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Genetic Terms
 Gene - a unit of inheritance that usually is directly
responsible for one trait or character.
 Allele - an alternate form of a gene. Usually there
are two alleles for every gene, sometimes as many a
three or four.
 Homozygous - when the two alleles are the same.
 Heterozygous - when the two alleles are different,
in such cases the dominant allele is expressed.
Genetic Terms
 Dominant - a term applied to the trait (allele) that is
expressed irregardless of the second allele.
 Recessive - a term applied to a trait that is only
expressed when the second allele is the same (e.g.
short plants are homozygous for the recessive
allele).
 Phenotype - the physical expression of the allelic
composition for the trait under study.
 Genotype - the allelic composition of an organism.
 Punnett squares - probability diagram illustrating
the possible offspring of a mating.
Genetic Code
Example of Pedigree
A1/A1
Male
A2/A2
Female
A1/A2
A1/A2
A2/A2
A2/A2
A1/A2
A2/A2
Two alleles model
 Let us assume a gene containing two mutually
exclusive alleles:A1,A2.
 There are three possible
combinations:A1/A1,A1/A2 and A2/A2, with initial
frequencies: u,v and w.
 u+v+w=1
 Let us compute their density after one division
First generation
Mating type
Offsprings
frequency
A1/A1xA1/A2 0.5A1/A1+ 0.5A1/A2
2uv
A1/A1xA2/A2 A1/A2
2uw
A1/A1xA1/A1 A1/A1
U2
A1/A2xA1/A2 0.25A1/A1+0.5A1/A2
+0.25A2/A2
A1/A2xA2/A2 0.5A1/A2+0.5A2/A2
V2
A2/A2xA2/A2 A2/A2
w2
2vw
In the next generation
 Hardy-Weinberg Equilibrium
 A1/A1=u2+uw+0.25v2=(u+0.5v)2=p12
 A2/A1=uv+2uw+0.5v2+vw=2(u+0.5v)(w+0.
5v)=2p1p2
 A2/A2=0.25v2+vw+w2=(w+0.5v)2=p22
Third generation
Mating type
A1/A1xA1/A2
A1/A1xA2/A2
A1/A1xA1/A1
A1/A2xA1/A2
Offsprings
0.5A1/A1+ 0.5A1/A2
A1/A2
A1/A1
0.25A1/A1+0.5A1/A2
+0.25A2/A2
A1/A2xA2/A2 0.5A1/A2+0.5A2/A2
A2/A2xA2/A2 A2/A2
frequency
2p13p2
p12p22
p 14
4p12p22
2p1p23
p 24
X linked loci
If an allele is present in the X chromosome, the
situation is more complicated.
If qn is the allele frequency in women in the
generation n, and rn the allele frequency in mens.
Rn=qn-1
Qn=0.5qn-1+0.5rn-1
2/3qn+1/3rn=2/3(0.5qn-1+0.5rn-1)+1/3qn-1
=2/3qn-1+1/3rn-1=p
Qn-p=-0.5(qn-1-p)
Dynamics to equilibrium
When the Hardy-Weinberg Law
Fails to Apply
 To see what forces lead to evolutionary change, we
must examine the circumstances in which the
Hardy-Weinberg law may fail to apply. There are
five:
 mutation
 gene migration
 genetic drift
 nonrandom mating
 natural selection
Mutation
 The frequency of gene B and its allele b will not
remain in Hardy-Weinberg equilibrium if the rate of
mutation of B -> b (or vice versa) changes.
 By itself, mutation probably plays only a minor role
in evolution; the rates are simply too low. But
evolution absolutely depends on mutations because
this is the only way that new alleles are created.
After being shuffled in various combinations with
the rest of the gene pool, these provide the raw
material on which natural selection can act.
Gene Migration
 Many species are made up of local populations whose members
tend to breed within the group. Each local population can develop
a gene pool distinct from that of other local populations.
 However, members of one population may breed with occasional
immigrants from an adjacent population of the same species. This
can introduce new genes or alter existing gene frequencies in the
residents. In many plants and some animals, gene migration can
occur not only between subpopulations of the same species but
also between different (but still related) species. This is called
hybridization. If the hybrids later breed with one of the parental
types, new genes are passed into the gene pool of that parent
population. This process, is called introgression.
