Population Genetics 2 Flashcards
Fitness differential NS can act one
Natural Selection can work on any fitness differential in the absence of other evolutionary forces
IMAGE – The curves all have different fitness differentials –> all of teh curves still show that b1 will increase in frequencey through time
- rate = function of the strength of selection
- Weaker selection takes longer BUT B1 will still increase
- regardless of the strength of selection – if you have a fitness differential = you wikll incerase the frequncey of the higher fitness allelel –> WIlLL LEAD TO FIXATION
Fitness differential NS can act one
Natural Selection can work on any fitness differential in the absence of other evolutionary forces
Weaker fitness differences
Weaker fitness diffreences lead to slower rates of change
Rate of change
Rate of change is a function of the strength of selection
- Weaker selection = takes long
STILL IN DIRECTIONAL SELECTION IT WILL END WITH FIXATING FOR HIGHER FITNESS ALLELE
When is the rate of chnage the fastest
The rate of chnage is the fatstest when the genetic varaition in fitness is highest (P=0.5)
- Place where the rate of evolution (rate of alelle frequcney change) is fatstest = in the steepest part of teh curve – always at the same place – alwats when p=0.5
IMAGE – even though all differentc urves (different fitness differential) – the rate of chnage is fasttest when P=0.5
Fisher’s Fundamental Theorem of Natural Selection
Change in popultion fitness is proportional to varaition in fitness
- Fastest rate of chnage in fitness from one generation to the next when variation is highest
- More varaition = more NS can sort through the variation = fatser evolution
Effects of NS
NS is determinanistic when acting by itself
- If we know the starting point = we can know the end + all of the intermeduary steps
- If we know what the conditions are we know what the outcomes will be - NS selection by itself is driven by straight foward mathematics towards a predictable outcome
Dominance Vs. recessive in Directional selections
Whether an alelle is domineant or recssive – NS will still push the alelle to increase in frequncey – will get fixation for higher fitness alele in populations over time (for dominant or recessive)
- the end point is still the same (for domiannet vs. recssive) – still goong to fixation
DIFFERENCE = the rate at which coming to fixation occurs
Directional Selections
One allele is beneficial and one allele is deletrious
Model of Purley Domeinnet Fitness Vs. Model of purley recessive fitness
IF start with p = 0.9 (Start with the dominent in high frequncey)
Selection against dominent – dp = -0.0038
Selection Against a purley recssive –
dP = 0.032
Against Dom –> Agaisnt recssive – X8 diffreence in the rate change
- Selection agsinst the recssive = stronger than the selection agsint the dominant
UNDER THESE CONDITIONS – ALLELE FREQINCEIES ARE CHNAGING MUCH MORE RPAIDLY IN THE PURLEY RECSSIVE CASE (SELECTION AGAINST THE RECESSIVE)
IF we changed allele frequency (NOW the A is in low frequncey) w
P = 0.1 s = 0.3
Selection against the dominant –
w/ = 0.943
dp = -0.026
Selection against the recessive allele –
w/ = .997
dp = -0.0027
NOW – Have bog difference BUT the alelle frequcney is changing much more rapdily in selection against the dominant alllel
-0.026 –> -0.0027 – pattern is now the opposite (selection gaainst the dominant is stronger)
Model of purley Dominent Fitness
P = 0.9 S = 0.3
Selection against A BUT A is recsisve – a is domient because Aa is like aa = a is the dominenat and has the highest foitness = sleection gaainst the recssive A
S = 0.3 P = 0.9
w/ = 0.757
dP = 0.032 (different from selection against a dominant allele because w/ is different)
Model of purley recssive fitness (Selection against Dominenat)
S= 0.3 and P = 0.9
We know that the selection is pruley recessive fitness because teh heterozygous has teh same selection coeficiant (same Relative fitness) as the AA – fitness affect of A = fitness affect of Aa –> means that the fitness affect of A is dominent (Because AA and Aa have the same fitness)
HERE – fitness for a = highest = 1
S = 0.3 P = 0.9
Need to find dP –> Need relative fitness
wAA = 0.7 (W = 1-s – have have S)
WAa = 0.7
Aaa = 1
W/ = 0.703 – use equation
dP = -0.0038 –> Have a decrease in A because A is the lowest fitness = deleterious = goes down
Meaning of S = 0.3
Means that 30% difference in fitness across phenotypes
Relative fitness = 0.7
Overall – Change of alllele frequcney in dominant vs. recessive
IF Start will dominent in high frequncey
Selection against the purley recssive alllele (Recessive allele is less fit) = stringer
High freqincey of deleteriuos allele = get rid of it faster when it is recessive
IF start with dominant in low frequcney
