Lecture 10. Natural Selection II

# Lecture 10 Natural Selection II

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Unformatted text preview: a single nucleo+de in a DNA sequence •  Indels – inser+ons/dele+ons in a DNA sequence •  Gene duplica+ons – duplica+ons of one or more protein‐coding genes •  Muta+ons can be in the germ line (passed on to the next genera+on) or the soma (normally not passed on) More useful dis+nc+ons: •  muta+on is a change in the gene+c material, usually occuring in a single individual and produces a mutant allele •  subs+tu+on = ﬁxa+on of a mutant allele in a popula+on or species, replacing previous alleles Reversible Muta+on •  Two ways to get an A allele in genera+on t: an A allele that escaped muta+on with probability (1‐μ), or an a allele that mutated with to A probability ν. pt = pt −1 (1 − µ) + (1 − pt −1 )ν 35 € Reversible Muta+on •  The general solu+on is: ν ν t pt − = p0 − (1 − µ − ν ) µ+ν µ+ν 36 Reversible Muta+on •  The general solu+on is: ν ν t pt − = p0 − (1 − µ − ν ) µ+ν µ+ν when t approaches inﬁnity, this becomes zero. 37 Reversible Muta+on •  Therefore, the equilibrium is reached when: ν pt − =0 µ+ν or, ν pt = µ+ν 38 Change in allele frequency with reversible muta+on 1.0 μ = 0.0001 ν = 0.00001 0.8 0.6 p 0.4 0.2 0.0 0 10 000 20 000 30 000 40 000 50 000 genera+ons (t) 39 Calcula+ng the Equilibrium (a second approach) The change in q over one +me step: Δq = µp − νq = u − q( u + v ) € 40 Exercise •  Use the formula provided to calculate the equilibrium frequency of q with forward and backward muta+on: Δq = u − q( u + v ) € 41 Calcula+ng the Equilibrium (review) The change in q over one +me step: Δq = µp − νq = u − q( u + v ) Sevng Δq = 0, and using p = 1‐ q, € 0 = µ(1 − q) − νq 0 = µ − µq − νq = µ − q(µ + ν ) µ ˆ q= µ+ν 42 Equilibrium q 0.0001 ν = 0.00001 0.00005 Δq 0.0000 - 0.00005 - 0.0001 0.2 0.4 0.6 0.8 1.0 ν = 0.0001 q 43 Beneﬁcial Muta4ons •  Fitness and cell size increased in a punctuated manner in an experiment with E. coli •  Advantageous muta+ons were rare – the authors e...
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## This note was uploaded on 11/20/2012 for the course BIO bio3124 taught by Professor Rezanokhbeh during the Spring '11 term at University of Ottawa.

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