Basic Graduate Evolution

nucleotide ≅ base

Bases

• purines (A T), 3 H bonds, less stable (fewer bonds)
• pyrimidine (GC), 3 H bonds

RNA	normally single stranded
DNA	double stranded

Each strand has a 5' end and a 3' end. The convention is to write from the 5' and to the 3' end when transcribing DNA. The strands are anti-parallel.

RNA (as compared to DNA)

• single stranded
• much shorter (often 20-24 nucleotides long)
• Bases: (A C G U)

• traditionally, something that codes for a protein, i.e., gene → messenger-RNA → protein (this was previously the only functionality known for DNA segments)
• now, genes also include sequences which do other things, e.g., transcribe RNA, some RNA sequences are functional as themselves

Types of Genes

• protein coding
• RNA
• regularity

Eukaryotic protein coding genes comprise both transcribed () and non-transcribed () parts.

Gene's are transcribed by polymerase, which first anchors to a "promoter region" which flanks the gene, and then travels the gene transcribing its contents.

A "codon" is 3 nucleatides which are transcribed into 1 amino-acid.

Gene Structure (we're talking about protein coding gene)

TATA box

in the promoter region -19 from the gene start, in a GC-rich region of the DNA. Not required, but prevalent

A Gene with the promoter region.

    promoter region       Gene->
  ---->  --  <---  --     ----------   --------   ---------
  GC    CAAT   GC  TATA    
  box    box  box  box   

RNA polymerase

I	RNA
II	protein coding
III	small RNA

• Genes specifying proteins
  

  Transcription and Translation process

  1. DNA -> pre-RNA (which does include non-coding introns)
  2. pre-RNA -> mature mRNA, this is done by the spicing machinery (these arose early in evolution and are very intricate machines). Genes are spliced using the "GT-AT rule" (introns often start with GT and end with AG)
  3. Mature mRNA -> the remainder of the gene is split up into codons and transcribed, it must start with one of three start codons (UGA UAA UAG). The start code does not code for an amino acid. This is still capped by small untranslated sections on either side.
  4. Protein -> only the translated regions converted to amino acids

  There are many other regulatory sequences in introns or between genes which do things like increase or decrease the speed of translation.

• RNA-specifying genes (transcribed to RNA, not translated to protein)
  
  • transfer RNA
  • ribosomal RNA
  • similar sequences between (eukaryotes and prokaryotes) which means they arose early and are important

  Degenerate genetic code

  • 20 Amino Acids
  • 64 codons (4 × 4 × 4)

• Regulatory Genes
  
  • regulate the expression of another gene
  • not transcribed or translated

  enhancers or repressors (change tempo of translation)

  notable examples

  replicator genes

  initialize and terminate replication

  telomeres

  "cap" at the end of a chromosomes, these erode with age, these don't erode as quickly in sea turtles

  segregator genes

  help split the DNA pair (sisters) for translation, this is where the zippers attach to unzip

  recombination genes

  sites for recombination during meiosis (crossover more likely to happen here)

Composed of

• a central carbon
• an amino end
• a carboxyl end
• a hydrogen
• a side chain – this is the most variable and the most important

Simplest is glycine

• single H side chain
• fits in nooks and crannies of proteins

Five classes

• positively charged
• negatively charged
• hydrophobic
• neutral
• special

string of amino acid

• secondary structure – two most common 2-D structures for folded proteins
  • α helix
  • β pleated sheet
• tertiary structure – these combine into 3-D structures of the protein
• quartinary structure – two tertiary molecules

Losing the phase (correct codon alignment) can be caused by mutations and garbles the translation resulting in a garbled protein. The phase is determined by the start or initiation codon, and is called the "reading frame" or "open reading frame" (ORF).

Genetic code is degenerate but not ambiguous.

Multiple codons coding for an amino acid will often differ in the third position.

Terminology

fourfold-degenerate site

any nucleotide in this position will specify the same amino acid.

twofold-degenerate site

two of the four nucleotides at this position will specify the same amino acid.

non-degenerate site

every nucleotide here results in a different amino acid, called an "amino-acid substitution".

synonymous codons

different codons which code for the same amino acid.

