©2000 Timothy G. Standish 1 Thessalonians 5:21 21 Prove [test] all things; hold fast that which is good.
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©2000 Timothy G. Standish
1 Thessalonians 5:21
21 Prove [test] all things; hold fast that which is good.
©2000 Timothy G. Standish
Timothy G. Standish, Ph. D.
Evolution OfEvolution OfPopulationsPopulations
©2000 Timothy G. Standish
Macro and Micro EvolutionMacro and Micro Evolution Macro evolution is the evolution of higher taxonomic
groups (formation of a new genus, family etc.) Micro evolution - Change in allele frequency within a
species or population of a species Micro evolution is population genetics Population genetics has been observed and this is what
is being talked about when scientists say that evolution has been observed
Macro evolution has not been observed in any definitive way
©2000 Timothy G. Standish
Speciation, Yes.Speciation, Yes.Natural Selection, ???Natural Selection, ???
After The Origin of Species was published in 1859, the scientific community quickly accepted that speciation occurred
Remember that speciation was not an entirely new idea; it had been proposed by Lamarck and Franz Unger (Mendel’s mentor) among others
The mechanism for speciation proposed by Darwin, natural selection, was not as quickly accepted
©2000 Timothy G. Standish
Other Ideas Other Ideas About SpeciationAbout Speciation
Many believed that new species resulted from hybridization between old species (not necessarily untrue)
Orthogenesis (ortho = straight genesis = beginning) - The idea that evolution was progressing along a predictable path toward some ideal. Really a throwback to Lamarckism
1920s After the rediscovery of Mendel's work, the idea that evolution occurred in rapid leaps due to mutations radically altering phenotype was popular
From Huxley’s book
©2000 Timothy G. Standish
The Modern SynthesisThe Modern Synthesis Darwin recognized that variation existed in populations and
suggested natural selection as a mechanism for choosing some variants over others resulting in survival of the fittest and gradual changes in populations of organisms.
Without a mechanism for generation of new variation, populations would be selected into a corner where only one variation would survive and new species could never arise.
The Modern Synthesis combines the mechanism of DNA mutations generating variation with natural selection of individuals in populations to produce new species.
©2000 Timothy G. Standish
Where Speciation OccursWhere Speciation Occurs Real acceptance of natural selection came after it was
realized that evolution occurs on the level of populations, not individuals
Individuals that have more success at reproducing than others are selected over others in a population
If one type of individual is chosen (selected) over another type, it will change the make up of the population by passing its genes on to more members of the next generation
Individuals are selected, populations evolve
©2000 Timothy G. Standish
What is a Population?What is a Population? A group of individuals of the same species in the
same geographical area:– Human population of Berrien Springs
– Chicken population of Hong Kong
– Human population of the United States What is a species? A group of populations that have the potential to
interbreed in nature We’ll come back to this question
©2000 Timothy G. Standish
Population GeneticsPopulation Genetics Is mathematics One definition: Algebraic description of population's genetic
makeup including allelic frequencies and genotypic frequencies
Emphasizes - Genetic variation within populations (on which selection can occur)
Recognizes - The importance of quantitative traits
©2000 Timothy G. Standish
HistoryHistory 1908 - G. H. Hardy, an English mathematician
and W. Weinberg, a German physician, simultaneously discovered an equation that relates allelic and genotypic frequencies in populations that meet certain requirements commonly found in real populations.
1920s - Developed very rapidly due to work by R. A. Fisher, J. B. S. Haldane, and S. Wright.
©2000 Timothy G. Standish
History Cont.History Cont. 1960+ Has become a major area of genetics
due to: Computers - Allowing rapid computation on
large data sets Electrophoresis - Allows the rapid gathering
of large amounts of empirical data Newer techniques that allow the analysis of
relationships among species
©2000 Timothy G. Standish
The Hardy-Weinberg TheoremThe Hardy-Weinberg Theorem The cornerstone of population genetics “The frequency of alleles in a population
will remain constant over time if certain conditions are met”1 Infinite (or at least very large) population size
2 Isolation from other populations - No migration
3 No net mutations
4 Random mating
5 No natural selection
©2000 Timothy G. Standish
The EquationThe EquationThat Says it allThat Says it all
If we look at one gene in a population with 2 alleles, A and a, and we let:
p = f(A) q = f(a) -> f(A) + f(a) = p + q = 1 and p = 1 - q and q = 1 - p Probability of getting an individual with a given genotype
can be calculated on the basis of the probability of getting parents with given genotypes: (p + q)(p + q) = 1 x 1 = 1
(p + q)2 = 1 2
p2 + 2pq + q2 = 1
©2000 Timothy G. Standish
pp22 + 2pq + q + 2pq + q22 = 1 = 1This equation allows us to predict genotypic
frequencies on the basis of allelic frequencies and allelic frequencies on the basis of genotypic frequencies
f(AA) = f(A) x f(A) = p2
f(aa) = f(a) x f(a) = q2
f(Aa) =2 [f(A) x f(a)] = 2pq
©2000 Timothy G. Standish
Does This Equation Fit Does This Equation Fit With Mendelian Genetics?With Mendelian Genetics?
