Population Structure and Drift Chapter 11. Conservation Genetics Illinois Greater Prairie Chicken Illinois Greater Prairie Chicken Tympanuchus cupido

Population Population Structure and DriftStructure and Drift

Population Population Structure and DriftStructure and Drift

Chapter 11Chapter 11Chapter 11Chapter 11

Conservation GeneticsConservation GeneticsConservation GeneticsConservation Genetics

Illinois Greater Prairie ChickenIllinois Greater Prairie Chicken Tympanuchus cupido pinnatusTympanuchus cupido pinnatus 200 years ago Illinois was covered with 200 years ago Illinois was covered with

prairie with millions of greater prairie prairie with millions of greater prairie chickenschickens

Introduction of steel plow decimated prairie Introduction of steel plow decimated prairie habitathabitat

By 1994 there were less than 50 greater By 1994 there were less than 50 greater prairie chickens leftprairie chickens left Two remnant populationsTwo remnant populations

Illinois Greater Prairie ChickenIllinois Greater Prairie Chicken Tympanuchus cupido pinnatusTympanuchus cupido pinnatus 200 years ago Illinois was covered with 200 years ago Illinois was covered with

prairie with millions of greater prairie prairie with millions of greater prairie chickenschickens

Introduction of steel plow decimated prairie Introduction of steel plow decimated prairie habitathabitat

By 1994 there were less than 50 greater By 1994 there were less than 50 greater prairie chickens leftprairie chickens left Two remnant populationsTwo remnant populations


Ban on hunting began in 1933Ban on hunting began in 1933 In 1960s the two populations were In 1960s the two populations were

established as sanctuariesestablished as sanctuaries In 1970s bird numbers increasedIn 1970s bird numbers increased By mid-1970s population began to crash By mid-1970s population began to crash

againagain In 1994 only 6 males were leftIn 1994 only 6 males were left Why did population decline when habitat Why did population decline when habitat

was restored?was restored?

Ban on hunting began in 1933Ban on hunting began in 1933 In 1960s the two populations were In 1960s the two populations were

established as sanctuariesestablished as sanctuaries In 1970s bird numbers increasedIn 1970s bird numbers increased By mid-1970s population began to crash By mid-1970s population began to crash

againagain In 1994 only 6 males were leftIn 1994 only 6 males were left Why did population decline when habitat Why did population decline when habitat

was restored?was restored?

Random Genetic DriftRandom Genetic DriftRandom Genetic DriftRandom Genetic Drift In finite populations, allele frequencies can In finite populations, allele frequencies can

fluctuate by chancefluctuate by chance

e.g. populations heavily structured by e.g. populations heavily structured by geography geography mating not random mating not random

In finite populations, allele frequencies can In finite populations, allele frequencies can fluctuate by chancefluctuate by chance

e.g. populations heavily structured by e.g. populations heavily structured by geography geography mating not random mating not random

ConsequenceConsequence the replacement of old alleles by new ones the replacement of old alleles by new ones

proceeds in a random fashion not influenced proceeds in a random fashion not influenced by natural selectionby natural selection

NONADAPTIVE evolution! NONADAPTIVE evolution!

Allele frequencies CAN & DO change from 1 Allele frequencies CAN & DO change from 1 generation to the nextgeneration to the next

ConsequenceConsequence the replacement of old alleles by new ones the replacement of old alleles by new ones

proceeds in a random fashion not influenced proceeds in a random fashion not influenced by natural selectionby natural selection

NONADAPTIVE evolution! NONADAPTIVE evolution!

Allele frequencies CAN & DO change from 1 Allele frequencies CAN & DO change from 1 generation to the nextgeneration to the next

Random Genetic DriftRandom Genetic DriftRandom Genetic DriftRandom Genetic Drift

What are the two MOST important What are the two MOST important causes of allele substitutions or causes of allele substitutions or

evolution in populationsevolution in populations

What are the two MOST important What are the two MOST important causes of allele substitutions or causes of allele substitutions or

evolution in populationsevolution in populations

Random Genetic DriftRandom Genetic Drift

Natural SelectionNatural Selection

Random Genetic DriftRandom Genetic Drift

Natural SelectionNatural Selection

CoalescenceCoalescenceCoalescenceCoalescence Given enough time, all gene copies in a Given enough time, all gene copies in a

population are ultimately descended from population are ultimately descended from a single ancestral gene copya single ancestral gene copy

However, this is also affected by:However, this is also affected by: MutationMutation ImmigrationImmigration Natural SelectionNatural Selection

Given enough time, all gene copies in a Given enough time, all gene copies in a population are ultimately descended from population are ultimately descended from a single ancestral gene copya single ancestral gene copy

However, this is also affected by:However, this is also affected by: MutationMutation ImmigrationImmigration Natural SelectionNatural Selection

EXAMPLE OF COALESCENCEEXAMPLE OF COALESCENCEEXAMPLE OF COALESCENCEEXAMPLE OF COALESCENCE

CoalescenceCoalescenceCoalescenceCoalescence Implies that the average degree of Implies that the average degree of

relationship among individuals increases relationship among individuals increases with the passage of timewith the passage of time