In most codons the first two positions are non-degenerate sites.

numbers of codons

• 61 sense codons (remaining 3 are STOP codons)
• 549 possible codon nucleotide substitutions
  • 61 codons × 3 positions × (4-1) alternatives for each position
• assuming equally probable mutations (not true), then 70% of all 3^{rd} position changes are synonymous
• 2^{nd} site is the most sensitive to substitution, 0% of changes are synonymous
• in the 1^{st} site only 4% of changes are synonymous

Main evolutionary forces (on populations)

• mutation
• selection
• migration (new alleles from outside)
• drift

Mutations are hereditary changes in the genetic material due to errors in DNA replication or DNA repair.

Types of mutations

• substitutions
• recombination (crossing-over and gene conversion)
• deletions/insertions ("indels")
• duplication
• inversions

Evolutionarily mutations that occur in germ cells are the only hereditary ones.

• classes of mutations
  
  • substitutions
    also called "point mutations"

    classifications

    1. transitions (purine to purine, pyrimidine to pyrimidine), there are four possibilities for this
       • a ↔ g
       • t ↔ c
    2. transversions change the type, there are eight possibilities for this

    If these were equally likely you would expect twice as many transversions as compared to transitions.

    You actually see many more transitions than translations.

    Also classified by effect (only applies to protein coding genes)

    1. silent or synonymous (no amino acid change)
    2. replacement or non-synonymous (cause aa change)
       • missense (now codes a new aa)
       • nonsense (changes to a termination codon, will prematurely terminate translation)
  • crossing-over and gene conversion
    

    homologous recombination

    occurs between strands which are similar through a shared common ancestry

    This happens most often during repair. Say a chromosome breaks (very common) there is a machine which comes along and repairs the broken chromosome (sometimes this causes a change).

    This also happens during meiosis.

    Two types of homologous recombination

    1. crossing over (reciprocal recombination), two chromosomes pair up and each gets a bit of the other
    2. gene-conversion (nonreciprocal recombination), a bit of one goes to another, but one remains unchanged
  • insertions and deletions
    

    unequal crossing over

    May be caused by unequal crossing over, this is often caused by similar sub-sequences, this could cause an insertion and a deletion. Generally 10-13 nucleotides long.

     -----=====-----                -------------
                             x
       ---------======-----     -----====---====------
    

    replication slippage

    (look up in a text book), when a repeating pattern is offset. These can be thousands of base pairs long

    retro-transposition

    Selfish elements which are prone to copy themselves anywhere throughout the genome (discovered by Barbara McKlintoc in corn). Sometimes these elements will grab a nearby section of the sequence and bring them along.

  • inversion
    A rotation of a double-stranded segment by 180.

     |     |
    a b c d e f g h
       to
    a d c b e f g h
    

    These often occur between genes where they don't have much effect.

• spatial distribution of mutation
  Often 100-fold differences in mutation rates between elements of the sequence. These are often very repetitive sequences of the genome.

  Some groups of nucleotides are prone to change. E.g., CG is easily methelated causing the C to become a T. TT is also a hot spot.

  palindromes

  epigenetics (non-genetic), e.g., chemical elements changing genetic interpretations.

  • chemicals inhibiting expression
  • proteins binding up DNA into little balls, by histomes, this inhibits transcription

• substitution in non-coding sequences and pseudo-genes
  important to determine the pattern of spontaneous mutation

  no selective pressure

  mutation accumulation experiments, you maintain the lowest possible population size

  you could bottleneck a population, no selection, only genetic drift

  Pseudo-genes are dead (premature STOP or something), these can also indicate baseline rates.

  • can compare to an active duplicate
  • can compare to a homolog (inactive in people, compared to active in chimps)

  Trend from GC to AT, so non-coding regions become AT-rich.

Big "macro-level" changes (e.g., between species) are results of the same small "micro-level" changes between individuals.

Four major evolutionary forces

• mutation
• random genetic drift – ∃! animal, the Atlantic eel, which has an effectively infinite population size, because they all come together to one place annually to mate.
• natural selection
• gene flow

The study of gene changes in populations is population genetics.

