ms – a program for generating samples under neutral models
Richard R. Hudson October 16, 2017
This document describes how to use ms, a program to generate samples under a variety of neutral models. The purpose of this program is to allow one to investigate the statistical properties of such samples, to evaluate estimators or statistical tests, and generally to aid in the interpretation of polymorphism data sets. The typical data set is obtained in a resequencing study in which the same homologous segment is sequenced in several individuals sampled from a population. The classic example of such a data set is the Adh study of Kreitman(1983) in which 11 copies of the Adh gene of Drosophila melanogaster were sequenced. In this case, the copies were isolated from 11 different strains of D. melanogaster collected from scattered locations around the globe.
The program ms can be used to generate many independent replicate sam- ples under a variety of assumptions about migration, recombination rate and population size to aid in the interpretation of such polymorphism studies. The samples are generated using the now standard coalescent approach in which the random genealogy of the sample is first generated and then mutations are ran- domly place on the genealogy (Kingman, 1982; Hudson, 1990; Nordborg, 2001). The usual small sample approximations of the coalescent are used. An infinite- sites model of mutation is assumed, and thus multiple-hits and back mutations do not occur. However, when used in conjunction with other programs, finite- site mutation models or micro-satellite models can be studied. For example, the gene trees themselves can be output, and these gene trees can be used as input to other programs which will evolve the sequences under a variety of finite-site models. These are described later.
The program is intended to run on Unix, or Unix-like operating systems, such as Linux or MacOsX. The next section describes how to download and compile the program. The subsequent sections described how to run the program and in particular how to specify the parameter values for the simulations.
If you use ms for published research, the appropriate citation is: Hudson, R. R. (2002) Generating samples under a Wright-Fisher neutral
model of genetic variation. Bioinformatics 18: 337-338.

Downloading and compilation
All relevant files including this pdf file are included in the tar file ms.tar available at 􏰁 rhudson1. Download this tar file to your machine then extract the files from the archive with: tar -xvf ms.tar . After extracting, type cd msdir, then compile the programs by typing:
gcc -o ms ms.c streec.c rand1.c -lm
gcc -o ms ms.c streec.c rand2.c -lm
or alternatively, typing ./clms, which contains this compilation line with rand1.c. The choice of these compilations depends on which random number generator one has available. rand1.c and rand2.c call drand48() and, rand(), respec- tively. I make no claims concerning the properties of these generators, and it would be straightforward to replace these by another generator, such as one of those described in Numerical Recipes in C (Press et al., 1992).
With rand1.c and rand2.c, one can specify the three seeds on the command line, with -seeds x1 x2 x3 where the x’s indicate the three integer seed values. If no -seeds switch appears on the command line, ms looks for the file “seedms” to find the seed values for initializing the random number generator. If no seedms file is found the generator is seeded with a default value. When the simulation is finished, the state of the random number generator is output to seedms. In this way, each time ms is invoked a new set of results is produced. If one wishes to produce the same set of samples, seedms can be edited to contain the value(s) indicated on the second line of the output file.
In all cases, the seeds are printed on the second line of the output file, so that the same set of samples can be generated again if desired.( The program can also be compiled with rand1t.c or rand2t.c, which use the system clock for seeding the generators and don’t utilize the file seedms at all.)
The basic command line:
ms nsam nreps -t θ
The above line shows the simplest usage of ms which generates samples under the basic neutral model, with constant population size, no recombination, panmixis, and an infinite-sites model. In this case there are three arguments to ms: nsam, nreps, and, following the switch “-t”, the parameter θ. The two arguments, nsam and nreps are required and must appear in this order.(Although there are exceptions, most of the switches can appear in any order.) nsam is the number of copies of the locus in each sample, and nreps is the number of independent samples to generate. The third parameter here is the mutation parameter, θ = (4N0μ) , where N0 is the diploid population size and where μ is the neutral mutation rate for the entire locus. (Note: As described later,when the -I switch

