Download 11. Gene350 Animal Genetics 18 August 2009

Gene350 Animal Genetics
Lecture 11
18 August 2009
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Genetic structure of animal populations
Hardy-Weinberg Equilibrium
Genetic variation in space and time
Variation in animal populations, Wright’s Fixation Index
(Fst)
Today
• Forces that change gene frequencies
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Non-random mating
Migration
Selection
Random genetic drift
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 evolutionary processes responsible for such changes:
1.
Mutation
1.
Genetic drift
1.
Migration
1.
Natural selection
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 neutral (no effect on reproductive fitness).
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Others are detrimental or lethal (depends on environment).
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If population size is large, effects of mutation act slowly (i.e.,
compared to selection).
.
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
Mutation:
Probability of fixation of a new
neutral mutation:
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= 1/2Ne
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Ne = effective population
size
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requires and average of
4N generations.
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Time between successive
fixations = 1/
generations.
Hartl & Clark (1997)
Principles of Population Genetics
Mutation:
Fixation of a new favorable mutation:
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May occur rapidly, depends on strength of selection and effective
population size.
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Selective sweep = process by which a favorable mutation becomes
fixed in a population due to force of positive selection.
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Tightly-linked neutral alleles can hitchhike during a selective sweep
(i.e., genetic draft).
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Linked regions of DNA around the favorable allele are
overrepresented in the population; leads to excess of rare alleles at
linked loci.
Genetic drift:
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Chance alone may result in changes in allele frequency, including
fixation and extinction.
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Genetic drift is analogous to sampling effect.
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Genetic drift has important consequences for small populations.
Example:
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Island population of 10 heads of cattle; 5 with black coat colour
(BB) and 5 with red (bb); f(B) = 0.5, f(b) = 0.5.
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Typhoon devastates the island; 5 head with black coat colour (BB)
die.
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Allelic frequency of b , f(b) = 1.0; chance events have radically
changed the allele frequencies and the population evolves.
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Now imagine the same scenario for an island of 10,000 head of
cattle.
Genetic drift:
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Chance deviations from expected ratios of gametes and zygotes also
produce genetic drift.
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Cross Aa x aa  expect 50% Aa and 50% aa, but not all of the time
insofar that sampling is limited (sampling error).
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Sampling variance: sp2 = pq/2N
*N = number of individuals in the population.
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Variance is large for small populations, and small for large
populations.
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Sampling occurs naturally:
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Which gametes fertilizes the egg?
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What proportion of offspring survive?
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What proportion of offspring contribute gametes to the next
generation?
Effective population size:
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Not all individuals contribute gametes to the next generation.
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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.
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Sampling variance: sp2 = pq/2Ne
Standard error: sp = √(pq/2Ne)
95% confidence limit = p  2sp
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e.g., Ne = ~8 for a population with 70 breeding females and 2 males.
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Other factors that reduce reduce Ne:
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Differential production of offspring
Fluctuating population size
Overlapping generations
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 small population size
(i.e., bottleneck) can dramatically reduce Ne, and it takes a long
time for Ne to recover.
Bottleneck and founder effects:
“Sampling effects” occurs in natural populations:
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Genetic drift can be pronounced when population size remains small
over many generations, especially when subpopulations are
isolated.
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Genetic drift also arises from founder effects = a population is
initially established by a small number of breeding individuals.
Chance plays a significant role in determining which genes are
present among the founders.
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Bottleneck effect = effects of genetic drift when a population is
dramatically reduced in size.
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Migration and gene flow in populations increase Ne and reduce
effects of genetic drift.
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Fluctuating population size through time may results in complex
patterns, as will interaction of drift and 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.
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. 24.14, Relationship between
 = 4 Ne 
and expected heterozygosity.
Hartl & Clark (1997) Principles of Population Genetics
Migration:
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Migration in genetic terms equates to gene flow - movement of
genes from one population to another.
Two major effects:
1.
Introduces and spreads unique alleles to new populations.
2.
If allelic frequencies of migrants and recipient populations differ,
gene flow changes allele frequencies of the recipient population.
Fig. 24.15, 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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Migration rate (m) >> mutation rate rate of ().
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Especially important to conservation of wild animals because habitat
fragmentation can prevent gene flow, and thus reduce effective
population size of isolated populations.
Natural selection (and process of adaptation):
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).
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.
Natural selection (and adaptation):
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 recessive
allele 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 (and adaptation):
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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Recessive allele is not eliminated; rare, lethal recessive alleles occur
in the heterozygote (protected polymorphism).
Fig. 24.20, 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. 24.22,
Distribution of
malaria and Hb-S
allele.
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 = √

Important related topics:
Assortative mating
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Individuals do not mate randomly but prefer one phenotype to
another.
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Affects allele frequencies.
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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 (heterozygosity
decreases and homozygosity increases).
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Self-fertilization is the most extreme example.
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.
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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.
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Natural selection
Increases or decreases genetic variation depending on the
environment, increases or decreases divergence, and continues to
act after equilibrium has been achieved; also balances with other
forces, e.g., mutation and drift.
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Non-random mating
Inbreeding decreases variation and fitness, and contributes to the
effects of other processes by decreasing effective population size.
Conservation of genetic diversity = conservation of biodiversity:
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Maintaining large interbreeding populations typically requires large
non-fragmented habitats.
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Earth’s animal species and most species-rich habitats are being
exterminated by humanity at rates ~1,000-fold greater than
historical background extinction rates.
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Currently experiencing the most massive extinction episode in 65
million years.
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Mutations that give rise to variation accumulate slowly over many
generations.
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Habitat loss and extinction occur much faster.
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Existent animal biodiversity is the result of a legacy of 4-5 billion
years of genetic information.
Hardy-Weinberg Equilibrium
(HWE)
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Can calculate whether the allele frequencies of a given population
of organisms deviates from those frequencies predicted by HWE
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In other words, are allele frequencies being affected by some
evolutionary force
E.g. Gene flow (emigration, immigration),
Natural selection
Hypothesis Testing
1.
Develop a null hypothesis and determine the level of
experimental error (Type 1 statistical error; rejecting null when
it is actually correct) that we are willing to accept while not
rejecting the null
i.e. Populations of animals are in Hardy-Weinberg equilibrium
using a confidence level of 0.95
In other words, we want to be 95% certain that populations
under consideration are in HWE; willing to allow 5%
(p=0.05) error in our data while still failing to reject the null
hypothesis
Hypothesis Testing
2.
3.
4.
Find the probability distribution for the event of interest
Calculate the observed p-value
Compare observed p-value to the preselected level of
Type 1 statistical error, or p= 0.05
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If observed p-value is less than 0.05, we reject our
null hypothesis
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If observed p-value is greater than 0.05, we fail to
reject our null hypothesis
Hardy-Weinberg Equilibrium
(HWE)
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Simplest method for testing for deviations from HWE
– Chi-square Goodness-of-fit Test
2
(
O

E
)
i
x2   i
Ei
i 1
k
O = observed number of individuals of a given genotype
E = expected number of individuals of a given genotype if population
is at HWE
degrees of freedom (df) = k – number of estimated
parameters – 1
DF determines the maximum observed chi-square value you can
obtain while still failing to reject the null hypothesis (i.e. p < 0.05)
Example
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Is this population in Hardy-Weinberg equilibrium?
p  2 pq  q  1
2
2
Genotype
Observed Number
A1A1
5000
A1A2
3000
A2A2
2000
Example