population statistics Flashcards
population
gene pool
polymorphism
fixation
localised group of interbreeding individuals of the same species.
All the alleles of a gene in a population make up the gene pool
Many traits show variation in a population
If only one allele in population - called monomorphic and allele is fixed in the population.
Variation or polymorphism in traits can be examined at different levels:
- Morphological
- Physiological
Biochemical
- Physiological
Biochemical Polymorphism
- Example: Alcohol dehydrogenase enzyme – breaks down ethanol.
- In Drosophila comes in different forms called allozymes
migrate differently in gel electrophoresis – called Fast and Slow forms
- In Drosophila comes in different forms called allozymes
Genotype and Allele Frequencies
- Can define genetic structure of a population by frequencies of different genotypes, or by frequencies of alleles.
- Example: one gene, two alleles that show incomplete dominance for flower colour.
○ Hypothetical population of 500 individuals: 320 red, 160 pink, 20 white.
§ Calculating genotype frequency - 320/500 = 0.64 red genotype frequency
Calculating phenotype frequency - 320x2 +160 /1000 = 0.8
- Example: one gene, two alleles that show incomplete dominance for flower colour.
Incomplete dominance
- Heterozygote has intermediate phenotype
Genotypic and phenotypic ratios of F2 coincide: 1: 2: 1
The Hardy-Weinberg Principle
- Describes gene pool of a population that is not evolving.
○ i.e. the allele and genotype frequencies remain constant from generation to generation
§ (so also called H-W equilibrium).- If mating is random, every male gamete unites at random with every female gamete, and frequencies of pairings depend on the allele frequencies.
Can think of all the alleles being in a “bin” or pool, and reproduction occurring by selecting two at random.
- If mating is random, every male gamete unites at random with every female gamete, and frequencies of pairings depend on the allele frequencies.
General Hardy-Weinberg equilibrium
- For two alleles A and a
○ Let p = freq A, q = freq a
Genotypic frequencies will be: A2 + 2Aa +a2 = 1
Applying the H-W Principle
- In many cases dominance is complete, so can’t determine genotype of all individuals.
- But can still use H-W theory to calculate allele frequencies and estimate genotype frequencies.
e. g. may want to estimate carrier frequency for recessive human disorder.
- But can still use H-W theory to calculate allele frequencies and estimate genotype frequencies.
Example: a human recessive disorder albinism occurs in 1/10,000 births. What is the expected frequency of carriers?
- p2 + 2pq +q2 = 1
- q = √1/10000
- q = 0.01
- p = 1-q
- p = 0.99
2pq = 0.0198
Five assumptions underly H-W
- Genotypes will stay in H-W equilibrium only if:
- the population is very large
- there is no gene flow
- there is no natural selection
- there is no mutation
- there is random mating
- If any of these do not apply then allele and genotype frequencies will change – microevolution.
The mechanisms that most commonly alter allele frequencies are due to violations of conditions 1-3.
Genetic drift
- If population size is not very large, genotype and allele frequencies can change due to random sampling effects, called genetic drift.
- In small populations genetic drift acts faster and with greater consequences
- causes fixation of one allele or the other (randomly).
- What causes genetic drift
○ (1) Bottleneck – sudden dramatic decrease in population size
○ (2) Founder Effect – isolation of a few individuals to form new population
E.g. amish people have high rate of Ellis-van Creveld syndrome (dwarfism, polydactyly, and heart disease). Incidence is 1/160 (worldwide ~ 1/60,000).
Gene flow
- Migration of individuals into and out of a population can alter allele frequencies if genotypes migrate differentially.
- Different effects if unidirectional or bidirectional.
If bidirectional tends to reduce differences between populations.
- Different effects if unidirectional or bidirectional.
Natural Selection
- If a particular genotype is better suited to an environment these individuals will produce more offspring than others, and contribute more to next generation.
- This will change allele frequencies.
We say this genotype has greater “relative fitness” than others, and other genotypes are “selected against”.
- This will change allele frequencies.
