Transcript Lec3

Variation
Lecture 4-5
Sources of Phenotypic Variation
Phenotype
Characteristic in an individual organism or group of individuals that are
alike
Level of gene expression is a phenotype
Sources of Phenotypic Variation
Phenotypic variation is the result of:
• Genetic differences among
individuals
Ex: Snow goose
• Environmental variation on
development
Ex: Ptarmigan
Because evolution consists of
genetic changes in populations over
time, evolutionary biologists are
most interested in those variations
that have genetic basis
Sources of Phenotypic Variation
Genotype
Genetic constitution at one or more loci of an individual organism or a
group of organisms that are alike
The number of alleles or loci that contribute to genetic variation in a
phenotypic trait differs from case to case
Sources of Phenotypic Variation
Variation comes in many forms:
• Two or three alleles at the
same locus
Ex: Snow goose and swallowtail
butterfly (color patterns of wings)
• Multiples alleles at different
loci
Ex: Land snail (color patterns of
shell bands)
• Multiple loci contributing to
continuous variation
Ex: Human (color of hair and skin)
Sources of Phenotypic Variation
Variation in a phenotypic character can have several sources other than
those encoded in DNA sequences
The environment directly affects the development or expression of many
features:
Permanent effects: environmental sex determination
Temporary effects: enzyme induction
Environmental Variance: Environmentally induced variation among
individuals
Developmental Noise: phenotypic variation observed even when genetic
and environmental variation are eliminated is caused by random events at
the molecular level: fluctuating asymmetry
Phenotype= Genes + Environment + Noise
Sources of Phenotypic Variation
Maternal effects: Effects of a mother on her offspring that are due not to
the genes they inherit from her but rather to non-genetic influences
Amount of yolk in eggs, amount of maternal care
Epigenetic inheritance: Some phenotypic differences that are not based
on DNA sequence differences are sometimes transmitted from parents to
offspring
Genomic imprinting
Because evolution depends on the genetic component of variation, it is
often critically important to determine whether variation in a characteristic
is genetic, environmental or both
Lecture Ideas
• Genetic variation is a necessary condition for evolution
• Variability is achieved through the process of mutation:
• Mutation rate (per individual gene per generation) is low but provides
abundant genetic variation within a population
• Recombination also generates variability
• Mutation is NOT the cause of evolution
• Phenotypic variation results from genotypic and environmental variation
Fundamental Principles of Genetic Variation in Pops
We are interested in genetic variation and the factors that cause evolution
within species
At any given gene locus a population may contain 2 or more alleles that
have arisen over time by mutation. WILD TYPE refers to the most common
allele
ALLELE FREQUENCY
Proportion of a population that has a certain allele
In sexually reproducing populations, the alleles, carried in eggs and
sperm, become combined into homozygous and heterozygous genotypes
GENOTYPE FREQUENCY
Proportion of a population that has a certain genotype
Fundamental Principles of Genetic Variation in Pops
Any alteration of the genotype frequencies in one generation will alter the
frequencies of the allele carried by the population’s gametes when
reproduction occurs, so the genotype frequencies of the following
generation will be altered in turn. Such alteration, from generation to
generation, is the central process of evolutionary change
However the genotype and allele frequencies do not change on their own;
something has to change them. The factors that can cause the
frequencies to change are the causes of evolution
Fundamental Principles of Genetic Variation in Pops
Frequencies of Alleles and Genotypes
Consider alleles A1 and A2
If there are 400 A1 A1, 400 A1A2, and 200 A2A2 individuals
What are the genotype and allele frequencies in this population?
Fundamental Principles of Genetic Variation in Pops
Frequencies of Alleles and Genotypes
Consider N, alleles A1 and A2, genotypes A1 A1, A1A2, A2A1, and A2A2
The parental genotype and allele frequencies are
Genotype
1000
N=1000
400
400
200
A1 A1
A1A2
A2A2
Allele
D
H
R
0.4
0.4
0.2
A1
A2
p=D+H/2
q=R+H/2
0.6
0.4
Fundamental Principles of Genetic Variation in Pops
Frequencies of Alleles and Genotypes
Assume genotype equally represented in females and males and random
mating
If the previous is the parental population
What is the frequency of each genotype among the offspring
generation ?