is used, ms can generate samples under models with population structure. In those cases N0 is the number of diploids in each subpopulation.) At least one of the options, -t -s , -T or -L must be used. The latter three options are described later. After nsam and nreps, any or all other switches with their parameters can be read from a file using -f filename.
Here is an example command line:
ms 4 2 -t 5.0
In this case, the program will output 2 samples, each consisting of 4 chromo- somes, generated assuming that θ = 5.0.
The output
The output from the example command in the previous section would look like this (the exact output will depend on the random number generator) :
ms 4 2 -t 5.0
27473 36154 10290
segsites: 4
positions: 0.0110 0.0765 0.6557 0.7571
segsites: 5
positions: 0.0491 0.2443 0.2923 0.5984 0.8312
The first line of the output is the command line. The second line shows the random number seeds(described in the “Downloading and compilation” section.) Following these two lines are a set of lines for each sample. Each sample is preceded by a line with just “//” on it. ( With tbs arguments some other numbers appear on this line following the “//” .) That line is followed by “segsites:” and the number of polymorphic sites in the sample. Following that line is a line which begins with “positions:” which is followed by the

positions of each polymorphic site, on a scale of (0,1). By default, the number of digits displayed after the decimal point is 4. The number of digits displayed can be modified with the switch -p. For example, to display six digits after the decimal point one includes, -p 6 on the command line. With no recombination, which is the default case, the positions are randomly and independently assigned from a uniform distribution. (With recombination, the distribution is somewhat more complex.) Following the positions, the haplotypes of each of the sampled chromosomes are given, each as a string of zeros and ones. The ancestral state is coded with a zero, and the mutant, or derived state, indicated with a one. When a sample has no polymorphic sites, the line with positions and the sample haplotypes are omitted.
When the option -L is used the output includes for each sample, a line giving the time of the most recent common ancestor of the sample and the sum of the lengths of the branches of the gene tree, each in units of 4N0 generations. This line appears right after the ”//” and begins with “time:”.
Output gene trees:
ms nsam nreps -T
When the option -T is used the trees representing the history of the sampled chromosomes are output. For example, the command line ms 5 2 -T results in the following output:
ms 5 2 -T
3579 27011 59243
This output represents the trees for two samples. The tree format is the Newick format utilized by Phylip and a number of other applications. The branch lengths are in units of 4N0 generations. The sampled chromosomes are labelled 1, 2 … corresponding to ordered sampled chromosomes. This labelling is irrelevant with unstructured models, but with island models described later, the labelling can be important. This command can be used together with the -t or -s commands.
With recombination a tree is output for each segment within which no re- combination has occurred in the history of the sample.
The gene trees output by ms can be used as input to other programs. To illustrate, we use seq-gen, the sequence evolution program of Rambaut and

Grassly(1997) which can simulate the evolution of sequences under a variety of mutation models. The following lines generate 2 samples of sequences 40 base pairs long, according to a simple finite-sites model with θ per base pair of 0.2.
ms 5 2 -T | tail +4 | grep -v // >treefile
seq-gen -mHKY -l 40 -s .2 seqfile
cat seqfile
5 40
5 40
The tail +4 command is used to strip off the first four lines output by ms.
The grep -v // command removes the lines with double slashes from the ms
output. The -mHKY command for seq-gen specifies (in this case) the Jukes-
Cantor mutation model. The -s command for seq-gen scales the branch lengths
so that θ per site is 0.2, in this case. This can also work with recombination but
seq-gen requires that one specify the maximum number of recombinational
segments. One cannot know this ahead of time but one can guess that the
number of segments will be less than say 10ρ􏰀n−1 1 Here is an example, for i=1 i
generating 2 samples of sequences 1000 base pairs long with ρ = 3.0: ms 5 2 -T -r 3. 1000 | tail +4 | grep -v // >treefile
seq-gen -mHKY -l 1000 -s .2 -p 50 seqfile
The -p option for seq-gen specifies the maximum number of recombinational segments. The argument of the -l option of seq-gen must match the number of sites of the -r option of ms. The -r option of ms is described in a later section.
It may be of interest to know the time of the most recent common ancestor of each sample. The command line switch, -L, will generate an additional line of output for each sample, containing the word, ”time: ” followed by the time back to the most recent common ancestor of the sample in units of 4N0 generations. With recombination, the time printed is the time of the most recent common ancestor for the site in the exact center of the segment simulated. Also printed on this line is the total tree length, that is, the sum of the lengths of the branches of the gene tree, also in units of 4N0 generations. With recombination, the total tree length printed is a weighted average across sites of total tree length, such that the product of the printed quantity and θ is the expected number of segregating sites, conditional on the coalescent history of the sample.