Directional selection
when individuals with traits on one side of the mean in their population survive better or reproduce more than those on the other
Stabilising selection
- a type of natural selection in which the population mean stabilizes on a particular non-extreme trait value
- E.g. birth weight
Infant deaths are higher at the lower end of birthweight and at the higher end - middle is favoured
- E.g. birth weight
Balancing Selection
- Sometimes natural selection maintains two or more forms in population
- E.g. Heterozygote advantage
○ heterozygote more fit than both homozygotes under certain conditions. - E.g. Frequency-dependent selection
○ the least common genotype is the most fit.
E.g. scale-eating fish in africa
- E.g. Heterozygote advantage
Effect of mutation
- Mutation is an evolutionary force as it creates new variation.
- mutation rate = μ
○ probability of mutation to a different allele per gene per generation
○ mutation rates are generally around 10-5 to 10-8 - Recurrent mutation can change allele frequencies
But mutation is extremely slow at changing allele frequencies, and so cannot account for rapid genetic changes.
- mutation rate = μ
Non random mating
- Bias towards choosing a similar mate
○ = positive assortative mating- Bias towards choosing a dissimilar mate
○ = negative assortative mating - Humans commonly show positive assortative mating for skin colour and height.
- Positive assortative mating increases the homozygosity of the population (reduces the numbers of heterozygotes)
- Inbreeding
Inbreeding increases the number of deleterious recessive individuals (aa) in a population - homozygosity
- Bias towards choosing a dissimilar mate
why do we use simple models
- We use simple models to study complex systems.
○ Models make studying populations tractable.
○ Models portray an idealised population.
How do we actually use a model?
○ Compare model to data from natural populations.
Simulate evolution through time.
Wright-Fisher Model
- Haploid (each individual has only one copy of its genetic information)
- Constant population size
- No mating (just asexual clonal reproduction)
- Discrete generations (an entire population is replaced by its offspring in a single generation)
- Genes are transmitted to the next generation by sampling with replacement.
No selection or mutation
fixed vs lost
Fixed is when the allelic frequency in a population reaches 1.0
Lost is when the allelic frequency in a population reaches 0.
time to fixation
Neutral alleles (0.5 frequency) must eventually become fixed or lost. Time to fixation is dependent on population size. In other words, genetic drift works much faster in small populations than large populations (remember bottle necks and founder effects).
Probability of fixation of a neutral allele
independent on population size.
The probability of fixation of a neutral allele is its current frequency.
As Population size (N) increases
the probability of a newly arising neutral allele fixing decreases proportionally.
Probability of fixation of a new neutral allele = 1/N
Synonymous substitution
- Substitutions on the third base can result in different amino acids.
- E.g. GAA and GAG might equal glutamine but
○ GAC and GAU might equal aspartate
○ They are synonymous if the substitutions at the third site produces the same amino acid
○ As 2/4 possible substitutions produce one amino acid it is called a 2 fold synonymous site - E.g. GUU, GUC, GUA, GUG all produce valine
○ As 4/4 possible substitutions are synonymous therefore it is called a 4 fold synonymous site - We can assume that most four-fold redundant sites are selectively neutral.
- E.g. GAA and GAG might equal glutamine but
Genetic variations with mutations
- We might expect from the previous models that eventually all variants would be fixed or lost.
- However, mutation resupplies populations with genetic variation.
- Mutation rates for a genome might seem high, but for any given locus in the genome, mutation rates are low~ 10-7-10-9.
Each individual in a population is a new opportunity for mutation to occur!
Mutation rates and rate of substitution
- New mutations enter the population at a mutation rate U
- U is the genomic mutation rate, or the expected number of mutation to occur in each new offspring.
Examples, for humans U is about 100, and for E. coli U is about 0.003
- U is the genomic mutation rate, or the expected number of mutation to occur in each new offspring.
Calculating rate of substitution of mutations in a population
- N.o mutations entering a diploid population = 2NU
○ 2 = diploid
○ N = population size
○ U = mutation rate- Chance that any of the mutations will go into fixation = 1/2N
- Expected number of mutations that we expect to fix every generation = 1/2N x 2NU
They cancel out using algebra to make it = U (the mutation rate)
How does a molecular clock work?
- The molecular clock was used to figure out the divergence time of Chimpanzees and humans (or when was the last common ancestor).
○ To calibrate the clock: the number of neutral differences between humans and macaques was counted, then divided by the number of years.