Selection against the purley dominent alllele (dominant is less fit) = Stronger
- Selection against the recessive – For benefical dominant alleles at low frequnceies selections acts quickly but slows down as the allele appraches fixation
Low frequencey of deleterious allele = get rid of it fatser when it is dominant
Depends on if teh deleterious allele is dom/rec AND the context of the alllele frequncey in a population (The dominant will not always have stringer seleection)
Graphs – Change of alllele frequcney in dominant vs. recessive
Selection agsint the recessive and for the dominant – concave shape
- Selection against the recessive – For benefical dominant alleles at low frequnceies selections acts quickly but slows down as the allele appraches fixation
- Selection occurs rapidly because any time the dominant alelle shows up it is seen by Nastural selection = NS can act on it BUT slows down as ut aporaches fixation becayse increase mean popultion fitness to bring it close to 1 = NS can only act on the deletrious recessive allele of which there are very few = Selection slows down
Selectin against the dominant and for the recessive = convex shape
-
END POINTS of both systems are the same – they still both fix for an allele with higher fitness BUT one starts slow and finshes fast and one starts fast and ends slow
Selection for benefcial dominant alleles at low frequncey
Selection acts quickly but then slows down as the alleles apprach fixation
- Selection occurs rapidly because any time the dominant alelle shows up it is seen by Nastural selection = NS can act on it BUT slows down as ut aporaches fixation becayse increase mean popultion fitness to bring it close to 1 = NS can only act on the deletrious recessive allele of which there are very few = Selection slows down
Selection for benefical recessive allles at low Frequency (The dominant allele is in high frequncey)
Seleection acts slowly but speeds up as the allele appraches
fications
- NS can only see the allele if it is in aa – if the allele freqeuncey if a is low THEN teh frequncey of aa is even lower because aa is q^2 = have less aa for NS to act on – NS can only act against the A alllele – as frequncey of a increases = maintain varaiance in fitness because of teh heterozygous = NS can accelerate through to end point
- NS is slow acting in favor of recssive because recssive won’t have phenotypic affect = NS cam’t fo anything (opposite for dominant because anytime you have dominant NS can act on it)
Why is there a difference in change in allele freqeuncey acting against dominent or against recessive
The difference is in the average excess –
at low frequencies recessive alleles are most likely to combine with dominant gametes –> Therefore, the fitness effect of the allele is invisible to selection because it is mased by the dominant allele
- Makes the benefical recessive at low frequencey hace slow chnage but then speed up as the alleles approach fixation
Vs.
At low frequencies the fitness effect of dominant alleles show up no matter who they combine with however, as they approach fixation, the population mean fitness gets
closer and closer to the fitness of the allele –
Therefore, the relative benefit of carrying the allele isn’t as strong
Quantifying the degree of doninace
Real cases often don’t follow that strict dichotomy – So we can quantofy the degree of doinance and define the dominence coefficant for an allele (h)
Directional Selection
The highest or lowest value of a trait/alelle frequncey has the highest mean popultion fitness
- Will always end up in the same place – fixing for one allele
P = 1 OR p=0 = has the highest mean population fitness
In the absenece of other forces this leads to fixation for the favored allele
When does directional selection apply
Only applies if teh relative fitness of Aa is between the bounds or equal to AA and aa
- can be the same as AA or aa or in between the values of AA and aa
Overdominance
Heterozygous advatage – Aa has teh highest fitness
Under dominance
Heterozygous infiriority – Aa has the lowest fitness
Forms of selection
- Overdominance
- Underdominance
- Directional selection
Example of Overdomiance
Here Aa has the higehst fitness = we set Aa equal to 1
s vs. t in selection coefficients
s and t keep track of the two selection coeffcinats seeprations
IMAGE
A = p –> use s – Selection coefficient acting against AA
a = t
P –> S
q –> T
Example for Underdominance
HERE WE MAKE THE LOWEST FITNESS EQUAL TO 1 – divide the absolute fitness by fitness of Aa
Selection coeficiants in underdominance
s and t are negitive – because the fitness of aa and AA should both be higher than Aa
1 - (-#) = gives a number greater than 1
In under dominencae - scale Aa to one (it will be the lowest – only time you scale the lowest value to 1)