Fixed number of segregating sites:
ms nsam nreps -s segsites
As described in Hudson(1993) , one may in some cases wish to generate samples in such a way that every sample has the same number of segregating sites (regardless of the size of the genealogy generated.) This is done by using the -s option on the command line. For example,
ms 10 3 -s 7
will output 3 samples, each consisting of 10 chromosomes. Each sample will have exactly 7 polymorphic sites. It should be emphasized that this method of generating samples is not equivalent to specifying a value of θ, and then condi- tioning on some fixed number of polymorphic sites. Rather, these samples are produced by randomly placing a fixed number of mutations on each genealogy generated.
If both the -s option and the -t option are used, there will be one additional line of output for each sample. This line, which appears after the segsites line, begins with prob: which is followed by the probability of the specified number of segregating sites given the genealogical history of the sample and the value of θ specified with the -t option. For example, ms 5 2 -t 3.0 -s 5 produces the following output:
ms 5 2 -t 3.0 -s 5
3579 27011 59243
segsites: 5
prob: 0.145142
positions: 0.0803 0.1516 0.2276 0.8501 0.8636
segsites: 5
prob: 0.0709507
positions: 0.0856 0.1591 0.2881 0.2901 0.6601

Crossing over:
ms nsam nreps -t θ -r ρ nsites
ms will generate samples under a finite-sites uniform recombination model (Hud- son, 1983). In this model, the number of sites between which recombination can occur is finite and specified by the user (with the parameter nsites). Despite the finite number of sites between which recombination can occur, the muta- tion process is still assumed to occur according to the ”infinite-sites” model, in that no recurrent mutation occurs, and the positions of the mutations are specified on a continuous scale from zero to one, as in the no-recombination case. To include crossing-over (recombination) in the model, one uses the -r switch and specifies the cross-over rate parameter, ρ which is 4N0r, where r is the probability of cross-over per generation between the ends of the locus being simulated. In addition, the user specifies the numbers of sites, nsites, between which recombination can occur. One should think of nsites as the number of base pairs in the locus. For example, to simulate samples of size 15 for a locus which is 2,501 base pairs long with cross-over probability between adjacent base pairs of 10−8 per generation, and assuming N0 = 106 one enters:
ms 15 1000 -t 10.004 -r 100.0 2501
In this case, ρ = 100, since the cross-over probability between the two ends of the locus is 10−8(2501−1) = 2.5×10−5, and thus ρ = 4×106 ×2.5×10−5 = 100. (In addition we have assumed that the neutral mutation rate is 10−9 per site to obtain θ.) Once again, although we obtained θ by multiplying the number of sites by the mutation rate per site, the program assumes an infinite-sites model in which no recurrent mutation occurs.
Crossing-over and gene conversion:
ms nsam nreps -t θ -r ρ nsites -c f λ
In addition to crossing-over, gene conversion (intra-locus non-cross-over ex- change) can be included in the simulations. We assume a model like that of Wiuf and Hein(2000). Gene conversion is assumed to initiate between a speci- fied pair of sites in a given chromosome with probability g. We let f denote the ratio, g/r, where r is the probability per generation of crossing-over between adjacent sites.(The parameters g and r are the same parameters that appear in Wiuf and Hein.) The parameter f is input to the program, as well as the mean conversion tract length, λ, after the -c switch. (The mean track length is equal to 1/q in the notation of Wiuf and Hein.) The conversion tract is assumed to