Thus becomes monomorphic, becomes Thus becomes monomorphic, becomes fixed (freq. of 1.0)fixed (freq. of 1.0)

Implies that the average degree of Implies that the average degree of relationship among individuals increases relationship among individuals increases with the passage of timewith the passage of time

Thus becomes monomorphic, becomes Thus becomes monomorphic, becomes fixed (freq. of 1.0)fixed (freq. of 1.0)

CoalescenceCoalescenceCoalescenceCoalescence If we have alleles pIf we have alleles p and q where p=0.5 and q=0.5and q where p=0.5 and q=0.5

What would be the probability that allele q is What would be the probability that allele q is passed on to the next generation? passed on to the next generation?

If we have alleles pIf we have alleles p and q where p=0.9 and q=0.1and q where p=0.9 and q=0.1

A population will eventually become A population will eventually become monomorphic and this equals the initial monomorphic and this equals the initial frequency of that allelefrequency of that allele


What would be the probability that allele q is What would be the probability that allele q is passed on to the next generation? passed on to the next generation?


A population will eventually become A population will eventually become monomorphic and this equals the initial monomorphic and this equals the initial frequency of that allelefrequency of that allele

CoalescenceCoalescenceCoalescenceCoalescence How long does it take?How long does it take?

The mean time back to common The mean time back to common ancestry of ancestry of allall gene copies in the gene copies in the population is 2N generationspopulation is 2N generations

Consider the probability of q being Consider the probability of q being passed to the next generation when passed to the next generation when there was a small number of mating there was a small number of mating individuals....say 10...??? individuals....say 10...???

How long does it take?How long does it take?

The mean time back to common The mean time back to common ancestry of ancestry of allall gene copies in the gene copies in the population is 2N generationspopulation is 2N generations

Consider the probability of q being Consider the probability of q being passed to the next generation when passed to the next generation when there was a small number of mating there was a small number of mating individuals....say 10...??? individuals....say 10...???

Genetic DriftGenetic DriftGenetic DriftGenetic Drift1.1. Alleles fluctuate at random, and eventually become Alleles fluctuate at random, and eventually become

fixed fixed

2.2. Genetic variation is lostGenetic variation is lost

3.3. Initially similar populations diverge in allele frequency, Initially similar populations diverge in allele frequency, and may become fixed for different alleles (all and may become fixed for different alleles (all individuals homozygous)individuals homozygous)

4.4. The probability, at time t, that an allele will eventually The probability, at time t, that an allele will eventually become fixed equals the frequency of the allele at that become fixed equals the frequency of the allele at that timetime

5.5. The rate at which these events occur is greater, the The rate at which these events occur is greater, the smaller the populationsmaller the population

1.1. Alleles fluctuate at random, and eventually become Alleles fluctuate at random, and eventually become fixed fixed

2.2. Genetic variation is lostGenetic variation is lost

3.3. Initially similar populations diverge in allele frequency, Initially similar populations diverge in allele frequency, and may become fixed for different alleles (all and may become fixed for different alleles (all individuals homozygous)individuals homozygous)

4.4. The probability, at time t, that an allele will eventually The probability, at time t, that an allele will eventually become fixed equals the frequency of the allele at that become fixed equals the frequency of the allele at that timetime

5.5. The rate at which these events occur is greater, the The rate at which these events occur is greater, the smaller the populationsmaller the population

N = 4N = 4

N = 40N = 40

N = 400N = 400

Drift SimulatorDrift SimulatorDrift SimulatorDrift Simulator

http://darwin.eeb.uconn.edu/http://darwin.eeb.uconn.edu/simulations/drift.htmlsimulations/drift.html

http://darwin.eeb.uconn.edu/http://darwin.eeb.uconn.edu/simulations/drift.htmlsimulations/drift.html

Evolution by Genetic DriftEvolution by Genetic DriftEvolution by Genetic DriftEvolution by Genetic Drift In an adult population there are 2N gene copiesIn an adult population there are 2N gene copies The variance in allele frequencies:The variance in allele frequencies:

V = p (1-p) / 2NV = p (1-p) / 2N

(where 2 refers to the diploid condition and N refers (where 2 refers to the diploid condition and N refers to the size of the population)to the size of the population)

What is this telling us?What is this telling us?

In an adult population there are 2N gene copiesIn an adult population there are 2N gene copies The variance in allele frequencies:The variance in allele frequencies:

V = p (1-p) / 2NV = p (1-p) / 2N

(where 2 refers to the diploid condition and N refers (where 2 refers to the diploid condition and N refers to the size of the population)to the size of the population)

What is this telling us?What is this telling us?

Evolution by Genetic Drift is Evolution by Genetic Drift is FASTER in small populationsFASTER in small populationsEvolution by Genetic Drift is Evolution by Genetic Drift is

FASTER in small populationsFASTER in small populations The smaller the N (pop. size) the greater the The smaller the N (pop. size) the greater the

genetic variance from generation to generation!genetic variance from generation to generation! The probability, at time t, that an allele will The probability, at time t, that an allele will

ultimately become fixed equals its frequency at ultimately become fixed equals its frequency at that time.that time.

