Population genetics - Migration Flashcards
What does migration usual conjur up
Organism moving across space
examples:
1. Wildbeasts across area – variation in raine = drives popultion shifting range
- Artic turns
What do we mean by migration
Emigration + imigration drynamics between sub popultions
- When indiviual in one popultions contrubutes to genes in other popultion
Movement of alleles from one breeding popultion to another breeding popultion
- Indiviouals departing from or arriving in a new breeding popultion
What does migration violate in H-W
H-W = no one can go in or out –> when you are born into a popultion you contrubute to that popultion and no one comes in
- Violating the 3rd assumption
This is the assumption we are violateing to model migration
NOW the gentic makeup of the new generation is NOT just a function of within popultion reproductive dynamics – NOW it also includes some input from other popultions
Migration example
Can get movemnt between the forest and evergaldes black bears or night not get any migration
Individuals going between popultions birng alleles to the other popultion –> move from one gene pool to another gene pool
Two models of migration
- Continent island model – larger popultion going to smaller
- Two island model – recpiprcal gene flow (this is the one we use)
Migration model
Start = have 2 subdivided popultions with difefrent alelles frequnceies
AT H-W –
Poplation 1 – P = 0.8 –> p1 = 0.8
Popultion 2 – P = 0.2 –> p2 = 0.2
At H-W the allele frequencies would stay the same (no migration) –> BUT THEN we can swap individulas at a rate of m
m = proportion of one population that will contrubute to reproduction pool of other popultion in the next generation
m in migration models
Proportion of popultion that contributes to the next generation of the other popultion
HERE = we assume that m is the same for both popultions
- We could do m1 and m2 for each popultion BUT we willl treat m symetrically
Things we need to account for in migration model
- m – proportion of popultion that contributes to the next generation of the other popultion
- Input
- m - 1 – need to account for individuals leaving popultion (need to take account loss)
- Loss from original population
- Loss of migrants from our focal popultions
Change in allele frequencey in migration model
Get chnage in allele frequency because move individuals in and out = undergo evolutionary change
Looking m and 1-m = allele frequencies change
Mathamatical model of migration
𝑝′1 = (1 − 𝑚) (𝑝1) + (𝑚)(𝑝2)
- 1-m X p1 – only have individulas with p1 allele frequncey
- m = migration rate
- m X p2 – get indiviuals at a raye of m at P2 allele frequncey
𝑝′2 = (1 − 𝑚) (𝑝2) + (𝑚)(𝑝1)
p’ = allele frequncey in the next generation
(1- 0.05) X (0.8) – only 95% f 0.8 allele frequncey contribute to next generation
(0.05) X o.2 - 5% of popultion have frequncey of 0.2
Because the system is symetrical migration chnage alelle in both popultion by same amount in different direction (because same m)
- Since we set up the system to be symetrcal (same m for both) = they change by the same amount
Change in alelle frequncey in both popultions
Because the system is symetrical migration chnage alelle in both popultion by same amount in different direction (because same m)
- Since we set up the system to be symetrcal (same m for both) = they change by the same amount
Popultion A – allele frequnceies are close together
- P goes up in ine popultin and down in the other by the same amount
- Allele frequncey chnage in A is smaller than B because allele frequncey in A is already similar to begin with
Popultion B the allele frequcneies are far apart
- Even though the allele frequncey is NOT the same = the allele frequcney chnage is still is –> means that suymetery in chnage is not because of p being mirrories it is becuase m is the same
Pop A vs. Pop B.