When do we set the lowest fitness value to 1
ONLY for underdominance (If the Aa has the lowest fitness)
Under dominance example – with work – calculating w
s = -0.2 t = -0.1
What do we calculate for over/under dominance
calculate an equilibrium point – static point in system (forces are balanced)
- Static point in otherwise dynamic system – forces are balanced to make it stationary
Do this by solving for dP = 0
Meaning of Equilbrium point
At that point evolution will no longer occur
- Solving for point where dp = 0
Calculating P> In overdominance
Given: s = 0.2 t = 0.1
AA = 1-s –> RF = 0.8
aa = 1-t –> RF = 0.9
Aa = 1 – hightest
p> = 0.1/().2 + 0.1) = 0.33
- Have equilbirum when p = 0.33 OR when the frequcney of q (a) = 0.67
P> in Overdominace vs. nder dominance
Might have the same P> value but the nature of p> is difefrent
P> for Overdominance is the highest point of fitness
P> for underdominance is the lowest point of mean fitness
- Fitness is lowest at p> for under dominance
Adaptive topography for Overdominance
value of P> is the peak – theer is no dP
- At the peak there is NO uphill to go = NS will stop (because NS always oushes uphill)
- If to the left of the point – then P will increase
- If to the right of the point P will decrease
- If you start at P> it will stay there –> if you move away from P> it will evolve to go back to P>
- The direction depends on alelle frequncey BUT will always fix for the same point
- The dP to the left will be posiutive (incvrease P) and dP to the right will be negitive (Push to decrease p)
Reason that P> is the highest population fitness in overdomainnece
Equillirbium in Overdominance
STABLE equillbirum
Fixing in Over vs. Underdominance
Overdomince = always fixing for one point
- No matter the allele frequcney – always fix for the same point
Under dominace = there are two points that you can fix for – don’t knwo what wilol be fixed for
- What will be fized for depends on allele frequcney
Adaptive Topogrphy of Under dominance
Still alwats going uphil
- if start to the left of p> = the popultrion will evolove to p=0
- If start to the right of P. = NS will push P = 1
- If start at P> and all H-W assumptions are true – it will stary there but only if we keep it there – if it is perturbed = then it wil go uphill in eitehr way depending on how it was perturbed
Equillibrium in Under dominance
Unstable Equillirbium – does not return when pushed
- if you start the poulation on one side it will go to fixation for p = 0
- If you start the population on the other side – it will go to fixation for P = 1
Harder to predict end point – depends on the starting allele frequencey
- Whether goes to P = 1 or P = 0 depends on the starting allele frequencey (Depends if the starting alelle frequncey starts above or below p>)
STILL – both will increase fitness
Drawing Topographies for Over dominance
Need to find P>
P> = 0.33
0.8 = 1 - s –> s = 0.2
0.9 = 1 - t –> t= 0.1
THEN can calculate relative fitness
p =0.33
q = 0.67
w/ = 0.933 (using equation)
Have 3 points:
P = 1 –> w/ = 0.8
P = 0 –> w/ = 0.9
P = 0.33 –> w/ = 0.933
Points for Adaptive topographies for over/under dominance
STILL NEED 3 points
P = 1
P = 0
P> –> Find w/
- Because P> is a critical value = needs to be our 3rd point
***P> = stable equilbbirum point in over BUT tipping point in unstable for under
Testing for NS in the lab
Expect the effect of NS to be the primary driver of change
can run selection experiment and compare the outcome to expectations from model – asking if they evolove based on the adaptive topography
Testing the math in the lab (Example – Flour Beetles)
Looking at selection against a lethal recessive
Populations = started with ONLY heterozygous (P=0.5) at the locus
- Start at p=0.5 (ALL heterozygotes)
THEN – get the H-W genotypes and track change in alllele frequncey iver time
s for lethal = 1 (1 - 1 = 0 RF)
- RF for aa = 0
- RF for AA and Aa = 1
THEN can find dP – get simplified expression for lethal recessives
LOOK at allele frequncies after 12 generations – compare the rate of chnage in allele freqncuencey with Adaptive Topographies
- They checked the data aginst the curve predicted by population genetics x
OVERALL – you are starting with a mid frequncey of A and you are selectingh against recesisve allele
IMAGE – as it gets rarer = only have issue in q^2 can’t affcet fitness unless in aa = rate of change tappers off
RESULTS – matched what is sepected for selection agaisnt recessive allle
- get fixation for A
Testing math in the lab (Example #2) – Drosphila
Start = Lethal resseive allele starting at p=0.5 (same starting point as the beetles)
Results = The A alelle did NOT go to fixation (insetad it stalled around 0.79)
- Stoped evoloving when lethal allele was still in frequncey of 21% of the population
WHY did it stall?