• what influences mutant allele over time
• how is genetic variability maintained
• probability of going to fixation
• how fast will replacement take place
• influence of chance effects on molecular genetic change

(see #terms)

locus, allele, allele frequencies, genotype, phenotype, discrete trait, continuous or quantitative trait, homozygous vs. heterozygous, genotypic vs. phenotypic ratios, dominant vs. recessive allele, evolution, natural selection, fitness (w)

• BB is homozygous
• Bb is heterozygous

Mendel bred purple × purple plants and got both purple and white plants. Specifically 705 purple and 224 white.

Diploid parent will produce single-ploid gametes (else there would be a combinatorial explosion in the ploidy of the offspring).

A Punnett Square

		pollen
		B	b
pistil	B	BB (purple)	Bb (purple)
	b	Bb (purple)	bb (purple)

• phenotypic ratio of above is
  • 3 purple
  • 1 white
• genotypic ratio of above is
  • 1 BB
  • 2 Bb
  • 1 bb

Problem

• 1000 peppered moths in Manchester
• dark melanic form of allele is dominant (M)
• ancestral is recessive (m)
• 825 melanic
• 175 peppered
• 512 of melanic are heterozygous

Some calculations

• Phenotypic ratio is 875/175 or 4.7 melanic to peppered
• Genotypic ratio is 313 MM, 512 Mm, 175 mm or 1.78 : 2.93 : 1
• Allele frequencies of M and m 616 + 512 / 2000 = 0.569 (2 * 175) + 512 / 2000 = 0.431

Allele frequencies are changed by

• selection
• drift
• migration

2 Mathematical approaches

deterministic

(analytic) can predict changes unambiguously. The first of these was "Harvey Weinberg".

stochastic

probabilistic, associates probability distributions with environmental conditions

Deterministic assumptions

• infinite population size
• constant environment

Needed for Darwinian selection (influenced by Menthusian principles)

• variation
• environmental limit to population size (carry capacity)
• differential reproduction (because of the above)

                +------------ mutation ------------------+
                |                  |                     |
                |                  |                     |
                |                  |                     |
           deleterious          neutral            advantageous
                |                  |                     |
                |                  |                     |
                |                  |                     |
                |                  |                     |
           purifying            chance             positive selection
           selection            events                   or
                                                    overdominant     
                                                     selection

Normally selection reduces genetic variation, however "overdominant" selection can increase genetic variation. This is when the heterozygote has the highest fitness.

1 locus, 2 alleles (A_{1} A_{2})

• 3 possibly diploid genotypes
• allelic frequencies are
  • f(A_{1}) = p
  • f(A_{2}) = q
  • p + q = 1

genotype	A_{1}A_{1}	A_{1}A_{2}	A_{2}A_{2}
	p^{2}	2pq	q^{2}

genotypic frequencies

• f(A_{1}) = p^{2}
• f(A_{2}) = 2pq
• p + q = q^{2}

This is the null model.

Back to our problem.

• melanic is dominant and is 87% (could be heterozygotes)
• → 13% is non-melanic
• → q = 0.13
• → q = \sqrt{0.13} = 0.36
• → p = 1 - q = 0.64
• → f(Mm) = 2pq = 2 × 0.36 × 0.64

Graph (frequency of a, by frequency of genotype in population)

set xrange [0:1]
set xlabel 'frequency of A'
plot x * x title 'AA', (1-x) * (1-x) title 'aa', 2 * x * (1-x) title 'Aa'

genotype	A1 A1	A1 A2	A2 A2
fitness	w11	w12	w22
frequency
after	p * p w11	2pqw12	q * q * w22
selection

\begin{equation*} q' = \frac{pqw_{12} + q^{2}w_{22}}{p^{2}w_{11} + 2pqw_{12} + q^{2}w_{22}} \end{equation*}

change in frequency \begin{equation*} \delta q = q' - q \end{equation*} \begin{equation*} \delta q = \frac{pq(p(w_{12} - w_{11}) + q(w_{22} - w_{12}))}{p^{2}w_{11} + 2pqw_{12} + q^{2}w_{22}} \end{equation*} Example

• heterozygous individuals have lighter eye spots (increased predation)
• relative fitness of genotypes

  SS	1
  Ss	0.9
  ss	0.6

• p(S) = 0.7

p = 0.7 q = 0.3

Frequencies in the original

p	0.49
pq	0.09
q	0.42

Relative fitness

p	1
pq	0.9
q	0.6

Next generation frequencies

• f(SS)' = p^{2}w_{11} = 0.49 × 1
• f(Ss)' = 2pqw_{12} = 0.42 × 0.9
• f(ss)' = q^{2}w_{22} = 0.09 × 0.6

