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In
population genetics Population genetics is a subfield of that deals with genetic differences within and between s, and is a part of . Studies in this branch of examine such phenomena as , , and . Population genetics was a vital ingredient in the of the . Its pri ...
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 gene variants 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 structu ...
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 Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland's national academy of science and Literature, letters, judged to ...

Sewall Wright
and
Ronald Fisher Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a subs ...
(1922, 1930) and (1931). Wright-Fisher
population Population typically refers the number of people in a single area whether it be a city or town, region, country, or the world. Governments typically quantify the size of the resident population within their jurisdiction by a process called a ...

population
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 * Mate (colloqu ...

mate
and
reproduce Reproduction (or procreation or breeding) is the biological process Biological processes are those processes that are vital for an organism In biology, an organism (from Ancient Greek, Greek: ὀργανισμός, ''organismos'') is ...
with any other member. Another example is a Moran model, which has overlapping
generation A generation is "all of the people born and living Living or The Living may refer to: Common meanings *Life, a condition that distinguishes organisms from inorganic objects and dead organisms ** extant taxon, Living species, one that is not ex ...

generation
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 number of individuals that an idealised population would need to have in order for some specified quantity of interest to be the same in the idealised population as in the real population. Idealised ...
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 (biology), cell, and hence the number of possible alleles for Autosome, autosomal and Pseudoautosomal region, pseudoautosomal genes. Somatic cells, Tissue (biology), tissues, and I ...
, 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 *B ...
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 biology, conservation research includes studies of the historical population siz ...
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 In biology, a species is the basic unit of biological classificati ...
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 is the number of individuals that an idealised population would need to have in order for some specified quantity of interest to be the same in the idealised population as in the real population. Idealised populations a ...
size of the females by two, assuming
sex ratio The sex ratio is the ratio In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, ...
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 The Middle Paleolithic (or Middle Palaeolithic) is the second subdivision of the Paleolithic The Paleolithic or Palaeolithic or Palæolith ...
. 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 stepping, a ...
, 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 models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulat ...

simulation
s, including in silica ones, to hypothesize evolutionary outcomes. As an example
PopG
is a free
computer program In imperative programming, a computer program is a sequence of instructions in a programming language that a computer can execute or interpret. In declarative programming, a ''computer program'' is a Set (mathematics), set of instructions. A comp ...
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