- Reached a static equillibrium point = even though it was lethal for aa it has a benifit for Aa
NOW – it is not directional selection (the heterozygotes have the highest fitness) = over dominancve
THEN – They started with different allele frequnceies to see if it would stable to the same pount –> Found that it did get to the same point
- Confimed that this was due to overdomincae by starting the population at a very low frequncey of the recessivee (at 0.025) –> q evolove to increase to 0.21 – the leathal allele increased in frequncey because of its adavatage in Aa
Had an increase in frequncey in the lethal allele because of overdominance (Heterozygous advantage)
- Depsite being lethal as aa – teh a allele was a benefit to Aa = get equilibirum ppint
Population genetics example in the real world with Over/under dominance
Sickle cell + Malaria
Malaria
One of the greatest public health crisis
- Big porblem
- Hot sopt = wet warm places
- The plasmodium parasite gers into RBCs – ability to iteract with RBCs = important for malaria
Anemia + malria
Sickle cell Anmeica = plats a role in malaria resistance
- hemoglobin peptides = bunch up = strtch out RBCs = wriong shaope RBCs –> hard for RBCs to pass through capilaries = decrease in oxygen + low Iron + low RBC count
Fitness of Sickle cell in malaria envirnmnets
CLEAR case of over dominance
AS = the highest fitness
AA = get malaria –> S = 0.11 (RF = 0.89)
AS = 1.0 – in malaria envirnemnt you are better tan AA because resistant to malaria
SS = 0.2 – same in malaria and non-malraia envoirnmemnts – still same fitness decrease as before
Calculating the P> + making Adaptive topography for Malaria (With two alleles)
Chart = shows that if to the right of equillibriounm in a place with malaria = will increase in S allele (Decrease A) THEN negitive affect of SS is overcome by the increase in fitness oif AS = the frequncey of S will increase until P>
Calculating the expected frequncey of Hemolytic Anermia Phenotypes in malarial Envirnments
We already know that P = 0.88 –> Q = 0.12
Then we can know the frequncey of indovodulas maintained by NS
q^2 = 0.12^2 = 0.014 –> means that 1% of the population is mainatined by NS
- If you decrease S NS will push it basck up and increase the number of Individulas that have the disease
Result of Heterozygous Advantage
The heterozygote advantage of the S allele results in natural selection maintaining a very negative trait – sickle cell anemia- at a rate of nearly 1.5% in those populations!
Malaria Example – Add in C Alelle
NOW have a 3 allele system
AC – C has no effect on fitness if with A (In a malaria envirnmmet or NOT)
SC – Have decrease in fitness in maalria + non-malaria envirnmemt
- Have some finess cost with AC
CC – Same in non-malaria envirnmemnt BUT best in A malaria envrinment
- In malaria envirnment it is alwamost entireley resistent to malaria
- Have no Anemia + Most resistant to malaria = C is the best alelle
Best genotype is CC – has the higehst w/ when population is fixed for C (w/ would be 1.31)
Question - why hasn’t C gone to fixation? How will NS act on C?
Equilibirum between A and S
Pa> = 0.879
Ps> = 0.121
Start with
Frequncey of A (pA) = 0.879
Frequncey of S (pS) = 0.121
THEN If we have C and we make Frequncey of C (pC) = 0.01
- take away from A
NOW
pA = 0.869
pS = 0.121
pC = 0.01
NOW
w/ = 0.903
dPc = pC/w/ (Avegrage excess)
dPc = -0.0314
What happens to C – dpC = -0.03 –> NS acts against C – decrease the frequncey of C
- Before w/ = 0.933 BUT now w/ is 0.903 –> w/ decreased – even though C is a good alelle w/ Decreased (hurt the population fitness to have the good allele)
REASON – only get the beneficial genotupoe 1% of the time – very small amount - most of the time the otehr copes if C make the w/ decrease (when will SC – decreases w/) –> MEANS that the C alelles end up in genoptypes that NS acts against (because ends up in genotypes that have lower fitness)
- Even thought C is the best alelle it won’t go to fixation because NS will act against it because it will only act in uphill directions to increase w/ BUT most of the time C decreases w/ = it will not go to fixation)
Even though C is the best aellle (it has the highest w/) –> natutral selection with act agaionst C in the population (NS is determianistic NOT ominpotent)