In the following cross:– Aa x Aa
0.5 of alleles in gametes will be A 0.5 of alleles in gametes will be a
Therefore:– f(A) = p = 0.5– f(a) = q = 0.5
p2 + 2pq + q2 = 1 (0.5)2 + 2(0.5)(0.5) + (0.5)2 = 1 0.25 + 0.5 + 0.25 = 1 f(AA) = 0.25, f(Aa) = 0.5, f(aa) = 0.25
AA0.01
Aa0.09
Aa0.09
aa0.81
A0.1
a0.9
A0.1a
0.9
AA0.25
Aa0.25
Aa0.25
aa0.25
A0.5
a0.5
A0.5a
0.5
©2000 Timothy G. Standish
Problem 1 Problem 1 MN Blood Types in US. WhitesMN Blood Types in US. Whites
MN blood types are inherited in a co-dominant fashion, thus heterozygous individuals can easily be detected
In a sample of the U.S. white population, blood types were determined as follows:–M (Genotype MM) = 1,787–MN (Genotype MN) = 3,039–N (Genotype NN) = 1,303
©2000 Timothy G. Standish
Problem 1 AProblem 1 AMN Blood Types in US. WhitesMN Blood Types in US. Whites
MM 1,787 MN 3,039 NN 1,303 A) What is the frequency of the M allele? Answer - As each individual is heterozygous and there are a total
of 6,129 in the sample there should be 2(6,129) = 12,258 alleles 2 M alleles in each MM genotype = 2(1,787) = 3,574 alleles 1 M allele in each MN genotype = 3,039 alleles Total M alleles/Total of all alleles = f(M) = p
p 2(MM) (MN)
2(Total)2(1,787) 3, 039
2(6,129) 3, 574 3, 039
12, 2580.54
or
p (MM) 1/ 2(MN)
Total
©2000 Timothy G. Standish
Problem 1 BProblem 1 BMN Blood Types in US. WhitesMN Blood Types in US. Whites
MM 1,787 MN 3,039 NN 1,303 B) What is the frequency of the N allele? Answer: As p + q = 1 q = 1 - p q = 1 - 0.54 q = 0.46
©2000 Timothy G. Standish
Problem 1 CProblem 1 CMN Blood Types in US. WhitesMN Blood Types in US. Whites
MM 1,787 MN 3,039 NN 1,303 C) Is this population described by the Hardy-Weinburg formula? Answer: Predicted genotypic numbers in a population of this size =
– f(MM)(Total) = p2 (Total) = (0.54)2(6,129) = 0.292 (6,129) = 1,790
– f(MN) (Total) = 2pq (Total) = 2(0.54)(0.46) (6,129) = 0.498 (6,129) = 3,052
– f(NN) (Total) = q2 (Total) = (0.46)2 (6,129) = 0.212 (6,129) = 1,299
Quick math check:– p2 + 2pq + q2 = 0.292 + 0.498 + 0.212 = 1.002 (Close enough)– 1,790 + 3,052 + 1,299 = 6,151 (off by about 12)– 0.002 x 6,129 ≈ 12
Do Chi square to decide
©2000 Timothy G. Standish
Problem 1 C Cont.Problem 1 C Cont.MN Blood Types in US. WhitesMN Blood Types in US. Whites
Degrees of freedom = N - 1 = 3 - 1 = 2 0.99 > p > 0.95 Yes, the population is probably in a Hardy-Weinburg equilibrium
d2
e (Obs. Ex.)2
ExChi Square:
0.0554
0.005
0.0123
3,052
1,790
1,299
3,039
1,787
1,303
0.0727X2 =
(O-E)2/EEx.Obs.
MN
MM
NN
O - E
-13
-3
4
©2000 Timothy G. Standish
What if pWhat if p22 + 2pq + q + 2pq + q22 = 1 = 1 Did not Describe the Population?Did not Describe the Population?
