Download Population genetics 2

Chapter 21 - Population genetics (part 2):
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Forces that change gene frequencies
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Balance between mutation, drift, selection, and migration
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Mutation-Drift
Mutation-selection
Migration-selection
Inbreeding & inbreeding depression
Forces that change gene frequencies:
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Natural populations harbor enormous amounts of genetic variation.
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If population is in Hardy-Weinberg equilibrium (large, random
mating, free from mutation, migration, and natural selection) allele
frequencies remain constant.
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Many, if not most populations, do not meet Hardy-Weinberg
equilibrium conditions, allele frequencies change, and the
population’s gene pool evolves.
Four main evolutionary processes responsible for such changes:
1.
Mutation
1.
Genetic drift
1.
Selection
1.
Migration
Mutation:
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Heritable changes within DNA .
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Source of all new genetic variation.
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Raw material for evolution.
Mutation rate varies between loci and among species:
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~10-4 to 10-8 mutations/gene/generation.
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Mutation rate is abbreviated
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Some mutations are selectively neutral (no effect on
reproductive fitness).
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Others are detrimental or lethal, or beneficial (depends on
environment).
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If population size is large, effects of neutral mutation act
slowly because new mutations are by definition initially rare.
Only selection can quickly increase the frequency of a new
mutation.
.
Mutation:
Irreversible mutation:
Allele A is fixed (p =1.0) and mutates A  a at rate of
Hartl & Clark (1997) Principles of Population Genetics
 = 10-4:
Mutation:
Reversible mutation:
Allele A is fixed (p =1.0) and mutates A  a at rate of
a mutates a  A at a rate of
 = 10-5.
Hartl & Clark (1997) Principles of Population Genetics
 = 10-4; but allele
Genetic drift and the fate of neutral mutations:
Neutral theory of molecular evolution:
Motoo Kimura (1924-1994)
Genetic drift causes allele frequencies to change over time and wander
randomly:
1.
Some alleles may go extinct: p  0
2.
Other alleles may become fixed: p  1
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Probability of fixation increases with time.
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Which allele becomes fixed is strictly random.
3.
Rare alleles are more likely to be lost (p  0).
4.
Time to fixation/loss varies with effective population size (Ne) and
initial allele frequency.
5.
Drift has much larger effects on small populations.
Effective population size (Ne):
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The population census size N is distinct from Ne.
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Not all individuals contribute gametes to the next generation, and
not all gametes survive.
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Effective population size (Ne) = equivalent number of adults
contributing gametes to the next generation.
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If sexes are equal in number and all individuals have an equal
probability of reproducing, Ne = N.
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Otherwise: Ne = (4 x Nf x Nm )/ (Nf + Nm )
Nf and Nm = numbers of breeding females and males (Ne = ~8 for a
population with 70 breeding females and 2 males).
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Sampling variance: sp2 = pq/2Ne
Standard error: sp = √(pq/2Ne)
95% confidence limit = p  2sp
Variance in Ne is large for small populations, and small for large
populations.
Fluctuations in effective population size:
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Population sizes change over time.
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Average effective population size (Ne) is a harmonic mean:
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1/Ne = 1/t (1/N0 + 1/N1 + … 1/Nt-1)
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Harmonic mean = reciprocal of the average of the reciprocals.
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Important consequence---one short period of of small population
size (i.e., bottleneck) can dramatically reduce Ne, and it takes a long
time for Ne to recover.
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Other factors that influence Ne:
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Differential production of offspring
Overlapping generations
Population structure
Natural selection
Fig. 21.11, Average time to
fixation/loss as a function of
population size and initial allele
frequency.
Fig. 21.10, Effect of drift on four
populations with initial allele
frequencies q = 0.5.
https://www.boundless.com/biology/textbooks/boundless-biology-textbook/the-evolution-of-populations-19/
Probability of fixation of a new
neutral mutation depends
on the population size:
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= 1/2Ne
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Ne = effective population
size
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Requires average of 4N
generations.
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Time between successive
fixations = 1/
generations.
Hartl & Clark (1997)
Principles of Population Genetics
Take home message - genetic drift has important consequences for
small populations:
•If Miami population had 10 individuals; 5 with brown eyes (BB) and 5
with green eyes (bb); f(B) = 0.5, f(b) = 0.5.
•Hurricane devastates Miami; 5 people with brown eyes (BB) die.
•Allelic frequency of b , f(b) = 1.0; chance events have radically changed
the allele frequencies and the population evolves.
•Now imagine the same scenario for a Miami of 5 million inhabitants.
•Probability of the same outcome is >6 orders of magnitude lower.
•This type of “sampling” occurs naturally:
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Which gametes fertilizes the egg?
What proportion of offspring survive?
What proportion of offspring contribute gametes to the next
generation?
Genetic drift acting through founder events, bottlenecks, and geographic
isolation can lead to rapid changes in gene frequency and
phenotype.
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Effects of Genetic drift can be pronounced when population size
remains small over many generations, especially when
subpopulations are isolated.
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Founder effect = a population is initially established by a small
number of breeding individuals.
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Chance plays a significant role in determining which genes are
present among the founders, can lead to rapid evolutionary
changes.
