gayle ferguson

Lecture 12

genetic drift gayle ferguson

•  allele frequencies and therefore genotype frequencies in a population remain constant

•  proportions are p2, 2pq, q2 and this equals the H-W distribution of genotype frequencies

•  principle holds whatever the initial genotype frequencies are: after one generation of random mating the genotype frequencies will be p2 : 2pq : q2

the H-W principle

If  you’re  s+ll  struggling  with  HWE,  take  a  look  at  this  tutorial  

H-W genotype frequencies as a function of allele frequency

Locus with two alleles

i.e. when alleles have equal

frequencies!

why do we care?

when a population is not in H-W equilibrium something interesting is happening! – mating is non-random (e.g. in-breeding) (recombination)

– population size is small (genetic drift is happening)

– immigration of new genes (gene flow/migration)

– new mutations arising

– natural selection is happening

change in allele frequencies over time by drift vs selection

•  genetic drift: a RANDOM, UNPREDICTABLE, NON-ADAPTIVE process

•  natural selection: a NON-RANDOM, DETERMINISTIC, ADAPTIVE process

“survival of the luckiest - differential reproductive success that just happens”

“survival of the fittest - differential reproductive success that happens for a ‘reason’”

change in allele frequencies over time by drift vs selection

•  All genes are subject to genetic drift (#yesallgenes); not all are subject to selection (#notallgenes)

•  Genetic drift accounts for much of the difference in sequence variation we see between organisms

“survival of the luckiest - differential reproductive success that just happens”

“survival of the fittest - differential reproductive success that happens for a ‘reason’”

genetic drift occurs due to sampling error

•  http://upload.wikimedia.org/wikipedia/commons/b/b6/Random_sampling_genetic_drift.gif"

•  because normal populations are finite, unlike ideal populations at H-W equilibrium.

•  due to random “sampling” of alleles during mating and random “sampling” of alleles by death.

•  the effects of genetic drift can be dramatic

“the random walk”

Analogy: the smaller the population, the narrower the platform

Figure 10.2, p. 259 Futuyma, Evolution, 2e

populus simulations

MONTE CARLO METHOD

“The use of randomly generated or sampled data and computer simulations to obtain approximate solutions to

complex mathematical and statistical problems.”

The Monte Carlo model simulates genetic drift using a random number generator to sample genes from a

small parental population and passes them on to offspring. Population size is assumed to be constant from generation to generation and gene frequency

changes the result of the random sampling process.

time to fixation: 30 simulations N = 20 52 ± 28 generations

time to fixation: 90 simulations N = 100 256 ± 159 generations

•  every population follows a unique evolutionary path •  different alleles are fixed by chance in different populations •  the expected mean number of generations until either loss or fixation

of an allele is 4N, 4x the population size.

2 alleles at each locus

Summary - the key consequences of genetic drift

•  due to genetic drift every population follows a unique evolutionary path

•  drift has a more rapid effect on allele frequencies in small populations than in large populations

•  given sufficient time, genetic drift can produce substantial changes in allele frequencies - even in larger populations

•  as allele frequencies in a finite population drift toward fixation or loss, the frequency of heterozygotes - and hence the genetic variation - in the population declines

more rapid effect on allele frequencies in small populations than in large populations

N = 100

N = 10

more rapid effect on allele frequencies in small populations than in large populations

In larger populations, fluctuations in allele frequencies at each generation due to random sampling are of smaller magnitude and

more easily corrected in the following generation because in a larger population the sample of the gene pool propagated at

each generation more closely approximates reality. In a small population the sample is less likely to be a true reflection of the population as a whole and the allele frequencies at the next

generation can change dramatically because of this.

what are the chances of an allele being fixed?

•  the probability that an allele will be fixed in the future is equal to the frequency of the allele at that moment in time

•  if a new allele arises by mutation in a diploid population of N individuals, its probability of fixation is 1/(2N) (and the mean number of generations ‘til either loss or fixation will be 4N)

A1A1

A1A1

A1A1

A1A2

A1A1 A1A1

A1A1 A1A1

A1A1

A1A1

what are the chances of an allele being fixed?

probability of fixation of A2 is 1/(2N)

N = 10

the probability that an allele will be fixed in the future is equal to the frequency of the allele at

that moment in time

locus 1 !!

mean generations until loss or fixation"

locus 1!!

% fixed"% lost"

locus 2!!

mean generations until loss or fixation"

locus 2!!

% fixed"% lost"

70 iterations" 70 iterations 70 iterations" 70 iterations"

191 ± 107! 87% fixed (F)!13% lost (E)! 154 ± 100! 7% fixed (F)!

93% lost (E)!

table 4: two loci, population size 100, initial frequency 0.9 (locus 1) and 0.1 (locus 2)

from Populus simulations

a history of descent of gene copies showing coalescence

coalescence

Figure 10.1, p. 258 Futuyma, Evolution, 2e Reading p. 257-9

mitochondrial eve

Mitochondrial Eve is the name given by researchers to the woman who is defined as the matrilineal most recent common ancestor (MRCA) for all currently living humans. All mtDNA in every living person is derived from hers. Mitochondrial Eve is believed to have lived about 170,000 years ago, or roughly 8,000 generations ago. This places her shortly after the speciation of Homo sapiens and the emergence of the first anatomically modern humans. Mitochondrial Eve would have been roughly contemporary with humans whose fossils have been found in Ethiopia near the Omo river and at Hertho. Mitochondrial Eve lived significantly earlier than the out of Africa migration which occurred some 60,000 years ago. The existence of Mitochondrial Eve and Y-chromosomal Adam does not imply the existence of population bottlenecks or a first couple. They each may have lived within a large human population at different times.

different alleles are fixed by chance in different populations

deme drift reduces genetic variation within each deme over time, but

increases variance in allele frequencies

between demes within a metapopulation

random genetic drift acts more rapidly in small effective population sizes

the effective population size (breeding) is often much smaller than the apparent population size (census).

