Population Genetics

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Population Genetics

• Alleles A a
• Genotypes AA Aa aa
• Frequencies 50 30 20
• Symbol P Q R
• Calculate the individual gene frequencies
• freq. A (p) P ½Q 0.5 0.15 0.65
• freq. a (q) R ½ Q 0.2 0.15 0.35
• p q 1, therefore 1 - p q or
• 1 q p

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• If we know gene freqs (p and q), how can we
  calculate the genotype frequencies?
• What is probability of getting an A gamete?
• gene freq of A p
• Therefore, freq of AA p2
• Probability of getting an a gamete? q
• Therefore, freq of aa q2

3

• How do we calculate the heterozygote freq?
• Probability of egg A (p) x sperm a (q) pq
• Probability of egg a (q) x sperm A (p) pq
• Therefore, freq of Aa 2pq
• So all 3 genotypes can be calculated by their
  gene freqs using the equation
• p2 2pq q2
• Hardy- Weinberg Equation!

4

• MN blood group and Hardy-Weinberg Eq.
• MM MN NN
• MM freq. 29
• Therefore, p2 0.29, and p 0.54
• If p 0.54, then q 0.46, so q2 0.21 and
• 2pq 0.50
• So MM MN NN
• 0.29 0.50 0.21
• And these are very close to the actual
  frequencies in the European American population

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Assumptions of the H-W Equilibrium

• No selective advantage of one allele over
  another, i.e., no natural selection
• No new alleles introduced via mutation
• No gain or loss of alleles due to immigration (no
  gene flow)
• No random changes in gene freqs assumes an
  infinite population size
• Totally random mating every individual has an
  equal chance of mating and producing equal
  numbers of offspring

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What is the value of H-W equaiton?

• Since not all of the assumptions will hold true
  in natural populations most of the time, the
  numbers predicted by the H-W equation wont be
  accurate
• Why use it?
• H-W equation can serve as a null model for a pop
  not undergoing evolution
• The ways in which a real pop deviate from the
  expected H-W values give us clues as to what
  evol. mechanisms are at work

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What if Natural Selection is working?

• AA Aa aa
• Lets say that aa is being selected against
• Selection coefficient s of population with
  that genotype selected against
• If s 0.1, then 10 of aa are lost in each
  generation and 90 survive
• So chances of aa survival is 1-s fitness of
• that genotype

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• So you can modify the H-W Equation to account for
  selection if you know the selection coefficient
• p2 2pq q2 (1-s)

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Can you lose a entirely?

• If all a alleles are lost and all genotypes are
  AA, we say that A has become fixed
• But as q declines, fewer aa individuals occur to
  be selected against, so the rate of loss of a
  declines
• Most a alleles occur in Aa heterozygotes
• As long as fitness of Aa AA, you cant lose a
  entirely the locus remains polymorphic

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What if heterozygote is more fit than either
homozygote?

• Selection coefficients for both homozygotes
• (s and t). Modify the H-W equation to account
  for selection
• AA Aa aa
• p2(1-t) 2pq q2(1-s)
• If st, rate of change of p will q gt
  equilibrium
• If sltt (fitness of AAltaa), p will decline rel. to
  q
• If sgtt (fitness of aaltAA), p will increase rel.
  to q

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Sickle-cell disease

• HbHb HbHbs HbsHbs
• In Nigeria, selection against sickle homozygote
  (s) 0.86 against normal (from malaria) (t)
  0.12
• HbHb HbHbs HbsHbs
• p2(0.88) 2pq q2(0.14)

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• If one gene or its homozygous genotype is
  consistently favored, selection will be
  directional no equilibrium gene freqs will
  shift
• If heterozygotes are consistently favored, the
  gene pool can reach a stable equilibrium, p q
• What if selection fluctuates, favoring one
  genotype at one time and another at a different
  time?
• gt Frequency-dependent selection fitness of a
  genotype varies with its frequency in a population

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Frequency-dependent selection

• Your fitness depends on how common you are in the
  population usually rare genotypes are favored

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How much can mutation affect the H-W equilibrium?

• Mutation rates at individual loci appear to be
  low 1 in 10K to 1 in 1M per generation
• So in one generation the effect on p or q will be
  very slight
• Over long periods of time these changes in
  frequency can accumulate

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How do mutations interact with natural selection?

