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Population genetics
Thinking like a population geneticist
!
Thinking like a population geneticist
Expectation!
The expected value of a random variable,
especially the average; a prediction or
forecast.!
T04_Thinking like a popgen.key - 25 September, 2014
Expectation of being hit by a meteorite?
Expectation of being hit by a meteorite?
Probably null. Why?!
!
!
Expectation of being hit by a meteorite?
Expectation of being hit by a meteorite?
Barringer Meteor crater, Arizona
http://www.barringercrater.com
T04_Thinking like a popgen.key - 25 September, 2014
Expectations
Expectations in population genetics attempt to
predict things like:!
You have combined your knowledge of the physical
world and your experience to arrive (perhaps
unconsciously) at a prediction or an expectation: !
!
meteorite strikes are possible but are so
infrequent that the risk of being struck is
minuscule.
1) how much genetic variation is present in a
population, !
2) how genetic variation in a population changes
over time,!
3) pattern of genetic variation that might be left
behind by a given biological process that acts over
time or through space
First principles
FIRST PRINCIPLES
T04_Thinking like a popgen.key - 25 September, 2014
Parameters and parameter estimates
Parameters and parameter estimates
Quantities in population genetics are
estimated with error. !
!
!
WHY?!
Parameters and parameter estimates
Parameters and parameter estimates
Parameter A variable or constant appearing in a
mathematical expression; a value (usually
unknown) used to represent a certain population
characteristic; any factor that defines a system and
determines or limits its performance.!
Parameter: exact value of some
measurement
!
Parameter estimate: value
measured on a sample
Estimate An indication of the value of an unknown
quantity based on observed data; an approximation
of a true score, parameter, or value; a statistical
estimate of the value of a parameter.!
T04_Thinking like a popgen.key - 25 September, 2014
Example
Example
p̂ = 0.483
p̂ = 0.474
p̂ = 0.464
p̂ = 0.490
p̂ = 0.498
p̂ = 0.531
p̂ = 0.518
p̂ = 0.483
p̂ = 0.521
p̂ = 0.460
p̂ = 0.483
p̂ = 0.517
SUM 3.980
AVERAGE 0.498
(SUM/ N)
SUM 7.896
S.D. 0.0271
(SUM/ N)
S.E. 0.0096
(SD/ √ N)
p̂ = 0.478
p̂ = 0.489
p̂ = 0.514
p̂ = 0.493
AVERAGE 0.494
(SUM/ N)
S.D. 0.0212
(SUM/ N)
S.E. 0.0053
(SD/ √ N)
S.E.: how far the true population
average (a parameter) may be
from the sample average (a
parameter estimate) by chance.
Example
p̂ = 0.483
p̂ = 0.474
p̂ = 0.464
p̂ = 0.490
p̂ = 0.498
p̂ = 0.531
p̂ = 0.518
p̂ = 0.483
p̂ = 0.521
p̂ = 0.460
p̂ = 0.483
p̂ = 0.517
p̂ = 0.478
p̂ = 0.489
p̂ = 0.514
p̂ = 0.493
SUM 3.9800
SUM 7.8960
AVERAGE 0.4980
AVERAGE 0.4940
S.D.
0.0271
S.D. 0.0212
S.E.
0.0096
S.E. 0.0053
Inductive and deductive reasoning
T04_Thinking like a popgen.key - 25 September, 2014
Inductive and deductive reasoning
Inductive and deductive reasoning
Inductive
Inductive
Observation/
Experiment
Observation/
Experiment
Inductive and deductive reasoning
Inductive and deductive reasoning
Inductive
Inductive
Observation/
Experiment
Observation/
Experiment
Generalizations
Generalizations
Paradigma / Theory
T04_Thinking like a popgen.key - 25 September, 2014
Inductive and deductive reasoning
Inductive and deductive reasoning
Inductive
Inductive
Deductive
Observation/
Experiment
Observation/
Experiment
Generalizations
Generalizations
Paradigma / Theory
Paradigma / Theory
Deductive
Paradigma / Theory
Inductive and deductive reasoning
Inductive and deductive reasoning
Inductive
Inductive
Deductive
Observation/
Experiment
Deductive
Observation/
Experiment
Observation/
Experiment
Generalizations
Predictions
Generalizations
Predictions
Paradigma / Theory
Paradigma / Theory
Paradigma / Theory
Paradigma / Theory
T04_Thinking like a popgen.key - 25 September, 2014
Inductive and deductive reasoning
Inductive
Observation/
Experiment
Observation: Every time
I’ve walked by that dog, he
hasn’t tried to bite me.
!
Generalizations
Paradigma / Theory
Generalization: the next
time I walk by that dog he
won’t try to bite me.
!
Theory: that dog will not
bite me.