Bottleneck effect = effects of genetic drift when a population is
dramatically reduced in size.
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Common in endangered species
Founder Effect
http://wallace.genetics.uga.edu/groups/evol3000/wiki/fb221/Bottlenecks_and_Founder_Effects.html
Founder Effect
Heterozygosity for eight populations of
Song Sparrows (Pruett & Winker 2005)
Bottleneck
http://wallace.genetics.uga.edu/groups/evol3000/wiki/fb221/Bottlenecks_and_Founder_Effects.html
Fig. 21.9, P. Buri’s study of genetic drift
in Drosophila.
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107 experimental populations.
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Randomly selected 8 males and 8
females from each population for the
next generation for 20 generations.
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Sequential Bottleneck
Natural selection:
1.
Populations growth occurs exponentially; more individuals are
produced than can be supported by available resources resulting in
a struggle for existence (e.g., Malthus, Swift).
2.
No two individuals are the same, natural populations display
enormous variation, and variation is heritable.
3.
Survival is not random, but depends in part on the hereditary
makeup of offspring. Over generations, this process leads to
gradual change of populations and evolution of new species.
Jonathan Swift (1729)
Thomas Malthus (1798)
Malthusian Population Catastrophe
Natural selection (and adaptation) in genotypic terms:
1.
Natural selection equates to the differential survival of genotypes.
2.
Darwinian fitness (W) = relative reproductive ability of a genotype
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Calculate the # of viable offspring relative to other genotypes.
3.
Selection coefficient (s) = 1 - W
4.
Contribution of each genotype to the next generation:
AA
Aa
aa
Initial
genotypic
frequencies
p2
2pq
q2
Fitness
WAA
WAa
Waa
Frequency after
selection
p2 WAA
2pq WAa
q2 Waa
Relative
frequency after
selection
p2 WAA/WMEAN
2pq WAa /WMEAN
q2 Waa /WMEAN
Natural selection (and adaptation):
Some conclusions:
1.
WAA = WAa = Waa: no natural selection
2.
WAA = WAa < 1.0 and Waa = 1.0: natural selection and complete
dominance operate against a dominant allele.
3.
WAA = WAa = 1.0 and Waa < 1.0: natural selection and complete
dominance operate against a recessive allele.
4.
WAA < WAa < 1.0 and Waa = 1.0: heterozygote shows intermediate
fitness; natural selection operates without effects of complete
dominance.
5.
WAA and Waa < 1.0 and WAa = 1.0: heterozygote has the highest
fitness; natural selection/codominance favor the heterozygote (also
called overdominance or heterosis).
6.
WAa < WAA and Waa = 1.0: heterozygote has lowest fitness; natural
selection favors either homozygote.
Natural selection:
Selection against recessive alleles:
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Recessive traits often result in reduced fitness.
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If so, there is selection against homozygous recessives, thus
reducing the frequency of the recessive allele.
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However, the recessive allele is not usually eliminated; rare, lethal
recessive alleles occur in the heterozygote (protected
polymorphism).
Fig. 21.17, Selection
against a recessive
lethal genotype.
Heterozygote superiority:
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If a heterozygote has higher fitness than the homozygotes, both
alleles are maintained in the population because both are favored by
the heterozygote genotype (e.g., sickle cell trait).
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Also known as: heterosis or overdominance
Fig. 21.19,
Distribution of
malaria and Hb-S
allele.
Effects of selection can override genetic drift leading to fixation of a new
favorable mutation:
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Drift will only rarely lead to fixation of a new mutation; the odds are
very much stacked against this outcome.
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However, fixation of a new favorable mutation may occur very
rapidly, depending on the strength of selection and effective
population size.
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When Ne is large, the effects of genetic drift are always small, but
the effects of selection can be large (directly proportional to Ne).
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Selective sweep = process by which a favorable mutation becomes
fixed in a population due to force of directional selection.
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Closely-linked neutral alleles can hitchhike during a selective sweep
(i.e., genetic draft, which is distinct from genetic drift).
Selective Sweep
Through genetic draft linked regions of DNA linked to the favorable allele
become overrepresented in the population. Effects of selection are apparent
not only at the selected locus but also in the flanking DNA sequences.
If there is a lot of linkage disequilibrium (LD) like in
humans, these markers can tell us a lot about the
general location of particular genes.
Summary of different types of selection (following Bamshad & Wooding 2003)
No Selection
Allele frequencies change
due to genetic drift
Directional
One particular allelic
variant is favored
Balancing/Diversifying
Purifying
Two or more allelic
Deleterious (lethal) alleles
variants are favored
are eliminated
Migration equates to gene flow - movement of genes from one
population to another.
Three major effects:
1.
Introduces and spreads unique alleles to new populations.
2.
If allelic frequencies differ between two populations, gene flow
changes allele frequencies of the recipient population.
3.
By increasing the effective population size, migration increases Ne
and reduces genetic drift.
Fig. 21.13, Effect of migration
on a recipient gene pool.
Change in allele frequency with one-way migration (m = 0.01)
Hartl & Clark (1997) Principles of Population Genetics
Migration (cont.):
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Increases the effective size of a population.
