Population structure and random changes

1
Population structure and random changes

• Hardy-Weinberg principle no change in allele
  frequencies if
• No mutation
• No selection
• Infinite population
• Random mating
• No immigration
• Mutations (chapt. 10)
• Selection (chapt. 12 and 13)
• Genetic drift is the effect of finite population
  size
• Inbreeding is the effect of non random mating
• Gene flow is the result of immigration

2

• 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
  16 17 18 19 20 21 22 23 24 25
• 2 3 4 4 4 5 6 6 6 7 8 10 11 11 12 13
  14 18 18 20 21 22 22 23 23 25
• 3 3 4 4 4 5 6 6 6 8 10 11 11 11 11 12
  13 13 14 18 18 18 18 20 23 23
• 4 3 3 4 5 6 8 10 10 10 11 11 11 11 13 13
  13 18 18 18 18 18 18 18 18 23
• 5 3 3 3 5 5 8 8 10 10 11 11 13 13 13 13
  18 18 18 18 18 18 18 18 23 23
• 6 3 3 3 3 3 3 5 5 5 8 8 10 11 13 13
  13 13 13 18 18 18 18 18 23 23
• 7 3 3 3 3 3 3 3 3 5 5 8 8 11 11 13
  13 13 13 13 18 18 18 18 18 18
• 8 3 3 3 3 3 3 3 3 3 8 8 8 11 13 13
  13 13 13 13 18 18 18 18 18 18
• 9 3 3 3 3 3 3 3 3 3 3 3 8 8 8 8
  8 13 13 18 18 18 18 18 18 18
• 10 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
  8 8 8 13 13 18 18 18 18 18
• 11 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
  3 8 8 8 8 13 13 18 18 18
• 12 3 3 3 3 3 3 3 3 3 3 3 3 3 3 8
  8 8 13 13 13 18 18 18 18 18
• 13 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
  3 3 8 8 13 13 13 18 18 18
• 14 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
  3 3 8 8 8 8 13 13 13 18
• 15 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
  3 3 8 8 8 8 8 13 13 18
• 16 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
  3 3 8 8 8 8 8 8 13 18
• 17 3 3 3 3 3 3 3 3 3 3 3 3 8 8 8
  8 8 8 8 8 8 13 13 13 18
• 18 3 3 3 3 3 3 3 3 3 3 3 3 3 8 8
  8 8 8 8 8 8 8 8 8 18
• 19 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
  3 3 8 8 8 8 8 8 8 18

3
Genetic drift

• Assume no differences in fitness, no selection,
  alleles are neutral
• In a finite population allele frequencies
  fluctuate by chance
• Genetic variability decreases and eventually
  disappears
• One allele becomes fixed it replaces all the
  others
• The probability of an allele to become fixed
  allele frequency
• Eventually all individuals in the population
  decend from a single ancestor
• Each individual has an equal chance to be the
  future ancestor of the whole population

4
Genetic drift more detailed
2N
Genetic diversity HT (1 1/2N) HT-1
Probability of identity FT 1/2N (1 - 1/2N)
FT-1
Average time to fixation 4N
5
More genetic drift

• Genetic drift is stronger in smaller populations
• Genetic diversity is lost more rapidly

Figure 11.5
HT (1 1/2N) HT-1
6
Several populations

• Genetic drift will make initially identical
  population different
• Eventually, each population will be fixed for a
  different allele
• If there are very many populations, the
  proportion of populations fixed for each allele
  will correspond to the initial frequency of the
  allele
• Small populations will get different more rapidly

7
Importance of genetic drift

• Two causes for allele substitutions
• Selection -gt adaptive evolution
• Genetic drift -gtnon-adaptive evolution
• Most populations are geographically structured
• All populations are finite in size
• All genetic variation is subject to genetic drift
  but not necessarely to selection
• Genetic drift as a null hypothesis against which
  evidence for selection has to be tested

8
Backwards the coalescent approach

• Simplification 0, 1 or 2 offspring
• Coalesce have the same parent
• Probability to coalesce 1/N
• Probability Not to coalesce 1 1/N
• t generations (1-1/N)t
• Average time to coalesce for 2 genes N
• For the whole population 2N

Figure 11.24
9
Bottlenecks and founder effect

• Bottleneck the population size is drastically
  reduced for one or more generations
• Founder effect a new population is founded by a
  few individuals
• Effect
• Loss of rare alleles
• Loss of heterozygozity
• Identification of bottlenecks
  important in conservation
  biology

Figure 11.6
10
Bottleneck example
Song sparrows on Mandarte Island (Canada) entire
population studied from 1974 1996.
Diversity estimted from 8 microsatellite loci
Consequences of the bottleneck Large reduction
in number of alleles Slight effect on the
heterozygozity
(Keller et al. 2001)
11
Repeated founder effect

• mtDNA CR sequences from Greenfinches from all
  over Europe
• Correlation of genetic diversity with latitude
• Explanation New populations were founded
  repeatedly during the northward expansion after
  the ice age

(Merilä et al. 1997)
12
Effective population size

• Effective population size lt Census size (in most
  cases)
• The effective population size is the size of an
  ideal population having the genetic properties
  of the studied population
• The effective population size is determined by
• Large variation in the number of offspring
• Unequal numbers of males and females
  contributing to reproduction
• Overlapping generation
• Fluctuations in population size

Ne lt N
1
1
1
S

n
Ni
Ne
(Harmonic mean)
13
Inbreeding

• Panmictic population mating is random
• Most species are geographically devided, and
  mating is local
• Inbreeding individuals are more likely to mate
  with relatives than with non related individuals
• Identity in state (IIS) having the same allele
  (e.g. A)
• Identity by descent (IBD) having a copy of one
  particular A allele (e.g. From Granfather Bill)