Inductive and deductive reasoning
Inductive
Observation/
Experiment
Isaac Newton used knowledge of how
objects fall to the surface of the Earth as
well as knowledge of the movement of
planets to arrive at the general
principles of gravity.
Deductive
Theory: All cars have tires
Prediction: Therefore, your
car has tires
Observation/
Experiment
Predictions
Generalizations
If the initial premise is correct,
Paradigma / Theory
the conclusion is correct…
Paradigma / Theory
T04_Thinking like a popgen.key - 25 September, 2014
Inductive and deductive reasoning
Theory: Every day, I leave
for work in my car at eight
o’clock. Every day, the drive
to work takes 45 minutes I
arrive to work on time.
Prediction: Therefore, if I
leave for work at eight
o’clock today, I will be on
time.
Theory and assumptions
Deductive
Observation/
Experiment
Predictions
• What is a theory and what are assumptions?!
• How can theories be useful with so many!
assumptions?!
If the initial premise is correct,
the conclusion is correct…
Paradigma / Theory
allele frequency !
how often a form of a gene appears in a
gene pool
T04_Thinking like a popgen.key - 25 September, 2014
allopatric speciation !
The formation of a new species as a result
of an ancestral population's becoming
isolated by a geographic barrier
biological species concept !
a species concept defining a species as a
population or group thereof whose
members potentially interbreed and
produce fertile offspring!
bell curve !
Bell-shaped curve; typically results from
graphing frequency versus distribution for
a trait that varies continuously in a
population!
directional selection !
occurs when natural selection favors one of
the extreme variations of a trait!
T04_Thinking like a popgen.key - 25 September, 2014
disruptive selection !
natural selection that favors individuals
with either extreme of a trait!
emigration !
movement of individuals out of a
population!
gene flow !
exchange of genes between populations!
gene pool!
combined genetic information of all the
members of a particular population!
T04_Thinking like a popgen.key - 25 September, 2014
genetic drift !
the gradual changes in gene frequencies in
a population due to random events!
geographic isolation!
form of reproductive isolation in which two
populations are separated physically by
geographic barriers such as rivers,
mountains, or stretches of water!
!
gradualism !
the theory that evolution occurs slowly but
steadily!
Hardy-Weinberg principle !
the principle that states that the frequency
of alleles in a population does not change
over generations unless outside forces act
on the population (mutation, genetic drift,
gene flow, natural selection and mate
selection)
T04_Thinking like a popgen.key - 25 September, 2014
immigration !
movement of individuals into an area
occupied by an existing population!
!
morphology !
the branch of biology that deals with the
structure of animals and plants!
microevolution evolution !
resulting from small specific genetic
changes that can lead to a new subspecies
phenotype !
frequency equal to the number of
individuals with a particular phenotype
divided by the total number of individuals
in the population
T04_Thinking like a popgen.key - 25 September, 2014
population genetics !
the study of genetic changes in
populations; the science of
microevolutionary changes in populations
prezygotic isolation !
reproductive isolation that occurs before a
zygote can be formed!
!
postzygotic isolation !
reproductive isolation that occurs after
members of two different species have
mated and produced a hybrid offspring.
Such hybrids are usually unable to
reproduce!
punctuated equilibrium !
pattern of evolution in which long stable
periods are interrupted by brief periods of
more rapid change!
T04_Thinking like a popgen.key - 25 September, 2014
reproductive isolation !
separation of species or populations so that
they cannot interbreed and produce fertile
offspring
speciation !
the formation of new species as a result of
evolution
sexual selection !
a form of natural selection in which
individuals with certain inherited
characteristics are more likely than other
individuals to obtain mates
stabilizing selection !
natural selection that favors intermediate
variants by acting against extreme
phenotypes
T04_Thinking like a popgen.key - 25 September, 2014
CONCLUSIONS
• General principles and direct
measurements taken in actual
populations combine to form
comprehensive expectations about
amounts, patterns, and cause-and-effect
relationships in population genetics.
• The theory of population genetics is the
collection of well-accepted expectations
used to articulate a wide array of
predictions about the biological
processes that shape genetic variation.
CONCLUSIONS
CONCLUSIONS
sympatric speciation !
the formation of new species in populations
that live in the same geographic area
T04_Thinking like a popgen.key - 25 September, 2014
CONCLUSIONS
• Population genetics is not a spectator
sport! Direct participation in computer
simulation provides the opportunity to
see population genetic processes in
action. You can learn by trial and error
and test your own understanding by
making predictions and then
comparing them with simulation
results.
CONCLUSIONS
CONCLUSIONS
• Parameters are idealized quantities that
are exact while parameter estimates
wear notational “hats” to remind us
that they have statistical uncertainty.
• !• ! Population genetics uses both
inductive reasoning to generalize from
knowledge of specifics and deductive
reasoning to build up predictions from
general principles that can be applied to
specific situations.
T04_Thinking like a popgen.key - 25 September, 2014