©2000 Timothy G. Standish 1 Thessalonians 5:21 21 Prove [test] all things; hold fast that which is...

©2000 Timothy G. Standish

1 Thessalonians 5:21

21 Prove [test] all things; hold fast that which is good.


Timothy G. Standish, Ph. D.

Evolution OfEvolution OfPopulationsPopulations


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


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


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


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.


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


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


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


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.


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


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


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


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


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


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


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


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


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


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


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:


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)


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)


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


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!


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


Natural SelectionNatural Selectionp= 0.1q= 0.9


Natural SelectionNatural Selectionp= 0.1q= 0.9

If selection (s)is 0.5 against aaand fitness = W=1-s


Natural SelectionNatural SelectionSecond GenerationSecond Generation

p= 0.17q= 0.83

AA=2Aa =30aa =68


Natural SelectionNatural SelectionThird GenerationThird Generation

p= 0.25q= 0.75

AA=3Aa =46aa =51


Natural SelectionNatural SelectionFourth GenerationFourth Generation

p= 0.34q= 0.66

AA=3Aa =62aa =35


Natural SelectionNatural SelectionFifth GenerationFifth Generation

p= 0.42q= 0.58

AA=4Aa =75aa =21


Natural SelectionNatural SelectionSixth GenerationSixth Generation

p= 0.46q= 0.54

AA=5Aa =83aa =12


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!


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


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


Frequency

Diversifying

DirectionalFrequency

Types of SelectionTypes of SelectionSelectionSelection

Frequency

StabilizingSelectionPseudopterix

pleiorostrum(many beaked fake bird)


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


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©2000 Timothy G. Standish 1 Thessalonians 5:21 21 Prove [test] all things; hold fast that which is...

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