This help page answers some questions about the
mechanics of Web PopGen. The function of buttons will be
described as well as some of the algorithms used in generating
the graphs. Evolutionary theory will not be covered.
Click on the links below to get information on a
particular aspect of the program
Display,
Stochastic/Infinite
populations,
Population Size,
Number of Populations,
Number of Generations,
Initial Allele Frequency,
Selection/Fitness,
Graphing Average Fitness,
Mutation,
Migration,
Inbreeding Bottle
Neck Effect,
Graph effects - Zoom and
Pan
How to copy and paste graphs into a Word Processor Document (
Macintosh,
Windows).
Please send any "Bug" reports, comments or suggestions to
Bob Sheehy
Introduction:
This program is a web based version of Joe
Felsenstein's Simul8
and PopG
programs. There are variations that make the this
program more attractive and some that may make it more painful
to use.
Variations of this program from PopG/Simul8
- Alleles are labeled A1 and A2.
There is no longer an implied dominance between the
alleles. The dominance relationship can be determined
by genotypic fitness.
- Populations are distinguishable by color.
- When more than one population is simulated the upper
graph depicts the frequency of the A1 allele (p)
and the lower graph mirrors the upper graph with the
frequency of the A2 allele (q).
- When a single population is simulated the upper graph
depicts the frequencies of both the A1 and A2 alleles while
the lower graph depicts the genotype frequencies (A1A1,
A1A2, and A2A2).
- Two models of migration are allowed.
- Bottleneck effects may be simulated. Starting and
ending generations determine the length of the
bottleneck. The population size within the bottleneck
may also be determined by the user.
- It is possible to compare the effects of different fitness
values among the different populations.
- When simulating an infinite population it is possible to
have each population start at a different initial allele
frequency.
- The user can click on a region of a graph to zoom in.
Future Changes
- Write data to an output file.
- Stepping stone model of migration
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Display:
The upper part of the display contains the input boxes for
setting variables (population size, fitness, migration rates
etc.). The lower portion contains two graphs. If 2
or more populations are modeled the upper graph will plot the
frequency of the A
1 allele for each population and
the lower graph will mirror the upper graph by plotting the
frequency of the A
2 allele. If a single
population is modeled the frequencies of both the A
1
and A
2 allele are plotted on the upper graph while
the genotype frequencies of the Homozygote A
1A
1,
the homozygote A
2A
2 and the heterozygote
A
1A
2 is plotted on the lower graph.
The simulation is started by clicking on the "
Go" button. If the effect you are
looking for (for example allele fixation) has not occurred by
the completion of the run you could extend the number of
generations.
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Finite
(Stochastic)/Infinite populations:
Simulation may be run either with a defined population size or
with a theoretically infinite population. Finite
populations are used to examine the effects of population size
on genetic drift. Some other factors which affect allele
frequency may become more apparent when using infinite
populations.
When running simulations with a finite population size there
will be a control population (
Infinite Population) that
will allow the user to compare the stocastic populations to an
infinite population.
The pull-down menu allows the user to toggle between finite and
infinite populations. When in infinite population size
mode the user may choose to set the starting allele frequency of
each population different from other populations. The number of
populations being simulated will determine the number of allele
frequency input boxes that are available. Below (center)
is what appears for 5 populations. Each population may
have a different starting allele frequency. If the user
wishes to have the initial allele frequency the same among all
populations she may set the allele frequency for the first
population and then click the "
Set Equal" button.
Note that when the population is in Infinite mode a
Reset
Freq button appears. This allows the user to reset
her starting allele frequency(ies) between runs.
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Population Size
Population size between 5 and 10,000 individuals work well.
The larger the population the slower the
program. Populations larger than 10,000 result in
much slower response time. When running the program in
stochastic mode all populations start with the same initial
allele frequency. Allele frequency will drift,
independently, in each population.
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Number of Populations
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1 to 10 populations may be simulated
at a time. If 1 population is chosen then both
the A1 and A2 allele
frequencies are plotted on the upper graph and the
three genotype frequencies (A1A1, A2A2
and A1A2) are plotted on
the lower graph. If 2 or more populations are
simulated then the frequency of the A1
allele for each population is plotted on the top
graph while the frequencies of the A2
allele for each population is plotted on the lower
graph. Each population is given a different
color and, in the absence of migration, each
population is independent of the others.
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Number of Generations
The number of generations may be set to any desired
value. The greater the number of generations
the longer it will take the simulation to run (the
time between clicking the "Go" button and
when the results appear in the graphs below.
Population size, population number, and the number
of generations to run are the most influential
variables on the speed of the program. |
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Initial Allele
Frequency
Web PopGen simulates
evolution at a single locus with two alleles (A1
and A2). Since allele frequencies
at a locus must sum to 1.0, knowing the frequency of
one allele (the A1 allele for example)
allows you to calculate the frequency of the
alternative allele.
freq(A1)
+ freq(A2) = 1.0
Given the
frequency of A1 it is not difficult to calculate
the frequency of the A2 allele.
freq(A2)
= 1-freq(A1)
Hence, the user need only enter
initial allele frequencies for the A1
allele. When simulating stochastic
populations all populations will start with the
same, user determined allele frequency.
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Selection/Fitness
Web PopGen may be used to
model natural selection of alleles and genotypes.
The fitness of a particular genotype may range from
0 to 1 inclusive. Fitness provides the relative
survival rate of a particular genotype with the most fit
genotype(s) being set to 1.0. For example, suppose
the finesses for the three genotypes are A1A1
= 1, A1A2 = 1 and A2A2
= 0.8. This would indicate that fitness of the A1
allele behaves as a dominant, That the A1A1
homozygote and the A1A2 heterozygote
have an equal fitness (leave, on average, the same number
of viable offspring) and that the A2A2
homozygote leaves, on average 80% of the number of viable
offspring as either the A1A1 and the
A1A2 genotypes.