- Allele frequncey chnage in A is smaller than B because allele frequncey in A is already similar to begin with
Affect of same m
If m is the same = p chnages by the same amount in different directions in both popultions
- Even though the allele frequncey is NOT the same = the allele frequcney chnage is still is –> means that suymetery in chnage is not because of p being mirrories it is becuase m is the same
dP = same –> sign is different but the absolute value is the same
- Even if allele frequncey is not symetric dP still is if m is the same for both popultions
What is happening with migration over time
Use general dP –
dP = m(p2 - p1)
- Assume m is the same
- p2 - p1 – Frequcney of same allele in popultions 2 vs population 1 –> drives magnitude of change
End point of migration
if dP = 0 –> get equillirbium point - get an end point of popultion
IF migration is ongoing dP = 0 when P2 = p1 (when the allele frequnceies are identical)
- Have end point in middle + know what endpoint is
END – P2 = P1 –> end is when dP = 0
Migration is…
Determanistic – have an endpoint and know what the endpoint os –> if you know the start you can know what effect will be
- Migration will go until p2 = p1
Effect of migration
Migration acts to decrease genetic diffeerntaion between popultions – homogenizes genetic varaition across subdivided popultions
- If migration keeps occuring popultions will evenually have the same alelle frequncey
- Makes allele requncies of popultion more similar through time until there is no difference between thwm
Homogenize until get equal Pt (will end equal to the frequncey across popultions Pt)
Pt
If two popultions were in one popultions what would overall p be
- Allelic varaition in total popultion if subdivided were in one popultion
- Pt = used to find Ht = Heterpzygosity across popultions
THIS is what migration pushes P to in each popultion – pushes to average of 2 alleles
- Migration acts to drive P1 and P2 towards PT
FST of drift vs. migration
Drift = increases FST towards 1
- Drift = makes Pt less similar
- Increases differences between popultions
Migration decreases FST towards 0
- decrwases difefrences between popultions
- Make popultions converge of Pt
Migration and drift = in direct opposition
- If migration acts to dirve P1 and P2 towards PT = acting in direct opposition of drift
Can find an equillirbium between the two
Meaning of FST
Increase difefrence between popultions
FST = 1 = no shared alleles (have P = 1 and P =0)
FST = 0 – ni allele frequency differences (they are the same)
FST
The measure of genetic differentiation between subdivided popultions
Drift vs. Migration
If migration acts to drive P1 and P2 towards Pt = acting in direct opposition to drift
- Effects can be viewed in terms of FST
Have an equillibrum point where forces balance out
Drift vs. migration equillbirum point
FST>
Size of m and FST>
If m is smalle (less than 10-15%)– can calculate FST at equillirbium between drift and migrayion –>
𝐹𝑆𝑇= 1/4𝑁𝑒𝑚+1
Nem = efefctive popultion size times the migraytion rate = the numver of effective migrants per generation
- Nem = improtant term
- Assume that level of FST = due to equillibrum between drift and migration = can use FST to see number of migrants moving in generation
***Ne and m = hard ot gte iun popultionn but they are meaningful
Use of FST
Assume that level of FST = due to equillibrum between drift and migration = can use FST to see number of migrants moving in generation
Given a value of FST = can find Nem = can find expected number of effective migrants
- Here we assuime that the popultions are at equillbirum
FST = 0.0476 –> FSt is much closer to 0 than 1 = these popultions are much more alike than they are different
Changing Ne
If increase Ne – loosing FST vakue = FST decreases
Increase Ne = FST decreases because ability for drift to maintain allele frequncey difefrences decreases and migration is strong
Increase Nem = favor of migration over drift = become similar
Decrease Nem = favor drift = miantain differences
FST> with larger popultion size
FST> = 0.0243
Increase Nem = favor of migration over drift = become similar
Decrease Nem = favor drift = miantain differences
FST at equillibrium
if m is small we can calculate FST at equillirium between drift and migration
FST> = 1/4Nem+1
Nem term
Effective population size times the migration rate – it is the number of effective migrants per generation
Meaning of FST
FST = equilibrium point between the effects of drift and effect of migration
