1)



When the Hardy-Weinberg Law Fails to Apply

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.

* Controversial when first proposed (Kimura 1968) , Incontrovertible in 2001:

* DNA sequence polymorphisms are abundant

* In Eukarya, most of the genome is noncoding

* most sequence polymorphism lies in noncoding regions

* Most sequence polymorphisms appear selectively neutral

[pic]

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.

Isolate communities

Worldwide, 1/3 of all marriages are between people born within 10 miles of each other

Cultures in which consanguinity is more prominent

Consanguinity is marriage between relatives e.g. second or third cousins

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.

1) 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.

[pic]

2) Fitness

The average fitness is:

[pic]

[pic]

3) Hetrozygote Advantage

[pic]

The difference decreases to zero only for positive r and s. Thus the scenario in which both alleles can survive is Hetrozygote Advantage

4) Recessive diseases

If r>0, and s=0, the disadvantage appears only homozygotic A1.

In this case:

[pic]

5) 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)

6) 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.

7) Genetic Variation

Three fundamental levels and each is a genetic resource of potential importance to conservation:

Genetic variation within individuals (heterozygosity)

Genetic differences among individuals within a population

Genetic differences among populations

Species rarely exist as panmictic population = single, randomly interbreeding population

Typically, genetic differences exist among populations—this geographic genetic differences=Crucial component of overall genetic diversity

8) heterozygosity

Several measures of heterozygosity exist. The value of these measures will range from zero (no heterozygosity) to nearly 1.0 (for a system with a large number of equally frequent alleles).  We will focus primarily on expected heterozygosity (HE, or gene diversity, D). The simplest way to calculate it for a single locus is as:

                            [pic]                                                        where pi is the frequency of the ith of k alleles

. If we want the gene diversity over several loci we need double summation and subscripting as follows

[pic]

In H.W heterozygosity is given by 2pq. The rest of the expression ([pic]) is the homozygosity.

The heterozgosity for a two-allele system is described by a concave down parabola that starts at zero (when p = 0) goes to a maximum at p = 0.5 and goes back to zero when p = 1. In fact for any multi-allelic system, heterozygosity is greatest when

p1 = p2 = p3 = ….pk                                                                    

The maximum heterozygosity for a 10-allele system comes when each allele has a frequency of 0.1 H then equals 0.9. 

9) Genetic Variation

HI, HS, HT refer to the average heterozygosity within individuals, subpopulations and the total population, respectively

HT = HP + DPT

where HT = total genetic variation (heterozygosity) in the species;

HP = average diversity within populations (average heterozygosity)

DPT = average divergence among populations across total species range

Divergence arise among populations from random processes (founder effects, genetic drift, bottlenecks, mutations) and from local selection).

Drop in heterozygosity defined as Wright’s F statistics:

[pic]

2 subpopulations of equal size, gene frequencies p1 = 0.8, p2 = 0.3.

Gene frequency in total population midway between them pt = 0.55

HS1 = 2p1q1 = 2 x 0.8 x (1-0.8) = 0.32

HS2 = 2p2q2 = 2 x 0.3 x (1-0.3) = 0.42

HS = average(HS1, HS2) = (0.32 + 0.42)/2 = 0.37

HT = 2 x 0.55 x (1 - 0.55) = 0.495

FST=(0.495-0.37)/0.495=0.252

10) Indentity

G1 and G2 are identical by descent (i.b.d) if they are physical copies of the same ancestor, or one of the other.

G1 and G2 are identical by state (i.b.s) if they represent the same allele.

The kinship between two relatives fij is the probability that random gene from autosomal loci in I and j are i.b.d.

The interbreeding coefficient is the probability that his or her two genes from autosomal loci are i.b.d

Every mutation creates a new allele

Identity in state = identity by descent (IBD)

[pic]

F=1-H (inbreeding coefficient) is probability of IBD = 1/2.

fAC is the coancestry of A with C etc., i.e. the probability of 2 gametes taken at random, 1 from A and one from C, being IBD.

The inbreeding is thus ,- fAA be the probability of 2 gametes taken at random from A being IBD.

[pic]

[pic]

Note that if mutations occurred twice indpendently

11) Back to genetic drift

Assume a population size of N, therefore 2N alleles in population. Imagine eggs and sperm released randomly into environment (e.g. sea)

What is the probability of 2 gametes drawn randomly having the same allele?

[pic]

◆ Therefore, after 1 generation the level of inbreeding is F1 = 1/2N

◆ After t generations the probability is [pic]

◆ [pic]

◆ Genetic drift will make initially identical population different

◆ Eventually, each population will be fixed for a different allele

◆ If there are very many populations, the proportion of populations fixed for each allele will correspond to the initial frequency of the allele

◆ Small populations will get different more rapidly

[pic]

◆ The effective population size is determined by

◆ Large variation in the number of offspring

◆ Overlapping generation

◆ Fluctuations in population size [pic]

◆ Unequal numbers of males and females contributing to reproduction[pic]

12) Founders effect

|Population |# of founders |# of generations |Current size |

|Costa Rica |4,000 |12 |2,500,000 |

|Finland |500 |80-100 |5,000,000 |

|Hutterites |80 |14 |36,000 |

|Japan |1,000 |80-100 |120,000,000 |

|Iceland |25,000 |40 |300,000 |

|Newfoundland |25,000 |16 |500,000 |

|Quebec |2,500 |12-16 |6,000,000 |

|Sardinia |500 |400 |1,660,000 |

13) Coalesence

◆ Simplification: 0, 1 or 2 offspring

◆ Coalesce: have the same parent

◆ Probability to coalesce: 1/N

◆ Probability Not to coalesce: 1 – 1/N

◆ t generations: (1-1/N)t

◆ Average time to coalesce for 2 genes: N

◆ For the whole population: 2N

◆

14) Genetic drift and mutation

◆ [pic]

◆ Probability of neither of 2 alleles being mutated is (1-μ)2

◆ [pic]

◆ If one also includes gene flow

◆ FT = [1/2N + (1 - 1/2N) * FT-1] * (1 – m- μ)2

15) Balance between Mutation and selection.

Mutations can provide a balancing force to selection.

Let us assume a mutation rate of μ from A2 to A1. The dynamics equation is:

[pic]

An equilibrium is obtained when

[pic]

-----------------------

A1A2

A1A2

A1A1

A1A2

A2A2

A1A1

A2 A2

alike in state (AIS)

not identical by descent

A2 A2 IBD

A2 A2 IBD

A1A2

A1A2

A؀ࠫ࠳࠴ਟਢਰ਱ഝഠഭമྉྊྐྵྼ႘႙ႰႱႲႳႴႵჅ჆ᆵᆶርሮሯሿቀዛዜᏃᏄᏕᏖᕂᕕᕖᛒᛥᛦᤏᦃ퓛퓐쓈뛈좮龍鿪���箂ﳵ矵ﳪᘆ땨癹ᔌ䕨ضᘀ䕨ضᔔ2A2

A1A2

A1A2

A2A2

A1A1

A1A2

A1A1

A1A1

A1A2

A1A1

A - B C - D

| |

P - Q

|

X

A - B

| |

P - Q

|

X

gen 1

gen 0

2N alleles

probability = 1/(2N)

(Harmonic mean)

Σ

1

Ni

1

n

=

1

Ne

4NfNm

(Nf + Nm)

Ne =

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download