If a new mutation arises in a population, the If a new mutation arises in a population, the probability it will be fixed in that population at probability it will be fixed in that population at time t is:time t is:

pptt = ½ N = ½ Nthis is the likelihood of reaching p=1 (fixation)this is the likelihood of reaching p=1 (fixation)

Clearly, if the population is small, fixation will Clearly, if the population is small, fixation will occur fasteroccur faster

The smaller the N (pop. size) the greater the The smaller the N (pop. size) the greater the genetic variance from generation to generation!genetic variance from generation to generation!

The probability, at time t, that an allele will The probability, at time t, that an allele will ultimately become fixed equals its frequency at ultimately become fixed equals its frequency at that time.that time.

If a new mutation arises in a population, the If a new mutation arises in a population, the probability it will be fixed in that population at probability it will be fixed in that population at time t is:time t is:

pptt = ½ N = ½ Nthis is the likelihood of reaching p=1 (fixation)this is the likelihood of reaching p=1 (fixation)

Clearly, if the population is small, fixation will Clearly, if the population is small, fixation will occur fasteroccur faster

Evolution by DriftEvolution by DriftEvolution by DriftEvolution by Drift

Random walk of the drunkRandom walk of the drunk

The probability, at time t, that an The probability, at time t, that an allele will ultimately be fixed equals it allele will ultimately be fixed equals it frequency (pfrequency (ptt) at that time.) at that time.

Random walk of the drunkRandom walk of the drunk

The probability, at time t, that an The probability, at time t, that an allele will ultimately be fixed equals it allele will ultimately be fixed equals it frequency (pfrequency (ptt) at that time.) at that time.

Structured PopulationsStructured PopulationsStructured PopulationsStructured Populations The Concept of Demes and metapopulationsThe Concept of Demes and metapopulations The Concept of Demes and metapopulationsThe Concept of Demes and metapopulations

Structured PopulationsStructured PopulationsStructured PopulationsStructured Populations

Structured PopulationsStructured PopulationsStructured PopulationsStructured Populations Demes and metapopulationsDemes and metapopulations the equation to predict the probability of a the equation to predict the probability of a

new mutation becoming fixed is still ½ Nnew mutation becoming fixed is still ½ N if if kk=# of populations=# of populations 2N2Nkk=total # gene copies in population=total # gene copies in population Overall number of populations fixed for p:Overall number of populations fixed for p:

ppkk(2N) [where 2N = #genes per population)(2N) [where 2N = #genes per population)

Demes and metapopulationsDemes and metapopulations the equation to predict the probability of a the equation to predict the probability of a

new mutation becoming fixed is still ½ Nnew mutation becoming fixed is still ½ N if if kk=# of populations=# of populations 2N2Nkk=total # gene copies in population=total # gene copies in population Overall number of populations fixed for p:Overall number of populations fixed for p:

ppkk(2N) [where 2N = #genes per population)(2N) [where 2N = #genes per population)

frequency of, say the allele p, is summed frequency of, say the allele p, is summed over all metapopulations over all metapopulations pp2N2Nkk / / 2N2Nkk

This equals This equals pp, the initial frequency! , the initial frequency!

frequency of, say the allele p, is summed frequency of, say the allele p, is summed over all metapopulations over all metapopulations pp2N2Nkk / / 2N2Nkk

This equals This equals pp, the initial frequency! , the initial frequency!


Thus one consequence of drift is the Thus one consequence of drift is the smaller the population size, the shorter the smaller the population size, the shorter the average time to fixationaverage time to fixation

For diploid populations, a newly arisen For diploid populations, a newly arisen neutral allele mutation takes (on average) neutral allele mutation takes (on average) 4N generations to become fixed4N generations to become fixed

Thus one consequence of drift is the Thus one consequence of drift is the smaller the population size, the shorter the smaller the population size, the shorter the average time to fixationaverage time to fixation

For diploid populations, a newly arisen For diploid populations, a newly arisen neutral allele mutation takes (on average) neutral allele mutation takes (on average) 4N generations to become fixed4N generations to become fixed


HeterozygosityHeterozygosityHeterozygosityHeterozygosity Heterozygosity is maximal when all alleles are Heterozygosity is maximal when all alleles are

equal (p=0.5 and q=0.5) equal (p=0.5 and q=0.5) Alleles may drift from low frequency to high Alleles may drift from low frequency to high

frequency or even fixation in which case:frequency or even fixation in which case: Heterozygosity initially increases (as the frequencies Heterozygosity initially increases (as the frequencies

start to approach 50% p and q) then starts to decrease start to approach 50% p and q) then starts to decrease as one of the two alleles drift toward fixationas one of the two alleles drift toward fixation

In a metapopulation, different alleles become In a metapopulation, different alleles become fixed in different demes (or metapopulations) fixed in different demes (or metapopulations) each of which declines in Heterozygosityeach of which declines in Heterozygosity