extend, say to the right, for a random number of sites (denoted L), which is geometrically distributed:
Prob[L=j]=pj−1(1−p), j=1,2,… . p= λ−1.
To carry out simulations with gene conversion but no crossing-over, one uses the -r option with ρ equal to zero, and the -c option. In this case value following the -c option is the value of 4N0g, rather than the ratio g/r.
Exponentially growing or shrinking population size:
ms nsam nreps -t θ -G α
The switch -G is used to specify that the population has been growing (or shrinking) exponentially. That is, the population size is given by: N(t) = N0 exp−αt, where t is the time before the present, measured in units of 4N0 generations. (A negative value of α means that the population was larger in the past than at present.) Negative values of α are allowed, however, other past demographic events must also be specified to prevent a situation where no coalescent event ever occurs. These additional demographic events are specified with the -e options described below.
It is important to realize that the parameters θ, ρ and 4N0m (described later) are defined in terms of the present population size, N0.
Under island models, specified with the -I option described below, the -G option specifies that all subpopulations grow at the same rate. (See switch -g for specifying different growth rates for different subpopulations.)
Spatial structure and migration:
ms nsam nreps -t θ -I npop n1 n2 …[4N0m]
The program, ms, can produce samples under island models with arbitrary mi- gration rates, and different population sizes. To produce samples under an island model, one adds the switch -I followed by the number of subpopulations, npop, and the sample configuration. The sample configuration is a list of npop integers (n1 n2 . . . ) indicating the number of chromosomes sampled from each subpopulation. (Note: The subpopulations are numbered from 1 to npop.) By default all subpopulations are assumed to consist of the same number of diploids, denoted N0. For a symmetric island model, one can enter the migration param- eter 4N0m after the sample configuration as illustrated in the template above. In this case, each subpopulation receives migrants at the same rate from each

of the other subpopulations. ( m is the fraction of each subpopulation made up of new migrants each generation.) The migration rate parameter is optional. If this parameter is not provided, the migration rate is set to zero. Thus the command line:
ms 15 1000 -t 2.0 -I 3 10 4 1 5.0
will generate 1000 samples of size 15, where the first 10 chromosomes in each sample are from subpopulation 1, the next 4 chromosomes are sampled from sub- population 2, and one chromosome is sampled from subpopulation 3. (If, in this example, the -T option were used, the chromosomes from the first subpopula- tion would be labelled 1 to 10, the chromosomes from the second subpopulation would be labelled 11 to 14, etc.) In this example all three subpopulations are assumed to be the same size, and receive migrants at the same rate from each of the other subpopulations. The migration parameter, 4N0m is 5.0 .
When the -I switch is employed, the mutation parameter and the recom- bination parameters, entered with the -t and -r options, are defined in terms of the subpopulation size rather than the total population size. That is, θ is defined as 4N0μ, with N0 being the subpopulation size, and similarly ρ is 4N0r, where N0 is the subpopulation size. Again, in the output, the first n1 haplotypes represent the sampled chromosomes from subpopulation 1, and the following n2 haplotypes are from subpopulation 2, etc.
ms will also produces samples under models with arbitrary backward mi- gration matrices. This is done by first using the -I option and its arguments (with or without the migration rate parameter.) This establishes the number of subpopulations, the sample configuration, and assigns preliminary values to the elements of the migration matrix. The elements of the migration matrix are Mij = 4N0mij, i,j = 1,…,npop , where mij is the fraction of subpopu- lation i which is made up of migrants from subpopulation j each generation. The -I option sets all elements of the migration matrix, Mij,i ̸= j, equal to 4N0m/(npop-1) (or to the default value zero.) To modify any non-diagonal elements of this matrix, one can use the -m or -ma options as described next.
The command line:
ms 15 1000 -t 2.0 -I 3 10 4 1 5.0 -m 1 2 10.0 -m 2 1 9.0
will generate samples as described in the last example but with a slightly modi- fied migration matrix. In this case all elements of the matrix are 2.5 (= 5.0/(3-1) ), except elements M12 and M21 which have been set to 10.0 and 9.0, respec- tively. Any number of -m commands can be specified. The -ma option is used to specify an entire migration matrix. The option is followed by a list of all the elements of the migration matrix: M11, M12, M13, M21, M22, . . . . As indicated, entries for the diagonal elements, Mi,i, must be included on the command line, but are meaningless and ignored by the program. Here is an example:
ms 15 1000 -t 10.0 -I 3 10 4 1 -ma x 1.0 2.0 3.0 x 4.0 5.0
6.0 x