• Neutral mutations will accumulate according to
  the natural mutation rate (low)
• Positive mutations will increase depending on
  their fitness, i.e., selection can amplify
  mutation
• Negative mutations should disappear quickly
  before they can accumulate

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Exception to loss of negative mutations

• Mutation-selection balance equilibrium
  frequency of a mutant allele if
• selection rate mutation rate
• q vm/s
• q equilibrium gene frequency
• m mutation rate
• s selection coefficient

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Example of mutation-selection balance

• Spinal muscular atrophy high mortality (s0.9)
  counting numbers in current pop, estimated gene
  freq is 0.01 (1 in 100) hi!
• If this mutant is maintained by m/s balance
• 0.01 vm/0.9, so m 0.9x10-4
• Looking at known family trees, 7 of 340 patients
  were new mutations
• From this m was calculated at 1.1 x 10-4

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Is cystic fibrosis governed by mutation-selection
balance?

• Frequency of cf allele is 0.02 (2 in 100)
• Selection coefficient is high (gt0.8)
• If the cf freq is maintained because of m/s
  balance, m 4 x 10-4
• Actual mutation rate 7 x 10-7
• What other factor(s) might cause the gene freq to
  be so high?

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Look at biology of cf

• cf homozygotes have very thick mucus that traps
  bacteria gt develop severe, chronic lung
  infections most die before age of reproduction
• Heterozygotes produce moderately thick mucus so
  have fewer lung infections, but it traps
  enteropathic bacteria like salmonella
• Normal homozygote has thin mucus no lung
  infections but also susceptible to gut infections
  from enteropathogens
• Heterosis!

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What if gene flow is going on?

• Few natural populations are totally isolated
• But gene flow may be low
• - due to random migration among pops
• - part of mating system, e.g., exclusion of
  young males plant pollination
• Gene flow maintains genetic variation within
  populations (demes) minimizes variation among
  demes - more later!

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What if gene freqs change at random?

• Random fluctuations in gene frequencies
• GENETIC DRIFT
• This is an evolutionary mechanism because it
  changes gene frequencies, but since the shifts
  are random, it is non-adaptive

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• Genetic drift derives from sampling error
• by chance, the gene pool does not remain in
  equilibrium from one generation to another
• E.g., heterozygote Aa should pass on equal
  numbers of A and a gametes, so ½ of its offspring
  should get A and ½ should get a
• By chance, it may not likelihood depends on
• of offspring (pop size)

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Strength of GD depends on population size

• Analogy to coin toss
• If you toss a coin 10,000 times you are likely to
  get a 5050 ratio of headstails (by chance if
  you toss several heads in a row, youll also toss
  several tails in a row)
• If you toss a coin only 10 times, what are the
  chances youll get 5 heads5 tails?
• Small sample gt random skewing of frequencies

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• Whats different about a coin toss vs.
  reproducing a gene pool?
• Drift is additive (will accumulate) unlike coin
  toss, starting freqs change in each generation
• Drift typically leads to loss of one allele
  fixation of the other gt monomorphic loci
• GD tends to decrease genetic diversity within
  populations

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Why does GD lead to fixation?

• Random walk model
• Drunk on a runway runway length time width
  pop size with enough time /or small pop, he
  will fall off (allele will be lost)
• So as GD gt fixation, heterozygosity will decline
  which may affect fitness

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GD may vary during the lifetime of a population
if its size varies

• 1) Bottleneck effect - E.g., snowshoe hares in
  the Arctic

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Variable effects of GD (cont.)

• 2) Founder effect small colony founds a new
  population
• - small colony not likely to be repre-sentative
  of parent gene pool (sampling error)
• - GD will quickly skew gene freqs in a small
  population

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What determines pop size?

