Chapter 21 - Population genetics (part 2):

• Forces that change gene frequencies

• Balance between mutation, drift, selection, and migration

• Mutation-Drift• Mutation-selection• Migration-selection

• Inbreeding & inbreeding depression

Forces that change gene frequencies:

• Natural populations harbor enormous amounts of genetic variation.

• If population is in Hardy-Weinberg equilibrium (large, random mating, free from mutation, migration, and natural selection) allele frequencies remain constant.

• Many, if not most populations, do not meet Hardy-Weinberg equilibrium conditions, allele frequencies change, and the population’s gene pool evolves.

Four main evolutionary processes responsible for such changes:

1. Mutation

1. Genetic drift

1. Selection

1. Migration

Mutation:

• Heritable changes within DNA .

• Source of all new genetic variation.

• Raw material for evolution.

Mutation rate varies between loci and among species: • ~10-4 to 10-8 mutations/gene/generation.

• Mutation rate is abbreviated .

• Some mutations are selectively neutral (no effect on reproductive fitness).

• Others are detrimental or lethal, or beneficial (depends on environment).

• If population size is large, effects of neutral mutation act slowly (i.e., compared to selection) because new mutations are by definition initially rare.

Mutation:

Irreversible mutation:

Allele A is fixed (p =1.0) and mutates A a at rate of = 10-4:

Hartl & Clark (1997) Principles of Population Genetics

Mutation:

Reversible mutation:

Allele A is fixed (p =1.0) and mutates A a at rate of = 10-4; but allele

a mutates a A at a rate of = 10-5.

Hartl & Clark (1997) Principles of Population Genetics

Effects of genetic drift on fate of neutral mutations:

Neutral theory of molecular evolution:

Motoo Kimura (1924-1994)

Genetic drift causes allele frequencies to change over time and wander randomly:

1. Some alleles may go extinct: p 0

2. Other alleles may become fixed: p 1

• Probability of fixation increases with time.

• Which allele becomes fixed is strictly random.

• Rare alleles are more likely to be lost (p 0).

• Time to fixation/loss varies with effective population size (Ne) and initial allele frequency.

Effective population size (Ne):

• The population census size N is distinct from Ne.

• Not all individuals contribute gametes to the next generation.

• Effective population size (Ne) = equivalent number of adults contributing gametes to the next generation.

• If sexes are equal in number and all individuals have an equal probability of reproducing, Ne = N.

• Otherwise: Ne = (4 x Nf x Nm )/ (Nf + Nm )

Nf and Nm = numbers of breeding females and males (Ne = ~8 for a population with 70 breeding females and 2 males).

• Sampling variance: sp2 = pq/2Ne

• Standard error: sp = √(pq/2Ne)• 95% confidence limit = p 2sp

• Variance in Ne is large for small populations, and small for large populations.

Fluctuations in effective population size:

• Population sizes change over time.

• Average effective population size (Ne) is a harmonic mean:

• 1/Ne = 1/t (1/N0 + 1/N1 + … 1/Nt-1)

• Harmonic mean = reciprocal of the average of the reciprocals.

• Important consequence---one short period of of small population size (i.e., bottleneck) can dramatically reduce Ne, and it takes a long time for Ne to recover.

• Other factors that influence Ne:

• Differential production of offspring• Overlapping generations• Population structure• Natural selection

Fig. 21.10, Effect of drift on four populations with initial allele frequencies q = 0.5.

Fig. 21.11, Average time to fixation/loss as a function of population size and initial allele frequency.

Fisher-Wright model of genetic drift:

Hartl & Clark (1997)Principles of Population Genetics

2N = 18

2N = 100

Fisher-Wright model of genetic drift:

Simulated using the software:

DRIFT An interactive program for teaching the concepts of genetic drift by Mark Young (Lincoln University, New Zealand). The program runs under DOS or WINDOWS 3.x on an IBM PC, with or without a mouse.

http://nitro.biosci.arizona.edu/zbook/general/gened.html

Probability of fixation of a new neutral mutation depends on the population size:

• = 1/2Ne

• Ne = effective population size

• Requires average of 4N generations.

• Time between successive fixations = 1/ generations.

Hartl & Clark (1997)Principles of Population Genetics

Take home message - genetic drift has important consequences for small populations:

•Island population of 10 individuals; 5 with brown eyes (BB) and 5 with green eyes (bb); f(B) = 0.5, f(b) = 0.5.

•Typhoon devastates the island; 5 people with brown eyes (BB) die.

•Allelic frequency of b , f(b) = 1.0; chance events have radically changed the allele frequencies and the population evolves.

•Now imagine the same scenario for an island of 10,000 inhabitants.

