mendelian genetics in populations – migration, drift & non- random mating migration – not in...

Mendelian Genetics in Populations – Migration, Drift & Non-Random Mating

Migration – Not in the ecological sense.

I like to call it gene flow – the transfer of alleles from the gene pool of one population to the gene pool of another population.

The alleles may travel in a spore, pollen, seeds or an organism.

Mendelian Genetics in Populations – Migration,

The one-island model of migration – a simple model

The arrows represent the relative magnitude and direction of gene flow.

What is the impact of alleles travelling from the continent on the allele pool of the island?

What is the impact of alleles travelling from the island on the allele pool of the continent?

Can migration take the allele and genotype frequencies on the island away from Hardy-Weinberg equilibrium?

Mendelian Genetics in Populations – Gene Flow


Start here

Have allele frequencies changed?

A1= A2=



Have genotype frequencies changed?

A1= 0.8 A2= 0.2 p2 = 2pq = q2 =



Have genotype frequencies changed?

A1= 0.8 A2= 0.2 A1A1 = 0.64 A1A2 = 0.32 A2A2 = 0.04

Note: A single bout of random mating will put the population back into H-W equilibrium.

Mendelian Genetics in Populations – Hardy Weinberg equilibrium

The Hardy-Weinberg equilibrium principle yields two fundamental conclusions:

Conclusion 1: The allele frequencies in a population will not change, generation after generation.

Conclusion 2: If the allele frequencies in a population are given by p and q, the genotype frequencies will be given by p2, 2pq, q2.

Both of these are violated by gene flow.


Gene flow homogenizes allele frequencies across populations.

Where m = fraction of island population comprised of mainland individuals.

Pi = frequency of A1 in island populationpc = frequency of A1 in mainland population

Δ pi = 0 m(pc – pi) = 0

No change in allele frequency of the island occurs when:• If there is no migration (m = 0) , then Pc does not change. • If (pi = pc), then Pi does not change.

Without any opposing mechanism, migration will eventually equalize the allele frequencies of island and mainland populations.Migration of alleles is what keeps populations from diverging genetically.


photographed by Kristian Peters

Red bladder campion (Silene dioica)

Colonizes islands of glacial material that have been underwater since last ice age.

Geological uplift raises the islands above water level.

New islands are constantly appearing.

The Skeppsvik Archipelago (Sweden) contains dozens of different islands, permitting testing of the homogenizing effect of gene flow.

Alleles can move via.1) Pollen (insect transported)2) Seeds (wind & water)

• In a few hundred years, patches of red campion are invaded by competitors and pollinator-borne disease.

• Establishment of seedlings stops.


photographed by Kristian Peters

Red bladder campion (Silene dioica)

FST – a measure of allele frequency among populations.

See lab handout on genetic drift.

Fst ranges between 0 - 1.

0 – 0.05 = little differentiation0.05 – 0.15 = moderate differentiation0.15 – 0.25 = great differentiation > 0.25 = very great differentiation


Giles and Goudet (1997) predict:

1) New islands will be unique, reflecting the chance of unique alleles arriving at any given island. Variation in allele frequencies will be large.

2) Intermediate aged populations will have the lowest variation in allele frequencies. (More homogenous). This will be due to gene flow (pollen and seeds) among islands.

3) The oldest islands will have greater variation in allele frequencies. This reflects that lack of gene flow from older islands and the allele frequency of survivors.

Mendelian Genetics in Populations – Genetic Drift

Natural selection is not a chance event.• The effect of the environment on phenotypes is real.• Survivorship is not always a chance event. An individual must

possess the most appropriate phenotype for the environment.

• This results in the adaptation of the population to the environment.


Genetic drift: the random discrepancy between the theoretical expectations (from H-W) and the actual results.• Results in non-adaptive evolution.• Can be considered the result of sampling error, or inadequate

sampling.• Whether an individual has an appropriate phenotype or not, it

may be lost from the population. Hence, genetic drift is a chance event that leads to changes in

the allele frequency of a population without leading to adaptation of the population.

Mendelian Genetics in Populations – Genetic Drift - Exercise

Mendelian Genetics in Populations – Genetic Drift - Exercise

The two conclusions of the Hardy – Weinberg equilibrium theory

1. The allele frequencies in a population will not change, generation after generation.

2. If the allele frequencies in a population are given by p and q, the genotype frequencies will be given by (p2 + 2pq + q2).