Fundamental Principles of Genetic Variation in Pops
Frequencies of Alleles and Genotypes
Assume genotype equally represented in females and males and random
mating
Mating
Prob Mating
Fem x Mal
Offspring Genotype
A1 A1
A1 A2
A2 A2
A1 A1 x A1 A1
D2
1
0
0
A1 A1 x A1 A2
2DH
½
½
0
A1 A1 x A2 A2
2DR
0
1
0
A1 A2 x A1 A2
H2
¼
½
¼
A1 A2 x A2 A2
2HR
0
½
½
A2 A2 x A2 A2
R2
0
0
1
The frequency of each genotype among the offspring is:
A1A1
A1A2
A2A2
D2 + ½2DH + ¼H2 = (D+H/2)2 = p2
½2DH + 2DR + ½H2 + ½2HR = 2[(D+H/2)+(H/2+R)] = 2pq
¼H2 + ½2HR + R2 = (R+H/2)2 = q2
Fundamental Principles of Genetic Variation in Pops
Frequencies of Alleles and Genotypes
If genotypes mate at random, gametes, and therefore genes, unite at
random to form zygotes
Sperm
A1 (p)
A2 (q)
Eggs A1 (p)
A1A1 (p2)
A1A2 (pq)
A2 (q)
A2A1 (pq)
A1A1 (q2)
What is the frequency of each allele among the offspring generation ?
Fundamental Principles of Genetic Variation in Pops
Frequencies of Alleles and Genotypes
If genotypes mate at random, gametes, and therefore genes, unite at
random to form zygotes
Sperm
A1 (p)
A2 (q)
Eggs A1 (p)
A1A1 (p2)
A1A2 (pq)
A2 (q)
A2A1 (pq)
A2A2 (q2)
The frequency of each allele among the offspring is:
A1 p2 + ½2pq = p
A2 ½2pq + q2 = q
The allele frequencies do not change from one generation to the next
Fundamental Principles of Genetic Variation in Pops
Frequencies of Alleles and Genotypes
The offspring genotype and allele frequencies are
If there are 400 A1 A1, 400 A1A2, and 200 A2A2 individuals
What are the genotype and allele frequencies in the offspring
population?
Fundamental Principles of Genetic Variation in Pops
Frequencies of Alleles and Genotypes
The offspring genotype and allele frequencies are
Genotype
A1 A1
A1A2
A2A2
Allele
p2
2pq
q2
0.36
0.48
0.16
A1
A2
p
q
0.6
0.4
The allele frequencies have not changed from one generation to the next ,
although the alleles have become distributed among the three genotypes
Fundamental Principles of Genetic Variation in Pops
Frequencies of Alleles and Genotypes
HARDY-WEINBERG PRINCIPLE
• Whatever the initial genotype frequencies for two alleles may be, after
one generation of random mating, the genotype frequencies will be
p2:2pq:q2
• Both these genotype frequencies and the allele frequencies will remain
constant in succeeding generations … unless some factor change them
When the genotypes at a locus have the frequencies predicted by the HardyWeinberg principle the locus is said to be in HARDY-WEINBERG EQUILIBRIUM
Example: Human MN Locus
Two alleles M, N. Sample 320. MM 187, MN 114, NN 19
Frequency of each genotype? Allele frequencies? Expected vs observed number of
individuals?
Fundamental Principles of Genetic Variation in Pops
The Significance of the Hardy-Weinberg Principle
The Hardy-Weinberg principle is the foundation on which almost all of the
theory of population genetics of sexually reproducing organisms rests
The study of genetic evolution consists of asking what happens when one or
more of the assumptions of the Hardy-Weinberg principle are relaxed
The most important assumptions are:
1.
