# Detecting intra-species divergent sequences at base pair resolution with PanCons

Matthias Zytnicki

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Matthias Zytnicki. Detecting intra-species divergent sequences at base pair resolution with PanCons. 2026. hal-05460361

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
Detecting intra-species divergent sequences at
base pair resolution with PanCons

Matthias Zytnicki

January 15, 2026

Abstract

Comparative sequence analysis is a powerful method for understanding func-
tional elements, and traces of conservation, or divergence, informs on the se-
lective constraint. While several methods have been successfully developed for
the comparison of different species, very few study the evolution of individuals
within a species. Yet, several pangenomes, which include several genomes of the
same species, are now available, and could be leveraged to assess evolutionary
constraints. In this work, we present a new method for computing conserva-
tion at base pair resolution. It includes the characterization of syntenic regions
in pangenome graphs, the creation of a new scoring system, and the develop-
ment of an efficient algorithm. We applied this method, name PanCons, to the
*Arabidopsis thaliana* pangenome, and we showed that it captures subtle infor-
mation, such as the least conservation of third nucleotide of the codons. We
also found a divergent region in an intron of the *FLC* region, a gene implicated
in the vernalization process.
1 Introduction

Sequence conservation between different species has been used to characterize
genomes. Indeed, sequence identity usually implies evolutionary constraints,
and, as such, functional elements like protein coding genes are expected to be
found in conserved regions. Methods like GERP [3] and GERP++ [4] use se-
quence alignment and a phylogenetic tree, and, for each position of the ref-
erence genome (the organism of interest, such as the human or *Drosophila
melanogaster*), computes the observed number of mutations, which is compared
to the expected number. PhastCons [16] uses a phylogenetic hidden Markov
model with two states, modeling conserved and nonconserved regions, where
the branch lengths of the phylogenetic tree differ. While the previous meth-
ods focus on conserved regions, PhyloP [12] treat conservation and divergence
alike: they estimate branch lengths at each position of the reference genome,
and compare it to the background length. Of note, this last work compares the
results of all the previously mentioned methods, and finds that they are similar,
even though the methods implement very different models.

With the advent of long, almost errorless reads, it is now possible to assemble
near telomere-to-telemore genome at an affordable price. Modeling intra-species
variability is usually done using pangenome graphs. Like genome alignments,
graphs explicitly capture conserved sequences, but they are easier to exploit, and
less biased toward a reference, than alignments. These graphs can be encoded
into de Bruijn graphs, but variation graphs [6] are today more commonly used for
multi-cellular eukaryotes, mostly because it is easier to retrieve haplotypes [1].
In these graphs, nodes represent sequences, and paths through these nodes
are haplotypes. As a result, a node traversed by two different paths means
that the sequence is conserved in the two haplotypes. Applying previously
described sequence conservation methods to the intra-species is not straight-
forward: they all require a phylogenetic tree, and this tree is usually not defined, since inbreeding is frequent.

In this work, we would like to extend the concept of conservation quantification to the intra-species case. PanSel [18] is, so far, the only tool for this. However, it uses sliding windows to do so, and best results are achieved with sizes of 10 000 base pairs. This makes detection of small elements, such as exons, or even single nucleotides, impossible.

The objective of this work is to provide a base pair quantification of the sequence conservation, at each position of the reference genome, using a pangenome graph. To do so, we compute an *average conservation score*, which is intuitive, and still accurately models the conservation level. We provide an algorithm and tool, PanCons, that efficiently computes it in linear time, and we used it on several species. The *Aradidopsis thaliana* use case, with 69 individuals [9], revealed that PanCons accurately finds distinctive traces of conservation in known genes. We also found a highly divergent region in an intron of the *FLC* gene, implicated in the vernalization process. This process depends on the presence of winter, and adaptation could have favored alternative gene structures.

PanCons is a C++ tool, available on https://github.com/mzytnicki/pancons.

# 2 Method

## 2.1 Algorithm

Previously presented conservation detection methods rely on a multiple sequence alignment. They suppose that base pairs from the same column share a common ancestor, and they compare the observed number of substitutions to the expected one. Pangenome graphs model these substitutions, but also insertions
and deletions, of any size. There is no established model for extracting the back-ground distribution of these events, especially at a base pair resolution. Our aim here is to develop an intuitive conservation score, which would be 1 if we observe a total conservation at a given locus, and a minimum score of $\frac{1}{n}$ if all the n sequences are different. Of note, we tried other score systems, based for instance on entropy, but they had less power to segregate functional elements (see Supplementary Data).

