Genepop Support in Biopython

The Genepop module allows to access Genepop functionality using a Python interface. This means that the vast majority of Genepop’s methods (exact tests for Hardy–Weinberg equilibrium, population differentiation, genotypic disequilibrium, F-statistics, null allele frequencies, allele size-based statistics for microsatellites and much more) can now be accessed from Python. Genepop needs to be installed for this as the code is only a wrapper.

A parser to Genepop files is also available (and documented in the Tutorial). Genepop formatted files can be processed without Genepop.

Two interfaces are supplied: A general, more complex and more efficient one (GenePopController) and a simplified, more easy to use, not complete and not so efficient version (EasyController). EasyController might not be able to handle very large files, by virtue of its interface. On the other hand it provides utility functions to compute some very simple statistics like allele counts, which are not directly available in the general interface.

The more complex interface assumes more proficient Python developers (e.g., by the use of iterators) and for now it is not documented. But even for experienced Python developers, EasyController can be convenient as long as the required functionality is exposed in EasyController and its performance is deemed acceptable.

For details on the methods used for calculations, check the Genepop documentation, which provides pointers to all papers from where the calculations are derived.

EasyController tutorial

Installation

In order for the controllers to be used, Genepop has to be installed in the system, it can be downloaded from here.

Before we start, lets test the installation (for this you need a Genepop formated file):

from Bio.PopGen.GenePop.EasyController import EasyController

ctrl = EasyController(your_file_here)
print(ctrl.get_basic_info())

Replace your_file_here with the name and path to your file. If you get a IOError: Genepop not found then Biopython cannot find your Genepop executable. If Genepop is not on the PATH, you can add it to the constructor line, i.e.

ctrl = EasyController(your_file_here, path_to_genepop_here)

If everything is working, now we can go on and use Genepop. For the examples below, we will use the Genepop file big.gen made available with the unit tests. We will also assume that there is a ctrl object initialized with the relevant file chosen.

We start by getting some basic info

pop_names, loci_names = ctrl.get_basic_info()

Returns the list of population names and loci names available on the file.

Caveat: Most existing Genepop files provide erroneous data regarding population names. In many cases that information might not be trusted. Assessing population information is, most of the times, done by the relative position of the population in the file, not the name. So the first population is the file is index 0, the second index 1, and so on…

Statistics

Heterozygosity

Lets get heterozygosity info for a certain population and a certain allele:

(exp_homo, obs_homo, exp_hetero, obs_hetero) = ctrl.get_heterozygosity_info(0, "Locus2")

Will get expected and observed homozygosity and heterozygosity for population 0 and Locus2 (of the file big.gen, if you are using another file, adjust the population position and locus name accordingly).

Existing alleles

It is possible to get the list of all alleles of a certain locus in a certain population:

allele_list = ctrl.get_alleles(0, "Locus2")

allele_list will be [3, 20] (i.e., alleles 3 and 20 are on the population).

The number of alleles is simply getting with len(allele_list).

It is also possible to get the list of all alleles of a certain locus for all populations:

all_allele_list = ctrl.get_alleles_all_pops("Locus2")

all_allele_list will be [3, 20].

Allele and genotype frequencies

It is possible to get the frequency of alleles in a certain population:

allele_data = ctrl.get_allele_frequency(0, "Locus2")

allele_data will be (62, {3: 0.88700000000000001, 20: 0.113}). That is there are 62 genes. 88.7% are 3 and 11.3% are 20.

We can get similar information for genotypes (diploid data). Expected frequencies will also be reported:

genotype_list = ctrl.get_genotype_frequency(0, "Locus2")

genotype_list will be: [(3, 3, 24, 24.3443), (20, 3, 7, 6.3114999999999997), (20, 20, 0, 0.34429999999999999)]

Lets interpret the first element: There are 24 individuals which have a genotype of (3, 3), whereas the expected number of individuals with that genotype is 24.2443.

F statistics

Lets start with general multilocus F statistics:

Fis, Fst, Fit = ctrl.get_multilocus_f_stats()

This gets multilocus Fis, Fst and Fit.

Lets get that (and a bit more) per locus:

Fis, Fst, Fit, Qintra, Qinter = ctrl.get_f_stats("Locus2")

This gets single locus Fis, Fst and Fit, Qintra and Qinter.

There are specific sections below for Fst and Fis (where pairwise and population specific variants are introduced). On the Fis section Qintra and Qinter are explained.

Fst

Lets get the pairwise Fst for a certain locus:

pair_fst = ctrl.get_avg_fst_pair_locus("Locus4")

Will return a map where the key is the pair composed of population1, population2 (the population Id). population2 is always LOWER than population1. Example: the pairwise Fst for Locus4 between population 0 and population 3 is given by pair_fst[(3,0)].

You can also get the multilocus pairwise Fst estimate:

multilocus_fst = ctrl.get_avg_fst_pair()

This will return the same data structure as above but with a multilocus pairwise Fst.