2.
3.
4.
5.
Infinite population (random genetic drift)
Random mating
No migration
No mutation
No natural selection
Thus the major factors that cause evolutionary change within populations
are chance, nonrandom mating, gene flow, mutation and selection.
Other assumptions: a. Autosomal loci (sex-linked loci) b. Mendelian
segregation (segregation distortion)
If these assumptions hold true for a particular locus, that locus will display Hardy-Weinberg genotype frequencies. But if we
observe that a locus fits the Hardy-Weinberg frequency distributions we cannot conclude that the assumptions hold true!
Fundamental Principles of Genetic Variation in Pops
Frequency of Alleles, Genotypes and Phenotypes
At Hardy-Weinberg equilibrium when is the frequency of
heterozygotes greatest?
Fundamental Principles of Genetic Variation in Pops
Frequency of Alleles, Genotypes and Phenotypes
At Hardy-Weinberg equilibrium, the
frequency of heterozygotes is greatest
when alleles have equal frequency
When an allele is rare almost all its
carriers are heterozygous:
A rare recessive allele may not be
detected: populations can carry
concealed genetic variation
Fundamental Principles of Genetic Variation in Pops
Inbreeding
INBREEDING is a form on non-random mating that occurs when the gene
copies in uniting gametes are more likely to be identical by descent than if
they joined at random
IDENTICAL BY DESCENT Gene copies that have descended from a common
ancestor
What is the probability that the two gene copies the offspring of a
brother and a sister are identical by descent?
Fundamental Principles of Genetic Variation in Pops
Inbreeding
INBREEDING is a form on non-random mating that occurs when the gene
copies in uniting gametes are more likely to be identical by descent than if
they joined at random
IDENTICAL BY DESCENT Gene copies that have descended from a common
ancestor
A1*A2 A1A2
A1*A1 A1*A2 A2A1
A1*A1* A1A1* A1*A2 A1A2
homozygote heterozygote
autozygous
allozygous
A2A2
AUTOZYGOUS Individuals that carry
two gene copies identical by
descent. They are necessarily
homozygous
ALLOZYGOUS Individuals that carry
two gene copies that are not
identical by descent. They might
be homozygous or heterozygous
Fundamental Principles of Genetic Variation in Pops
Inbreeding
Fundamental Principles of Genetic Variation in Pops
Inbreeding
He was born physically and mentally disabled, and disfigured. Possibly through
affliction with mandibular prognathism, he was unable to chew. His tongue was so
large that his speech could barely be understood, and he frequently drooled. It has
been suggested that he suffered from the endocrine disease acromegaly, or his
inbred lineage may have led to a combination of rare genetic disorders such as
combined pituitary hormone deficiency and distal renal tubular acidosis.
Consequently, Charles II is known in Spanish history as El Hechizado ("The
Hexed") from the popular belief that his physical and mental disabilities were
caused by "sorcery." The king went so far as to be exorcised
Fundamental Principles of Genetic Variation in Pops
Inbreeding
Fundamental Principles of Genetic Variation in Pops
Inbreeding
The inbreeding coefficient (F) is the probability that an individual taken at
random from the population will be autozygous :
• Not inbred
F=0
• Inbred
F=1
In a population in which there might be inbreeding what are the
genotype frequencies?
Fundamental Principles of Genetic Variation in Pops
Inbreeding
The inbreeding coefficient (F) is the probability that an individual taken at
random from the population will be autozygous :
• Not inbred
F=0
• Inbred
F=1
Taking into account the allozygous and autozygous fractions of the
population, the genotype frequencies are
Allozygous
Autozygous
Genotype
Frequency
A 1 A1
(1-F) p2
Fp
p2 + Fpq = D
A 1 A2
(1-F) 2pq
A 2 A2
(1-F) q2
2pq (1-F) = H
Fq
q2 + Fpq = R
The consequence of inbreeding is that the frequency of homozygotes is
higher, and the frequency of heterozygotes is lower than in a HardyWeinberg equilibrium
Fundamental Principles of Genetic Variation in Pops
Inbreeding
We can estimate the inbreeding coefficient by two measurable quantities :
• The observed frequency of heterozygotes H
• The expected frequency of heterozygotes H0
If p=0.4, q=0.6 and the observed frequency of heterozygotes is 0.24
What is the inbreeding coefficient in this population?
