Editing Selfish genetic element (section)

== Mathematical theory ==
Much of the confusion regarding ideas about selfish genetic elements center on the use of language and the way the elements and their evolutionary dynamics are described.<ref name=":24">{{cite journal | vauthors = Gardner A, Welch JJ | title = A formal theory of the selfish gene | journal = Journal of Evolutionary Biology | volume = 24 | issue = 8 | pages = 1801–13 | date = August 2011 | pmid = 21605218 | doi = 10.1111/j.1420-9101.2011.02310.x | s2cid = 14477476 }}</ref> Mathematical models allow the assumptions and the rules to be given ''a priori'' for establishing mathematical statements about the expected dynamics of the elements in populations. The consequences of having such elements in genomes can then be explored objectively. The mathematics can define very crisply the different classes of elements by their precise behavior within a population, sidestepping any distracting verbiage about the inner hopes and desires of greedy selfish genes. There are many good examples of this approach, and this article focuses on segregation distorters, gene drive systems and transposable elements.<ref name=":24" />

=== Segregation distorters ===
The mouse t-allele is a classic example of a segregation distorter system that has been modeled in great detail.<ref name=":14" /><ref>{{cite journal | vauthors = Lewontin RC, Dunn LC | title = The Evolutionary Dynamics of a Polymorphism in the House Mouse | journal = Genetics | volume = 45 | issue = 6 | pages = 705–22 | date = June 1960 | doi = 10.1093/genetics/45.6.705 | pmid = 17247957 | pmc = 1210083 }}</ref> Heterozygotes for a t-haplotype produce >90% of their gametes bearing the t (see [[#Segregation distorters|Segregation distorters]]), and homozygotes for a t-haplotype die as embryos. This can result in a stable polymorphism, with an equilibrium frequency that depends on the drive strength and direct fitness impacts of t-haplotypes. This is a common theme in the mathematics of segregation distorters:virtually every example we know entails a countervailing selective effect, without which the allele with biased transmission would go to fixation and the segregation distortion would no longer be manifested. Whenever sex chromosomes undergo segregation distortion, the population sex ratio is altered, making these systems particularly interesting. Two classic examples of segregation distortion involving sex chromosomes include the "Sex Ratio" X chromosomes of ''Drosophila pseudoobscura''<ref name=":11" /> and Y chromosome drive suppressors of ''Drosophila mediopunctata''.<ref>{{cite journal | vauthors = Carvalho AB, Vaz SC, Klaczko LB | title = Polymorphism for Y-linked suppressors of sex-ratio in two natural populations of Drosophila mediopunctata | journal = Genetics | volume = 146 | issue = 3 | pages = 891–902 | date = July 1997 | doi = 10.1093/genetics/146.3.891 | pmid = 9215895 | pmc = 1208059 }}</ref> A crucial point about the theory of segregation distorters is that just because there are fitness effects acting against the distorter, this does not guarantee that there will be a stable polymorphism. In fact, some sex chromosome drivers can produce frequency dynamics with wild oscillations and cycles.<ref>{{cite journal | vauthors = Clark AG | title = Natural selection and Y-linked polymorphism | journal = Genetics | volume = 115 | issue = 3 | pages = 569–77 | date = March 1987 | doi = 10.1093/genetics/115.3.569 | pmid = 3569883 | pmc = 1216358 }}</ref>