Next generation's allelic frequencies

• f(SS) × 2 + f(Ss)
• f(ss) × 2 + f(Ss)

• Overdominance is also called heterozygote superiority.
• When the heterozygote has a higher fitness than either homozygote.
• this is one of the few times (along with frequency dependent selection) in which selection increases genetic diversity
• called "balancing" or "stabilizing" selection

The equilibrium frequency (\(\hat{p}\)) is given by \begin{equation*} \hat{p} = \frac{w_{11} - w_{22}}{2w_{12} - w_{11} - w_{22}} \end{equation*} When w11=0.9, w12=1, and w22=0.8 then \(\hat{p} = 0.667\).

\(\bar{w}\) is the average fitness of the entire population.

"find them and grind them" ← experimental identification of overdominant selection. Cavalli-Sforza is prolific in this area.

type	codon	amino-acid	cell shape
wild type	GAG	glu	doughnut
mutant	GTG	val	cycle

The wild type allele is more dominance, but it is not a perfect dominance relation.

alleles	anemia	malaria	fitness
SS	normal	vulnerable	0.9
Ss	slight	resistant	1.0
ss	severe		0.2

This is an unstable equilibrium, any deviation from equilibrium will fall away.

This is another instance of a valley which selection can not traverse.

• Changes in allele frequency due solely to chance effects.
• Moral is not to assume that every trait is adaptive.
• Especially important in our currently world of many species with severely reduced population sizes. Note: this will reduce the likelihood that these populations will be able to adapt to climate change.

Stochastic events from ecology have huge effects on small populations.

• alley effect
• catastrophe

;; the above generated with the following
(loop :for pop-size :in '(100000 1000000) :do
   (with-open-file (out (format nil "/tmp/pop~d.data" pop-size) :direction :output)
     (gen-drift out :pop-size pop-size)))

• depiction of the sampling process in populations of finite size
• the distribution of frequencies of gametes is expected to follow a binomial distribution

Process

1. N individuals in P_{0}produce ∞ gametes
2. 2N gametes are selected from the pool of ∞ gametes
3. N individuals in P_{1}

Consider a diploid population of N individuals w/2N genes

when 2N gametes are sampled from the ∞ gamete pool the probability P_{i} of i genes of type A is given by

\begin{equation*} P_{i} = \frac{(2N)!}{i! (2N-i)!} p^{i}q^{2N-i} \end{equation*}

Make some graphs of a population of a given size with some number of genes, should the frequency of each gene over a number of generations to show the increased effect of chance in smaller populations.

A pot of 100 seeds, 50 round and 50 wrinkled.

Enumerate all possible samples and the related probability of such a sample.

• Probability of four round seeds = \(\frac{4!}{4! 0!} 0.5^{4} 0.5^{0} = 2^{-4}\)
• Probability of three round seeds = \(\frac{4!}{3! 1!} 0.5^{3} 0.5^{1} = 4 \times 2^{-3} \times 2^{-1}\)
• Probability of two of each = \(\frac{4!}{2! 2!} 0.5^{2} 0.5^{2} = 4 \times 2^{-2} \times 2^{-2}\)

N individuals → ∞ gametes → N individuals → ∞ gametes

\begin{equation*} P_{i} = \frac{(2N)!}{i! (2N-i)!} p^{i}q^{2N-i} \end{equation*}

For an idealized population and makes the following assumptions

• all individuals contribute gametes equally to the next generation
• population size is constant
• non-overlapping generations

N_{e}: The size of an idealized population which would have the same effect of random sampling on gene frequency as that in the actual population.

N: The observed actual population size (census size).