The general formula for selection is:
- Average Fitness (w):
- w =
p2 * w11 + 2pq * w12
+ q2 * w22
- where p = the frequency of the A1
allele, q = the frequency of the A2
allele, w11 = the fitness of the A1A1
homozygote, w12 = the relative
fitness of the A1A2
heterozygote and w22 = the
relative fitness of the A2A2
homozygote.
- The frequencies of the various
genotypes after selection:
- Frequency of the A1A1
homozygote = (p2 * w11)/ w
- Frequency of the A1A2
heterozygote = (2pq * w12)/ w
- Frequency of the A2A2
homozygote = q2 * w22)/ w
Selecting Infinite
population will cause a check box to appear in the Fitness
box. Initially, the fitness for each genotype is the
same for all populations.
Initially, all
populations share the same fitness values as placed in
the various boxes. Clicking on the check box
reveals a drop down menu which allows the user to
enter different genotypic fitnesses for each of the
populations.
After entering the
desired values clicking on the "OK" button will close the
dialogue box. Only the fitness values for
population 1 will be visible. Note:
Fitnessees for population 1 will not change until
the simulation is started.
When the "GO" button is clicked,
starting the simulation, a key to the various
populations will appear to the right of the upper
graph.
Clicking on the
fitness check box will return to all
populations sharing the same fitness values.
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Graphing Average Fitness w, or Δp
When simulating infinite populations with varied
fitness the frequency of the A1 allele will be depicted in the
upper graph. The user has the option to choose which
data are depicted in the lower graph. By default the
frequency of the A2 allele is depicted here, but by choosing
from the drop-down menu in the Set fitnesses window you may
choose to graph wBar (w) or the absolute
value of the rate of change in p (abs(Δp)).
Migration
Currently two models of migration are possible.
- The Island model
in which migration occurs at random among a group of
small populations.
- The Source-sink or Continent-island model in which there
is effectively one-way movement from a large ("source")
population to a smaller, isolated ("sink") population.
In this case there is no migration among the sub
populations. The allele frequency(s) of the Source
population may be different than the allele frequency of the
sink populations.
The migration option can be chosen by clicking on the
Migration pull-down menu.
Choosing the
Island model you will
see the input data box asking for the rate of migration.
This is a number between 0 and 1 inclusive (0 = no
migration, 1 = every individual is a migrant). If you
choose the Source/Sink model you will see an input box for rate
of migration and another box for the A1 allele frequency in the
source population. Frequency of the A
1 allele
in the source population may vary between 0 and 1 inclusive.
The general formula for migration is:
- Island model:
- Average frequency of the A1 allele (p) is calculated
across all populations.
- pn = pn*(1-m) + m*p
- where pn in the frequency of the A1
allele in population n, m is the frequency of migrants
to the population and 1-m is the frequency of
individuals which do not migrate.
- Source/Sink model
- p'n = pn*(1-m) + m*ps
- where pn is the frequency of the A1
allele in population n, p'n in the frequency
of the A1 allele in population n in the next
generation, m is the frequency of migrants to the
population, 1-m is the frequency of individuals which do
not migrate and ps in the frequency of
the A1 allele in the source population.
Mutation
Mutation allows you to
convert a proportion of one allele type to another
allele type at a given frequency of mutation per allele
per generation. Both forward mutations (A1 A2) and reverse mutations (A1 A2) are allowed.
The frequency of forward and reverse mutations may
vary.
The general formula for mutation is:
- p' = p*(1-µ) + (1-p) * v
- where p is the frequency of
the A1 allele in population, p' is
the frequency of the A1 allele in the
next generation, µ is the frequency of the forward
mutation (A1 A2) and v is
the frequency of the reverse (A1 A2)
mutation.
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Inbreeding occurs when
there is mating between two relatives. This can
be by mate choice (Assortative mating) or by
chance. The degree of inbreeding in a population
is quantified by the inbreeding coefficient, F which
can range from 0 (no inbreeding) to 1 (complete
inbreeding).
In population genetics there are
several F statistics, also called the fixation
statistics, depending on the comparisons being made
(FIS - Individual vs Sub
Population, FST - Sub population vs
total population, FIT - individual vs
Total populations). In this simulator the F
statistic is equivalent to Wright's FIS. and
is the average kinship coefficient between mating
pairs of individuals in the previous generation.
Inbreeding does not change allele
frequency within a population and therefore, by
itself, does not lead to evolution. It does
however alter the genotype frequencies expected
under the assumptions of Hardy-Weinberg.
Coupled with selection, inbreeding may affect the
rate at which allele frequencies change relative to
a population without inbreeding.
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Note that inbreeding will result in, on
average, the increase in homozygotes and a decrease in
heterozygotes. The F statistic is calculated by
comparing the frequency of heterozygtes with a
population to the expected frequency under the
assumption of Hardy-Weinberg (2pq).
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Bottle Neck
Bottlenecks can be simulated for stochastic (finite)
populations. When the bottle neck check box is clicked
four input boxes become available. Start represents the
starting generation (the generation where the population crash
occurs). End is the last generation of the bottleneck where
the population begins returns to the
initial population size. The length of the bottleneck
is determined by values entered into the End and Start
boxes. The size of the population will remain constant
during the bottleneck and is determined by the value placed
in the Pop Size. box. The growth rate determines how
fast the population increases in size. A growth rate
of 1 means the population will remain the size of the
bottleneck population. A growth rate of 2 means the
population doubles each generation until the original
population size is reached.
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