- It is a function of migration rate and strength of drift
THIS IS A PUSHING EAQUILLIBRIUM = stable equillirbium between the two forces
Looking at how connected the 2 popultions are
IF FST = 0.5 – assume equillirbium
Nem = 1/FST/4FST
Nem = 1-0.5/4X0.5 = 0.25
- Nem = effective number of migrants
0.25 –> means have 0.25 individuaks (can be decimal because its an average)
- Means – 1 indiviuals every 4 generations (the popultions ate quite isolated)
- 0.25 is NOT the migration rate – it is the avergae number of migrations per generation
Looking at how indepent the popultions are –> you can find genotype frequncey –> use that to find FST –> get Nem
FST = 0.203 –> pretty intermediate
Nem = 0.981 –> If allelic varaition is driven by long term drift + migration = get 0.981 deer each generation
- 0.981 deer going from one to other (Since symetric = goes both ways)
Pairwise effects of forces
- Mutation selection balance
- Mutation adding alleles and NS getting rid of them
- s and u
- The dual effect of drift and mutation driving neutral molecular evolution
- Drift regarless of popultion size drives genotypic variation between two species
- u and N
- Drift regarless of popultion size drives genotypic variation between two species
- The tension between drift and migration in subdivided populations
- m and N
Drift and selection interaction
IMAGE:
- Left of 0 = selection predominates (negitive selection)
- Line at 0 = drift predominates
- Right of 0 = positive selection – selection predominantes
- INtersection of lines – point where drift = acting soley on alleles – there is no difefrence between drift affect on alleles and NS affect
Deviation from balance between Drift and mutation (deviation from intersection) = based on 2Nes
Probability of mutation being lost due to drift = more likley (1-1/2N)
Image = shows drift + selection simultaneously in a system (violating infinate popultion size)
Overall – there are osme parameters where selection will predominate and spme where drift will
- Popultion size decreases = stringer strength of ____ for selection to be predominante dirver of allele frequncey chnage
- Selection needs to act alongside drift – relative strength pf 2 ffoces = affects if selection can occur
Take home message – the relative magnitude of selection and drift matter – they often behave as if one force is predominant over the other
Is pushing of adopative peaks always a bad thing?
If have scenerio in image –> You can go to w/ = 0.35 OR can go to w/= 1
IF p goes to p> = it will stay there – this is bad because low w/ – NS can’t move it from the valley BUT other evolutionary forces can
- If went to the right of valley = would go to p = 1 – would end at w/ = 0.35
- If have other forces with selection = won’t get stuck there –> drift can chnage { and can drift acros equillirbium to the left and NS can then bring it to P = 1
- Selection can’t do this by itself but it can with other forces – drift opens up posibility
- Selection + drift = two step process involoving chnage in predominance of first (first drift predominates then selection)
OR migration can come in – other population with benefical allele can come in – they can send migrants –> migrants can go to the focal popultion and can bring P across equillibrium and allow NS to bring P = 0 and w/ = 1
NS by itself can’t bring the popultion to the global optimum but selection in conjuction with other forces can
How to think about Rugged topographies
It is more realistic to think in multiple dimensions
Example – image
- Can see two traits
- Rugged topography because 2 points of high fitness states –> Can’t go between points without decrease w/ –> NS can’t go between them itself
- Have local optimum at combination of low values or trait 2 and moderate values of trait 1
- Have global optimum at combination of moderatley high values of trait 2 and highest values of trait q
- Highest fitness = high trait 2 and high trait 1
- There are two possibilities on high w/ based on right combination of trait values –> need right combo to have right value
Example – 2 locus fitness epistasis
Has two fitness peaks + 2 low vallues
A1 has high fitness in presence of B1
- A1 = only high fitness with B1
A2 only has high fitness in the presence of B2
- High A2 and B2 = high fitness
Wrong combo of alleles = decrease fitness
If to the left of valley = fix for A1B1 BUT if to the firght of balue fix for A2B2
Have Adaptive topography for A with w/ and Adaptive topography with B for W/ –> put them together to see interaction