Generally N_{e} << N, or roughly \(\frac{N}{3}\), because of

• Pre- and post-reproductive individuals should not be counted.
• difference in ratio of males to females, in which case \begin{eqnarray*} N_{e} &=& \frac{4N_{m}N_{f}}{N_{m}+N_{f}}, where\\ N_{m} &=& \text{num males}\\ N_{f} &=& \text{num females} \end{eqnarray*}

Also due to long-term variations in pop-size

• environmental catastrophes
• cyclical model of reproduction
• local extinction and re-colonization events

The long term size is the harmonic mean of population sizes (where n is the number of generations). Thus dips in population size affect the long term size more than temporary peaks. \begin{equation*} N_{e} = \frac{n}{(\frac{1}{N_{1}} + \frac{1}{N_{2}} + \ldots + \frac{1}{N_{n}})} \end{equation*} Long bottlenecks have much more of an impact on maintained genetic diversity than short bottlenecks. It is impressive how much variation may be maintained even through very narrow short bottlenecks.

gene substitution

the process whereby a mutant allele completely replace the predominant or wild-type allele in the population

fixation time

time (usually measured in # generations) it takes for a mutant allele to become fixed in a population

fixation probability

the chance that a new mutant allele will reach fixation in a population

rate of gene substitution

number of substitutions or fixations per unit time

• fixation probability determined by
  1. initial frequency (often 1/2N)
  2. selective advantage
  3. the effective population size N_{e} ← very important

Fitness for an allele is equal to a combination of S and N_{e}

• Selection coefficient (S) or (w - S)

  S=0	neutral
  S>0	beneficial
  S<0	deleterious

• in small populations basically everything is neutral

P probability of fixating

neutral

p = \frac{1}{2N}

small selection coefficients

P = \frac{2s}{(1 - e^{-4Ns})}

positive values of s and large N

P = 2s

• example of fixation probability
  
  • N_{e} = 1000 = N
  • a new mutant arises

  so initial frequency = 1/2000

  1. let this new mutant be neutral, so s = 0

     then probability of fixation P = 1/2000.

  2. with a slight selective advantage, e.g., s=0.01

     then P = \frac{2s}{(1 - e^{-4Ns})} ≅ 2s = 0.02

  3. with a slight selective disadvantage, e.g., s=-0.001

     then P = \frac{2s}{(1 - e^{-4Ns})} ≅ 2s = 3.7314723e-5

  (defun adv (s N) (/ (* 2 s) (- 1 (exp (* -4 N s)))))
  

the time required for fixation or loss of a neutral allele depends upon

• initial frequency
• population size N

times shorten as frequency approaches 1 or 0

For a new mutation (Kimura and Ohta 1969) with initial frequency 1/2N, the mean time to fixation is ≈

neutral allele

\(\bar{t} = 4N generations\)

allele with a selective advantage of S

\(\bar{t} = \frac{2}{s}\ln{\left(\frac{2}{N}\right)}\)

• example (lets say a mouse)
  
  • N_{e} = 10^{6}
  • generation time = 2 years

  For a neutral mutant allele in will take 4N = 4(10^{6}) = 8 mil. years.

  For a slightly selective allele (s=0.01)

  \frac{2}{0.01} × ln{(2/N)} = 5,800 years

Rate of gene substitutions (reaching fixations) per unit time.

neutral mutations

• neutral mutation rate = μ per gene per generation
• number of mutations arising at a locus in a diploid pop of size N = 2Nμ per generation
• but the probability of fixation of each mutation is P = 1/2N

Therefore the substitution rate is

K = (number of mutations)(probability of fixation)

or

\begin{equation*} K = 2 N \mu P = (2N\mu)(1/2N) = \mu \end{equation*}

substitution rate = mutation rate (thanks Kimura)

• advantageous mutation rate μ per gene per generation
• mutations per locus is 2Nμ per generation
• probability of fixation is P=2s

therefore

K = (num of mutations) (probability of fixation) (selection coefficient)

\begin{equation*} K = 2N\mu P = (2N\mu)(2s) = 4Ns\mu \end{equation*}

Rates and patterns of nucleotide substitutions, and molecular clock.

Darwin didn't know the mechanisms of heredity.

Mendel was treated as a crackpot because most people studied bio-metric continuous quantitative traits with normal distributions. So Mendel went back to gardening.

New-Darwinian theory Darwin and Mendel combined.

• mutation ultimate source of genetic variation
• natural selection given the dominant "creative" role in shaping genetic make-up of populations

Selectionism

• natural selection only evolutionary force
• polymorphism must be maintained by balancing selection
• gene substitution must be due to selection of advantageous mutations