We describe a pangenome graph as a set of paths $P_i$, where each path is a list of nodes $P_i = (n_1^i, \dots, n_m^i)$. Since each path is a list, its elements are ordered in $P_i$: $n_\ell^i <_i n_{\ell+1}^i$. If $n_\ell^i$ and $n_{\ell'}^i$ are nodes of $P_i$, then $P_i[n_\ell^i : n_{\ell'}^i]$ denotes the sub-list starting and ending at these nodes. We denote $P_i(n_\ell^i : n_{\ell'}^i)$ the same sub-list, where the first and last nodes are removed. Nodes can be shared between different paths, and if a node $n_\ell^i$ of $P_i$ is shared with $P_j$, we will simply write $n_\ell^i \in P_j$. By convention, we will name the reference path $P_0$.

We first give a conservation score $s(n)$ to each node $n$: the number of paths that traverse it, divided by the total number of paths. Now, we would like to extract all the nodes that are syntenic to a reference node, and compute the average conservation score of all these nodes.

Given a node $n_\ell^0$ of the reference path, the syntenic node(s) of the non-reference path $P_i$, is $n_\ell^0$ if $n_\ell^0 \in P_i$, and is otherwise:

$$S_i(n_\ell^0) = P_i \left( \max_{n \in P_0 \cap P_i} n <_i n_\ell^0 : \min_{n \in P_0 \cap P_i} n >_i n_\ell^0 \right)$$

Note that, in case of a SNP, the syntenic node is the other allele. The conservation score of a reference node $n_\ell^0$ is the average of the conservation scores of all the syntenic nodes: $\text{mean}_i(\text{mean}_{n \in S_i(n_\ell^0)}(s(n)))$. An example of syntenic nodes is given in Figure 1. Once the scores of the nodes are computed, we scan the list of reference nodes, and we project scores of the nodes to scores
<figure><img src="image_2.png" /><figcaption>Figure 1: Description of average conservation score. This graph contains seven nodes (we will suppose that they have the same size of 1) and three paths (red, blue, and green). We will suppose that the reference path is the red one. Since nodes $n_1$ and $n_7$ are traversed by all paths, their scores are 1. Nodes $n_2$ and $n_6$ have a score of $\frac{2}{3}$, and the remaining nodes, which are only traversed by one path, is $\frac{1}{3}$. Node $n_1$ is traversed by the non-reference blue and green paths, therefore the syntenic node of $n_1$ with respect to these green paths is itself. We will now compute the syntenic node of $n_3$ with respect to the blue path. We find the closest, encompassing common nodes from the red and blue path, which are $n_2$ and $n_6$. We thus state that all the nodes between $n_2$ and $n_6$ in the blue path (here, $n_4$) are declared syntenic to $n_3$. Likewise, $n_5$ is syntenic to $n_2, n_3$ and $n_6$ in the green path. Without considering the Jaccard normalization factors, the average conservation scores are 1 for nodes $n_1$ and $n_7$, $\frac{5}{9}$ for nodes $n_2$ and $n_6$, and $\frac{1}{3}$ for node $n_3$.</figcaption></figure>

on genomic intervals. The output of PanCons is thus a value for each position of the genome.

We added two improvements to the previous methods. First, the average of the node scores is weighted by the node size, since smaller nodes should have less impact than larger nodes. If the size of a node $n$ is $w(n)$, then the average score used here, named $wmean$, of a set of nodes $N$ is $wmean(N) = (\sum_{n \in N} s(n) \times w(n)) / (\sum_{n \in N} w(n))$.

Second, we wanted to take into account the proximity distance between individuals. Indeed, some individuals may be very distant from the reference; their variants are thus more likely, and should have less impact on the overall score. We thus compute the weighted Jaccard index $j$ between each non-reference path and the reference, which is the number of common nodes divided by the union of the nodes, weighted by the node sizes. The Jaccard distance is $1 - j$. We will name the Jaccard distance weighted average $jmean$: if $a_i$ is the average score of the genome $i$, and $j_i$ is the jaccard distance,
jmeanᵢ = (∑ᵢ jᵢ × aᵢ) / (∑ᵢ jᵢ). To summarize, the conservation score of a reference node n<sub>ℓ</sub><sup>0</sup> is jmeanᵢ(wmean<sub>n∈Sᵢ(n<sub>ℓ</sub><sup>0</sup>)</sub>(s(n))). We tried other scoring schemes (see Supplementary Data), but none of them gave a good discriminative power. Of note, using the Jaccard distance did not provide visible improvement.