A simulation of drawing alleles from (the same) gene pool.

3 replicate runs.

Mendelian Genetics in Populations –Genetic Drift – Founder effect

Founder effect: When a small population is founded from a larger population. • The allele frequency of the new population is likely,

simply due to chance, to be different from the source population.

• The source population was randomly sub-sampled to found the new population.


The Amish in PA. The frequency of the allele responsible for Ellis-van Creveld syndrome is 0.07 in the Amish, but 0.001in most populations.

• The condition is inherited in an autosomal recessive pattern.

• Ellis-van Creveld syndrome can be caused by mutations in the EVC or EVC2 gene. They appear to play important roles in cell-to-cell signaling during development. In particular, the proteins produced from the EVC and EVC2 genes are thought to help regulate the Sonic Hedgehog signaling pathway. This pathway plays roles in cell growth, cell specialization, and the normal shaping (patterning) of many parts of the body.

• Researchers traced 50 cases of Ellis-Van Creveld in Lancaster County to a couple who emigrated to eastern Pennsylvania in 1744.


Ellis-van Creveld syndrome is an inherited disorder of bone growth that results in

• Very short stature (dwarfism)- short forearms and lower legs

• A narrow chest with short ribs. • Also characterized by the presence of extra fingers

and toes (polydactyly), • Malformed fingernails and toenails, and dental

abnormalities. • More than half of affected individuals are born with

a heart defect, which can cause serious or life-threatening health problems.

Mendelian Genetics in Populations –Genetic Drift

Random fixation of alleles and loss of heterozygosity


Because the fluctuation in allele frequency is due to a sampling error, then each generation will experience a different allele frequency due to chance. • Consequently, over time, each population

will follow a unique evolutionary path that will change its allele frequency solely due to chance alone (barring no selection, mutation or migration).

• The effects of drift are greater for small populations than large populations (compare 7.15 a c.)

• Given sufficient time, even large populations can experience a change in allele frequencies


Random fixation- predicting which allele goes to fixation.

As the frequency of an allele fluctuates between 0 and 1, it will inevitably meet one of two fates.• The frequency of the allele will reach 0, and the allele will be

lost forever (unless it is introduced through mutation or migration).

• The frequency of the allele will reach 1, in which case, the allele is said to be fixed.

• Consequently, allelic diversity declines.



Sewell Wright developed a very simple method for predicting the probability that an allele will drift toward fixation.• A population of N individuals.• There are thus 2N alleles in the population• Every allele is unique• Genetic drift is the only mechanism at work.• At some point, one of the alleles will have drifted to fixation,

and all others will have been lost.• Each allele began with an equal probability of being the allele

to drift toward fixation. • Each allele’s chance of becoming fixed is



But, as is often the case, each allele is not represented in equal proportions. There are often more of one type of an allele than another.

• If there are x copies of A1 and y copies of A2 and z copies of A3.

• And each allele has a chance of being the one that drifts to fixation.

• Then the probability that A1 drifts to fixation is

x x = • This is equal to the initial frequency of that allele.



As the frequency of an allele goes to 0 or 1, the frequency of heterozygotes goes to “0”.


Loss of heterozygosity.

As any allele drifts towards 0 or 1, the frequency of heterozygotes declines.

Heterozygosity is defined as 2(p)(1-p). This is the same as 2pq.

Consider a 2 allele system with A1= 0.5, then A2 = 0.5

Heterozygosity is equal to 2(0.5)(0.5) = 0.50

• If A1 = 0.2 and A2 = 0.8, then Heterozygosity = 2(0.2)(0.8) = 0.32.

• If A1 = 0.8 and A2 = 0.2, then Heterozygosity = 2(0.2)(0.8) = 0.32.

• So as soon as one allele drifts away from the intermediate value of 0.5, (and towards 0 or 1) heterozygosity declines.


Predicting the loss of heterozygosity (Hg ).• The value of is always between 0.5 and 1.0, so the value for

heterozygosity must always decline.• Consider the consequences for trying to resuscitate a captive

population of breeding animals that is small, N = 50.• Even with random mating, there would be a loss of

heterozygosity of 1% every generation just due to genetic drift.

𝐻𝑔+1=𝐻𝑔[1 −𝑥

2𝑁 ]

The gray line is the predicted loss in heterozygosity.


Assessing differentiation among populations due to drift.

