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Broad-Sense Heritability Index
The heritability index estimates that part of variation
due to all genetic influences, which is calculated as
H2 = VG/VP
Again, a heritability index close to 1.0 indicates that
a large portion of the variation is due to genetic
Narrow-Sense Heritability
Heritability and the heritability index is most useful
as an estimate of the predicted response to
selection. In order to make this estimate, VG must
be subdivided to separate the effects of additive
variance and dominance variance.
VG= VA + VD (+ VI)
(The interaction between the two is usually
negligible and can be dropped from the equation)
Narrow-Sense Heritability
VA is that portion of the variance due to the average
effect of additive components of genes.
VD is the portion of variance that results when
expression in heterozygotes is not precisely
intermediate between that of homozygotes.
h2 = VA/VP
Putting It All Together
Remember, heritability is due to the effects of
environment and genetics. Having partitioned the
effects of genetics into additive and dominance
effects, we can put the equations together.
VP = VE + VG and
V G = V A + VD
h2 =
Based on our knowledge of parental phenotypes, a
value closer to 1.0 indicates a greater response to
Twin Studies
How are heritability estimates created in humans?
Study of identical (monozygotic) twins allows
researchers to infer genetic and environmental
effects. (Characteristics that remain similar are
presumed to have a strong genetic component)
Data can then be compared to fraternal (dizygotic)
Concordance values of phenotypic expression can also be
used to make estimates.
Twins are concordant for a trait if both express it or
neither express it (i.e. are the same)
Twins are discordant if one expresses it and the other does
Concordance values for identical vs fraternal twins reared
together then allows calculation of a heritability estimate.
Concordance Estimates—Caveats
Concordance estimates must be evaluated carefully
to ensure that environmental effects are not in fact
responsible for phenotypes observed.
Concordance values are most useful when used to
identify differences between identical and fraternal
Generally, a greater difference between monozygotic
and dizygotic twins indicates a higher genetic
component controlling the phenotype.
Quantitative Trait Mapping
Because most quantitative traits are controlled by multiple
genes, researchers are interested in identifying where
genes are located in the genome.
Are they on the same chromosome?
If so, how closely are they linked?
Genes controlling a quantitative trait that are on the same
chromosome are called quantitative trait loci
QTL are mapped relative to markers, or other known genes
with known inheritance patterns.
Population Genetics
Basic observations by geneticists (Wallace, Darwin
and Mendel)
1. Phenotypic variations exist among individuals
within populations
2. These differences are passed on from parents to
3. More offspring are born than will survive to
4. Some variants are more successful at surviving
and reproducing than others.
Population Genetics
In populations where all four factors are in effect, the
frequency of different phenotypes will change across
Changes in abundance of particular phenotypes in a
population is tied to changes in abundance of the alleles
that control the phenotype.
Population Genetics is that portion of genetic research
dedicated to study of changes in allele frequency.
Forces that Alter Gene Frequencies
Selection—Both natural and artificial
Random genetic drift
Population: a group of individuals from the same
species, living in the same geographic area and that can
Gene pool: All gametes made by all the breeding
members of a population in a single generation. (These
gametes will combine to form zygotes that become the
next generation) Remember, each gamete is haploid and
only contains one allele for each locus, and different
gametes carry different alleles.
3. Allele frequency: The proportion of gametes in the
gene pool that carries a particular allele.
Populations are dynamic; they change over
generations such that over time, the gene pool can
Calculating Allele Frequency
Genotypes may be inferred from phenotypes
Protein or DNA sequences are analyzed
Different protein forms (e.g. ABO blood type)
Different size mRNA transcripts (splice variants)
Small differences in DNA sequences that produce
different size fragments when digested by enzymes
(RFLP or restriction fragment length polymorphism)
Single nucleotide differences (SNP or single
nucleotide polymorphisms)
Calculate Allele Frequency
Populations are tested to determine the genotypes.
When all the allele frequencies are added together
and the total equals 1.0, then all possible alleles
(for a given population) have been accounted for.
The Hardy-Weinberg Law
We are interested in determining or predicting
changes in allele frequencies.
The Hardy-Weinberg law is a mathematical model
that shows what happens to alleles and genotypes
in an ideal population (free of the complications
that actually affect real populations).
The Hardy-Weinberg law has a set of assumptions
that must be kept in mind.
Hardy-Weinberg Assumptions
Individuals of all genotypes are equal in capacity to
survive and reproduce (no selection).
No new alleles are created or converted from one to
another (no mutation).
Individuals do not migrate out or into a population
The population is infinitely large such that sampling
errors and random effects are negligible
Individuals in a population mate randomly.