=== Gene-drive systems ===
The idea of spreading a gene into a population as a means of population control is actually quite old, and models for the dynamics of introduced compound chromosomes date back to the 1970s.<ref>{{cite journal | vauthors = Fitz-Earle M, Holm DG, Suzuki DT | title = Genetic control of insect population. I. Cage studies of chromosome replacement by compound autosomes in Drosophila melanogaster | journal = Genetics | volume = 74 | issue = 3 | pages = 461–75 | date = July 1973 | doi = 10.1093/genetics/74.3.461 | pmid = 4200686 | pmc = 1212962 }}</ref> Subsequently, the population genetics theory for homing endonucleases and CRISPR-based gene drives has become much more advanced.<ref name=":15" /><ref name=":28">{{cite journal | vauthors = Deredec A, Burt A, Godfray HC | title = The population genetics of using homing endonuclease genes in vector and pest management | journal = Genetics | volume = 179 | issue = 4 | pages = 2013–26 | date = August 2008 | pmid = 18660532 | pmc = 2516076 | doi = 10.1534/genetics.108.089037 }}</ref> An important component of modeling these processes in natural populations is to consider the genetic response in the target population. For one thing, any natural population will harbor standing genetic variation, and that variation might well include polymorphism in the sequences homologous to the guide RNAs, or the homology arms that are meant to direct the repair. In addition, different hosts and different constructs may have quite different rates of non-homologous end joining, the form of repair that results in broken or resistant alleles that no longer spread. Full accommodation of the host factors presents considerable challenge for getting a gene drive construct to go to fixation, and Unckless and colleagues<ref>{{cite journal | vauthors = Unckless RL, Clark AG, Messer PW | title = Evolution of Resistance Against CRISPR/Cas9 Gene Drive | journal = Genetics | volume = 205 | issue = 2 | pages = 827–841 | date = February 2017 | pmid = 27941126 | pmc = 5289854 | doi = 10.1534/genetics.116.197285}}</ref> show that in fact the current constructs are quite far from being able to attain even moderate frequencies in natural populations. This is another excellent example showing that just because an element appears to have a strong selfish transmission advantage, whether it can successfully spread may depend on subtle configurations of other parameters in the population.<ref name=":28" />

=== Transposable elements ===
To model the dynamics of transposable elements (TEs) within a genome, one has to realize that the elements behave like a population within each genome, and they can jump from one haploid genome to another by horizontal transfer. The mathematics has to describe the rates and dependencies of these transfer events. It was observed early on that the rate of jumping of many TEs varies with copy number, and so the first models simply used an empirical function for the rate of transposition. This had the advantage that it could be measured by experiments in the lab, but it left open the question of why the rate differs among elements and differs with copy number. Stan Sawyer and Daniel L. Hartl<ref>{{cite journal | vauthors = Sawyer S, Hartl D | title = Distribution of transposable elements in prokaryotes | journal = Theoretical Population Biology | volume = 30 | issue = 1 | pages = 1–16 | date = August 1986 | pmid = 3018953 | doi = 10.1016/0040-5809(86)90021-3}}</ref> fitted models of this sort to a variety of bacterial TEs, and obtained quite good fits between copy number and transmission rate and the population-wide incidence of the TEs. TEs in higher organisms, like ''Drosophila'', have a very different dynamics because of sex, and [[Brian Charlesworth]], [[Deborah Charlesworth]], Charles Langley, John Brookfield and others<ref name=":13" /><ref>{{cite journal | vauthors = Brookfield JF, Badge RM | title = Population genetics models of transposable elements | journal = Genetica | volume = 100 | issue = 1–3 | pages = 281–94 | date = 1997 | pmid = 9440281 | doi = 10.1023/A:1018310418744| s2cid = 40644313 }}</ref><ref>{{cite journal | vauthors = Charlesworth B, Charlesworth D | title = The population dynamics of transposable elements. | journal = Genet. Res. | date = 1983 | volume = 42 | pages = 1–27 | doi = 10.1017/S0016672300021455 | doi-access = free }}</ref> modeled TE copy number evolution in ''Drosophila'' and other species. What is impressive about all these modeling efforts is how well they fitted empirical data, given that this was decades before discovery of the fact that the host fly has a powerful defense mechanism in the form of piRNAs. Incorporation of host defense along with TE dynamics into evolutionary models of TE regulation is still in its infancy.<ref>{{cite journal | vauthors = Lu J, Clark AG | title = Population dynamics of PIWI-interacting RNAs (piRNAs) and their targets in Drosophila | journal = Genome Research | volume = 20 | issue = 2 | pages = 212–27 | date = February 2010 | pmid = 19948818 | pmc = 2813477 | doi = 10.1101/gr.095406.109 }}</ref>