Download Biology 4974/5974 Evolution

Populations: Equilibrium and Inbreeding
Evolution
Biology 4974/5974
D.F. Tomback
Biology 4974/5974
Evolution
Population genetics:
equilibrium and inbreeding
Smith & Smith 1998 Ecology and Field Biology, 6th ed.,
Benjamin Cummings
Figures are from M.W. Strickberger (2000) Evolution,
3rd ed., Jones and Bartlett, unless indicated
otherwise.
Smith& Smith 1998
Learning goals
Understand the following:
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How natural selection sorts among individuals but
populations are the unit that evolves over time.
How to calculate allele frequencies given genotype
information.
The conditions required for Hardy-Weinberg equilibrium.
The implications of equilibrium for evolution.
Whether most populations meet H-W conditions.
The definitions of inbreeding.
How inbreeding violates H-W conditions.
How inbreeding affects populations genetically and in
fitness.
Definitions
Population: “….a group of organisms belonging to one species
(conspecific) occupying a more or less well-defined geographical
region and exhibiting reproductive continuity from generation to
generation.”
Mendelian population: A group of sexually interbreeding or
potentially interbreeding individuals.
Deme: Local population, within which individuals are most likely
to mate with one another.
Gene pool: The sum total of genes represented by a population.
It includes all the different kinds of genes in the genome of the
species, plus all the different alleles for each gene, at their
represented frequencies.
Gene frequencies: The proportion of the different alleles of a
gene in a population. (Total diploid individuals x 2 = total “slots”
for a given gene; total haploid individuals x 1 = total “slots” for a
given gene.)
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Populations: Equilibrium and Inbreeding
Evolution
Biology 4974/5974
D.F. Tomback
Individual vs. population in evolution
See p. 365-6
• Variation among individuals comes
from multiple genetic sources.
• Natural selection is based on the
differential survival and reproduction
of individuals in relation to prevailing
conditions.
• Populations respond to selection,
with changes in allele frequencies
over time.
• Other genetic mechanisms change
gene frequencies in populations over
time, including mutation, gene flow,
and genetic drift.
• Individuals cannot evolve but
populations and species evolve
over time.
Calculating gene frequencies for diploid populations
Two methods:
• Based on total gene
counts within a gene
pool.
• Based on genotype
frequencies.
Example (see right):
Gene with two alleles,
T and t, T dominant.
Possible genotypes:
TT Tt tt (T=tasting
phenylthiocarbamide)
Hardy-Weinberg Equilibrium
Genetic definition of evolution: “Genetic changes in
populations through time that lead to differences among
them.”—Strickberger’s Evolution. “Changes in allele
frequencies over time.” –Price (1996)
The Hardy-Weinberg equilibrium is the fundamental principle
of population genetics (“founding theorem,” p. 376).
• In 1908, G.H. Hardy and W. Weinberg independently
determined that for a population where mating is random, allele
frequencies do not change over time.
• If genes are not linked and natural selection, genetic drift,
mutation, and gene flow, are not affecting a particular gene
locus, then the allele frequencies at that gene will not change.
Hardy-Weinberg equilibrium demonstrates which conditions
are necessary so gene frequencies do not change--that is,
conditions for no evolution at a gene locus.
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Populations: Equilibrium and Inbreeding
Evolution
Biology 4974/5974
D.F. Tomback
Hardy-Weinberg Equilbrium
In sexually-reproducing populations, under conditions of
stability, the frequencies of genes remain constant from
generation to generation. Stability no evolution
“Frequencies of genes” refers to relative proportions
of all alleles for any gene.
 Frequency of T = 0.60 = p
 Frequency of t = 0.40 = q
 p + q =1
Thus, under conditions of “stability,” the values for p and q
should stay the same generation after generation.
No evolution is occurring at this gene if p and q remain
the same over time.
Hardy-Weinberg Equilbrium
Equilibrium genotype using
the binomial expansion for a
one gene, two allele system:
• T = 0.60 = p; t = 0.40 = q
• (p + q)2 = p2 + 2pq + q2 = 1
• p2 (TT) + 2pq(Tt) + q2(tt) = 1
• (0.60)2 (TT) + 2(0.60)(0.40)
(Tt) + (0.40)2(tt) = 1
• Equilibrium genotype
frequencies are: 0.36 TT,
0.48 Tt, 0.16 tt
Fig. 18.10
Hardy-Weinberg Equilibrium assumptions
For allele frequencies to
remain stable from
generation to generation,
these conditions must be
met.
These conditions result in
“random mating.”
Fig. 18.9
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Populations: Equilibrium and Inbreeding
Evolution
Biology 4974/5974
D.F. Tomback
Conditions for stable gene frequencies
from Fig. 18.9
• Parents represent a random sample of gene
frequencies in the population.
• Genes segregate normally into gametes…
• Parents are equally fertile…
• The gametes are equally fertile…
• The population is very large…
• Mating between parents is random….
• Gene frequencies are the same in both male and
female parents.
• All genotypes have equal reproductive ability.
Interpretation of these assumptions
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Population is large enough so chance does not alter
gene frequencies.
Mutations must not occur, or the rate of forward and
back mutations are equal.
Allele frequencies are not altered by gene immigration
or emigration.
Mating is random with respect to that gene.
All genotypes have equal survival value; all genotypes
leave the same number of offspring.
How realistic is each assumption?!
What does this tell us?
Most populations experience some change in gene
frequencies over time at some gene loci.
• This varies with the gene locus.
• Most populations are evolving at one or more genes.
• However, only a relatively small number of genes violate
the Hardy-Weinberg Equilibrium conditions—many are
neutral, assuming a population is large enough and
mutation is rare.
