains constant population size, such population will be called an ideal population.[4][5] No natural population exhibits all characteristics of ideal population.[6] So, mostly all models that are based on idealized population have their limitations of which their users need to be aware of.[7] Despite several limitations, idealised population models are rather useful as direct measurements of populations dynamics are often very time consuming and expensive.[8] From this point of view, idealised population allows to track natural population dynamics and provide with significant amount of information about populations, using only limited sample size. 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 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 1:1, and then multiply by mitochondrial genes substitution rate, per generation. Making several assumptions according 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.[9]

## Usage in Natural History

Idealised population models could not only provide us with information about present populations conditions but as well are useful in revealing natural history and population dynamics in the past. Using 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.[10]

## Computer Simulations

Usage of models, also allows to perform simulations, including in silica ones, to hypothesize evolutionary outcomes. As an example, PopG is a free computer program that is capable of simulating simultaneous evolution of populations based on Wright-Fisher 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 is Genetic Drift simulator (Requires an updated Java version), which is designed to visualize influence of genetic drift on natural populations.

## References

1. ^ . Nielsen, Rasmus, and Montgomery Slatkin. An Introduction to Population Genetics: Theory and Applications. Sunderland, MA: Sinauer Associates, 2013. Print.
2. ^ 2. Огородников, Владимир Петрович, and В. П. Огородников. История и философия науки: учебное пособие для аспирантов. Издательский дом" Питер", 2013.ISBN 5423701317, 9785423701314
3. ^ . Crow, James F. "Population genetics history: a personal view." Annual review of genetics 21, no. 1 (1987): 1-22.
4. ^ . Harmon, Luke J., and Stanton Braude. "12 Conservation of Small Populations: Effective Population Sizes, Inbreeding, and the 50/500 Rule." (2009).
5. ^ . Van Dyke, Fred. Conservation biology: foundations, concepts, applications. Springer, 2008.
6. ^ .Sadava, David E., David M. Hillis, H. Craig Heller, and M. Berenbaum. Life: The Science of Biology. New York: W.H. Freeman, 2014. Print.
7. ^ Gillespie, Rosemary G., and David A. Clague, eds. Encyclopedia of islands. No. 2. Univ of California Press, 2009.
8. ^ . Whitlock, Michael C., and David E. McCauley. "Indirect measures of gene flow and migration: FST≠ 1/(4Nm+ 1)." Heredity 82, no. 2 (1999): 117-125.
9. ^ Roman, Joe, and Stephen R. Palumbi. "Whales before whaling in the North Atlantic." science 301, no. 5632 (2003): 508-510.
10. ^ 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.
• Hanage, W. P.; Spratt, B. G.; Turner, K. M. E.; Fraser, C. (2006). "Modelling bacterial speciation". Philosophical Transactions of the Royal Society B: Biological Sciences 361 (1475): 2039. doi:10.1098/rstb.2006.1926. edit