Fundamental Principles of Genetic Variation in Pops
Inbreeding
We can estimate the inbreeding coefficient by two measurable quantities :
• The observed frequency of heterozygotes H
• The expected frequency of heterozygotes 2pq
Example: p=0.4, q=0.6, H=0.24, F?
Fundamental Principles of Genetic Variation in Pops
Inbreeding
If consanguineous mating is a consistent feature of a population, F will
increase over generations at a rate that depends on how closely related
the average pair of mates is
The most extensive form of inbreeding, self-fertilization or selfing, occurs
in many species of plants and a few animals
Genotype frequencies
observed at two loci of
wild Oat (Avena fatua)
Genetic Variation in Natural Populations
Polymorphism
GENETIC POLYMORPHISM is the presence in a population of two or
more variants (alleles or haplotypes)
MONOMORPHIC character is a character that is not polymorphic
Genetic Variation in Natural Populations
Genetic Variation in Viability
RECESSIVE LETHAL ALLELE Allele that causes death before the
carrier reaches the adult stage
Frequency distribution of
relative viabilities of
chromosomes extracted
from a wild population of D.
pseudoobscura
Greater viability of
heterozygotes
Presence of recessive
deleterious alleles
The average person carries heterozygously the equivalent of 3-5
recessive lethal alleles acting between late fetal and early adult stages
Disease and Variation
Genetic Variation in Natural Populations
Inbreeding Depression
Because populations of humans and other diploid species harbor
recessive alleles that have deleterious effects, and because inbreeding
increases the proportion of homozygotes, populations in which many
matings are consanguineous often manifest a decline in components of
fitness, such as survival and fecundity. Such a decline is called
INBREEDING DEPRESSION
Marriages 19031907 in Italian
populations
Genetic Variation in Natural Populations
Inbreeding Depression
Small Swedish population of adders. Population decline due to inbreeding followed by
increase due to introduction of new individuals
Genetic Variation in Natural Populations
Variation in Proteins
Evolution would be very slow if populations were genetically uniform, and
if only occasional mutations arose and replaced pre-existing genotypes. In
order to know what the potential is for rapid evolutionary change, it would
be useful to know how much genetic variation natural population contain
Lewontin and Hubby
How much variation?
Genetic Variation in Natural Populations
Variation in Proteins
Drosophila
Humans
H=0.12
H=0.07
Humans between 1400 and 1750 (from estimates of 20 to 25 thousand
genes) polymorphic loci
Considering 2 alleles per locus this yields 31400 to 31750 different genotypes
Populations are far more genetically diverse than almost anyone imagined
What are the factors responsible for such variation?
