# Structure and group labels¶

## Principle¶

Many statistics, including $$F_{ST}$$, require that a structure is defined.

In EggLib, the structure is controlled by an instance of a specific class (Structure) that defines the groups and identifies the samples that belong to them. These structure objects define which samples belong to the outgroup and, how the other samples are organized in individuals and/or populations and/or clusters of populations. In this way, a three-level hierarchical structure can be defined. It is not required to provide information for either of the three levels.

The rationale of this system is to allow processing the same data set assuming different structurations (in order to either compare the effect of different ways to group samples, or analyze different subsets of the data separately). The approach is to keep the data set static, and provide a separate Structure instance holding the description of the structure for each analysis.

There are threes ways of creating a Structure instance. First, based on group labels of an Align instance. Second, by providing the sample size of each population. Third, from a more flexible explicit description of the structure as a dict instance. Those approaches are described in the next paragraphs.

## Group labels¶

To account for structure, EggLib uses a specific system that consists in attaching labels to each samples. All samples bearing the same label are supposed to belong to the same group. There can be several labels per samples. We sometimes refer to an index among group labels as a level. Different levels of structure are aimed to represent either nested levels of structure (clusters of populations and/or populations and/or individuals) or alternative levels of structure. There are little restrictions on group labels besides being strings.

All Align and Container instances have a list of labels attached to each sample. They can be set or edited using either LabelView which is a part of SampleView (see Principle of proxy types) or direct class-level methods get_label() and set_label(). By default, this list of labels is empty.

The aim of these group labels is essentially to be interpreted by the class Structure (actually through the method from_labels()) to be used for computing diversity statistics or restrict an operation to a given subgroup.

In the following we explain how to specify group labels in Fasta files such as EggLib will properly interpret them and store them within an Align or Container instance.

## Group labels in Fasta files¶

### Single group label¶

Let align2.fas be a Fasta file with six samples, the first three belonging to population “pop1” and the other three belonging to population “pop2”. EggLib supports a specific system of tags within sequence headers in the Fasta format to indicate group labels. The tags must appear as suffix starting with a @ followed by a string, as in the following example:

>sample1@pop1
ACCGTGGAGAGCGCGTTGCA
>sample2@pop1
ACCGTGGAGAGCGCGTTGCA
>sample3@pop1
ACCGTGGAGAGCGCGTTGCA
>sample4@pop2
ACCGTGGAGAGCGCGTTGCA
>sample5@pop2
ACCGTGGAGAGCGCGTTGCA
>sample6@pop2
ACCGTGGAGAGCGCGTTGCA


To import group labels, one is required to set the labels option of from_fasta() to True:

aln2 = egglib.io.from_fasta('align2.fas', alphabet=egglib.alphabets.DNA, labels=True)
print(aln2.get_name(0), aln2.get_label(0, 0))

sample1 1


If labels have not been imported like in the following:

aln2 = egglib.io.from_fasta('align2.fas', alphabet=egglib.alphabets.DNA)
print(aln2.get_label(0, 0))


In that case, print(aln2.get_label(0, 0)) would cause an error because, by default, there is no group labels at all included in Align instances.

Note

io.from_fasta() has an option (label_marker) to use a different character than @ to separate the name and the tag.

### Multiple group labels¶

There can be any number of group levels, either nested or not. To specify several labels for a sample, one can write several strings separated by commas, as in the following example:

>sam1@c1,i1
ACCGTGGAGAGCGCGTTGCA
>sam2@c1,i1
ACCGTGGAGAGCGCGTTGCA
>sam3@c1,i2
ACCGTGGAGAGCGCGTTGCA
>sam1@c1,pop1,i1
ACCGTGGAGAGCGCGTTGCA
>sam5@c2,pop1,i1
ACCGTGGAGAGCGCGTTGCA
>sam6@c2,pop1,i2
ACCGTGGAGAGCGCGTTGCA


The example above also demonstrate that it is possible to omit group labels for part of the samples, although it is probably better to avoid it (because it is error-prone). Labels absent for a given level are not added or initialised in any way. As a result, if the file shown above is saved as align3.fas, the code:

aln3 = egglib.io.from_fasta('align3.fas', alphabet = egglib.alphabets.DNA, labels=True)
print(aln3.get_name(0))
print(aln3.get_label(0, 0))
print(aln3.get_label(0, 1))


will yield:

sample1
c1
i1


but the code:

print(aln3.get_label(0, 2))


will result in an error.