where the migration parameters are M12 = 1.0,M13 = 2.0,M21 = 3.0,M23 = 4.0, M31 = 5.0 and M32 = 6.0. It is handy to indicate the diagonal elements with x’s, or any symbol one chooses to make the matrix more readable.
It is the user’s responsibility to provide sample configurations, migration matrices and past demographic events for which the sampled chromosomes will eventually coalesce. If the user specifies a sample configuration from subpop- ulations that do not communicate, the program will, in some cases, happily continue tracing the lineages back in time, forever.
Another suboption of -I is the -n option which allows the user to specify that a particular subpopulation has a different size relative to N0. For example, following a -I option with its required arguments, the option -n 3 .5 sets the population size of the third subpopulation to 0.5∗N0. (Note that this command does not change N0 and will not change any of the parameters, mij, or any of the elements of the migration matrix, Mij, which are defined in terms of N0 and the mij. However the number of migrant copies arriving each generation from a particular population, or from all other subpopulations, to population 3 is half as large as a consequence of this command. This is because the fraction of migrants is the same, but the total number of individuals is half what it would have been without the -n command.) To set other subpopulations to other sizes, additional -n i size commands are appended.
The -G option sets the growth rate of all subpopulations to one value (as indicated before.) To set individual subpopulations to have different growth rates, the -g i αi command is used to set the growth rate of subpopulation i to αi.
It is important to realize that -m, -ma, -n and -g are suboptions of -I and must appear only after the -I option has been used to establish the number of subpopulations (npop) and the sample configuration. -G α commands can appear before or after -I commands, and will in either case set the growth parameters for all subpopulations to the same value. Note however, that a -g i αi command that precedes a -G command on the command line will be overridden by the -G command and thus will have no effect. Thus -g options should only appear after any -G options.
Past demographic events
To specify that demographic parameters change at specific times in the past, the -e switches are used. These switches are: -eG, -eg, -eN, -en, -em, -ema, -es and -ej. In each case the first parameter following the switch is the time when the demographic change occurred, measured from the present in units of 4N0 generations. In all cases, the parameter values specified apply to the time interval immediately farther in the past from the time point specified. (Henceforth, the term ”past-ward” will be used to indicated farther in the past.) The arguments which follow the time parameter specify subpopulations and other relevant parameters, as indicated in the following list:
-eG t α Set all growth rates to α at time t. 10