Alleles may drift from low frequency to high Alleles may drift from low frequency to high frequency or even fixationfrequency or even fixation

Heterozygosity is maximal when all alleles are Heterozygosity is maximal when all alleles are equal (p=0.5 and q=0.5) equal (p=0.5 and q=0.5)

Alleles may drift from low frequency to high Alleles may drift from low frequency to high frequency or even fixation in which case:frequency or even fixation in which case: Heterozygosity initially increases (as the frequencies Heterozygosity initially increases (as the frequencies

start to approach 50% p and q) then starts to decrease start to approach 50% p and q) then starts to decrease as one of the two alleles drift toward fixationas one of the two alleles drift toward fixation

In a metapopulation, different alleles become In a metapopulation, different alleles become fixed in different demes (or metapopulations) fixed in different demes (or metapopulations) each of which declines in Heterozygosityeach of which declines in Heterozygosity

Alleles may drift from low frequency to high Alleles may drift from low frequency to high frequency or even fixationfrequency or even fixation

During this process in a metapopulation or During this process in a metapopulation or deme system of structured populations, deme system of structured populations, heterozygosity and homozygosity retain heterozygosity and homozygosity retain apparent H-W equilibrium genotype apparent H-W equilibrium genotype frequencies within each population BUT frequencies within each population BUT the metapopulation suffers a net the metapopulation suffers a net DECREASE in Heterozygosity!DECREASE in Heterozygosity!

During this process in a metapopulation or During this process in a metapopulation or deme system of structured populations, deme system of structured populations, heterozygosity and homozygosity retain heterozygosity and homozygosity retain apparent H-W equilibrium genotype apparent H-W equilibrium genotype frequencies within each population BUT frequencies within each population BUT the metapopulation suffers a net the metapopulation suffers a net DECREASE in Heterozygosity!DECREASE in Heterozygosity!

Heterozygosity and DriftHeterozygosity and DriftHeterozygosity and DriftHeterozygosity and Drift

What is Predicted based on What is Predicted based on Genetic Drift Simulations...Genetic Drift Simulations...What is Predicted based on What is Predicted based on Genetic Drift Simulations...Genetic Drift Simulations...

p = 0.5q = 0.5N = 162N = 32

Estimates fixationby 19 generations!

p = 0.5q = 0.5N = 162N = 32

Estimates fixationby 19 generations!

The Real Experimental DataThe Real Experimental DataThe Real Experimental DataThe Real Experimental Data

Effective population size Effective population size NNeeEffective population size Effective population size NNee

The reality of population ecology and The reality of population ecology and demography can affect the reality of demography can affect the reality of chance mating within populations, chance mating within populations, decreasing the effective population sizedecreasing the effective population size

1.1. Variation in number of progenyVariation in number of progeny

2.2. skewed sex ratiosskewed sex ratios

3.3. overlapping generationsoverlapping generations

4.4. fluctuations in population sizefluctuations in population size

The reality of population ecology and The reality of population ecology and demography can affect the reality of demography can affect the reality of chance mating within populations, chance mating within populations, decreasing the effective population sizedecreasing the effective population size

1.1. Variation in number of progenyVariation in number of progeny

2.2. skewed sex ratiosskewed sex ratios

3.3. overlapping generationsoverlapping generations

4.4. fluctuations in population sizefluctuations in population size

Genetic DriftGenetic DriftGenetic DriftGenetic Drift

Experimental study on Drosophila Average heterozygosity fell over time Decrease in heterozygosity did not match

predictions exactly Fell at rate predicted for population size of 9, not

16!!! Effective population size was only 9

Some individuals could have died Some males may have been rejected by females

Theory of genetic drift can make testable predictions about behavior of alleles in finite populations

Experimental study on Drosophila Average heterozygosity fell over time Decrease in heterozygosity did not match

predictions exactly Fell at rate predicted for population size of 9, not

16!!! Effective population size was only 9

Some individuals could have died Some males may have been rejected by females

Theory of genetic drift can make testable predictions about behavior of alleles in finite populations

Founder EffectsFounder EffectsFounder EffectsFounder Effects Genetic bottlenecksGenetic bottlenecks

population going through a population crash, population going through a population crash, followed by a population increasefollowed by a population increase

This has massive consequences on the size of This has massive consequences on the size of the gene pool after population increase, and the gene pool after population increase, and thus, drastically affects Nthus, drastically affects Nee

Genetic bottlenecksGenetic bottleneckspopulation going through a population crash, population going through a population crash,

followed by a population increasefollowed by a population increase

This has massive consequences on the size of This has massive consequences on the size of the gene pool after population increase, and the gene pool after population increase, and thus, drastically affects Nthus, drastically affects Nee

FounderFounderEffectsEffectsFounderFounderEffectsEffects

N = number of foundersr = pop. increase

WE SEE:if “r” is small, Heterozygosity declines faster!

N = number of foundersr = pop. increase

WE SEE:if “r” is small, Heterozygosity declines faster!