The algorithm used to compute the score is given in Supplementary Data.
Its space and time complexities are linear with respect to the number of paths,
and the number of nodes.

2.2 Data

We applied PanCons to an *Arabidopsis thaliana* pangenome graph, using sequences published in [9]. Pan1C pipe-line [11], which provides a Minigraph-Cactus graph [7], was applied to the available genome assemblies. This graph is ideal to benchmark our tool, since it includes 69 individuals, usually more than current pangenome graphs, although we can expect that this will be common in a near future. We also observed a large genomic diversity between individuals, and this is another main advantage of this dataset.

We used Col-PEK [8], a Col-0 near telomere-to-telomere genome assembly,
as the reference. We transferred the TAIR [14] annotation to Col-PEK using
LiftOn [2].

PanCons was run on a Linux computer equipped with Intel(R) Xeon(R) Gold 6248R CPU at 3.00GHz, on each chromosome separately, in less than 20 minutes, using slightly less than 50GB RAM.

Of note, we also tried PanCons on a human pangenome [10], but, due to the
lack of diversity, we could not extract meaningful results (see Supplementary
Data).
# 3 Results

We first checked that our proximity distance was consistent with previous published results. Indeed, [9] computed a phylogeny based on the amino-acid sequences of the unique genes. We plotted our Jaccard index between each chromosome of each ecotype and the reference chromosomes (here, Col-0). We also added the published phylogeny results (see Figure 2a). Since our distance is computed on the nucleotides, our results tend to show that individuals are closer to the reference. We also plotted the correlation between the phylogeny results and the Jaccard distances (see Figure 2b, where the former is the *x* value, and the latter is the *y* value for each chromosome of each ecotype). It confirms that our Jaccard distance delivers results which are consistent with phylogenetic approaches, with a *R*² of 0.41.

A first striking result is that most of the genome is clearly conserved (see Figure 3a). As a result, it is not possible to find conserved elements at base pair resolution, and longer ranges, such as windows, should be used instead [18]. However, divergent regions clearly appear on the left side of the distribution.

We tried to model this distribution, but the underlying model is unknown: events such as insertions and deletions are difficult to estimate. We tried several usual distributions, but none gave a good fit (see Supplementary Data).

We extracted the conservation score for known annotations (see Figure 3b). We plotted the cumulative distribution of several features, which include introns, UTRs, and coding sequences of genes. The three nucleotides of each codon of the coding sequences were plotted separately. We also included the most populous transposable element (TE) family: gypsy. We can clearly see that transposable elements are much less conserved than genes, as expected. Likewise, introns and UTRs are less conserved. More interestingly, the first and second nucleotides showed a similar conservation pattern, but the third nucleotide is slightly less
conserved. This reflects known results on the third nucleotide usage, but, more interestingly, the fact that our conservation score captures even subtle signals.

We then wanted to assess how the conservation score was distributed along the genes (see Figure 3c) using the DeepTools [13]. The conservation clearly showed an increase of conservation on the gene, between the transcription start size (TSS) and the transcription end site (TES), compared to a depletion in the close upstream and downstream regions.

We then wanted to focus on divergent regions on the reference genome, i.e. intervals with low conservation scores. Given that no model can extract significantly divergent regions, we just focused on the 5% lowest scores, forming genomic intervals of size not less than 100bp, possibly merging candidate regions if they are distant by at most 10bp. This strategy is somewhat arbitrary and offers no statistical guarantee, but we can safely assume that the selected regions are very divergent, considering the conservative parameters. We thus selected 4,943 intervals, forming about 3.5% of the reference genome.

As seen on Figure 4, most of the divergent regions are found in intergenic regions, as expected. Of note, we found more divergent regions in upstream regions, compared to downstream regions. This could suggest that some promoters have seen drastic changes, and may play a role in a differentiated regulation of the gene. We also found that the divergent regions overlapped with 839 protein coding genes, out of 26,925 in the reference genome. Most of these genes have no functional annotation, and are thus poorly characterized. Using Panther [17], we found no functional annotation in this set of genes.