Why?

effective population sizes may be smaller than census population sizes 1. Variation in numbers of progeny produced by males, females, or both -- e.g. elephant seal extreme example: most males may as well not exist from a genetic point of view! 2. Sex ratio is different from 1:1 3. Increased variation in progeny number (i.e. not a normal, bell-shaped curve), e.g. if larger individuals have more off-spring than smaller we see a very biased sampling of the gene pool 4. If generations overlap (progeny mate with parents) --- loss of heterozygosity and effective number of genes propagated is reduced (clones)

examples of genetic drift operating in natural populations

1. eastern collared lizard -- small, reproductively isolated populations

Human actions disrupt the normal equilibrium between genetic drift (purges genetic diversity) and gene flow by

migration (increases diversity within populations and decreases diversity between populations)

•  Lives in glades (rocky outcrops) within what was once desert, but is now Oak-Hickory forest (In the past 8,000-4,000 years, Missouri has become wetter and isolated these desert habitats into glades)

•  Templeton et al (1990) examined the distribution and population structure of the collared lizard (Crotaphytus collaris)

•  Human suppression of wild fires that used to occur at ~ 5 year intervals has caused habitat fragmentation, reducing gene flow and increasing loss of variation by genetic drift - prevents lizards from migrating from one glade to another - resulted in tiny populations of lizards with reduced genetic diversity

Example - the collared lizard Ozark Mountains (Missouri, USA)

Example - the collared lizard Ozark Mountains (Missouri, USA)

PREDICTION: lizard populations strongly affected by genetic

drift

Example - The collared lizard Ozark Mountains (Missouri, USA)

•  7 distinct multi-locus genotypes found in the lizard •  most glades fixed for a single multi-locus genotype with

different genotypes fixed in different populations

Example - The collared lizard Ozark Mountains (Missouri, USA)

•  populations too small to

adapt to pathogens.

•  likely to become extinct

•  controlled burns of forest resulted in immediate migration of lizards

•  hopefully the species will now have a greater chance of survival

bottlenecks the gene pool randomly drifts when the population is drastically reduced by a disaster that kills unselectively

the effects of bottlenecking can be easily demonstrated with bacteria

start a culture with a single bacterium

incubate overnight

propagate culture from a single bacterium

propagate culture from a single bacterium

incubate overnight

incubate overnight

measure fitness relative to ancestor after many generations of passage

Bo:lenecks  occur  naturally  in  wild  bacterial  popula+ons  -­‐-­‐  selec+on  by  the  immune  system  and  an+bio+cs  are  examples.  

 

Mutation accumulation by bottlenecking in bacteria

Lind et al. PNAS 2008 200 cycles = 5000 generations

population bottlenecks also occur in nature, with profound effects: the cheetah

•  so closely related that skin grafts from one animal to another do not cause immune response

•  no genetic heterozygosity

•  no polymorphic loci

•  suffer genetic effects including low fertility through in-breeding

•  thought to have gone through 2 bottlenecks --- 10,000 years ago --- 100 years ago

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The failure rate rate for egg hatch is greater in NZ bird species that have suffered a bottleneck in population size. Data for 22 native species of birds, many of which approached extinction after European settlement. Some are still highly endangered, such as #17, the Kakapo. The trend is the same for introduced bird species, where higher hatching failures are correlated with small numbers of individuals at the time of introduction to NZ. These are examples of the Founder effect.

Why do bottlenecks lead to hatchling failure?

the founder effect •  A slightly different sort of genetic bottleneck can occur

if a small group becomes reproductively separated from the main population. This is called a founder effect

•  Populations are often small when they have just been founded by a group of individuals that have moved to a new location

•  The allele frequencies of the new population are likely, by chance, to be different to the source population ---- for example, if a continental population of lizards has 35 alleles at a single locus, then the probability = 0 that 15 lizards floating away from that population contains all of the alleles

•  Dutch South Africans - Huntington’s disease

•  silvereye (taho or waxeye)

•  small birds native to australia and tasmania - colonized new zealand, chatham and norfolk islands over the last 200 yrs. - as the birds hopped from island to island the allele diversity declined

•  clegg et al (2002) estimated the rate of genetic change by comparing the level of neutral genetic variation in island populations that have been established over a range of time periods

founder effect example: the waxeye

"Six loci were examined in each population

1. results indicate that single founder events do not affect

levels of heterozygosity or allelic diversity, nor do they result in immediate genetic

differentiation between populations. Instead, four to

five successive founder events are required before

indices of diversity and divergence approach that seen in evolutionarily old

forms.

founder effect example: the waxeye

2. single colonization events in this species complex are rarely accompanied by severe founder effects, and multiple founder events and/or long-term genetic drift have been of greater consequence for neutral genetic diversity.

Flocks of ~100 birds colonized at each migration

Summary Genetic Drift

• Genetic drift vs. natural selection

•  Acts more rapidly in small populations

•  Coalescence

•  Bottlenecks, founder effects

•  Effective vs. census population size