•This type of “sampling” occurs naturally:

• Which gametes fertilizes the egg?• What proportion of offspring survive?• What proportion of offspring contribute gametes to the next

generation?

Genetic drift acting through founder events, bottlenecks, and geographic isolation can lead to rapid changes in gene frequency and phenotype.

• Effects of Genetic drift can be pronounced when population size remains small over many generations, especially when subpopulations are isolated.

• Founder effect = a population is initially established by a small number of breeding individuals.

• Chance plays a significant role in determining which genes are present among the founders, can lead to rapid evolutionary changes.

• Bottleneck effect = effects of genetic drift when a population is dramatically reduced in size.

• Migration and gene flow in populations increase Ne and reduce effects of genetic drift.

• Fluctuating population size through time may results in complex patterns, as will interaction of drift and selection.

Fig. 21.9, P. Buri’s study of genetic drift in Drosophila.

• 107 experimental populations.

• Randomly selected 8 males and 8 females from each population for the next generation for 20 generations.

Heterozygosity for eight populations of Song Sparrows (Pruett & Winker 2005)

Natural selection:

1. Populations growth occurs exponentially; more individuals are produced than can be supported by available resources resulting in a struggle for existence (e.g., Malthus).

2. No two individuals are the same, natural populations display enormous variation, and variation is heritable.

3. Survival is not random, but depends in part on the hereditary makeup of offspring. Over generations, this process leads to gradual change of populations and evolution of new species.

Natural selection (and adaptation):

1. Natural selection equates to the differential survival of genotypes.

2. Darwinian fitness (W) = relative reproductive ability of a genotype

• Calculate the # of viable offspring relative to other genotypes.

3. Selection coefficient (s) = 1 - W

4. Contribution of each genotype to the next generation:

AA Aa aa

Initial genotypic frequencies

p2 2pq q2

Fitness WAA WAa Waa

Frequency after selection

p2 WAA 2pq WAa q2 Waa

Relative frequency after selection

p2 WAA/WMEAN 2pq WAa /WMEAN q2 Waa /WMEAN

Natural selection (and adaptation):

Some conclusions:

• WAA = WAa = Waa: no natural selection

• WAA = WAa < 1.0 and Waa = 1.0: natural selection and complete dominance operate against a dominant allele.

• WAA = WAa = 1.0 and Waa < 1.0: natural selection and complete dominance operate against a recessive allele.

• WAA < WAa < 1.0 and Waa = 1.0: heterozygote shows intermediate fitness; natural selection operates without effects of complete dominance.

• WAA and Waa < 1.0 and WAa = 1.0: heterozygote has the highest fitness; natural selection/codominance favor the heterozygote (also called overdominance or heterosis).

• WAa < WAA and Waa = 1.0: heterozygote has lowest fitness; natural selection favors either homozygote.

Natural selection:

Selection against recessive alleles:

• Recessive traits often result in reduced fitness.

• If so, there is selection against homozygous recessives, thus reducing the frequency of the recessive allele.

• However, the recessive allele is not usually eliminated; rare, lethal recessive alleles occur in the heterozygote (protected polymorphism).

Fig. 21.17, Selection against a recessive lethal genotype.

Heterozygote superiority: • If a heterozygote has higher fitness than the homozygotes, both

alleles are maintained in the population because both are favored by the heterozygote genotype (e.g., sickle cell trait).

• Also known as: heterosis or overdominance

Fig. 21.19, Distribution of malaria and Hb-S allele.

Effects of selection can override genetic drift:

Fixation of a new favorable mutation:

• Fixation of a new favorable mutation may occur very rapidly, depending on the strength of selection and effective population size.

• When Ne is large, the effects of genetic drift are always small, but the effects of selection can be large (directly proportional to Ne).

• Selective sweep = process by which a favorable mutation becomes fixed in a population due to force of positive selection.

• Closely-linked neutral alleles can hitchhike during a selective sweep (i.e., genetic draft, which is distinct from genetic drift).

• Linked regions of DNA around the favorable allele become overrepresented in the population; leads to excess of rare alleles at linked loci.

• Effects of selection become apparent not only at the selected locus but also in the flanking DNA sequences.

Migration equates to gene flow - movement of genes from one population to another.

Three major effects:

1. Introduces and spreads unique alleles to new populations.

2. If allelic frequencies differ between two populations, gene flow changes allele frequencies of the recipient population.

3. By increasing the effective population size, migration reduces the effects of genetic drift.

Fig. 21.13, Effect of migration on a recipient gene pool.

Hartl & Clark (1997) Principles of Population Genetics

Change in allele frequency with one-way migration (m = 0.01)

Migration (cont.):

• Increases the effective size of a population.

• Prevents allelic fixation.

• If migration rate (m) >> mutation rate rate of (), effects of genetic drift that tend to cause populations to diverge in allelic frequencies will be offset.