• Census accurate in random-mating pop
• But in many pops, census is not accurate does
  not reflect actual number of breeding adults
  effective pop size
• Limited by
• Assortative mating
• Unequal sex ratios
• Overlapping generations
• Bottleneck effect

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• Most species comprised of many small demes
• Each is drifting randomly with respect to A a
• GD tends to lead toward fixation (? diversity)
  within demes, but since each deme is drifting
  randomly, we get maximum diversity among demes

1000
3565 Aa
8020
7030
1090
0100
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Sewall Wrights Model

• Small demic structure with low gene flow is best
  to respond to evolution
• Maximizes genetic diversity among pops
• Even rare alleles can ? and become fixed in some
  demes
• Small amount of gene flow among demes will keep
  all pops from becoming monomorphic
• Thus, survival and local adaptation of pops is
  possible if natural selection is acting, e.g., if
  environment changes this variation will increase
  likelihood that at least one deme has the right
  gene combinations to be able to respond to
  selection

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Neutralists vs. selectionists

• If most variation is neutral then GD is the only
  evolutionary mechanism (i.e., freqs of neutral
  alleles change at random) favored by
  Neutralists (NS only gets rid of deleterious
  mutants)
• Selectionists argue that many (or most) mutant
  alleles have selective value and NS is the
  primary force governing gene frequencies

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What if mating isnt random?

• Non-random mating is seen in inbreeding
  relatives mating
• Most extreme case
• AA x AA Aa x Aa aa x aa

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25
50
aa
AA
Aa
Inbreeding gt ? in heterozygosity and ? in
homozygosity
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• If pure inbreeding is going on (no GD or NS), the
  H-W equation can be modified with an inbreeding
  coefficient (F) probability that 2 alleles came
  from the same ancestor (low diversity)
• If all genotypes are equally fit (no NS), p and q
  dont change only the genotype frequencies
  shift toward the two homozygotes (no evolution)

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Inbreeding Natural Selection

• NS usually will select against the homozygous
  recessive genotype gt ? q
• Since inbreeding increases likelihood of many aa
  individuals being born, it causes ? fitness
  inbreeding depression
• If aa is highly lethal (s is high), A may
  increase rapidly
• If you add GD to the mix, fixation and loss of
  genetic diversity may happen very quickly in the
  population

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Outbreeding mechanisms

• Plants perfect flowers (both ? ? parts)
• Protandry/protogyny male (anthers) and female
  (stigma) flower parts mature at different times
• Heterostyly e.g., stigma taller than anthers
• Self-incompatibility self-sterility alleles
  prevent pollen from forming pollen tube on its
  own stigma/pistil

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Outbreeding mechanisms (cont.)

• Animals
• Protandry in hermaphroditesgtcross-breeding
• Behavior!
• Young males banished from natal group
• Mate recognition preference for the unfamiliar

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Summary of GD Inbreeding

• GD changes gene freqs (evol. mechanism)
• Inbreeding changes genotype freqs (no evolution
  if only inbreeding)
• Both have strongest effects in small pops
• Both ? genetic diversity GD by random fixation
  and loss inbreeding by ?ing homozygosity gt
  inbreeding depression
• Gene flow is major counteracting force to bring
  new diversity into demes, but keep it low so GD
  /or NS can gt divergence among demes gt local
  adaptation gt new species

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GD and Inbreeding in a real population Greater
Prairie Chickens

• Large, relict pops remain in KS, MN, NE
• In IL (Jasper Co.) they are in trouble!
• farming caused pop ? thru 19th century
• 1933 total hunting ban, but pop continued ?
• only a few 100 left by 1960
• 1960s habitat sanctuaries established small
  rebound of pop s
• 1980s crashed again only 6 adults found in 1990

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Why the pop decline?

• Hypothesis small, isolated pop w/o gene flow
• gt high GD with ? genetic diversity high
  inbreeding with ? homozygosity
• gt unmasks lethal recessives
• gt inbreeding depression w/? fitness
• gt fewer survivors gt smaller pop
• EXTINCTION VORTEX

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Is an Extinction Vortex affecting Greater Prairie
Chickens?

• Evidence for decreased genetic diversity
• Normal pop. has mean of 5.5 alleles/locus
• Jasper Co. pop has mean of 3.7 alleles/locus
• Evidence for decreased fitness
• Hatching rates normal (KS, MN, NE) 90
• Jasper Co 40
• Thus, ? genetic diversity due to GD and
  inbreeding depression appear to be causing an
  extinction vortex among the Greater Prairie
  Chickens of Jasper Co., IL

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How do we counter the problem?