14
Inbreeding coefficient

• Inbreeding coefficient F probability of identity
  by descent probability of an individual to be
  autozygous
• Genotype frequencies with inbreeding
• In inbred populations
• Frequency of heterozygotes is reduced relative to
  HW
• Frequency of homozygotes is increased relative to
  HW
• F can be measured by the difference between
  observed and expected heterozygozity

15
Estimation of F from a pedigree

• Chain-counting technique
• Trace a path from I through each common ancestor
  and back to I.
• Count the number of individuals (n) in each
  patch, excluding I
• Inbreeding due to a particular path (common
  ancestor) f (1/2)n
• F sum of f from each path
• Coefficient of relationship r expected
  proportion of genes IBD 2F of their potential
  offspring

Figure 11.13
16
Selfing

• Selfing is the most extreme form of inbreeding
• It is common in plants and occurs in some animals
  (e.g. flatworms and snails)
• The degree of selfing varies between species
• Selfing can be advantageous in some situations
  (isolated habitat)
• Animals capable of selfing, usually prefer to
  mate with another individual if they find a
  partner
• Many plants have adaptations to prevent selfing,
  e.g. Flower morphology or self-incompatibility

17
Consequences of inbreeding

• Decrease in heterozygozity
• The genetic variance of a quantitative character
  is usually increased by inbreeding
• Inbreeding depression reduced average fitness
  due to increased expression of deletrious
  recessive alleles in the population
• Linkage disequilibrium non-random associations
  of alleles at different loci. With less
  heterozygotes, the opportunities for
  recombination get fewer.

Figure 11.10
18
Song sparrows
Average inbreeding coefficient F (calculated from
pedigree)
Distribution of inbreeding coefficients for birds
that died in the crash (white) and birds that
survived (black)
Keller et al. 1994, 2001
19
Inbreeding depression

• Armbruster et al. (2000)
• Equivalent inbreeding depression under laoratory
  and field conditions in a tree-hole-breeding
  mosquito

20
Inbreeding genetic drift

• Consider a finite population of unique
  individuals which reproduces for several
  generations (random mating)
• The average probability of identity (ISS and IBD
  in this case) F increases each generation
• This is a result as well of genetic drift as of
  inbreeding
• Heterozygozity (1 F) in the population
  decreases
• This is again a result of both inbreeding and
  genetic drift
• If inbreeding occurs within the population, the
  effective population size will be reduced and
  drift will be more rapid
• Inbreeding has also a meaning at the individual
  level Individual F

21
Several demes differentiation

• A large population is divided into local demes
• Genetic drift will occur in each deme and make
  allele frequencies diverge
• The probability of IBD in each deme will increase
• After t generations on average F 1 (1
  1/2N)t
• When in all demes all individuals are descendent
  from one ancestor F 1
• FST is used as measure for population
  differentiation

Two etimates
22
Migration gene flow

• Contrary to selection and genetic drift gene flow
  homogenizes allele frequencies
• Genetic diversity is restored if immigrants carry
  new alleles or alleles which are rare in the
  population
• Differentiation among populations gets weaker
• m migration rate corresponds to the proportion
  of individuals entering the population and
  breeding (the proportion of genes having been
  carried into the population by immigrants in that
  generation)

23
Gene flow
2N
m
24
(Mutation has the same effect)
2N
µ
Assumes that each mutation creates a new allele
Infinite allele model
Mutation also retards the loss of genetic
variability due to genetic drift
25
Equilibrium

• After a long time (the longer the larger the
  population) there will be an equilibrium between
  genetic drift, gene flow and mutation
• F and H will not change any more (if everything
  remains constant !!)

FT 1/2N (1 - 1/2N) FT-1 (1 m- µ)2
Mutation drift equilibrium
Migration drift equilibrium
26
Back to gene flow

• Different models of gene flow
• Continent island model
• Island model
• Stepping stone model
• Continuous populations model
• Extinction and recolonization
• Groups of small populations inhabiting habitat
  patches. Some populations go extinct and the
  patches get recolonized Metapopulation
• Genetic diversity and differentiation among local
  populations depend on the extinction rate, the
  mode of recolonization a.o...

27
Estimating gene flow

• Direct estimates observation. e.g.
  Capture-mark-recapture, radio-telemetry
• Measure dispersal or migration, not necessarely
  gene flow
• Problem of scale
• Indirect (genetic) estimates Measure allele
  frequencies at some neutral loci (markers). Infer
  gene flow from the population structure and the
  level of differentiation at different distances
• One has to assume equilibrium
• Difficult to distinguish between historical
  association and gene flow in some cases
• Problem of sampling design

28
Collared lemmings on small islands (1)
Microsatellite data (4 loci) Average He
0.83 Kent region FST 0.047
(Ehrich et al. 2001)
29
Collared lemmings on small islands (2)

• In isolated small populations, variation is lost
  by genetic drift

at equilibrium
30
Collared lemmings on small islands (3)

• Isolated small populations diverge under the
  effet of genetic drift

FT 1/2N (1 - 1/2N) FT-1 (1 m)2
31
Summary

• Genetic drift In a finite population allele
  frequencies fluctuate at random and eventually
  one allele will be fixed
• After 4N generations all individuals descend from
  one ancestor
• Genetic diversity is lost more rapidly in small
  populations
• Inbreeding reduces the number of heterozygotes
• Inbred individuals can have lower fitness
  inbreeding depression
• The genetic composition of isolated populations
  diverges under the effect of genetic drift
• Gene flow homogenizes allele frequencies among
  populations
• After a long time, the genetic variability in a
  population reaches an equilibrium level mutation
  immigration drift equilibrium