If the Hardy-Weinburg equation does not describe the population, it is probably evolving due to violation of one of these conditions
1 Infinite (or at least very large) population size
2 Isolation from other populations - No migration
3 No net mutations
4 Random mating
5 No natural selection
Remember that the Hardy-Weinburg theorem is true only if certain conditions are met:
©2000 Timothy G. Standish
Infinite Population SizeInfinite Population Size This same assumption is made in most descriptive statistics Small population sizes can lead to sampling errors so that the next
generation is not an accurate representation of the previous generation– Genetic drift - With each generation each allele has a fixed probability
of not being passed on; in small populations this probability is significant– Founder effect - A small number of individuals from a large population
populate an area. Only the alleles of the few founders are represented in their descendants, not the entire population from which they came (i.e., the human population of Finland)
– Bottleneck effect - A large population is reduced to a very small number then recovers, but only those alleles that made it through the bottleneck are in the recovered population (i.e., cheetahs in Southern Africa)
©2000 Timothy G. Standish
Isolation From Other PopulationsIsolation From Other Populations If members of another population with different allelic frequencies are
migrating in, the population being studied will not be in equilibrium Example: Two populations of 100 individuals:
– 1 p1 = 0.1 q1 = 0.9 AA=1, Aa=18, aa=81
– 2 p2 = 0.9 q2 = 0.1 AA=81, Aa=18, aa=1
Combined together: p1+2 = 0.5 q1+2 = 0.5
Predicted genotypic frequency:– f(AA) = p2 = 0.25 or 50/200 (actual 0.41 or 82/200)– f(Aa) = 2pq = 0.50 or 100/200 (actual 0.18 or 36/200)– f(aa) = q2 = 0.25 or 50/200 (actual 0.41 or 82/200)
©2000 Timothy G. Standish
No Net MutationsNo Net Mutations In reality, heritable mutations are very rare events. Remember that most mutations are not a good thing for
the organism, so it is in the best interest of all living things to avoid damage to their DNA
Even if mutation was common, an equilibrium would be reached:
Let A and a be alleles for a given gene, mutation from A to a = and mutation from a to A =
A a
©2000 Timothy G. Standish
Random MatingRandom Mating If mates are chosen on the basis of a genetic trait,
then that trait or allele will be passed to the next generation at higher frequencies than alternative alleles; thus allelic frequencies will change over time, and the population will not be in equilibrium
Sexual Selection - Choosing a mate on the basis of their genotype Hi there
sweetie!
©2000 Timothy G. Standish
Natural SelectionNatural Selection Natural selection is thought to be the most common
cause of changes in allelic frequencies and thus populations being out of equilibrium
It is important to note that for the effect of natural selection to be detected on the basis of violation of Hardy-Weinburg, selection would have to be fairly stringent at the point in time data was collected
Hardy-Weinburg can be used to compare populations of the same species and may infer that selection has occurred assuming the other factors previously mentioned are not at play
©2000 Timothy G. Standish
Natural SelectionNatural Selectionp= 0.1q= 0.9
©2000 Timothy G. Standish
Natural SelectionNatural Selectionp= 0.1q= 0.9
If selection (s)is 0.5 against aaand fitness = W=1-s
©2000 Timothy G. Standish
Natural SelectionNatural SelectionSecond GenerationSecond Generation
p= 0.17q= 0.83
AA=2Aa =30aa =68
©2000 Timothy G. Standish
Natural SelectionNatural SelectionThird GenerationThird Generation
p= 0.25q= 0.75
AA=3Aa =46aa =51
©2000 Timothy G. Standish
Natural SelectionNatural SelectionFourth GenerationFourth Generation
p= 0.34q= 0.66
AA=3Aa =62aa =35
©2000 Timothy G. Standish
Natural SelectionNatural SelectionFifth GenerationFifth Generation
p= 0.42q= 0.58
AA=4Aa =75aa =21
©2000 Timothy G. Standish
Natural SelectionNatural SelectionSixth GenerationSixth Generation
p= 0.46q= 0.54
AA=5Aa =83aa =12
©2000 Timothy G. Standish
Natural SelectionNatural SelectionSixth GenerationSixth Generation
After 6 generations, the population is not in equilibrium:
p= 0.46 q= 0.54 p2 + 2pq + q2 = 0.212 + 0.497 + 0.292 =1.001 Expected genotype numbers: AA = 21 (Actual =5) Aa = 50 (Actual = 83) aa = 29 (Actual = 12) No need to do a Chi square on this one!
©2000 Timothy G. Standish
Rate of Change With Rate of Change With SelectionSelection
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Frequency
1 2 3 4 5 6 7 8 9 10
Generations
p
q
Alleles
Even with heavy selection (s=0.5) the rate of change in allele frequency declines rapidly after a few generations
©2000 Timothy G. Standish
1 2 3 4 5 6 7 8 9 10
pq0
0.10.20.30.40.50.60.7
0.80.9
Frequency
Generations
Alleles
s = 0.1
Rate of Change With SelectionRate of Change With SelectionThe heavier the selection, the faster the change and the quicker the decline in rate of change.
00.10.20.30.40.50.60.70.80.9
Frequency
1 2 3 4 5 6 7 8 9 10Generations
pqAlleles
s = 0.9
©2000 Timothy G. Standish
Frequency
Diversifying
DirectionalFrequency
Types of SelectionTypes of SelectionSelectionSelection
Frequency
StabilizingSelectionPseudopterix
pleiorostrum(many beaked fake bird)
©2000 Timothy G. Standish
When the Data SpeaksWhen the Data Speaks“For example, researchers have calculated that
‘mitochondrial Eve’--the woman whose mtDNA was ancestral to that in all living people--lived 100,000 to 200,000 years ago in Africa. Using the new clock, she would be a mere 6,000 years old.
No one thinks that's the case, but at what point should models switch from one mtDNA time zone to the other?”
Gibbons, A. 1998. Calibrating the mitochondrial clock. Science 279:28-29
©2000 Timothy G. Standish
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