mendel

was genetics important

• It was needed to clarify why selection works and overturn a theoretical objection to evolution by natural selection 

• It provided a rigorous basis for understanding how evolution works 

• It enormously enriched our understanding of how evolution works, providing often counter-intuitive, but empirically correct, results 

theoretical objection to evolution by natural selection

• The decline of black pepper moths was not by itself enough evidence for natural selection 

• e.g. could have just been covered in soot 

• Needed to know that you are tracking an allele 

why was Darwin confused about inheritance

• Darwin understood natural selection but did not know the genetic mechanism of inheritance.

• Blending inheritance was the belief that offspring inherit a mixture of their parents' traits.

• This suggested advantageous traits could become diluted over generations.

• Natural selection requires heritable variation within populations.

• Darwin struggled to explain how useful variations could persist across generations.

• He proposed pangenesis, an incorrect theory that body parts produced particles passed to offspring.

• Gregor Mendel demonstrated particulate inheritance, where inherited factors remain distinct.

• Rediscovery of Mendel's work around 1900 helped explain how genetic variation persists for natural selection to act upon.

Jenkin’s objection - blending inheritance destroys variation

• Assumed phenotypes were inherited by blending inheritance (also wrong) 

  • Offspring look like a mix of both parents 

  • e.g. short + big = in the middle 

• a new 'type' cannot easily increase in frequency because the mode of inheritance dilutes it each generation 

  • e.g white + red flower = pink 

  • White + pink flower = less pink 

• Eventually the population moves to a position – through 'rules' of inheritance alone, in which there is no variation 

• No variation = no one is fitter = natural selection cannot work 

blending inheritance

• Wrong 

• Inheritance is mendelian 

	R	r
R	RR	Rr
r	Rr	rr

• 1:2:1 

• Understanding that inheritance is mendelian rescued natural selection as a concept by showing why selection matters and inheritance doesn't 

• Our understanding of genetics has become a framework for understanding the fate of new mutations 

  • This has been central to the clarification of the process of evolution : when, how and on what selection acts 

maths

Let there be two alleles (A and a) hence three genotypes (AA, Aa and aa) 
 
Let us assume frequency of A is p, of a q (p=1-q) 
Let us assume frequency of AA, Aa and aa, are x, y and z. 
 
Note freq of A = x +y/2 = p 

• 
  A major advangtage of this insight is that we can do the same calculations using gamete not genetype frequencies (P2 +q2 = 2pq) 

• If p is the frequency of A and q the frequency if am then in the next generation 

  • p’ = p²+pq = p(p+q) = p 

  • q’ = q²+pq = q(p+q) = q 

what if we add in selection

• 
  Assume AA has fitness 1+s, Aa fitness 1+hs and aa fitness 1 

• p'= [p² (1+s) + 0.5 (2 pq) (1+hs)]/w 

• W is the weighted mean fitness – weighted in proportion to the abundance of each of the 3 genotypes. 

• Finding invasion conditions 

  • Will the allele invade when rare? 

  • We take the slope on the line relating p' and p  

    • Dp' /dp 

  • When p is rare, this is greater than 1 

• Invasion happens if 1+t > 1, t>0 

• p’ = p²(1+s)+pq(1+t) /W