class: center, middle, inverse, title-slide .title[ # Long-term results and interpretation ] .author[ ### Jinliang Yang ] .date[ ### April 19, 2024 ] --- # Theoretical maximum limit ### Without considering mutation `\begin{align*} & R_{max} = 2N_eih^2\sigma_P = 2N_e i \frac{V_A}{V_P}\sigma_P = 2N_e i \frac{V_A}{\sigma_P}\\ \end{align*}` Set an upper limit to what can be expected. -- ----- Long-term selection is expected to reduce the phenotypic variance of a population because of gradual shifts in allele frequency toward 0 or 1. -- ### Unexpected results However, the variance often surprisingly remains the same over long-term selection - Conversion of variance due to epistasis to `\(V_A\)` - Generation of new alleles through __mutation__ --- # Response upon long-term selection ### Considering mutation Dr. __W. G. Hill__ in 1982, developed theory to include mutations as a wellspring of continuing new variation upon which selection could produce response. -- Analogous to `\(R=2 N_e \times i \frac{V_A}{\sigma_P}\)`, he got: `\begin{align*} & R = 2N_e \times \frac{iV_M}{\sigma_P} \\ \end{align*}` - Where `\(V_M\)` is the __additive genetic variance__ arising from __new mutations of each generation__. --- # Considering mutation `\begin{align*} & R = \frac{2N_eiV_M}{\sigma_P} \\ \end{align*}` - Where `\(V_M\)` is the __additive genetic variance__ arising from new mutations of each generation. -- - And `\(V_M = 2pq(a_M + d_M(q-p))^2\)` -- ### Important notes: 1. Additive variance of new mutation is a function of allele frequency. 2. It takes at least 20 generations for mutations to be __high enough in frequency__. -- ### Take home message: Increasing the mutation rate through __mutagenesis__ is not expected to enhance response in the short term. --- # Number of effective factors `\begin{align*} & n = \frac{R_T^2}{8\sigma_A^2} \\ \end{align*}` Where `\(n\)` is the number of loci with many assumptions: - 1) unrelated loci - 2) same effect size -- If takes LD into consideration, the above equation actually defines __the number of effective factors__. - The numer of loci affecting a trait is larger than the number of effective factor, resulting from __LD between loci__ -- If considering __large differences__ in effect size between loci - Not to actually using the above formula, but rather understanding the nature of genetic variation --- # Definition of Evolvability ### General definition: The ability for a species or breeding population - to adapt to its environment through __natural selection__ - to be improved through __artificial selection__ is known as __evolvability__. -- ### Other possible definition: - The ability of a population to respond to selection - The ability of a genomic architecture to facilitate change - The ability of a genetic system to produce and maintain potentially adaptive genetic variants - Propensity to evolve novel structures --- # Definition of Evolvability ### General definition: The ability for a species or breeding population - to adapt to its environment through __natural selection__ - to be improved through __artificial selection__ is known as __evolvability__. ### __Is evolvability evolvable?__ - Or is evolvability genetically determined? - Does natural selection in favor populations that are more evolvable? --- # E. Coli Long-term selection experiment (LTEE) .pull-left[ - Richard Lenski and co-workers, at Michigan State University since 1988 - Selection for fitness under glucose-limited conditions for __> 50,000 generations__ with __12 independent populations__ - Transferring 0.1 ml of culture into 9.9 ml of fresh medium __each day (about 6.6 life cycles)__ ] .pull-right[ <div align="center"> <img src="ecoli.png" height=350> </div> Rich makes the 10,000th transfer. ] --- # E. Coli Long-term selection experiment __Response__: - They store a sample every 75 days, or about 500 generations. - The __relative fitness__ can be compared to ancestral populations by competing two populations one another and counting the number of cells from each population. -- <div align="center"> <img src="response.png" height=250> </div> The figure is from Dawkins 2009. - Left: the response for 1/12 populations. - Right: responses of all 12 populations. --- # Mutations <div align="center"> <img src="mut.png" height=300> </div> > Tenaillon et. al., 2016. Mutations accumulated over time. - Left: total mutations over time in the 12 LTEE. - Right: total mutations rescaled to reveal the trajectories for the six populations that did not become __hypermutable__ for point mutations, and for the other six before they evolved hypermutability. --- # Mutations accumulated over time <div align="center"> <img src="mutmap.png" height=380> </div> > Barrick et. al., 2009. - Inside ring represents genome of clone from 2K generations. - Outside ring represents clone from 20K generations. - In between, intermediate clones. ??? Note that, mutations in the form of SNPs, deletions, insertions, and inversions have accumulated across the generations. --- # Large effect mutation <div align="center"> <img src="largeeffect.png" height=250> </div> > Dawkins et. al., 2009. -- - Increase in bacterial population density after 33,000 generations of one of the twelve populations. - This population accumulated the __large effect mutations__ necessary to metabolize citrate, greatly increasing the food source availability. - And thus greatly increase in the bacterial population. --- # Mutations affecting mutation rate Recently, Wielgoss et al., 2013 reported an interesting interaction between __mutations affecting mutation rate__, which involves mutations falling in genes controlling the cellular repair machinery. <div align="center"> <img src="mm.png" height=350> </div> > Wielgoss et. al., 2013. --- # Mutations affecting mutation rate <div align="center"> <img src="mm.png" height=300> </div> > Wielgoss et. al., 2013. -- - A mutation in __mutT__ between 20,000 and 30,000 generations dramatically increased the mutation rate. - Then, two mutations in __mutY__ (__mutY-E__ and __mutY-L__) between generations 35,000 and 40,000, which decreased the mutation rate --- # Mutations affecting mutation rate <div align="center"> <img src="mm.png" height=300> </div> > Wielgoss et. al., 2013. - The interesting part is that because __mutY__ is involved in DNA repair, mutations in __mutY__ are expected to be hypermutators themselves. -- - But in the background of the __mutT__, it actually decrease the mutation rate, because these mutations coincidentally repair the mutations made by __mutT__.