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Prevents allelic fixation.
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Can be a much stronger force than mutation.
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If migration rate (m) >> mutation rate rate of (), effects of genetic
drift that tend to cause populations to diverge in allelic frequencies
will be offset by gene flow.
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Measure migration scaled to the mutation rate (m/).
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Important to conservation biology because habitat fragmentation
can prevent gene flow, and thus reduce effective population size of
isolated populations, increasing the effects of genetic drift.
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Maintaining natural corridors between populations is essential.
Very bad agricultural landscape!
Better agricultural landscape!
Roadside Vegetation Activity in U.S!
Roadside Vegetation Act
in Australia!
Balance between evolutionary forces – equilibrium models:
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Mutation & genetic drift
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Mutation & selection
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Migration & selection
Balance between mutation and genetic drift:
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Mutation adds genetic variation/genetic drift removes variation.
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Infinite alleles model predicts that mutation and drift balance each
other to result in a steady state of heterozygosity.
Assumptions of the infinite alleles model:
1.
Each mutation is assumed to generate a novel allele never observed
(and the probability that two mutations will generate the same
mutation is infinitely small).
2.
Genetic drift operates as normal, affecting smaller populations
disproportionately.
3.
Heterozygosity: H = (4 Ne )/ (1 + 4 Ne )
4.
Neutral parameter
 = 4 Ne 
*describes balance between mutation and drift (if Ne doubles and
is halved  H remains the same).

Fig. 21.12, Relationship between
 = 4 Ne 
and expected heterozygosity.
Hartl & Clark (1997) Principles of Population Genetics
Lewontin’s Paradox
Selection Constrains Variation in Larger Populations
http://www.trevorbedford.com/tree_topology/
Balance between mutation and selection:
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When an allele becomes rare, changes in frequency due to natural
selection are small.
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Mutation occurs at the same time and produces new rare alleles.
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Balance between mutation and selection results in evolution.
For a complete recessive allele at equilibrium:
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q = √ (/s)
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If homozygote is lethal (s = 1) then q = √
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Lethal alleles never go away because they are always reintroduced
to the population by mutation.
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Allele frequencies may only increase greatly if the allele is
beneficial.

Balance between migration (gene flow) and selection:
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High levels of gene flow (>2 effective migrants per generation) will
counter the tendency for isolated populations to differentiate or
speciate.
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High rates of gene flow (>10 effective migrants per generation) will
typically result in low FST values between two populations for most
loci in genome.
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Populations might generally be indistinguishable (cryptic).
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But that doesn’t mean that individual populations don’t evolve and
adapt to their local environment.
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If the effects of selection are stronger than migration (s >> m),
specific alleles that are well-suited (beneficial) to their environment
can still become disproportionally represented in one population but
not the other.
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Gene flow is locus-specific and a function of “migration/selection
balance”.
Genic View of Speciation
Safran, R. J. & Nosil, P. (2012) Speciation: The Origin of New Species.
Nature Education Knowledge 3(10):17
Leads to heterogeneity creating “genomic islands of
divergence” against a neutral background
Safran, R. J. & Nosil, P. (2012) Speciation: The Origin of New Species.
Nature Education Knowledge 3(10):17
Threespine Stickleback
Hohenlohe PA, Bassham S, Etter PD, Stiffler N, Johnson
EA, et al. 2010 Population Genomics of Parallel
Adaptation in Threespine Stickleback using Sequenced
RAD Tags. PLoS Genet 6(2): e1000862.
doi:10.1371/journal.pgen.1000862
Finally, one more important and related topic:
Assortative mating
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Individuals do not mate randomly but prefer one phenotype to
another. Affects allele frequencies. Assortative mating may be
positive or negative.
Inbreeding
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Preferential mating of close relatives.
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Small populations may show this effect even with no tendency to
select close relatives.
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Acts on allele frequencies like genetic drift by decreasing Ne.
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Heterozygosity decreases and homozygosity increases.
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Self-fertilization is the most extreme example.
Effects of inbreeding:
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Effects of inbreeding are generally thought to be maladaptive.
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Outbreeding is usually beneficial.
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But interestingly, inbred population do not always show evidence of
inbreeding depression (harmful effects).
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Repeated cycles or persistent periods of small population size are
thought to purge populations of deleterious alleles.
Review Slide - Summary of effects of evolutionary forces:
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Mutation
Occurs at low rate, creates small changes, and increases genetic
variation; balanced with natural selection and drift.
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Genetic drift
Decreases variation due to loss of alleles, produces divergence and
substantial changes in small populations through bottlenecks,
founder events and geographic isolation; balanced with mutation.
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Migration
Rates and types of migration vary, increases effective population
size and decreases divergence by encouraging gene flow (and
reduces drift), but also creates major changes in allele frequencies;
balanced with selection.
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Natural selection
Increases or decreases genetic variation depending on the
environment, continues to act after equilibrium has been achieved;
balanced with other forces, e.g., mutation and migration.
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Non-random mating
Inbreeding decreases variation and in some cases fitness (but not
always), and contributes to the effects of other processes by
decreasing effective population size.