So, at this point, one should understand labels as list of 0, 1 or more arbitrary identifiers attached to each sample. How this labels will be used to group samples in individuals, populations or possibly multi-level hierachical structure is up to the Structure class.

Note

The separator can also be changed. This can be done using the label_separator of the io.from_fasta() method.

#### Outgroup specification¶

Tools analysing diversity in EggLib can account for one or more outgroup samples. If individuals are defined in the main group (ingroup), it is required that outgroup samples also come as one or more individuals sharing the same ploidy.

Individuals must be specified by the label # (obligatory as the only or first label), followed by maximum one other label (if the individual level is to be considered). This, outgroup samples are denoted by the tag @# or @#,IND where IND is an individual label. Note that if there are individuals in the ingroup then there must be also individuals in the outgroup (with the same ploidy).

Very importantly, one must keep in mind that neither io.from_fasta() nor Align have a notion of the outgroup. They don’t interpret the # label as special and don’t process outgroup samples differently of other samples. It will be the job of Structure to separate the outgroup from the rest of the samples. This means that, if you have outgroup samples including in your data, you must use a Structure instance. Also, if you want to use another label than # to identify outgroup samples, you need to tell it to Structure (or to the method struct_from_labels()).

## Creating a structure from an alignment¶

To present the usage of the Structure class, we will use a complete, albeit over-simplified example. Consider the Fasta alignment below:

>sample01@c1,p1,i01
CTTCCGGGAAGCGCCAGCAGAAGGTTGCTGCTAAGGCCCGCACACGTCTGCAGCACTTCG
>sample02@c1,p1,i01
CTTCCGCGCAGGGCCAGGAGCATGTAGCTTCTAAGGCTTGCACAGGTCTTCAGCACTACG
>sample03@c1,p1,i02
CTTCCGCGCAGGGCCAGGAGCATGTAGCTTCTAAGGCTTGCACAGGTCTTCAGCACTACG
>sample04@c1,p1,i02
CTTCCGCGCAGGGCCAGGAGCATGTAGCTTCTAAGGCTTGCACAGGTCTTCAGCACTACG
>sample05@c1,p1,i03
CTACCGTGACGAGCTAGCCGAGCCTGACGCAGGGGGCGAGTAAGGGAGATTACGACTTGG
>sample06@c1,p1,i03
CTTCCGCGCAGGGCCAGGAGAATGTTGCTTCTAAGGCTTGCACAGGTCTTCAGCACTAAG
>sample07@c1,p2,i04
CTGCTATGACGAACTACCCGAGCCTGGGGCATGGGGCGTGTATGGGAGCTTACAACTTGG
>sample08@c1,p2,i04
CTTACGCGACGTGCCAGCATAGGGAAGCTGCTAAGGCCTGCACACGTCCGCAGCACTACG
>sample09@c1,p2,i05
CTGCTATGACGAACTACCCGAGGCTGGGGCATGGGGCGTGTATGGGAGCTTACAACTTGG
>sample10@c1,p2,i05
CTGCTATGACGAACTACCCGAGGCTGGGGCATGGGGCGTGTATGGGAGCTTACAACTTGG
>sample11@c1,p2,i06
CTTACGCGACGCGCCAGCAGAGGGATGCTGCTAAGGCCTGCACACGTCCGCAGCACTACG
>sample12@c1,p2,i06
CTTACGCGACGCGCCAGCAGAGGGATGCTGCTAAGGCCTGCACACGTCCGCAGCACTACG
>sample13@c1,p2,i07
CTGCTATGACGAACTACCCGAGCCTGGGGCATGGGGCGTGTATGGGAGCTTACAACTTGG
>sample14@c1,p2,i07
CTGCTATGACGAACTACCCGAGGCTGGGGCATGGGGCGTGTATGGGAGCTTACAACTTGG
>sample15@c2,p3,i08
CTCCGGGGCCGGTTTCGCATAACGTCGCGCAGGGGACGTGTAGGGGCGCATACACCTGGG
>sample16@c2,p3,i08
CTCCGGGGCCGGTTTCGCATAACGTCGCGCAGGGGACGTGTAGGGGCGCATACACCTGGG
>sample17@c2,p3,i09
TTGCCGGGTCGAACTAGCCGACCTTGGCGCAGGGGTCGTTTAAGGGTCCTTACAACTTGG
>sample18@c2,p3,i09
TTGCCGGGTCGAACTAGCCGACCTTGGCGCAGGGGTCGTTTAAGGGTCCTTACAACTTGG
>sample19@c2,p3,i10
CTCCGGCGCCGGTTTCGCATAACGTCGCGCAGGGGACGTGTAGGGGCGCATACACCTGGG
>sample20@c2,p3,i10
TTGCCGGGTCGAACTAGCCGACCTTGGCGAAGGGGTCGTTTAAGGGACCTTACAACTTGG
>sample21@c2,p4,i11
TTGCCAGGACGAACTAGCCGCGCCTGGCGCAGGGGTCGTTTAAGGGAGCTTACAACTTGG
>sample22@c2,p4,i11
TTGCCAGGACGAACTAGCCGCGCCTGGCGCAGGGGTCGTTTAAGGGAGCTTACAACTTGG
>sample23@c2,p4,i12
TTGCCGGGACGAACTAGCCGAGCCTGGCGCAGGGGTCGTTTAAGGGAGCTTACAACTTGG
>sample24@c2,p4,i12
TTGCCGGGACGAACTAGCCGAGCCTGGCGCAGGGGTCGTTTAAGGGAGCTTACAACTTGG
>sample25@c2,p5,i13
CTACCGTGACGAACTAGCCGAGCCTGGCGCAGGGGGCGAGTAAGGGAGAGTACAACTTGG
>sample26@c2,p5,i13
CTACCGTGACGAACTAGCCGAGCCTGGCGCAGGGGGCGAGTAAGGGAGAGTACAACTTGG
>sample27@c2,p5,i14
CTACCGTGACGAACTAGCCGAGCCTGGCGCAGGGGGCGAGTAAGGGAGAGTACAACTTGG
>sample28@c2,p5,i14
CTACCGTGACGAACTAGCCGAGCCTGGCGCAGGGGGCGAGTAAGGGAGAGTACAACTTGG
>sample29@c2,p5,i15
TTGCCGCGACGAACTAGCCGAGCCTGGCGCAGGGGTCGTTTAAGGGAGCTAACAACTTGG
>sample30@c2,p5,i15
CTACCGTGACGAACTAGCCGAGCCTGGCGCAGGGGGCGAGTAAGGGAGAGTACAACTTGG
>sample31@#,i98
CATACCACCTTGGCCCGGAGAGTGCGGAGTACCGGGCGTGGAAGGCTGCATGCAAATGGA
>sample32@#,i98
CATACCACCTTGGCCCGGAGAGTGCGGAGTACCGGGCGTGGAAGGCTGCATGCAAATGGA
>sample33@#,i99
CATACCACCTTGGCCCGGAGAGAGCGCAGTGCCGGGCGTGGAAGGCTGCATTCAAATGCG
>sample34@#,i99
CATACCACCTTGGCCCGGAGAGAGCGCAGTGCCGGGCGTGGAAGGCTGCATTCAAATGCG


It has a total of 30 ingroup samples and 4 outgroup samples. These are actually respectively 15 and 2 individuals, and the ingroup is organized in two clusters of respectively two and three populations, themselves composed of two, three, or four individuals each. Remember the labels are arbitrary. In this case, cluster labels are c1 and c2, population labels p1 to p5 and individual labels i01 to i15 (i98 and i99 for the two outgroup individuals).

Let use name this file align5.fas and import it with group labels:

>>> aln = egglib.io.from_fasta('align5.fas', alphabet=egglib.alphabets.DNA, labels=True)


Now, we will directly show a Structure instance incorporating all structure information (all three levels) can be created:

>>> struct = egglib.struct_from_labels(aln, lvl_clust=0, lvl_pop=1, lvl_indiv=2)
>>> print(struct.as_dict())
({'c2': {'p3': {'i09': [16, 17], 'i08': [14, 15], 'i10': [18, 19]},
'p5': {'i13': [24, 25], 'i15': [28, 29], 'i14': [26, 27]},
'p4': {'i11': [20, 21], 'i12': [22, 23]}},
'c1': {'p1': {'i01': [0, 1], 'i03': [4, 5], 'i02': [2, 3]},
'p2': {'i05': [8, 9], 'i04': [6, 7], 'i07': [12, 13], 'i06': [10, 11]}}},
{'i99': [32, 33], 'i98': [30, 31]})


We used the function struct_from_labels() that generates a new Structure instance based on group labels of an Align (or Container). To use this method, it is necessary to tell which group level corresponds to the clusters, populations, and individuals in such a way that they are properly hierarchical. It is possible to skip any of these three levels of structure, simply by dropping the corresponding option parameter(s).