• HT is the expected heterozygosity under H-W equilibrium by combining separate populations into one large population.

• HS is the average heterozygosity across the separate populations (subpopulations)

Fst ranges between 0 - 1. 0.00 – 0.05 = little differentiation

0.05 – 0.15 = moderate differentiation 0.15 – 0.25 = great differentiation > 0.25 = very great differentiation

• HT and HS both start out at 0.5. But HS declines every generation to “0”. Hence goes to “0”

The fixation index


Seminal experiment – Peter Buri (1956)Buri established 107 populations of Drosophila.

• 8 males and 8 females.• All are heterozygous for brown eye color.

bw75/bw• The frequency of each allele is 0.5• The populations are maintained for 19

generations.• 8 males and 8 females are randomly

selected each generation to start the next.• With the frequency of the bw75 allele at 0.5,

it has an equal probability of going up or down.

• The rate of decline should follow Sewell Wright’s equation.

• At the end of the experiment, there had been dramatic selection.

• bw75 became lost in 30 populations and became fixed in 28. Very close to 1:1.


Seminal experiment – Peter Buri (1956)As expected, average heterozygosity declined.

But the heterozygosity of the population of 16 flies declined more rapidly than expected using Wright’s equation, .

Buri’s population behaved more like a population of 9 flies.


Effective Population SizeUnder genetic drift, • The population has become so small that not all of the

members participate equally in the mating, effectively reducing its size.

• This may be attributed to death of individuals, or some aspect of sexual selection that prevents males from reproducing.

• When males = 5 and females = 5, Ne = 10.

• When males = 1 and females = 9, Ne = 3.6

• When males = 1 and females = 1000, Ne = 4.0

fm

fm

NN

NN

4Ne =


The rate of evolution when genetic drift is the only process.

When selection is absent, what is the probability that a new allele created by mutation will become fixed?

When an allele created by mutation becomes fixed, that is known as substitution.

A population of 5 individuals. Therefore the population contains 10 alleles.


When genetic drift is the only mechanism of evolution at work, the rate of substitution is equal to the mutation rate.

A diploid population of N has 2N alleles. v = rate of neutral mutations, per allele, per generation. 2Nv – number of new alleles created by mutation that have not previously existed.

This rate holds no matter the size of the population. • More mutations occur in a larger population.• But this is offset by the lower probability that any one allele will drift to fixation.

( becomes smaller as N increases.)

Because these new alleles are selectively neutral, genetic drift is the only force at work. As each allele fluctuates, it has an equal chance of arriving at fixation as any other

allele. - the probability of going to fixation.

Combining the two probabilities: 2Nv x = v = mutation rate of neutral alleles.

Genetic Drift vs. Natural Selection


So why are deleterious and advantageous alleles ignored?

Deleterious alleles will be quickly eliminated by natural selection and never be fixed.



Neutral theory versus selectionist theory.

Motoo Kimur (1983) – Neutral theory• Advantageous mutations – exceedingly rare.• Rate of evolution = rate of mutation of neutral alleles




Neutral theory versus selectionist theory.

Motoo Kimura (1983) – Neutral theory• Advantageous mutations – exceedingly rare.• Rate of evolution = rate of mutation of neutral alleles

John Gillespie (1991) – Selectionist theory• Advantageous mutations - common enough not to be ignored. • Substitution rate will reflect action of N.S. on advantageous mutations.

This is largely a debate in molecular evolution, because that is where neutral and advantageous mutations can be detected.


Mutation, selection and drift in molecular evolution.Computing Consequences 7.5

The overall mutation rate at a locus L amino acids long is: u = uL(d + a+ f )

This can be rewritten as: u = uLd + uLa + uLf

d – fraction of codon changes that are deleteriousa – fraction of codon changes that are advantageousf – fraction of codon changes that are neutral


Mutation, selection and drift in molecular evolution.Computing Consequences 7.5

The overall mutation rate at a locus L amino acids long is: u = uL(d + a+ f )

This can be rewritten as: u = uLd + uLa + uLf

Based on neutral theory, a is “0” and d, though not “0”, is quickly eliminated by natural selection. So d could be “0”.

d – fraction of codon changes that are deleteriousa – fraction of codon changes that are advantageousf – fraction of codon changes that are neutral

u = uLf = v - rate of neutral mutations, per allele, per generation.



Which is more important in the outcome of evolution?