• We must ? genetic diversity ? pop size
• Gene flow individuals from MN, KS and NE were
  introduced to Jasper Co. in 1992
• By 1998 hatching rates were up to 90
• No new data on allelic diversity, but the pop
  size has rebounded into the 1000s

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Gene flow as an evol. mechanism

• Amount of gene flow is often dependent on spatial
  organization of populations
• Island model individuals may move to any other
  pop with equal frequency gt random gene flow among
  demes

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• Stepping stone individuals move to deme closest
  to them probability of mating ? with distance

In a continuous pop model this can lead to
isolation by distance
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Estimating gene flow rates

• Did genes get exchanged?
• GF is probably overestimated methods
• Mark recapture bird banding, ear tags, etc.
• Release genetically marked (mutant) individuals
  to study dispersal and infiltration of gene pools
• Measure genetic diversity among continuous pops
  to see how similar/different they are

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GF varies with habits of species

• Sedentary species have very low GF but mobile
  species have higher GF
• Slow movers or small animals disperse little vs.
  coyotes other highly mobile species (e.g.,
  planktonic vs. benthic)
• Seed dispersal is often low unless large carriers
  (mammals birds)
• Pollen dispersal is better but pollinators may be
  localized (bees)

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What do the studies show?

• GF in most species is low to moderate
• Few species form a unitary gene pool among
  populations
• Even if geographic distances are not great, many
  species have low GF
• Implications
• GD may gt strong divergence among demes
• Demes may easily adapt to local conditions gt
• Polymorphic species

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Polymorphism

• Freq-dependent selection (balanced polymorphism)
• Heterosis maintains multiple alleles
• Sexual dimorphism
• Environmental heterogeneity gt adaptation to
  microhabitats (different genotypes have different
  fitness in microhabitats)
• E.g., iron-adapted plants color polymorphs gt
• Ecotypes

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Ecotypic variation

• Clinal ecotypes occur in a linear pattern
• e.g., with altitude, latitude, rainfall (Glogers
  Rule, Bergmans Rule)
• Mosaic ecotypes occur wherever appropriate
  habitat occurs

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Are ecotypes always genetic?

• Genetic ecotypes vary because of NS and can
  evolve
• Ecophenotypes vary because of environ-mental
  effects non-heritable variation, e.g., stunted
  growth in cold or windy habitats height affected
  by nutrition eunuchs
• Ecophenotypic variation does not play a role in
  evolution so we need to identify it

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Design experiments to test genetic vs.
ecophenotypic ecotypes

• Salmon vertebrae story
• Potentilla glandulosa (sticky cinquefoil)

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Another example of NS producing polymorphism

• Character displacement

Allopatric pops
Sympatric pops
What is the selective force? Low hybrid fitness
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• Another pattern of polymorphism is geographic
  races geographically distinguishable pops with
  consistent and correlated patterns of
  polymorphism subspecies
• This may be adaptive (ecotypic)
• It may also be due to random differences
  accumulated during reproductive isolation (e.g.,
  oriental eye fold in humans curly vs. straight
  hair in mammals)
• If mating of subspecies gt ? hybrid fitness gt
  character displacement, then gt speciation

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Can we use H-W to look at more than one locus?
Lets say we have genes at 2 loci A,a and
B,b What are the haploid genotypes
(haplotypes)? AB, Ab, aB and ab If all the
alleles are independent of each other, i.e., A is
not found with B any more freq than with b, etc.,
then haplotype frequency is predictable based on
the freq of the individual alleles
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• pA 0.6 AB pAxpB 0.48
• qa 0.4 Ab pAxqb 0.12
• pB 0.8 aB qaxpB 0.32
• qb 0.2 ab qaxqb 0.08
• Of 60 of individuals carrying A (0.480.12)
• 80 (0.48/0.60) carry B and 20 (0.12/0.60)
  carry b
• Of 40 carrying a (0.320.08), 80 (0.32/0.40)
  carry B and 20 (0.08/0.40) b

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• Linkage equilibrium B and b do not segregate
  with A or a more frequently than their gene
  frequencies would predict (same proportions as
  their allele freqs)
• In this case we can use H-W for haplotype freqs

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• pA 0.6 but AB pAxpB 0.44 B in 73
• qa 0.4 Ab pAxqb 0.16 b in 27
• pB 0.8 aB qaxpB 0.36 B in 90
• qb 0.2 ab qaxqb 0.04 b in 10
• So haplotypes occur in higher or lower
  pro-portions than expected of their gene freqs
• B is less freq linked to A and more freq linked
  to a than Bs gene freq predicts, etc.
• Linkage disequilibrium haplotypes are over or
  under-represented have to adjust H-W equation
  with LD coefficient

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Why linkage disequilibrium?