○ We found out that macaque diverged 7% in 25 million years and the chimpanzee 1.2%
○ Using algebra 25m/7% = x/1.2%
X = 4.28m years
Palaeontological evidence found the clock was slightly wrong
- Age of the bone was correct but some assumptions underlying the clock were wrong
- Mutation rates could have change
○ If U = 1/2, it should take twice as long to accumulate mutations - Generation times, the per generation rate might be the same for some generations, therefore the clock would slow down
Population size - prolonged periods of small population size can cause to increased variation of the molecular clock.
- Mutation rates could have change
What is fitness
- Survival of the fittest
- Who are the fittest? Those that survive. Survival of the fittest is therefore a tautology.
- Fitness is the capacity to contribute offspring to the next generation.
An individual with a high fitness contributes more offspring than average to the next generation.
Beneficial allele
- A new mutation starts a frequency of 1/N.
- If it is beneficial, it will increase in frequency with every generation.
When the frequency goes to 1, it is said to have fixed, or substituted in the population
- If it is beneficial, it will increase in frequency with every generation.
Selection coefficient
- the measure of the strength of selection acting on a genotype
- Time to fixation is proportional to the strength of selection
○ So with twice the ‘s’ it will take roughly half the time to fix - We can use species with a fast generation time to calculate fitness,
We measure the frequency at a given generation then measure it again at a later generation and calculate the slope for s
- Time to fixation is proportional to the strength of selection
Humans modify their environment, reducing the action of selection.
- Enzyme replacement (Insulin for type I diabetes and clotting factors for Hemophilia)
- Antibiotics
- Sanitary living conditions
- Detection of heart and vascular defects
- Surgery
- Fixing of optical disorders
This will not effect all mutations, just those that are ameliorated by the treatment.
The capacity of selection to discern between fitness also depends
on population size
- If s < 1/N, then the natural selection cannot distinguish between that allele and the neutral allele
○ If n=10, 1/n = 0.1
○ Widens the range so that more alleles, that have a S of -0.06 (less than 0.1), are seen as neutral
How does it look in real populations?
- Three examples:
- Laboratory experimental populations
- Clonal expansion in human cancer
Modern human evolution
- Clonal expansion in human cancer
Laboratory experimental populations
- Take sample of bacteria grow it, dilute it into another solution and keep the process so you get many different generations to track their mutations through different generations
They found that beneficial mutations kept being acquired through different samples
Clonal expansion in human cancer
- Bacteria don’t have sex
- Evolution of cancer
○ The mutations that drive cancer evolution are called “driver” mutations instead of beneficial mutations.
○ Cancer is a somatic disease, there is no recombination between lineages.
Since cancer spreads from a single cell by mitotic (not meiotic) cell divisions, it is called a “clonal expansion” and shares characteristics with bacterial evolution
- Evolution of cancer
How to identify the “driver” mutations in complex sequence data?
○ Whole genome sequencing has become common
○ Genomes of tumours are found to contain tens of thousands of mutations
○ Due to high mutation rate
○ We need to know this to develop strategies to account for tumour evolution in treatments
○ Parallel evolution - if you treat many tumours with the same drug, you should see the same mutations drive resistance
Parallel evolution is the independent evolution of the same trait, or the fixation of mutations in the same gene.
Parallel evolution in:
- In animals
○ Species develop traits like wings independently so this trait must be favoured- Natural selection is strong and drives the same mutations again and again
- In experiments
In whole genome sequencing we can see mutations in the same beneficial genes again and again
Modern human evolution
- Beneficial mutations in recent human evolution
○ Lactase persistence
§ Mutation in LCT to keep lactase and keep capacity to utilise lactase in adults
Tooth number
Case study: EPAS1
○ Tibetans are better suited for high altitude
○ Polymorphism in EPAS1 gene that reduces its function
○ Its function is involved in response to hypoxia
○ Sometimes a loss of function can be beneficial
○ Has a high fitness at high altitude
○ For a population like Han Chinese (with genetic flow with the Tibetans) may be deleterious in low altitude
§ It could also be neutral we don’t know
Denisovans (distant relative to humans) shared the same 5 mutations that confer adaptation to high altitude - gene flow between Denisovans and humans