Tribolium castaneumb+ b+ – redb+ b – brownb b – black

Determined by: Size of the population The strength of selection.


Three notable patterns can be observed from the data in the graphs.

1. Black lines (, n = 12) indicate increase in frequency of b+ allele.

Fitnessb+ b+ – 1.0b+ b – 0.95b b – 0.90

2. Tan lines indicate considerable variation among populations – consistent with genetic drift.

3. Small populations travel more diverse evolutionary paths than large populations.

The influence of selection can be offset by the influence of drift in a small population.


How large should natural selection be to overcome genetic drift?

A new allele has a frequency of The allele is rare. The probability of drifting to fixation is: The allele is likely to quickly disappear.

Y-axis scale is in multiples of

No selection

Under no selection, the probability of an allele going to fixation is 1 x





No selection

Under negative selection, (deleterious allele) the probability of an allele going to fixation is tiny.





No selection

• If population (Ne) is large

or

• Selection (s) is strong

Then probability of fixation can be large.


Genetic Drift vs. Molecular Evolution

Neutral Theory of molecular evolution

Observations by Kimura (1968) and Zuckerkandl and Pauling (1965) had observed that:

1) Mutations in amino acid replacement had risen to fixation at a rate too high to be the result of natural selection.

2) The rate of change in amino acid sequences over time was constant. If it was due to natural selection then:• Changes should have been episodic• Should be correlated with environmental changes

Observations of molecular evolution were not consistent with natural selection.

What then could be the mechanism?

Genetic Drift


Neutral Theory of molecular evolution

Mutations that are deleterious tend to be eliminated by natural selection – not important to molecular evolution.

Mutations that are beneficial are low in frequency at first, and tend to be lost to genetic drift. (If not lost, then rise to fixation due to natural selection.)

Mutations that are neutral rise and fall due to drift. Many are lost. Some are fixed.

Neutral mutations that rise to fixation by drift vastly outnumber beneficial mutations that rise to fixation by natural selection.

Genetic drift, not natural selection, is thus the mechanism responsible for most molecular evolution.

Based on calculations, u = uLd + uLa + uLf, Kimura has postulated that the rate of molecular evolution = mutation rate.

Totally counterintuitive - Population size not important to the rate of evolution!


Evidence for the Neutral Theory of molecular evolution

Pseudogenes – functionless stretches of DNA – neutral with respect to fitness – go to fixation solely as a results of drift

The divergence rates recorded in pseudogenes between taxa are some of the highest for loci in the nuclear genome – consistent with neutral theory.


Evidence for the Neutral Theory of molecular evolution

Substitution rate for silent-site (synonymous) 3x greater than for replacement (nonsynonymous) mutations – consistent with neutral theory.

Both kinds of substitutions accumulated in a linear, clock-wise manner – not consistent with natural selection.

Molecular evolution in influenza viruses.


Evidence for the Neutral Theory of molecular evolution Rates of replacement vs silent substitutions

when comparing humans to mice/rats

If nonsynonymous and synonymous mutation rates were the same. (slope = 1)

Functional traits have low substitution rates.


Evidence for the Neutral Theory of molecular evolution Rates of replacement vs silent substitutions

when comparing humans to mice/rats

If nonsynonymous and synonymous mutation rates were the same. (slope = 1)

Non-functional traits have higher substitution rates.

Non-random mating does not cause evolution.

Most common type of non-random mating - inbreeding

Mendelian Genetics in Populations – Non-random Mating

But it does violate one of the conclusions of Hardy-Weinberg


At Generation 3, have allele frequencies changed? No. A1 = 0.5 A2 = 0.5

At Generation 3, have genotype frequencies changed? Yes.

At Generation 3, do allele frequencies predict genotype frequencies? No.

Which conclusion of Hardy-Weinberg has been violated?

If the allele frequencies in a population are given by p and q, the genotype frequencies will be given by p2, 2pq, q2.


• California sea otter population severely reduced by fur trade in 18th and 19th centuries.

• Population reduced to fewer than 50.

• Put under protection in 1911. By end of 20th century, there were 1500.

• 31 allozyme loci examined by Lidicker and McCollum (1997).

S = 0.6 F = 0.4

Actual SS SF FF 0.485 0.212 0.303

PAP locus; S and F alleles

Under Hardy – Weinberg SS SF FF

More homozygotes and fewer heterozygotes

0.36 0.48 0.16What pattern do you observe?