• In population genetics, genes are assumed to be in
H-W equilibrium.
• If not, then natural selection or linkage disequilibrium or
another process become the hypotheses for testing.
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Populations: Equilibrium and Inbreeding
Evolution
Biology 4974/5974
D.F. Tomback
Inbreeding
Hardy-Weinberg Equilibrium condition requires that
mating be random. If mating is random, the population
is panmictic.
• But, random mating is the exception and not the rule.
• Most populations experience some degree of
inbreeding: mating between relatives.
• Whether inbreeding occurs and how much depends on
dispersal patterns in populations and population size.
• If individuals do not move far from where they were born,
hatched, or germinated, they have a good chance of
encountering relatives when they breed.
• Also, the smaller the population, the greater the chance
for inbreeding.
Inbreeding definition
Relatives are defined as individuals who carry genes that are
identical by descent--that is, the same allele from a common
ancestor. The inbreeding coefficient F expresses the
probability that offspring inherit two gene copies that are
identical by descent. Here, F = 1/8.
Fig. 18.EB2
Relatives and inbreeding
A population is inbred if the probability that offspring
inherit two gene copies that are identical by descent is
greater than would be expected under random mating.
The Inbreeding Coefficient F ranges from 0 to 1 in
value:
• 0 = random mating. No genes identical by descent.
• 1.0 = complete inbreeding (e.g., selfing). All genes
identical by descent.
• When F > 0, the population is inbred.
• F also indicates the proportion of heterozygosity
reduced each generation by inbreeding relative to a
randomly breeding population.
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Populations: Equilibrium and Inbreeding
Evolution
Biology 4974/5974
D.F. Tomback
Effect on gene vs. genotype frequencies
Inbreeding does not change allele frequencies but it
does change genotype frequencies.
The frequency of homozygotes increases and the
frequency of heterozygotes decreases.
• Random mating: p2 + 2pq + q2 = 1
• Inbreeding: (p2 + Fpq) + (2pq – 2Fpq) + (q2 + Fpq) = 1
• TT genotype frequency is now p2 + Fpq
• Tt genotype frequency is now 2pq - 2Fpq
• tt genotype frequency is now q2 + Fpq
The allele frequencies p and q remain the same despite
continous inbreeding. However, the genotype
frequencies shift each generation, depending on the
magnitude of F.
Inbreeding
As inbreeding continues, F increases over time and the frequency of
heterozygotes decreases.
• The rate of increase of F and rate of loss of heterozygosity is faster the
smaller the population.
• The closer the relatives mating, the faster the increase in F.
Fig. EB18 2.2
Fig. EB18 2.3
The consequences of inbreeding
Inbreeding increases the probability that lethal and
deleterious recessive alleles are exposed in
homozygous genotypes.
Heterozygotes are actually considered the most fit for
many traits.
Case history: Song Sparrows on Mandarte Island, BC.
Keller et al. 1994. Selection against inbred Song Sparrows during a
natural population bottleneck. Nature 372:356-7.
• All birds on Mandarte Island were color-banded and of
known pedigree.
• Population crash in 1988; only 11% (n = 12) of
population survived.
• The mean F of the dead birds was 0.0312.
• The mean F of the survivors was 0.0065.
So what did this study show about the relationship
between survival and inbreeding for Song Sparrows on
this island?
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Populations: Equilibrium and Inbreeding
Evolution
Biology 4974/5974
D.F. Tomback
Comparison of survival among Song Sparrows
Case history: Greater Prairie Chicken
The Greater Prairie Chicken (Tympanuchus cupido)
has a lek mating system, where males establish small
territories and display to attract females.
• The Illinois population has been declining drastically with
conversion of prairie to cropland.
• Numbers in Illinois dwindled from 25,000 in 1933 to 50
birds in 1994 (Westemeier et al. 1998).
Freeman and Herron 2004
Greater Prairie Chicken
The remaining birds occurred in two remnant
populations in Jasper and Marion County.
• Grassland restoration increased the population in the
1960’s and 1970’s, but the population dropped to only 5
or 6 males in the 1990’s.
• The few prairie chickens remaining were isolated in
small populations within farmland.
• These had little or no gene flow. The populations were
suffering from genetic drift, inbreeding, and a general
loss of heterozygosity.
Freeman and Herron 2004
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Populations: Equilibrium and Inbreeding
Evolution
Biology 4974/5974
D.F. Tomback
Greater Prairie Chicken
Loss of genetic variation and inbreeding was reflected in
• Declining hatching success
• Low allelic variation.
Researchers began trapping Greater Prairie Chickens in other
states and moving them to Jasper County in the 1990’s.
Hatching success improved immediately.
WHY?
Freeman and Herron
2004
Study questions
• Define: gene frequencies, gene pool, evolution from the
genetic perspective, and inbreeding.
• Calculate gene frequencies based on a) genotype
frequencies and b) numerical counts? Try this problem:
AA(0.49) + Aa (0.42) + aa(0.09) = 1.0 and 98AA + 84Aa +
18aa = 200 individuals
• If a population meets Hardy-Weinberg conditions for a
given gene, what happens to allele frequencies over time?
• What is the binomial expansion for a one gene, two allele
system to determine genotype frequencies?
• What are the main assumptions of Hardy-Weinberg
Equilibrium? How realistic are they?
Study questions, continued
• How is F defined as a probability?
• What are the effects of inbreeding on gene
frequencies vs. genotype frequencies?
• What effect does population size have on rate of loss
of heterozygosity?
• Why is inbreeding generally bad?
• What did the study of Song Sparrow survival tell us
about the effects of inbreeding?
• Why did hatching success improve in the Greater
Prairie Chicken after new individuals were
introduced into the population?
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