variation lecture 4-5. phenotype characteristic in an individual organism or group of individuals...

VariationLecture 4-5

PhenotypeCharacteristic in an individual organism or group of individuals that are alikeLevel 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


GenotypeGenetic 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


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)



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 determinationTemporary 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


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 influencesAmount 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

• 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

Lecture Ideas

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 FREQUENCYProportion of a population that has a certain allele

GENOTYPE FREQUENCYProportion of a population that has a certain genotype

In sexually reproducing populations, the alleles, carried in eggs and sperm, become combined into homozygous and heterozygous genotypes

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

Fundamental Principles of Genetic Variation in PopsFrequencies 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?


Consider N, alleles A1 and A2, genotypes A1 A1, A1A2, A2A1, and A2A2

Allele

A1 p=D+H/2 0.6A2 q=R+H/2 0.4

Genotype

1000 N=1000

400 A1 A1 D 0.4400 A1A2 H 0.4200 A2A2 R 0.2

The parental genotype and allele frequencies are


Assume genotype equally represented in females and males and random mating

What is the frequency of each genotype among the offspring generation ?

If the previous is the parental population


Assume genotype equally represented in females and males and random mating

Mating Prob Mating Offspring Genotype

Fem x Mal A1A1 A1A2 A2A2

A1A1 x A1A1 D2 1 0 0

A1A1 x A1A2 2DH ½ ½ 0

A1A1 x A2A2 2DR 0 1 0

A1A2 x A1A2 H2 ¼ ½ ¼

A1A2 x A2A2 2HR 0 ½ ½

A2A2 x A2A2 R2 0 0 1The frequency of each genotype among the offspring is:

A1A1 D2 + ½2DH + ¼H2 = (D+H/2)2 = p2

A1A2 ½2DH + 2DR + ½H2 + ½2HR = 2[(D+H/2)+(H/2+R)] = 2pqA2A2 ¼H2 + ½2HR + R2 = (R+H/2)2 = q2


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 ?


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 = pA2 ½2pq + q2 = q

The allele frequencies do not change from one generation to the next


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?


The offspring genotype and allele frequencies are

Allele

A1 p 0.6A2 q 0.4

Genotype

A1 A1 p2 0.36A1A2 2pq 0.48A2A2 q2 0.16

The allele frequencies have not changed from one generation to the next , although the alleles have become distributed among the three genotypes


When the genotypes at a locus have the frequencies predicted by the Hardy-Weinberg principle the locus is said to be in HARDY-WEINBERG EQUILIBRIUM

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

Example: Human MN LocusTwo alleles M, N. Sample 320. MM 187, MN 114, NN 19Frequency of each genotype? Allele frequencies? Expected vs observed number of individuals?

Fundamental Principles of Genetic Variation in PopsThe 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. Infinite population (random genetic drift)2. Random mating3. No migration4. No mutation5. 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 PopsFrequency of Alleles, Genotypes and Phenotypes

At Hardy-Weinberg equilibrium when is the frequency of heterozygotes greatest?

Fundamental Principles of Genetic Variation in PopsFrequency 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 PopsInbreeding

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?


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

A1*A1

* A1*A2A1A1

* A1A2

autozygous allozygous

homozygote heterozygote

A1A2

A1*A2A1

*A1 A2A2A2A1

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

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



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?


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

A1A1 (1-F) p2 F p p2 + Fpq = D

A1A2 (1-F) 2pq 2pq (1-F) = H

A2A2 (1-F) q2 F q 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 Hardy-Weinberg equilibrium


We can estimate the inbreeding coefficient by two measurable quantities :

• The observed frequency of heterozygotes H• The expected frequency of heterozygotes H0

What is the inbreeding coefficient in this population?

If p=0.4, q=0.6 and the observed frequency of heterozygotes is 0.24


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?


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 PopulationsPolymorphism

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 PopulationsGenetic 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 PopulationsInbreeding 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 1903-1907 in Italian populations

Genetic Variation in Natural PopulationsInbreeding Depression

Small Swedish population of adders. Population decline due to inbreeding followed by increase due to introduction of new individuals

Genetic Variation in Natural PopulationsVariation 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

How much variation?

Lewontin and Hubby

Genetic Variation in Natural PopulationsVariation in Proteins

Drosophila H=0.12Humans 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 PopulationsMultiple 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 non-random association of alleles at two or more loci, not necessarily on the same chromosome

Recombination during meiosis reduces the level of linkage disequilibrium and brings the loci toward linkage equilibrium


A1B1/A1B1 pA2pB

2

Whether loci are in linkage equilibrium or disequilibrium, the genotype frequencies at each locus conform to H-W frequencies

Mating Prob Offspring Genotype

Egg x Spe A1B1 A1B2 A2B1 A2A2

A1B1 x A1B1 x12 1 0 0 0

A1B1 x A1B2 2x1x2 ½ ½ 0 0

A1B1 x A2B1 2x1x3 ½ 0 ½ 0

A1B1 x A2B2 2x1x4 ½(1-r) ½r ½r ½(1-r)

A1B2 x A1B2 x22 0 1 0 0

A1B2 x A2B1 2x2x3 ½r ½(1-r) ½(1-r) ½r

A1B2 x A2B2 2x2x4 0 ½ 0 ½

A2B1 x A2B1 x32 0 0 1 0

A2B1 x A2B2 2x3x1 0 0 ½ ½

A2B2 x A2B2 x42 0 0 0 1


x1’=x1-r(x1x4-x2x3)


Linkage disequilibrium: Interpretationx1-pA1pB1=D

Linkage disequilibrium: DecayD’=x1’x4’-x2’x3’

x1’=x1-rDx2’=x2+rDx3’=x3+rDx4’=x4-rD

D’=(1-r)DDt=(1-r)tD0


Linkage disequilibrium is common in:

• Asexual populations

• Very close molecular markersLinkage disequilibrium mapping

In panmictic sexually reproducing populations is rare

Length of stamens and style in the European primrose

Genetic Variation in Natural PopulationsVariation 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


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)


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 Quantifies the spread of individual values around the mean value

Xi Characteristic of an individualni Number of individuals

21

1

xXnn

V ii

Vs

Standard Deviation


Var[P]= Var[G]+Var[E]+2 Cov[G,E]

AssumingCov[G,E]=0

Dividing by Var[P]1=Var[G]/Var[P]+Var[E]/Var[P]+2 Cov[G,E]/Var[P]

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


EG

G

VV

Vh

2


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

variation lecture 4-5. phenotype characteristic in an individual organism or group of individuals...

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