Genetic Drift
 As we have seen, interbreeding often is limited to
the members of local populations. If the population
is small, hardy-Weinberg may be violated. Chance
alone may eliminate certain members out of
proportion to their numbers in the population. In
such cases, the frequency of an allele may begin to
drift toward higher or lower values. Ultimately, the
allele may represent 100% of the gene pool or, just
as likely, disappear from it. Drift produces
evolutionary change, but there is no guarantee that
the new population will be more fit than the original
one. Evolution by drift is aimless, not adaptive.
Rate of Genetic Drift
Nonrandom Mating
 One of the cornerstones of the Hardy-Weinberg
equilibrium is that mating in the population must be
random. If individuals (usually females) are choosy
in their selection of mates the gene frequencies may
become altered. Darwin called this sexual
selection.
 Assortative mating -Humans seldom mate at
random preferring phenotypes like themselves (e.g.,
size, age, ethnicity). This is called assortative
mating.
Natural Selection
 If individuals having certain genes are better able to
produce mature offspring than those without them,
the frequency of those genes will increase. This is
simple expressing Darwin's natural selection in
terms of alterations in the gene pool. (Darwin knew
nothing of genes.) Natural selection results from
 differential mortality and/or
 differential fecundity.
Mortality Selection
 Certain genotypes are less successful than others in
surviving through to the end of their reproductive
period.
 The evolutionary impact of mortality selection can
be felt anytime from the formation of a new zygote
to the end (if there is one) of the organism's period
of fertility. Mortality selection is simply another
way of describing Darwin's criteria of fitness:
survival.
Fecundity Selection
 Certain phenotypes (thus genotypes) may make a
disproportionate contribution to the gene pool of the
next generation by producing a disproportionate
number of young. Such fecundity selection is
another way of describing another criterion of
fitness described by Darwin: family size. In each of
these examples of natural selection certain
phenotypes are better able than others to contribute
their genes to the next generation. Thus, by
Darwin's standards, they are more fit. The outcome
is a gradual change in the gene frequencies in that
population.
Effect of Natural Selection on
Gene Frequencies.
 Let us define the frequency of each genotype
in the population as: w, and the initial allele
distribution as p and q for A1 and A2.
 wA1/A1=1-r
 wA1/A2=1
 wA2/A2=1-s
Fitness
The average fitness is:
W=(1-r)p2+2pq+(1-s)q2=1-rp2-sq2
DP=([(1-r)p2+pq]/W)-p=pq[s-(r+s)p]/W
0,1


[ p, q ]  
1,0
s /( r  s), r /( r  s)

Hetrozygote Advantage
Pn+1-(s/(r+s))=[(1-r)pn2+pnq]/W -(s/(r+s))
=[(1-r)pn2+pnq]-(s/(r+s))W]/W=
=[(1-r)pn2+pnq]-(s/(r+s)) (1-rpn2-sqn2)]/W
= (1-rpn-sqn)/W[pn-(s/(r+s)]
The difference decreases to zero only for
positive r and s. Thus the scenario in which
both alleles can survive is Hetrozygote
Advantage
Recessive diseases
If r>0, and s=0, the disadvantage appears only
homozygotic A1.
In this case: pn+1=pn(1-rpn)/(1-rpn2)
1/pn+1-1/pn=1/pn[(1-rpn2)/(1-rpn)-1]=
[r(1-pn2)/(1-rpn)]
1/pn-1/p0=nr
Fitness Summary
 Third fix point is in the range [0,1] only if r
and s have the same sign.
 It is stable only of both r and s are positive
 In all other cases one allele is extinct.
 If r>0 and s=0 then the steady state is still
p=0, but is is obtained with a rate
pn=1/(nr+1/p0)
Balance between Mutation and
selection.
 Mutations can provide a balancing force to
selection.
 Let us assume a mutation rate of m from A2
to A1. The dynamics equation is:
DP=[(1-r)p2+pq]/W-p+(1-m)*q
 An equilibrium is obtained when
q=[pq+(1-s)q2]/W(1-m)1+m(1-s)/s
Summary
 In the absence of selection an allele
concentration equilibrium is obtained after
one generation.
 In the presence of selection, usually a single
allele survives.
 There are many mechanisms which can lead
to the failure of the hardy weinberg
equilibrium.