InbreedingInbreedingInbreedingInbreeding AutozygousAutozygous

homozygous only and identical by descenthomozygous only and identical by descent

AllozygousAllozygous either homozygous or heterozygous but not identical either homozygous or heterozygous but not identical

by descentby descent

An inbred population is one in which the An inbred population is one in which the probability that an individual is autozygous is probability that an individual is autozygous is greater, as a consequence of mating among greater, as a consequence of mating among relatives, than in a panmictic populationrelatives, than in a panmictic population

AutozygousAutozygous homozygous only and identical by descenthomozygous only and identical by descent

AllozygousAllozygous either homozygous or heterozygous but not identical either homozygous or heterozygous but not identical

by descentby descent

An inbred population is one in which the An inbred population is one in which the probability that an individual is autozygous is probability that an individual is autozygous is greater, as a consequence of mating among greater, as a consequence of mating among relatives, than in a panmictic populationrelatives, than in a panmictic population

InbreedingInbreedingInbreedingInbreeding

Inbreeding coeffecient = F Inbreeding coeffecient = F the probability the probability that an individual taken at random from a that an individual taken at random from a population that is autozygouspopulation that is autozygous

F is the fraction that is autozygous and 1-F F is the fraction that is autozygous and 1-F is the fraction that is allozygousis the fraction that is allozygous

Inbreeding coeffecient = F Inbreeding coeffecient = F the probability the probability that an individual taken at random from a that an individual taken at random from a population that is autozygouspopulation that is autozygous

F is the fraction that is autozygous and 1-F F is the fraction that is autozygous and 1-F is the fraction that is allozygousis the fraction that is allozygous

InbreedingInbreedingInbreedingInbreeding With two alleles AWith two alleles A11 and A and A22 with frequencies p and with frequencies p and

q q the probability that an individual is the probability that an individual is allozygous allozygous andand A A11AA11 = (1-F)p = (1-F)p22

AA11AA22 = (1-F)2pq = (1-F)2pq the fraction of heterozygotes the fraction of heterozygotes

(although by definition, they are allozygous)(although by definition, they are allozygous) AA22AA22 = (1-F)q = (1-F)q22

Thus the fraction that is autozygous and AThus the fraction that is autozygous and A11AA11 = =

F(p) and thus, AF(p) and thus, A22AA2 2 = F(q)= F(q)

With two alleles AWith two alleles A11 and A and A22 with frequencies p and with frequencies p and

q q the probability that an individual is the probability that an individual is allozygous allozygous andand A A11AA11 = (1-F)p = (1-F)p22

AA11AA22 = (1-F)2pq = (1-F)2pq the fraction of heterozygotes the fraction of heterozygotes

(although by definition, they are allozygous)(although by definition, they are allozygous) AA22AA22 = (1-F)q = (1-F)q22

Thus the fraction that is autozygous and AThus the fraction that is autozygous and A11AA11 = =

F(p) and thus, AF(p) and thus, A22AA2 2 = F(q)= F(q)

InbreedingInbreedingInbreedingInbreeding

Notice, the frequency of Notice, the frequency of homozygotes is higher!homozygotes is higher!

F increases over generationsF increases over generations

Frequency of Heterozygosity is ½ Frequency of Heterozygosity is ½ in each successive generationin each successive generation

Notice, the frequency of Notice, the frequency of homozygotes is higher!homozygotes is higher!

F increases over generationsF increases over generations

Frequency of Heterozygosity is ½ Frequency of Heterozygosity is ½ in each successive generationin each successive generation

Genetic Consequences of Genetic Consequences of InbreedingInbreeding

Genetic Consequences of Genetic Consequences of InbreedingInbreeding

1.1. Inbreeding redistributes the alleles to the Inbreeding redistributes the alleles to the homozygous conditionhomozygous condition

genotype freqs. change but allele frequencies do genotype freqs. change but allele frequencies do not changenot change

2.2. Genetic variance of a phenotypic character Genetic variance of a phenotypic character within a population is usually increased within a population is usually increased

3.3. inbreeding depression inbreeding depression increase in increase in homozygous recessive alleles (likely to homozygous recessive alleles (likely to increase deleterious phenotypes)increase deleterious phenotypes)

4.4. Inbreeding promotes linkage disequilibrium Inbreeding promotes linkage disequilibrium nonrandom association of alleles at nonrandom association of alleles at different locidifferent loci

1.1. Inbreeding redistributes the alleles to the Inbreeding redistributes the alleles to the homozygous conditionhomozygous condition

genotype freqs. change but allele frequencies do genotype freqs. change but allele frequencies do not changenot change

2.2. Genetic variance of a phenotypic character Genetic variance of a phenotypic character within a population is usually increased within a population is usually increased

3.3. inbreeding depression inbreeding depression increase in increase in homozygous recessive alleles (likely to homozygous recessive alleles (likely to increase deleterious phenotypes)increase deleterious phenotypes)

4.4. Inbreeding promotes linkage disequilibrium Inbreeding promotes linkage disequilibrium nonrandom association of alleles at nonrandom association of alleles at different locidifferent loci

Genetic Drift VS InbreedingGenetic Drift VS InbreedingGenetic Drift VS InbreedingGenetic Drift VS Inbreeding

Genetic DriftGenetic Drift Allele frequencies change Allele frequencies change

InbreedingInbreeding Allele frequencies do not change but Allele frequencies do not change but

genotype frequencies (homozygous vs. genotype frequencies (homozygous vs. heterozygotes) DO change!heterozygotes) DO change!