Properties of an “Ideal” H-W
The frequency of alleles does not change from
generation to generation
After one generation of random mating, offspring
genotype frequencies can be predicted from the
parent allele frequencies (and would be expected
to remain constant from that point)
Uses of H-W Assumptions and the
“Ideal” Population
By identifying and specifying the assumptions under
which a population cannot evolve, the H-W law
identifies the forces at work in the real world that
cause allele frequencies to change.
In other words, the H-W law holds some forces
constant in order to identify and quantify other
Putting H-W to Work: An Example
Consider the A locus, which has two alleles, A and a.
The frequency of A is 0.7 and a is 0.3 in both eggs
and sperm.
0.7 + 0.3 = 1.0, indicating all alleles are accounted
Given the assumption that all individuals mate
randomly, gametes are paired to make zygotes to
create the next generation.
The A Locus
For any one zygote, the probability of the AA genotype (both
egg and sperm donate A):
0.7 x 0.7 = 0.49
The probability of A from sperm and a from egg:
0.7 x 0.3 = 0.21
The probability of A from egg and a from sperm:
0.7 x 0.3 = 0.21
Overall, probability of the Aa genotype: 0.21 + 0.21 = 0.42
The A locus, continued
Probability of the aa genotype (both egg and sperm
donate a): 0.3 x 0.3 = 0.09
Added together, all probabilities add up to 1.0:
0.49 + 0.42 + 0.09 = 1.0
(All possible zygotes have been accounted for)
What Happens in the Next
Our zygotes are 49% AA, 42% Aa, and 9% aa.
Remember, we assume all genotypes have an equal
chance of surviving and reproducing. What will
happen in the next generation?
AA individuals are 49% of the population and the
gametes they produce will constitute 49% of the
gene pool, all containing the allele A.
Frequency from homozygote = 0.49
The Next Generation, continued
Likewise, the Aa individuals are 42% of the
population, half (0.5) of which will contribute the
A allele
Frequency from heterozygotes = (0.5)0.42
The frequency of A is therefore
0.49 + (0.5)0.42 = 0.7
The Next Generation, Continued
What about the frequency of the a allele?
9% were aa and will donate only the a allele
42% were Aa, half of which will donate the a allele
Frequency of a = 0.09 + (0.5)0.42 = 0.3
So, after just one generation, genotype frequencies can be
predicted. (The population does not evolve)
The Hardy-Weinberg Law
The example just used illustrates the law in general.
The H-W law uses variables instead of numerical
values for the allele frequencies: p and q
The frequency of A = p and the frequency of a = q
such that p + q = 1.0
The Hardy-Weinberg Law
If we randomly draw a sperm and an egg from the
gene pool, then pair them to make a zygote, the
probability that both sperm and egg will carry the
A allele = p x p, or p2.
The Hardy-Weinberg Law
Next, the probability that the egg carries A and the
sperm carries a = p x q,
and that the sperm carries A and the egg carries a
Thus, the frequency of the Aa genotype is 2pq.
The Hardy-Weinberg Law
Lastly, the frequency at which both sperm and egg
will carry the a allele is q x q, or q2.
In total, the distribution of genotypes among the
zygotes is
p2 + 2pq + q2 = 1.0
The Hardy-Weinberg Law
The Hardy-Weinberg law works for any frequencies
of A and a, provided
1. The frequencies add up to 1.0 and
2. The five H-W assumptions are invoked.
A population in which the allele frequencies remain
constant from generation to generation and in
which the genotype frequencies can be predicted
from allele frequencies is said to be in Hardy-
Weinberg equilibrium for that locus.
Implications of the Hardy-Weinberg
Dominant traits do not necessarily increase in
frequency from one generation to the next.
Genetic variability can be maintained in a
population since, once established, allele
frequencies can remain unchanged.
If the H-W assumptions are invoked, knowing
the frequency of only one genotype allows
calculation of all other genotypes.
Implications, continued
For example, by knowing the frequency of
homozygous recessive individuals allows
calculation of heterozygous carriers for the
condition caused by the homozygous recessive
Implications, continued
The Hardy-Weinberg Law is the foundation upon
which the entire study of population genetics is
By demonstrating loci within populations that do not
evolve, we can use the H-W law to identify forces
that cause populations to evolve by examining loci
that do show changes in allele frequencies over
Implications, continued
In other words, when the assumptions of the HardyWeinberg Law are broken, allele frequencies
change over the generations.
Therefore, the forces that are held constant in HardyWeinberg ideal populations are the very forces that
cause genetic change.
Implications, continued
For example, non-random mating does not in and of
itself change alter allele frequencies, but by
altering genotype frequencies, it indirectly affects
the course of evolution.
The Hardy-Weinberg Law tells geneticists where to
look to find sources driving evolution in