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What is Evolution?
BIOL2007 Evolutionary Geneticscourse website: http://ucl.ac.uk/~ucbhdjm/courses/
(searching for “BIOL2007 timetable” on Google is easier!)
Darwin: “descent with modification”
A change in morphology, ecology, behaviour, physiology
Change must be genetic
Modern, genetic definition:“evolution is change in gene frequencies between generations”
a) Natural selectionb) Mutationc) Genetic drift, or neutral,
random evolutione) Migration, or gene flow
This lecture: simple examples of evolution by natural selection
What causes evolution?
What is natural selection?
“a consistent bias in survival or fertility between genotypes within generations”
Selection often causes evolution, but may also prevent evolution (e.g. stable polymorphism)
Evolution does not require selection (e.g. drift --important: > 95% of genome maybe "junk"!)
However, many interesting types of evolution involve natural selection
The peppered moth Biston betularia
Left: form typica (left, and carbonaria (right) on lichen-coveredtrunk in Dorset.
Right: on soot-covered tree near Birmingham
A flow diagram for evolution by ns
Random mating
Offspring genotypes in Hardy-Weinberg ratios
Offspring after selection
Natural selection
So now you can write anevolution computer program!
Numerical vs. analytical theory
Selection against recessive alleleSelection AGAINST recessive allele (= selection FOR dominant allele)
Suppose there is “viability selection” (i.e. survival affected) so that …
Genotypes AA Aa aa Total
Relative fitness, W 1 1 1-s -
Genotype frequenciesbefore selection p2 2pq q2 1(Hardy-Weinberg law)
Rel. frequencies p2 2pq q2(1-s) <1after selection
in this simple model, s is the “selection coefficient” (≈ fraction dying)
BIOL2007 – SELECTION AND THE SINGLE GENE SELECTION AGAINST RECESSIVE ALLELE (EQUIVALENT TO SELECTION FOR DOMINANT ALLELE) Suppose there is viability selection so that … Genotypes AA Aa aa Total Relative fitness, W 1 1 1-s Frequencies before selection p2 2pq q2 1 (Hardy-Weinberg law) Relative genotype frequencies p2 2pq q2(1-s) ≠1 after selection
Frequencies should sum to 1! Therefore, need to divide by “mean fitness,” 222 1)1(2 sqsqpqpW −=−++=
Genotype frequencies
after selection 2
2
1 sqp
− 21
2sqpq
− 2
2
1 sqq (1-s)
− 1
WHAT IS THE NEW FREQUENCY OF THE A ALLELE (p’)? p’ = new frequency of AA + ½ new frequency of Aa
( ) 222
2
2212
22
2
11)(
112
12
21
1 '
sqp
sqqpp
sqpqp
sqpqp
sqpq
sqpp
−=
−+=
−+=
−+=
−+
−=
WHAT IS THE RATE OF EVOLUTION PER GENERATION? We need to know the CHANGE OF GENE FREQUENCY, ∆p (obtained by subtracting old gene frequency from the new gene frequency).
2
2
2
2
2 1)1()1(
1 '-
sqspq
sqsqppp
sqpppp
−+=
−−−=−
−==∆
This is the basic equation for all of evolution by natural selection!
2
The basic equation for evolution
Natural selection at a dominant gene
22
2
1 '- spq
sqspqppp ≈−
+==∆
(if s is small)
In words:
The change in gene frequency per generation is proportional to spq2
Dominance vs. recessivesWe can now answer the question: How fast do populations respond
to natural selection?
Answer: (p is frequency of A, q is freq. a)
If p is small, ~0.01 or less, , i.e. RAPID
If p is large, so that q ≈ 0.01 or less, , i.e. very SLOW
(q2 is a square of a very small number � is itself even smaller!)
RESULT:Selection for/against a DOMINANT gene at low frequency is RAPID (∝ p)Selection for/against a RECESSIVE gene at low frequency is SLOW ((∝ q2)
…. many new single genes for resistance (melanism, insecticide resistance and so on) are dominant!
2
2
1
sqspqp−
=∆
ssppqq−
≈∆→→1 :1;1 2
1 :1
2sqpp ≈∆→
The speed of evolution
p
(the rate of gene frequency change per unit time)
time (generations)
rare gene recessive rare gene dominant
(from a programme written by a former B242 student, Wei-Chung Liu, available from the B242 website)
More generally …Complications – many!
Many different kinds of selection- fertility selection- sexual selection
Non-random mating- inbreeding- mate choice
Overlapping generations
Dominance not completeAA Aa aa1 1–hs 1–s
Multiple genes …
&c &c….
But the basic principle remains the same!
Take-home points
Evolution to a geneticist: a change in gene frequencies.
Natural selection: a consistent bias favouring some genotypes over others.
Evolution can occur in the absence of natural selection, via genetic drift or neutral evolution.
Natural selection can stabilize the status quo; zero evolution.
Evolution at a single dominant gene: rate can be predicted
If selected, dominant alleles evolve quickly when rare, slowly when common; recessive alleles evolve slowly when rare, quickly when common.
We can estimate selection coefficients (s), fitnesses (W=1-s) and predict rates of evolution from data on survival or fecundity.
Mathematical theory makes evolution a predictive science
Further reading
FUTUYMA, DJ 2005. Evolution. Chapter 12:270-280.
For readings on examples, see: Science Library: View BIOL2007 or B242 Teaching Collection by going to eUCLid; use Keyword, Basic Search, All Fields: B242.
ESTIMATING SELECTION 1) Change of gene frequencies per generation; result of selection, estimate ∆p; e.g. peppered moth; JBS Haldane estimated s = 0.5. 2) Distortion of Hardy-Weinberg ratios - problems? see next lecture 3) Comparison of birth or death rates between individuals
W = RELATIVE fitness MOST DIRECT METHOD
USING METHOD 3 TO ESTIMATE SELECTION IN PEPPERED MOTH e.g. survival in a field experiment on the peppered moth A) Central Birmingham
number number proportion relative (W, the other released recaptured recaptured fitness, W way round)
typica 144 18 0.125 0.43 1.00 carbonaria 486 140 0.288 1.00 2.30 B) Dorset wood
number number proportion relative released recaptured recaptured fitness
typica 163 67 0.411 1.82 carbonaria 142 32 0.225 1.00 SUMMARY OF FITNESSES:
(Wc = 1 - sc) typica carbonaria selection
coefficient against c Wcc WCc WCC sc
City 0.43 1 1 +0.57 Wood 1.82 1 1 -0.82 HOW FAST WILL CARBONARIA INCREASE IN FREQUENCY in a city? ∆p = spq2/(1-sq2); suppose p = 0.5 to start with:
= 0.57 x 0.5 x 0.52 / (1 - 0.57x0.52) = 0.08, or 8% per generation.
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