Genetic DriftGenetic Drift Allele frequencies change Allele frequencies change

InbreedingInbreeding Allele frequencies do not change but Allele frequencies do not change but

genotype frequencies (homozygous vs. genotype frequencies (homozygous vs. heterozygotes) DO change!heterozygotes) DO change!

Gene flowGene flowGene flowGene flow

Natural populations of a species Natural populations of a species typically are not completely isolated, typically are not completely isolated, but instead exchange genes with one but instead exchange genes with one another to a greater or lesser extentanother to a greater or lesser extent

Gene flow, if unopposed by other Gene flow, if unopposed by other factors, homogenizes a populationfactors, homogenizes a population

Natural populations of a species Natural populations of a species typically are not completely isolated, typically are not completely isolated, but instead exchange genes with one but instead exchange genes with one another to a greater or lesser extentanother to a greater or lesser extent

Gene flow, if unopposed by other Gene flow, if unopposed by other factors, homogenizes a populationfactors, homogenizes a population

Models of Gene flowModels of Gene flowModels of Gene flowModels of Gene flow

Island modelsIsland models

Stepping stone modelsStepping stone models

Isolation by distance modelsIsolation by distance models

Island modelsIsland models

Stepping stone modelsStepping stone models

Isolation by distance modelsIsolation by distance models


Homogenizes the populations within a Homogenizes the populations within a species (unopposed by other forces)species (unopposed by other forces)

Rate of gene flow = Rate of gene flow = mm AA11 varies among populations (p varies among populations (pii) ) residentresident

ppii and the average allele frequency is p and the average allele frequency is p (source)(source)

within population within population i i (p(pii), a proportion of ), a proportion of mm of of

the gene copies enter from other the gene copies enter from other populations, and the frequency is ppopulations, and the frequency is p

Homogenizes the populations within a Homogenizes the populations within a species (unopposed by other forces)species (unopposed by other forces)

Rate of gene flow = Rate of gene flow = mm AA11 varies among populations (p varies among populations (pii) ) residentresident

ppii and the average allele frequency is p and the average allele frequency is p (source)(source)

within population within population i i (p(pii), a proportion of ), a proportion of mm of of

the gene copies enter from other the gene copies enter from other populations, and the frequency is ppopulations, and the frequency is p


p pm

Source

resident


A proportion 1-m of the gene copies are A proportion 1-m of the gene copies are non-immigrants and among these the non-immigrants and among these the frequency is frequency is pp

After 1 generation the populations new After 1 generation the populations new allele freq (allele freq (p’p’) is:) is:

p’ = pp’ = p(1-(1-mm)) + pm + pm oror

p’ = p-pm + pmp’ = p-pm + pm

So........So........ΔΔp = mp = m((p – pp – p))

A proportion 1-m of the gene copies are A proportion 1-m of the gene copies are non-immigrants and among these the non-immigrants and among these the frequency is frequency is pp

After 1 generation the populations new After 1 generation the populations new allele freq (allele freq (p’p’) is:) is:

p’ = pp’ = p(1-(1-mm)) + pm + pm oror

p’ = p-pm + pmp’ = p-pm + pm

So........So........ΔΔp = mp = m((p – pp – p))


p=0.3 p=0.1m=0.001

Source

resident

1 in a 1000 is a migrant


Δp = m(p-p) = 0.001(0.3-0.1) =.0002Δp = m(p-p) = 0.001(0.3-0.1) =.0002

p’ = p(1-m) + pm = 0.1(1-0.001)+0.3*0.001p’ = p(1-m) + pm = 0.1(1-0.001)+0.3*0.001

=0.1002=0.1002

Δp = m(p-p) = 0.001(0.3-0.1) =.0002Δp = m(p-p) = 0.001(0.3-0.1) =.0002

p’ = p(1-m) + pm = 0.1(1-0.001)+0.3*0.001p’ = p(1-m) + pm = 0.1(1-0.001)+0.3*0.001

=0.1002=0.1002

Equilibrium FrequencyEquilibrium FrequencyEquilibrium FrequencyEquilibrium Frequency

Equilibrium frequency is found by setting Equilibrium frequency is found by setting p’p’ = 0 = 0 (or (or ΔΔpp = 0) = 0), which is where , which is where pp’ is not changing ’ is not changing between generations and is, thus, in equilibrium between generations and is, thus, in equilibrium

So... So... ΔΔpp = 0 = = 0 = mm((p-pp-p) thus ) thus pp = = pp

Therefore, each population will ultimately Therefore, each population will ultimately attain the same allele frequencies showing attain the same allele frequencies showing that that gene flow homogenizes populationsgene flow homogenizes populations