• 1) At random in a small pop, GD can lead to LD,
  e.g., by chance one of the haplotypes may be
  lost, or a mutation shows up changing Agta in only
  one individual that carries B but not b gt skews
  haplotype freqs away from predicted

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• 2) Gene flow mixing populations with different
  haplotype freqs may gt LD
• Say aB occurs at higher freq compared to AB in
  one pop than in another if the 2 pops merge you
  add both aB and AB, but in different proportions
  than in the original pop gt LD
• 3) Natural selection if it favors certain
  haplotypes over others, one will ? and another ?,
  e.g., if the abab homozygote is lethal, the ab
  haplotype may disappear altogether

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Why does LD matter?

• If 2 loci are in LD, a change in freq at one
  locus gt a change in freq at the linked locus that
  may be independent of its fitness gt
• E.g., if A and B are linked in LD (A occurs
• more freq than expected with B than with b)
• say NS favors A because its linked to B,
• B will automatically ? even if B has no
• selective advantage
• So selection cannot independently change the freq
  of A without B being carried along

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• In linkage disequilibrium we cannot assess the
  independent fitness of the linked loci we dont
  know whether freq of A B are ?ing because both
  are being favored, or whether one is along for
  the ride!
• LD can also act as a brake on evolution gt if A
  has high fitness but B has low fitness, it might
  be impossible to ? A because LD would also ? B
• As long as they remain linked NS may not be able
  to optimize the freq of A

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How common is LD?

• Most studies show it is uncommon
• Why?
• Sexual reproduction automatically ? LD
• Recombination shuffles genes to randomize alleles
  at the two loci and recreate any missing or
  low-freq haplotypes
• How long does it take to eliminate LD?
• Depends on pop size (? effects of GD) rates of
  crossing over (location on chromosomes) how
  strong NS is in favoring certain haplo-types over
  others

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Sexual vs. asexual reproduction why sex?

• Sexual reproduction is energy consuming gt Meiosis
  vs. mitosis
• gt finding and securing a mate
• It is risky gtaggression from potential mates
• gt exposure to predators
• Wasteful gt mate may be infertile
• gt gametes may be damaged

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• Asexual repro should swamp out sexual
  reproduction
• Asexuals produce 2X as many offspring as do
  sexuals (high fitness potential)
• Asexuals should ? rel. to sexuals and ultimately
  take over a population
• Vast majority of multicellular species reproduce
  sexually even if they use both asexual and
  sexual modes (e.g., aphids, cnidaria, most
  plants)
• Sex must be good!

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Why reproduce sexually?

• 1) Sex decreases Genetic Load accumulation of
  deleterious mutations
• in asexuals new mutations are eliminated only by
  NS and GD high mortality
• in sexuals these are also lost thru out-crossing
  and recombination
• e.g., AA x Aa, with a deleterious mutation

A
a
A
Some of offspring would not carry a at all (½
in this cross ¼ in heterozygote cross
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• 2) Recombination breaks LD and contin-uously
  shuffles genes gt genetic diversity
• in unchanging environment there is no sexual
  advantage asexuals should ?
• in changing environment, asexuals will either all
  do well or all do poorly
• Because of genetic diversity in sexuals, unique
  gene combinations will develop that may ?
  potential to respond to changing environment
• Downside is that sex breaks up favorable gene
  combinations

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Evidence for value of sex

• Most multicellular organisms have sexual
  reproduction either exclusively or as part of an
  alternation of generations
• In forms with alternation of generations, the
  asexual forms predominate during good times when
  rapid ? in s is beneficial when environment
  becomes unstable, they switch to the sexual form