-eN t x
-entix zero.
-eM t x
1) at time t.
subpopulation i made up of migrants each generation from subpopulation j.
-ema t npop M11 M12 M13 M21 … Assign new values to all elements of the migration matrix.
-es t i p Split subpopulation i into subpopulation i and a new sub- population, labeled npop + 1. Each ancestral lineage in subpopulation i is randomly assigned to subpopulation i with probability p and subpopula- tion npop + 1 with probability 1 − p. The size of subpopulation npop + 1 is set to N0. Migration rates to and from the new subpopulation are as- sumed to be zero and the growth rate of the new subpopulation is set to zero. Subpopulation i retains the same growth rate and migration rates as before the event. In the forward direction this corresponds to popu- lation admixture. The size, growth rates and migration parameters for the new subpopulation can be immediately modified by following the -es command with appropriate additional -e commands. Remember, that if changed population size and growth rates are desired at the same time point, that one must put the size change command first followed by the growth rate change command. This is because the size change command changes the growth rate to zero.
-ej t i j Move all lineages in subpopulation i to subpopulation j at time t. Migration rates from subpopulation i (Mki,k ̸= i) are set to zero. (Prior to May 19, 2007, ms left migration rates unchanged .) In the forward direction this corresponds to population splitting. Population growth rates are unchanged.
It is important to note that ms generates genealogical histories by working back from the present, and that each of these -e commands changes the pa- rameters for the period immediately past-ward (farther back in the past from) the time point specified. For example, ms 10 30 -t 4.0 -eN 0.2 .02 spec- ifies that the population size was constant at size N0 from the present back to time 0.2 ∗ 4N0, and farther back in time the population size was 0.02 ∗ 4N0. The population size change was instantaneous and occurred at time 0.2 ∗ 4N0 generations before the present.
Also, note that the -eN and -en commands change the population size(s), but also have the side-effect of changing the growth rate(s) to zero. If one desires
Setgrowthrateofsubpopitoαi attimet.
Set all subpop’s to size x ∗ N0 and growth rates to zero. Setsubpopisizetox∗N0 attimetandgrowthrateto
Set all elements of the migration matrix, Mij, to x/(npop−
SetMij(=4N0mij)toxattimet. mij isthefractionof

the growth rate to be non-zero in the time period immediately past-ward of a population size change, one needs to add a -eG or -eg command right after the -eN t x or -en t i x command. For example,
ms 15 1000 -t 6.4 -eN 0.3 0.5 -eG .3 7.0
In this case, the order of switches on the command line is crucial. The following is INCORRECT:
ms 15 1000 -t 6.4 -eG .3 7.0 -eN 0.3 0.5
since the the effect of the change-in-growth-rate command, -eG .3 7.0 would be canceled by the following -eN 0.3 0.5 command which has the side-effect of changing the growth rate to zero. Moving backward in time, ms invokes simultaneous demographic events in the order that the are specified on the command line. (The only other command with a side-effect is the -ej switch which sets some of the migration rates to zero.)
And finally, note that changes in subpopulation sizes do not change m, the migration fraction for any subpopulation. Thus, if one changes a subpopula- tion size, it implicitly changes the number of migrants that arrive per genera- tion into a subpopulation. For example, consider the command: ms 10 100 -t2.0-I2556.0-en0.12.25. Thephrase,-I2556.0,speci- fies that there are two subpopulations, each of size N0, with migration rate 4N0m = 6.0 . If we denote the subpopulation sizes by N1 and N2, these sizes in the most recent interval of time are N1 = N2 = N0. And each subpopulation receives 2N0m = 3.0 migrant copies of the gene per generation. (Recall that m is the fraction of the population which are new migrants each generation, and since the subpopulation size is N0 diploids, the number of migrant copies is 2N0m.) The phrase -en 0.1 2 .25 specifies that past-ward of this event, the size of subpopulation 2, call it N2, is one quarter of its size in recent times. But m is not changed so the fraction of subpopulation 2 which are new migrants each generation is still m. So the number of migrants arriving in subpopulation 2, 2N2 ∗ m, which is only 0.75 per generation, past-ward of time point 0.1. If one wishes the number of migrant copies to be maintained at 3 per genera- tion, one must increase the migration parameter, -em 0.1 2 1 24.0. With or without the later phrase, subpopulation 1 still receives three migrant copies per generation.
Ancient DNA
ms nsam nreps -t θ -eA t i n
To include n ancient chromosomes sampled at time t from subpopulation i the -eA switch is added to the command line as indicated above. t is measured in units of 4N0 generations. If there is no population substructure, the subpop- ulation index is indicated as one. The ancient DNA haplotypes are output after