Equilibrium frequency is found by setting Equilibrium frequency is found by setting p’p’ = 0 = 0 (or (or ΔΔpp = 0) = 0), which is where , which is where pp’ is not changing ’ is not changing between generations and is, thus, in equilibrium between generations and is, thus, in equilibrium

So... So... ΔΔpp = 0 = = 0 = mm((p-pp-p) thus ) thus pp = = pp

Therefore, each population will ultimately Therefore, each population will ultimately attain the same allele frequencies showing attain the same allele frequencies showing that that gene flow homogenizes populationsgene flow homogenizes populations

Gene flow and driftGene flow and driftGene flow and driftGene flow and drift In the absence of gene flow populations tend to In the absence of gene flow populations tend to

diverge due to driftdiverge due to drift

FFstst = fraction of autozygotes in a sub-population = fraction of autozygotes in a sub-population at time at time tt

Another way to look at this is that Another way to look at this is that FFstst is a measure is a measure of the observed variation in allele frequency of the observed variation in allele frequency among populationsamong populations

FFstst = 1- (1-= 1- (1-½½N)N)tt

see page 315, box 11.Dsee page 315, box 11.D

In the absence of gene flow populations tend to In the absence of gene flow populations tend to diverge due to driftdiverge due to drift

FFstst = fraction of autozygotes in a sub-population = fraction of autozygotes in a sub-population at time at time tt

Another way to look at this is that Another way to look at this is that FFstst is a measure is a measure of the observed variation in allele frequency of the observed variation in allele frequency among populationsamong populations

FFstst = 1- (1-= 1- (1-½½N)N)tt

see page 315, box 11.Dsee page 315, box 11.D

Gene flow and DriftGene flow and DriftGene flow and DriftGene flow and Drift

FFstst must reach an equilibrium must reach an equilibrium

between drift and gene flowbetween drift and gene flow

Thus Thus FFstst = 1 / (4N= 1 / (4Nmm + 1) + 1)

FFstst must reach an equilibrium must reach an equilibrium

between drift and gene flowbetween drift and gene flow

Thus Thus FFstst = 1 / (4N= 1 / (4Nmm + 1) + 1)

Gene flowGene flowGene flowGene flow We can rearrange We can rearrange FFstst = 1 / (4N= 1 / (4Nmm + 1) + 1) so that so that

we can estimate the average # of we can estimate the average # of immigrants into a population per immigrants into a population per generationgeneration

Nm = 1 / (Nm = 1 / (FFstst – – 1)1) Notice! This tells us that the higher the rate Notice! This tells us that the higher the rate

of gene flow, the more similar the allele of gene flow, the more similar the allele frequencies between populationsfrequencies between populations

Conversely, observing a strong divergence Conversely, observing a strong divergence indicates that the balance between gene indicates that the balance between gene flow and drift is tipped toward drift flow and drift is tipped toward drift

We can rearrange We can rearrange FFstst = 1 / (4N= 1 / (4Nmm + 1) + 1) so that so that we can estimate the average # of we can estimate the average # of immigrants into a population per immigrants into a population per generationgeneration

Nm = 1 / (Nm = 1 / (FFstst – – 1)1) Notice! This tells us that the higher the rate Notice! This tells us that the higher the rate

of gene flow, the more similar the allele of gene flow, the more similar the allele frequencies between populationsfrequencies between populations

Conversely, observing a strong divergence Conversely, observing a strong divergence indicates that the balance between gene indicates that the balance between gene flow and drift is tipped toward drift flow and drift is tipped toward drift

Estimating Estimating FFststEstimating Estimating FFstst

Direct estimates of gene flowDirect estimates of gene flow Mark-recapture studies...Mark-recapture studies...

Indirect estimates of gene flowIndirect estimates of gene flow Alleles used to calculate FAlleles used to calculate Fstst are neutral are neutral Allele frequencies must have reached Allele frequencies must have reached

equilibrium between gene flow and driftequilibrium between gene flow and drift

Direct estimates of gene flowDirect estimates of gene flow Mark-recapture studies...Mark-recapture studies...

Indirect estimates of gene flowIndirect estimates of gene flow Alleles used to calculate FAlleles used to calculate Fstst are neutral are neutral Allele frequencies must have reached Allele frequencies must have reached

equilibrium between gene flow and driftequilibrium between gene flow and drift

Gene Flow Example!Gene Flow Example!Gene Flow Example!Gene Flow Example!

Water snakes of Lake Erie Nerodia sipedon Live on mainland and on several islands Color pattern variable

Strongly banded to unbanded Banding controlled by a single locus with two

alleles Banded is dominant over unbanded On mainland most snakes are banded On island many are unbanded

Water snakes of Lake Erie Nerodia sipedon Live on mainland and on several islands Color pattern variable

Strongly banded to unbanded Banding controlled by a single locus with two

alleles Banded is dominant over unbanded On mainland most snakes are banded On island many are unbanded

Gene Flow...Gene Flow...Gene Flow...Gene Flow...