• Measure migration scaled to the mutation rate (m/).

• Important to conservation biology because habitat fragmentation can prevent gene flow, and thus reduce effective population size of isolated populations, increasing the effects of genetic drift.

• Maintaining natural corridors between populations is essential.

Balance between evolutionary forces – equilibrium models: • Balance between mutation & genetic drift

• Balance between mutation & selection

• Balance between migration & selection

Balance between mutation and genetic drift:

• Mutation adds genetic variation/genetic drift removes variation.

• Infinite alleles model predicts that mutation and drift balance each other to result in a steady state of heterozygosity.

Assumptions of the infinite alleles model:

1. Each mutation is assumed to generate a novel allele never observed (and the probability that two mutations will generate the same mutation is infinitely small).

2. Genetic drift operates as normal, affecting smaller populations disproportionately.

3. Heterozygosity: H = (4 Ne )/ (1 + 4 Ne )

4. Neutral parameter = 4 Ne

*describes balance between mutation and drift (if Ne doubles and is halved H remains the same).

Fig. 21.12, Relationship between = 4 Ne and expected heterozygosity.

Hartl & Clark (1997) Principles of Population Genetics

Balance between mutation and selection: • When an allele becomes rare, changes in frequency due to natural

selection are small.

• Mutation occurs at the same time and produces new rare alleles.

• Balance between mutation and selection results in evolution.

For a complete recessive allele at equilibrium:

• q = √ (/s)

• If homozygote is lethal (s = 1) then q = √

Balance between migration (gene flow) and selection: • High levels of gene flow (>2 effective migrants per generation) will

counter the tendency for isolated populations to differentiate or speciate.

• High rates of gene flow (>10 effective migrants per generation) will typically result in low Fst values between two populations for most loci in genome.

• Populations might generally be indistinguishable (cryptic).

• But that doesn’t mean that individual populations don’t evolve and adapt to their local environment.

• If the effects of selection are stronger than migration (s >> m), specific alleles that are well-suited (beneficial) to their environment can still become disproportionally represented.

• Gene flow is locus-specific and a function of “migration/selection balance”.

Safran, R. J. & Nosil, P. (2012) Speciation: The Origin of New Species. Nature Education Knowledge 3(10):17

Genic View of Speciation

Safran, R. J. & Nosil, P. (2012) Speciation: The Origin of New Species. Nature Education Knowledge 3(10):17

Leads to heterogeneity creating “genomic islands of divergence” against a neutral background

Yellow-billed pintail

Locus FST

mtDNA 0.00OCD1 0.01ENO1 0.01FGB 0.00GRIN1 0.02*PCK1 0.03*HBA2 0.01

* = significant P-value

A subunit4 amino acid substitutionsST = 0.65

Cause a beneficial increase in Hb-O2 affinity in the presence of phosphate and chloride.

Hohenlohe PA, Bassham S, Etter PD, Stiffler N, Johnson EA, et al. 2010 Population Genomics of Parallel Adaptation in Threespine Stickleback using Sequenced RAD Tags. PLoS Genet 6(2): e1000862. doi:10.1371/journal.pgen.1000862

Threespine Stickleback

Finally, one more important and related topic: Assortative mating

• Individuals do not mate randomly but prefer one phenotype to another. Affects allele frequencies. Assortative mating may be positive or negative.

Inbreeding

• Preferential mating of close relatives.

• Small populations may show this effect even with no tendency to select close relatives.

• Acts on allele frequencies like genetic drift by decreasing Ne.

• Heterozygosity decreases and homozygosity increases.

• Self-fertilization is the most extreme example.

Effects of inbreeding: • Effects of inbreeding are generally thought to be maladaptive.

• Outbreeding is usually beneficial.

• But interestingly, inbred population do not always show evidence of inbreeding depression (harmful effects).

• Repeated cycles or persistent periods of small population size are thought to purge populations of deleterious alleles.

Review Slide - Summary of effects of evolutionary forces:

• MutationOccurs at low rate, creates small changes, and increases genetic variation; balanced with natural selection and drift.

• Genetic driftDecreases variation due to loss of alleles, produces divergence and substantial changes in small populations through bottlenecks, founder events and geographic isolation; balanced with mutation.

• Migration Rates and types of migration vary, increases effective population size and decreases divergence by encouraging gene flow (and reduces drift), but also creates major changes in allele frequencies; balanced with selection.

• Natural selectionIncreases or decreases genetic variation depending on the environment, continues to act after equilibrium has been achieved; balanced with other forces, e.g., mutation and migration.

• Non-random matingInbreeding decreases variation and in some cases fitness (but not always), and contributes to the effects of other processes by decreasing effective population size.