If we mate two individuals that are heterozygous (e.g., Bb) for a trait, we find that
25% of their offspring are homozygous for the dominant allele (BB)
50% are heterozygous like their parents (Bb) and
25% are homozygous for the recessive allele (bb) and thus, unlike their parents, express the

recessive phenotype.
This is what Mendel found when he crossed monohybrids [Link]. It occurs because
Meiosis separates the two alleles of each heterozygous parent so that 50% of the gametes

will carry one allele and 50% the other.
When the gametes are brought together at random, each B (or -carrying egg will have a 1 in 2

probability of being fertilized by a sperm carrying B (or . (Left table)
Results of random union of the two gametes produced by two individuals, each heterozygous

for a given trait. As a result of meiosis, half the gametes produced by each parent with

carry allele B; the other half allele b. Results of random union of the gametes produced by

an entire population with a gene pool containing 80% B and 20% b.
0.5 B 0.5 b 0.8 B 0.2 b
0.5 B 0.25 BB 0.25 Bb 0.8 B 0.64 BB 0.16 Bb
0.5 b 0.25 Bb 0.25 bb 0.2 b 0.16 Bb 0.04 bb

But the frequency of two alleles in an entire population of organisms is unlikely to be

exactly the same. Let us take as a hypothetical case, a population of hamsters in which
80% of all the gametes in the population carry a dominant allele for black coat ( and
20% carry the recessive allele for gray coat (.
Random union of these gametes (right table) will produce a generation:
64% homozygous for BB (0.8 x 0.8 = 0.64)
32% Bb heterozygotes (0.8 x 0.2 x 2 = 0.32)
4% homozygous (bb) for gray coat (0.2 x 0.2 = 0.04)
So 96% of this generation will have black coats; only 4% gray coats.
Will gray coated hamsters eventually disappear?

No. Let's see why not.
All the gametes formed by BB hamsters will contain allele B as will
one-half the gametes formed by heterozygous (Bb) hamsters.
So, 80% (0.64 + .5*0.32) of the pool of gametes formed by this generation with contain B.
All the gametes of the gray (bb) hamsters (4%) will contain b but
one-half of the gametes of the heterozygous hamsters will as well.
So 20% (0.04 + .5*0.32) of the gametes will contain b.
So we have duplicated the initial situation exactly. The proportion of allele b in the

population has remained the same. The heterozygous hamsters ensure that each generation will

contain 4% gray hamsters.

Now let us look at an algebraic analysis of the same problem using the expansion of the

binomial (p+q)2.
(p+q)2 = p2 + 2pq + q2
The total number of genes in a population is its gene pool.
Let p represent the frequency of one gene in the pool and q the frequency of its single

allele.
So, p + q = 1
p2 = the fraction of the population homozygous for p
q2 = the fraction homozygous for q
2pq = the fraction of heterozygotes
In our example, p = 0.8, q = 0.2, and thus
(0.8 + 0.2)2 = (0.8)2 + 2(0.8)(0.2) + (0.2)2 = 064 + 0.32 + 0.04
The algebraic method enables us to work backward as well as forward. In fact, because we

chose to make B fully dominant, the only way that the frequency of B and b in the gene pool

could be known is by determining the frequency of the recessive phenotype (gray) and

computing from it the value of q.

q2 = 0.04, so q = 0.2, the frequency of the b allele in the gene pool. Since p + q = 1, p =

0.8 and allele B makes up 80% of the gene pool. Because B is completely dominant over b, we

cannot distinguish the Bb hamsters from the BB ones by their phenotype. But substituting in

the middle term (2pq) of the expansion gives the percentage of heterozygous hamsters. 2pq =

(2)(0.8)(0.2) = 0.32

So, recessive genes do not tend to be lost from a population no matter how small their

representation.

So long as certain conditions are met (to be discussed next),
gene frequencies and genotype ratios in a randomly-breeding population remain constant from

generation to generation.
This is known as the Hardy-Weinberg law in honor of the two men who first realized the

significance of the binomial expansion to population genetics and hence to evolution.

Evolution involves changes in the gene pool. A population in Hardy-Weinberg equilibrium

shows no change. What the law tells us is that populations are able to maintain a reservoir

of variability so that if future conditions require it, the gene pool can change. If

recessive alleles were continually tending to disappear, the population would soon become

homozygous. Under Hardy-Weinberg conditions, genes that have no present selective value will

nonetheless be retained.
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.

Link to Mutations
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.

It is simply gene migration between species rather than within them.

In either case, gene immigration increases the variability of the gene pool.

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.

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.

Nonrandom mating seems to be quite common. Breeding territories, courtship displays,

"pecking orders" can all lead to it. In each case certain individuals do not get to make

their proportionate contribution to the next generation.

Assortative mating
Humans seldom mate at random preferring phenotypes like themselves (e.g., size, age,

ethnicity). This is called assortative mating.

Marriage between close relatives is a special case of assortative mating. The closer the

kinship, the more alleles shared and the greater the degree of inbreeding. Inbreeding can

alter the gene pool. This is because it predisposes to homozygosity. Potentially harmful

recessive alleles - invisible in the parents - become exposed to the forces of natural

selection in the children.
It turns out that many species - plants as well as animals - have mechanisms be which they

avoid inbreeding. Examples:

Link to discussion of self-incompatibiity in plants.
Male mice use olfactory cues to discriminate against close relatives when selecting mates.

The preference is learned in infancy - an example of imprinting. The distinguishing odors

are
controlled by the MHC alleles of the mice;
detected by the vomeronasal organ (VNO).
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. Link

to an example of powerful mortality selection in a human population causing a marked

deviation from Hardy-Weinberg equilibrium.

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.

Calculating the Effect of Natural Selection on Gene Frequencies.
The effect of natural selection on gene frequencies can be quantified. Let us assume a

population containing
36% homozygous dominants (AA)
48% heterozygotes (Aa) and
16% homozygous recessives (aa)
The gene frequencies in this population are
p = 0.6 and q = 0.4
The heterozygotes are just as successful at reproducing themselves as the homozygous

dominants, but the homozygous recessives are only 80% as successful. That is, for every 100

AA (or aa) individuals that reproduce successfully only 80 of the aa individuals succeed in

doing so. The fitness (w) of the recessive phenotype is thus 80% or 0.8.
Their relative disadvantage can also be expressed as a selection coefficient, s, where

s = 1 − w
In this case, s = 1 − 0.8 = 0.2.
The change in frequency of the dominant allele (Äp) after one generation is expressed by the

equation

s p0 q02
Äp = __________
1 - s q02

where p0 and q0 are the initial frequencies of the dominant and recessive alleles

respectively. Substituting, we get

(0.2)(0.6)(0.4)2 0.019
Äp = ________________ = ______ = 0.02
1 − (0.2)(0.4)2 0.968
So, in one generation, the frequency of allele A rises from its initial value of 0.6 to 0.62

and that of allele a declines from 0.4 to 0.38 (q = 1 − p).
The new equilibrium produces a population of

38.4% homozygous dominants (an increase of 2.4%) (p2 = 0.384)
47.1% heterozygotes (a decline of 0.9%)(2pq = 0.471) and
14.4% homozygous recessives (a decline of 1.6%)(q2 = 0.144)
If the fitness of the homozygous recessives continues unchanged, the calculations can be

reiterated for any number of generations. If you do so, you will find that although the

frequency of the recessive genotype declines, the rate at which a is removed from the gene

pool declines; that is, the process becomes less efficient at purging allele a. This is

because when present in the heterozygote, a is protected from the effects of selection.

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