• California sea otter population compared to Alaskan sea otter population that experienced a less severe population reduction

• Deficit of heterozygotes could be due to underdominance, but ruled out by Lidicker and McCollum.


Coefficient of inbreeding (F) – the probability that the two alleles in an individual are identical by descent (came from the same ancestor).

A1A1 A1A2 A2A2 p2(1-F) + pF 2pq(1-F) q2(1-F) + qF

Genotype frequency for an inbred population that otherwise obeys H-W

How did we arrive at this? First, pick an egg.

The sperm in the gene pool consist of two fractions:• (1-F) A fraction carrying alleles that are not identical by descent

to the one in the egg .

There are two ways that homozygotes can be generated.

• (F) A fraction carrying alleles that are identical by descent to the one in the egg.


One • Need to consider the probability that two A1 alleles come

together from two unrelated individuals, from chance alone. This would be p2.

• But! Must consider the frequency of A1 alleles in the population due to chance alone.

• If F is the frequency of related alleles, then (1-F) is the frequency of unrelated alleles.

• The egg: picking any A1 allele from the population is p. • The sperm: The probability of picking an A1 allele unrelated to

the first (in the egg) is p(1-F).

Probability of getting a homozygote by chance- p x p(1-F) = p2(1-F)

egg sperm


Two- • The second way to obtain a homozygous A1 is to have an egg

with probability p of having the A1 allele

• and being fertilized by a sperm with the A1 allele because of common descent (an event with the probability of F).

• The probability of obtaining A1A1 in this manner is pF

Therefore, the probability of obtaining a homozygous A1A1 either one way or the other is the sum of their probabilities.

p2(1-F) + pF

If allele A1 is not due to shared ancestry at all, then F is 0 and the term = p2

Egg Sperm


In summary – • Inbreeding doesn’t change the allele frequencies• But inbreeding does alter the genotype frequencies.• Alone, this does not lead to evolutionary change.

• But the change in genotype frequencies increases homozygosity (heterozygosity is decreased). This means that:• There is an increase in the number of loci at which the

average individual is homozygous.• There is an increase in the proportion of individuals

homozygous for an individual locus in the population.


In summary –

If we compare the heterozygosity of an inbreed population with that of a randomly mating population, then

HF = H0(1-F)

Essentially, the heterozygosity of the inbred population is reduced by the percentage of alleles in the population that have a shared ancestry.


Inbreeding depression = a decrease in average fitness of individuals in a population.

An increase in homozygosity means an increase in the chances that an individual will be homozygous for deleterious recessive alleles.

In humans, infant mortality is ~ 4% greater among children of first cousins than among children of unrelated parents.


Three consequences of inbreeding have been emerged from experiments with plants.

1. The effects of inbreeding are most easy to detect when plants are under some sort of environmental stress. Why?

A: Consider the benefits of outbreeding – the acquisition of new alleles that might be beneficial in a new environment. The old combination of alleles worked fine for the parent and its environment, but stress represents a new environmental condition for which the old (inbred) allele combination is not well suited.


Three consequences of inbreeding have been emerged from experiments with plants.2. The effects of inbreeding are more likely to show up later in

the life cycle of plants, rather early in development, such as germination and the seedling stage.

• This may be because of maternal effects (seed provisioning).

• It is more likely that the seedling is dependent upon the endosperm initially for its resources.


Three consequences of inbreeding have been emerged from experiments with plants.3. The impact of inbreeding varies among plant families. Some

show large negative effects, some are neutral with respect to it, others actually benefit from inbreeding.

That some plants cannot be selfed reflects this negative impact of inbreeding and the mechanism by which plants will avoid it.


Inbreeding depression in great tits.

As the inbreeding coefficient, F, increases, the number of eggs that hatch decreases.

Ecology example of great tits in Wytham woods (UK). Nestling mortality was greater for inbreeding pairs (27.7%) vs. outbreeding pairs (16.2%).


Both plants and animals have mechanisms for avoiding inbreeding:

Mate choiceSelf-incompatibilityDispersal of gametes (recall compromise in dispersal for Delphinium]

In Summary:• Nonrandom matings that result in inbreeding

do not alter allele frequencies, so they are not mechanisms of evolutionary change.

• Because inbreeding does alter genotype frequencies, it can have major evolutionary consequences, such as inbreeding depression.

mendelian genetics in populations – migration, drift & non- random mating migration – not in...

Documents