Genetic Variation in Natural Populations
Multiple Loci and the Effects of Linkage
Each gene is LINKED to certain other
genes, meaning that they are
physically associated on the same
chromosome
This linkage is important because
under some circumstances changes
in allele frequencies at one locus
cause correlated changes at other
loci with which that locus is linked
LINKAGE DISEQUILIBRIUM is the nonrandom association of alleles at two
or more loci, not necessarily on the
same chromosome
Genetic Variation in Natural Populations
Multiple Loci and the Effects of Linkage
Recombination during meiosis
reduces the level of linkage
disequilibrium and brings the loci
toward linkage equilibrium
A1B1/A1B1
pA2pB2
Whether loci are in linkage equilibrium or disequilibrium, the genotype
frequencies at each locus conform to H-W frequencies
Genetic Variation in Natural Populations
Multiple Loci and the Effects of Linkage
Mating
Prob
Egg x Spe
Offspring Genotype
A1 B 1
A1 B 2
A2B 1
A2 A2
A1 B 1 x
A1 B 1
x1 2
1
0
0
0
A1 B 1 x
A1 B 2
2x1x2
½
½
0
0
A1 B 1 x
A2 B 1
2x1x3
½
0
½
0
½(1r)
½r
½r
½(1-r)
A1B1 x A2B2 2x1x4
A1 B 2 x
A1 B 2
x2 2
0
1
0
0
A1 B 2 x
A2 B 1
2x2x3
½r
½(1r)
½(1r)
½r
AB x
2x x
0
½
0
½
2
0
0
1
0
1 2
2 4
x1’=x
-r(x
x
-x
x3)
1
1
4
2
AB
2 2
A B xA B
x
Genetic Variation in Natural Populations
Multiple Loci and the Effects of Linkage
Linkage disequilibrium: Interpretation
x1-pA1pB1=D
Linkage disequilibrium: Decay
D’=x1’x4’-x2’x3’
x1’=x1-rD
x2’=x2+rD
x3’=x3+rD
x4’=x4-rD
D’=(1-r)D
Dt=(1-r)tD0
Genetic Variation in Natural Populations
Multiple Loci and the Effects of Linkage
Linkage disequilibrium is common in:
• Asexual populations
• Very close molecular markers
Linkage disequilibrium mapping
In panmictic sexually reproducing
populations is rare
Length of stamens and style in the
European primrose
Genetic Variation in Natural Populations
Variation in Quantitative Traits
SOURCES OF VARIATION
Discrete genetic polymorphisms in phenotypic traits are much less
common than slight differences among individuals
Quantitative/Continuous/Metric variation often fits a normal distribution
The genetic component of such variation is often polygenic: due to
variation at several or many loci each of which contributes to the variation
in phenotype
Genetic Variation in Natural Populations
Variation in Quantitative Traits
Quantitative characters often vary both because of genes and because of
nongenetic environmental factors
The relative amounts of genetic and environmental variation can differ
with different circumstances even in the same population.
Phenotype (P)= Genotype (G) + Environment (E)
Genetic Variation in Natural Populations
Variation in Quantitative Traits
ESTIMATING COMPONENTS OF VARIATION
The description and analysis of quantitative variation are based on
statistical measures because the loci that contribute to quantitative
variation generally cannot be singled out for study
VARIANCE
V
Quantifies the spread of individual values around the
mean value
1
2


n
X

x
 i i
n 1
Xi
ni
Characteristic of an individual
Number of individuals
Standard Deviation
s V
Genetic Variation in Natural Populations
Variation in Quantitative Traits
Var[P]= Var[G]+Var[E]+2 Cov[G,E]
Assuming
Cov[G,E]=0
Dividing by Var[P]
1=Var[G]/Var[P]+Var[E]/Var[P]+2 Cov[G,E]/Var[P]
Genetic Variation in Natural Populations
Variation in Quantitative Traits
In simple cases the variance in a phenotypic character VP is the sum of
genetic variance VG and environmental variance VE
VP = VG + VE
VG Amount of variation among the averages of the different
genotypes
VE Average amount of variation among individuals with the same
genotype
HERITABILITY
Proportion of phenotypic variance that is genetic variance
VG
h 
VG  VE
2
Genetic Variation in Natural Populations
Variation in Quantitative Traits
One way of estimating h2 is as the regression coefficient of offspring mean
on the mean of the two parents
Genetic Variation in Natural Populations
Phenotypic variation has a genetic component and an environmental
component
In an ideal population where natural selection is not acting Population is in
Hardy Weinberg equilibrium after one generation
Reductions in variation:
Inbreeding: increases homozygosity
Reduced recombination: generates linkage disequilibrium
Heritability explains the fraction of the variation that can be explained by
genetic factors