the haplotypes sampled in the present. nsam parameter is the number of chro- mosomes sampled at the present time. If multiple -eA switches are employed the ancient DNA haplotypes are output after the present day haplotypes in order from most recent to most ancient. If ancient DNA is sampled at the same time from two or more different subpopulations, the haplotypes are output in order of the -eA switches on the command line.
To illustrate this option consider an example with one chromosome sample from the present time and one ancient chromosome sampled two time units in the past. Two replicates of this kind of sample would be simulated with the following command line:
ms 1 2 -t 4.0 -eA 2.0 1 1 The output from such a command might be:
ms 1 2 -t 4.0 -eA 2.0 1 1
26011 5159 4807
segsites: 11
positions: 0.0602 0.1381 0.2014 0.2740 0.3161 0.3321 0.3382 0.6287 0.6770 0.7941 0.9333
segsites: 6
positions: 0.3078 0.3383 0.4466 0.4639 0.5795 0.7275
In this example, the ancient haplotypes are mostly zeroes indicating that they bear the ancestral allele at most polymorphic sites, as expected.
Using ”tbs” arguments
ms nsam nreps -t tbs -r tbs nsites
In some cases, it may be useful to permit parameter values to change from one sample to the next. For example, one may want to have the parameter values for each sample, drawn from a probability distribution. One could do this by using a separate program to generate many shell commands, each running ms to generate a single sample, with the random parameter values being specified. This would be inefficient and slow. ms can do this more efficiently using what I call ”tbs” arguments. This is done as follows. On the command line, instead of specifying a single value for a parameter, one simply types ”tbs”, without the quotes. The string ”tbs” indicates that the parameter value is ”to be specified” later. For each sample to be generated the program will read in the parameter

values from stdin. This can be done for any number of numerical parameters on the command line (but not for nsam, nreps, the number of segregating sites specified with the -s switch, or the number of populations, specified after a -I switch.) In the example above this paragraph, both theta and rho values are to be read in for each sample. For example, if file thetarho contains the two lines:
3.0 5.0
3.5 8.5
then the following command:
ms 5 2 -t tbs -r tbs 1000 sample_stats | cut -f 6 | stats .025 .5 .975

will output the estimated mean, standard deviation, 2.5th percentile, median, and the 97.5th percentile of the distribution of Tajima’s D for a model in which the population has experienced a recent rapid increase in size. ( In this example, the population size was one-tenth the current size until 0.2 ∗ 4N0 generations ago.)( cut is a Unix utility which can “cut” out a specified column of a file. Since Tajima’s D is output in the 6th column of the output of sample stats we use “cut -f 6” to get the D values.)
Hudson, R. R. (1983). Properties of a neutral allele model with intragenic recombination. Theoretical Population Biology, 23:183–201.
Hudson, R. R. (1990). Gene genealogies and the coalescent process. In Futuyma, D. and Antonovics, J., editors, Oxford Surveys in Evolutionary Biology, Vol. 7, pages 1–43. Oxford University Press, Oxford.
Hudson, R. R. (1993). The how and why of generating gene genealogies. In Takahata, N. and Clark, A. G., editors, Mechanisms of Molecular Evolution, pages 23–36. Sinauer Associates, Sunderland, MA.
Kingman, J. F. C. (1982). On the genealogy of large populations. J. Appl. Probab., 19A:27–43.
Kreitman, M. (1983). Nucleotide polymorphism at the alcohol dehydrogenase locus of drosophila melanogaster. Nature, 304:412–7.
Nordborg, M. (2001). Coalescent theory. In Balding, D. J., Bishop, M. J., and Cannings, C., editors, Handbook of Statistical Genetics, pages 179–212. John Wiley and Sons, Chichester, UK.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical Recipes in C. Cambridge University Press, Cambridge.
Rambaut, A. and Grassly, N. C. (1997). Seq-gen: An application for the monte carlo simulation of dna sequence evolution along phylogenetic trees. Com- put. Appl. Biosci., 13:235–238.
Wiuf, C. and Hein, J. (2000). The coalescent with gene conversion. Genetics, 155:451–62.

Leave a Reply

Your email address will not be published. Required fields are marked *