Water snakes of Lake Erie Banding pattern due to natural selection

On islands snakes bask on rocks On mainland stay closer to vegetation

Why is the unbanded allele not fixed on islands?

Banded snakes migrate from mainland each generation

Bring banded alleles to island gene pool Migration works in opposition to natural

selection

Water snakes of Lake Erie Banding pattern due to natural selection

On islands snakes bask on rocks On mainland stay closer to vegetation

Why is the unbanded allele not fixed on islands?

Banded snakes migrate from mainland each generation

Bring banded alleles to island gene pool Migration works in opposition to natural

selection


Westermeier’s hypothesisWestermeier’s hypothesis Destruction of prairie did two thingsDestruction of prairie did two things

Reduced population sizeReduced population size Fragmented remaining populationFragmented remaining population

Remaining prairie chickens were trapped in Remaining prairie chickens were trapped in two islands in seas of farmlandtwo islands in seas of farmland

Genetic drift caused decline in heterozygosityGenetic drift caused decline in heterozygosity Inbreeding depression occurredInbreeding depression occurred

Westermeier’s hypothesisWestermeier’s hypothesis Destruction of prairie did two thingsDestruction of prairie did two things

Reduced population sizeReduced population size Fragmented remaining populationFragmented remaining population

Remaining prairie chickens were trapped in Remaining prairie chickens were trapped in two islands in seas of farmlandtwo islands in seas of farmland

Genetic drift caused decline in heterozygosityGenetic drift caused decline in heterozygosity Inbreeding depression occurredInbreeding depression occurred


Accumulation of deleterious recessives Accumulation of deleterious recessives leads to reduction in population sizeleads to reduction in population size

Effectiveness of genetic drift is increasedEffectiveness of genetic drift is increased Speed and proportion of deleterious Speed and proportion of deleterious

mutations going to fixation increasesmutations going to fixation increases Population size decreases morePopulation size decreases more Mutational MeltdownMutational Meltdown

Accumulation of deleterious recessives Accumulation of deleterious recessives leads to reduction in population sizeleads to reduction in population size

Effectiveness of genetic drift is increasedEffectiveness of genetic drift is increased Speed and proportion of deleterious Speed and proportion of deleterious

mutations going to fixation increasesmutations going to fixation increases Population size decreases morePopulation size decreases more Mutational MeltdownMutational Meltdown


Prairie chickens caught in mutational Prairie chickens caught in mutational meltdownmeltdown

Reproductive success decreasedReproductive success decreased Hatching success lowHatching success low

Birds had fallen into extinction Birds had fallen into extinction vortexvortex

Birds needed gene flowBirds needed gene flow

Prairie chickens caught in mutational Prairie chickens caught in mutational meltdownmeltdown

Reproductive success decreasedReproductive success decreased Hatching success lowHatching success low

Birds had fallen into extinction Birds had fallen into extinction vortexvortex

Birds needed gene flowBirds needed gene flow


In 1992 conservationists trapped birds In 1992 conservationists trapped birds from Minnesota, Kansas, and Nebraska from Minnesota, Kansas, and Nebraska and moved them to Jasper County, Illinoisand moved them to Jasper County, Illinois

Hatching rate increased and population Hatching rate increased and population began to growbegan to grow

Migration, genetic drift, and nonrandom Migration, genetic drift, and nonrandom mating all contributed to fate of Illinois mating all contributed to fate of Illinois greater prairie chickensgreater prairie chickens

In 1992 conservationists trapped birds In 1992 conservationists trapped birds from Minnesota, Kansas, and Nebraska from Minnesota, Kansas, and Nebraska and moved them to Jasper County, Illinoisand moved them to Jasper County, Illinois

Hatching rate increased and population Hatching rate increased and population began to growbegan to grow

Migration, genetic drift, and nonrandom Migration, genetic drift, and nonrandom mating all contributed to fate of Illinois mating all contributed to fate of Illinois greater prairie chickensgreater prairie chickens

Conclusions about Gene FlowConclusions about Gene FlowConclusions about Gene FlowConclusions about Gene Flow

1.1. Certain taxa display substantial gene Certain taxa display substantial gene flow over long distancesflow over long distances

2.2. The average level of gene flow is greatly The average level of gene flow is greatly restricted over short distancesrestricted over short distances

Implies local populations can diverge Implies local populations can diverge substantially due to driftsubstantially due to drift

Thus, species can adapt to local Thus, species can adapt to local conditions!!!!conditions!!!!

1.1. Certain taxa display substantial gene Certain taxa display substantial gene flow over long distancesflow over long distances

2.2. The average level of gene flow is greatly The average level of gene flow is greatly restricted over short distancesrestricted over short distances

Implies local populations can diverge Implies local populations can diverge substantially due to driftsubstantially due to drift

Thus, species can adapt to local Thus, species can adapt to local conditions!!!!conditions!!!!

Documents

Population Structure and Drift Chapter 11. Conservation Genetics Illinois Greater Prairie Chicken Illinois Greater Prairie Chicken Tympanuchus cupido