Fis

We will now get the Fis of a certain locus/population plus a few other statistics:

allele_dict, summary_fis = ctrl.get_fis(0, "Locus2")

Lets have a detailed look at the output of get_fis:

summary_fis = (62, -0.1111, -0.11269999999999999)

allele_dict = {3: (55, 0.8871, -0.1111), 20: (7, 0.1129, -0.1111)}

summary_fis holds a triple with: total number of alleles, Cockerham and Weir Fis, Robertson and Hill Fis.

allele_dict holds for each allele (being each allele the key), number of repetitions of the allele, frequency and Cockerham and Weir Fis.

So, from the above results the following can be read: there are 62 genes with 2 different alleles (55 are of type 3, and 7 of type 20). Type 3 has frequency 0.89 and type 20 of 0.11. All CW Fis are -0.111 and the RH Fis is -0.112.

Lets now get multilocus Fis:

pop_list = ctrl.get_avg_fis()

pop_list will return an element per population. Each element is a quadruple containing:

1. population name (again, population names are not to be trusted)
2. 1 - QIntra: Gene diversity between individuals
3. 1 - QInter: Gene diversity among individuals within populations
4. Fis

Migration

We can get an estimation of the number of migrants:

samp_size, priv_allele_freq, mig10, mig25, mig50, migcorr = ctrl.estimate_nm()

samp_size is mean sample size, priv_allele_freq is the mean frequency of private alleles, mig10 is the number of migrants for Ne=10, mig25 for Ne=25, mig50 for Ne=50 and migcorr is the number of migrants after correcting for expected size.

Tests

Tests are normally computationally intensive as they are normally based on a Markov Chain algorithm. In some cases full enumeration approaches are available but those can only be applied for locus with a very low number of alleles. This means that most tests will take quite some time to complete.

For more details about Markov Chain parameters below (dememorization, batched and iterations) please consult the Genepop manual. Also consult the manual to understand when full enumeration is applicable.

Hardy-Weinberg equilibrium

Lets start by testing Hardy-Weinberg equilibrium for each loci in each population:

loci_map = ctrl.test_hw_pop(1, "excess")

The second parameter can be probability, excess or deficiency. probability is the standard Haldane HW test. Use deficiency when you are interested in heterozygote deficiency or excess if you are interested in excess.

The output is a map where the key is the locus name. The content is a tuple containing P-value, Standard Error, Fis (Weir and Cockerham), Fis (Robertson and Hill) and steps.

pop_test, loc_test, all_test = ctrl.test_hw_global("deficiency")

Use deficiency when you are interested in heterozygote deficiency or excess if you are interested in excess. probability does not apply here like in test_hw_pop.

The output is a triple:

1. pop_test is a list with an element per population including P-value, Standard error and switches.
2. loc_test is the same list, but with one element per locus including locus name, P-value, Standard error and switches.
3. all_test are the overall results consisting of a triple P-value, standard error and switches.

Linkage Disequilibrium

We can test if 2 loci are in linkage disequilibrium using the log likelihood ratio statistic (G-test).

chi2, df, pval = ctrl.test_ld_all_pair(
    "Locus1", "Locus2", dememorization=1000, batches=10, iterations=100
)

Returns the Chi square value, degrees of freedom and P value for the G statistic.

Isolation By Distance (IBD)

Isolation By Distance (IBD) analysis requires a special form of Genepop files:

1. One individual per population
2. The name of the individual has to be its coordinates

Example:

...
Pop
0 15, 0201  0303 0102 0302 1011
Pop
0 30, 0202  0301 0102 0303 1111
Pop
0 45, 0102  0401 0202 0102 1010
Pop
0 60, 0103  0202 0101 0202 1011
Pop
0 75, 0203  0204 0101 0102 1010
POP
15 15, 0102 0202 0201 0405 0807
...

Note that the example file that we are using, cannot be used for this case.

There is a single call for IBD analysis:

estimate, distance, (a, b), (bb, bblow, bbhigh) = ctrl.calc_ibd(
    self, is_diplo=True, stat="a", scale="Log", min_dist=0.00001
)

• is_diplo specifies if data is diploid (True) or haploid (False).
• stat is either 'a' or 'e' (see the Genepop manual for details).
• scale is either 'Log' or 'Linear'. 'Log' is used for 2D coordinates and 'Linear' for 1D.

Only pairwise comparisons above min_dist are used to compute regression coefficients.

The method returns:

• estimate, a triangular matrix containing genetic distances among samples according to the chosen statistic.
• distance, a triangular matrix containing distances (log or linear) among smamples.
• a and b *are the parameter fits for the regression. *bblow and bbhigh are the bootstrap confidence intervals for the b parameter (bb should be very close to b).

Interpretation of the triangular matrices should be done like this: Pythonwise, a matrix is implemented with a list of lists of numbers, like this:

[[0.1], [0.2, 0.3], [0.4, 0.5, 0.6]]

The above data structure corresponds to the following triangular matrix:

      1    2    3
2   0.1
3   0.2  0.3
4   0.4  0.5  0.6