The method as_dict() is aimed to provide an intuitive representation of the structure held by the instance. In practice, it is as intuitive as possible while being flexible enough to represent all possible cases.

### Dictionary representation of Structure instances¶

It is a tuple containing two items, each being a dict. The first one represents the ingroup and the second represents the outgroup.

The ingroup dictionary is itself a dictionary holding more dictionaries, one for each cluster of populations. Each cluster dictionary is a dictionary of populations, populations being themselves represented by a dictionary. A population dictionary is, again, a dictionary of individuals. Finally individuals are represented by lists or integers.

An individual list contains the index of all samples belonging to this individual. For haploid data, individuals will be one-item lists. In other cases, all individual lists are required to have the same number of items (consistent ploidy). Note that, if the ploidy is more than one, nothing enforces that samples of a given individual are grouped within the original data, meaning that you can shuffle labels in Align instances (or in your Fasta file) if you need to.

The keys of the ingroup dictionary are the labels identifying each cluster. Within a cluster dictionary, the keys are population labels. Finally, within a population dictionary, the keys are individual labels.

The second dictionary represents the outgroup. Its structure is simpler: it has individual labels as keys, and lists of corresponding sample indexes as values. The outgroup dictionary is similar to any ingroup population dictionary. The ploidy is required to match over all ingroup and outgroup individuals.

If we go back to our example, we see that the returned dictionary for the ingroup has two items, with keys c1 and c2, respectively, and that the correct structure appears at lower levels, with two-item (diploid) individuals within populations withing clusters. Similarly, the two outgroup individuals, labelled i98 and i99, appear as expected in the second dictionary returned by the as_dict() method. Ultimately, the values contained by the lists are the lowest levels are the index referring to the original Align instance (from 0 to 29 in the ingroup, 30 to 33 in the outgroup).

### Alternative structure¶

Occasionally, one will want to generate different Structure instances based on different levels of structure in group labels (for example if there are alternative structurations of the data). It is not required that all levels of a Structure instances are populated, and it is not necessary to import all structure levels of an Align. The example below demonstrates all this by importing the first level (previously, clusters) as populations in a new instance, skipping all other information:

>>> struct2 = egglib.struct_from_labels(aln, lvl_pop=0)
>>> print(struct2.as_dict())
({None: {'c2': {'24': [24], '25': [25], '23': [23], '27': [27],
'15': [15],'14': [14], '17': [17], '16': [16],
'19': [19], '18': [18], '22': [22], '28': [28],
'26': [26], '29': [29], '20': [20], '21': [21]},
'c1': {'11': [11], '10': [10], '13': [13], '12': [12],
'1': [1], '0': [0], '3': [3], '2': [2], '5': [5],
'4': [4], '7': [7], '6': [6], '9': [9], '8': [8]}}},
{'33': [33], '32': [32], '31': [31], '30': [30]})


Note that it is also possible to recycle an already existing Structure instance instead creating a new one (with the method from_labels() of Structure instances.).

Since we did not specify any group label index for the cluster level, there is no information regarding clusters, and all populations are placed in a single cluster. The default label is None in that case. The two labels c1 and c2 are now considered as population labels. At the lowest level (also in the outgroup), all samples are placed in a single-item individuals because, likewise, no index has been provided for the individual level. Then, haploidy is assumed, and the sample index is used as default value for individual labels (incremented in the outgroup).

This example demonstrates that the group labels in Align instances have no particular meaning per se until they are interpreted while configuring a Structure instance.

## Creating a structure manually¶

### Simple structure¶

If your data are organized in an intuitive way (that is, samples organized per individual and individuals grouped per population), and if the cluster level is not needed, you can use the function struct_from_samplesizes(). This function takes a list of sample sizes (one item per population). For example, if your dataset contains two populations of 20 haploid individuals, you can enter simply:

>>> struct = egglib.struct_from_samplesizes([20, 20])
>>> print(struct.as_dict())
({None: {'pop1': {'idv1': [0], 'idv2': [1], 'idv3': [2], 'idv4': [3],
'idv5': [4], 'idv6': [5], 'idv7': [6], 'idv8': [7],
'idv9': [8], 'idv10': [9], 'idv11': [10],'idv12': [11],
'idv13': [12], 'idv14': [13], 'idv15': [14], 'idv16': [15],
'idv17': [16], 'idv18': [17], 'idv19': [18], 'idv20': [19]},
'pop2': {'idv21': [20], 'idv22': [21], 'idv23': [22], 'idv24': [23],
'idv25': [24], 'idv26': [25], 'idv27': [26], 'idv28': [27],
'idv29': [28], 'idv30': [29], 'idv31': [30], 'idv32': [31],
'idv33': [32], 'idv34': [33], 'idv35': [34], 'idv36': [35],
'idv37': [36], 'idv38': [37], 'idv39': [38], 'idv40': [39]}}}, {})


This function supports ploidy and outgroup individuals, so you can also declare, for example, two populations of 10 diploid individuals plus one outgroup individual:

>>> struct = egglib.struct_from_samplesizes([10, 10], ploidy=2, outgroup=1)
>>> print(struct.as_dict())
({None: {'pop1': {'idv1': [0, 1], 'idv2': [2, 3], 'idv3': [4, 5],
'idv4': [6, 7], 'idv5': [8, 9], 'idv6': [10, 11],
'idv7': [12, 13], 'idv8': [14, 15], 'idv9': [16, 17],
'idv10': [18, 19]},
'pop2': {'idv11': [20, 21], 'idv12': [22, 23], 'idv13': [24, 25],
'idv14': [26, 27], 'idv15': [28, 29], 'idv16': [30, 31],
'idv17': [32, 33], 'idv18': [34, 35], 'idv19': [36, 37],
'idv20': [38, 39]}}}, {'idv21': [40, 41]})


Be careful that the order of samples in the Align or Site you’ll be analyzing with the resulting Structure instance must be consistent. Populations must be grouped together in the order indicated (if sample sizes differ), as well as individuals in populations, and the outgroup must be at the end.

### Fully flexible dictionary¶

It is possible to create a Structure instance from user-provided data formatted as dictionaries, using either the function struct_from_dict() or the equivalent method of Structure instances to recycle an existing instance. This approach allows maximal flexibility but requires that you create a properly formatted dictionary. Both methods take an ingroup and an outgroup arguments, which are formatted exactly as the output of as_dict() (see Dictionary representation of Structure instances). This feature can be used to import structure information without relying on EggLib’s tag system of Fasta sequence names.

## Using the structure¶

Once a Structure has been configured to represent the structuration of the data set, it can be used as a descriptor while computing diversity statistics. This will make available a wide array of statistics requiring this type of information. For example, the statistics with codes Fis, Snn, WCist, and WCisct require individual and/or population structure information and won’t be computed if no structure is provided:

>>> cs = egglib.stats.ComputeStats()
>>> print(cs.process_align(aln))
{'Snn': None, 'Fis': None, 'WCisct': None, 'WCist': None}


To provide the Structure to stats.ComputeStats, one just needs to pass the instance as a value for the struct argument of the class constructor (or the configure() method of ComputeStats instances):

>>> cs.configure(struct=struct)
>>> print(cs.process_align(aln))
{'Snn': 0.5111111111111112, 'Fis': 0.6442024052643518,
'FistWC': (0.39885944313988586, 0.4485871173702674, 0.6685233526761218),
'FisctWC': (0.39885944313988575, 0.4964142771064885, 0.2339234438730581, 0.6972741981129913)}


The code above shows that, with proper structure, we can compute statistics taking into account the individual, population, and cluster levels. In particular, FisctWC takes all levels into account. In comparison, FistWC ignores the cluster level, but nothing prevents you from computing it at this point. The code below shows that we can analyse the same data with a different structure (using the second instance we created before, using the clusters as populations and ignoring other levels):

>>> cs.configure(struct=struct2)
>>> print(cs.process_align(aln))
{'Snn': 0.9666666666666667, 'Fis': None, 'FistWC': None, 'FisctWC': None}


Since the individual level is not available, the statistics Fis, WCist, and WCisct (which also requires the cluster level) cannot be computed. Only Snn can. It is still possible to call for statistics that cannot be computed, but their value will be set to None.