Among these genes, we nevertheless found the well-studied *FLC* gene, implicated in vernalization [15]. Since the vernalization process is highly dependent of the location of the plant, it is likely that ecotypes have evolved in order to adapt to local weather. We thus plotted the conservation score (see Figure 5a),
and compared it to the structural annotation of the gene. We observed a sudden
drop of conservation in the first intron. We noted that this intron contained sev-
eral alternative paths (see Figure 5b, and Supplementary Data for an alternative
representation), which represent variations in the individuals, and explain the
drop of conservation.

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# 4 Discussion

PanCons is an efficient tool for finding divergent regions. Once of its aims
is to find possible traces of adaptation, which lead to structural variation. A
main advantage of the method is that it can detect small patterns, such as a
least conservation of the third nucleotides of the codons, or small structural
variations.

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So far, it does not have the power to find conserved regions, because of
the lack of genetic variability within a species at base pair resolution. Here, one
strategy to use windows [18], but the signal is more diluted. It is also possible to
leverage multiple-species alignments [3, 4, 16, 12], but the expected results is the
set of conserved elements within the phylum, not the species in consideration.

An advantage of the method is that it models substitutions and indels alike.
So far, usual method do model substitution, but hardly ever indels. This would
make it impossible to find deleted regions, or sequences that are not aligned
because they are too divergent. The shortcoming is that there is no model to
capture both substitutions and indels. It is thus impossible to find statistically
significantly divergent regions. Yet, we devised a simple, probably conserva-
tive, method to find some of these regions, and we found among them a large
divergent intron of the *FLC* gene, implicated in vernalization of *A. thaliana*.

We also suggested a conservation scoring system. Intuitively, we tried to
model an average conservation, computed as the proportion of individuals that
contain a given variation, for each base pair of the reference genome. This
conservation also includes the syntenic regions of the non-reference genomes.
Whereas syntenic nucleotides are located on the same column of a multiple
alignment, finding syntenic regions is not as straight-forward for pangenome
graphs. We defined a method that captures the different syntenic nucleotide in
case a SNPs, and extends it to the case of indels. Although it proved to have
a good discriminating power, it is possible that other methods (which include
finding syntenic nodes, and computing a conservation score) could be a better
fit.

It is important to note that PanCons heavily relies on a pangenome graph.
There are so far two lossless pangenome graph builders, namely Minigraph-
Cactus [7] and PGGB [5], with the former being the most used one, mostly
because the graphs it produces are easier to exploit. It is clear that errors in the
construction of the graphs, and more particularly alignments of the genomes,
will impact the outcome of PanCons. For instance, alignments of low complexity
or repeated regions are sometimes incorrect, or even skipped, and could yield to
over-divergent predictions. Yet, these methods are improving at a rapid pace,
and the graphs are expected to be more accurate after each release of the tools.

In the future, we hope that PanCons will be even more useful to the commu-
nity. With dropping sequencing prices, we can expect more telomere-to-telomere
genome assemblies, and thus more pangenome graphs, but also more individuals
in graphs. With more samples, divergent regions will be better characterized,
and a method finding conserved regions could be possible.

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<figure><img src="image_3.png" /><figcaption>(a) Similarity of ecotypes with the reference genome. Red dots are results computed by [9] using phylogeny. Blue dots are computed using our Jaccard index, for each chromosome.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>(b) Comparison between the phylogenetic and the Jaccard method. Each dot is the chromosome of an ecotype, the *x* value is the phylogenetic distance, and the *y* value is the Jaccard distance. The *R*² is 0.41.</figcaption></figure>

<caption>Figure 2: Comparison with similarities (1 being identical) computed by the Jaccard index (this work), and a phylogenetic approach, based on coding genes. In our method, we provided the Jaccard index between the chromosome of each ecotype, and the reference chromosome 6.</caption>
<figure><img src="image_5.png" /><figcaption>(a) Raw distribution of the conservation score.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>(b) Cumulative distribution of the conservation scores of several annotations. Genes were decomposed into different features: UTRs, introns, and we separated the three nucleotides of each codon of the coding sequences ("genes frame0" thus refers to the first nucleotide of each codon). Of note, "genes frame 0" and "genes frame 1" distributions are almost identical. Transposable elements were restricted to the most populous family, gypsy. The figure is zoomed to focus on the [0 - 0.7] y scale.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>(c) Average distribution of the conservation score over coding genes. Each gene is split into 1000 bins of equal sizes from the 5' end to the 3' end. We also included upstream and downstream regions up to 3kb. The TSS and TES are transcription start and end sites respectively.</figcaption></figure>

<caption>Figure 3: Several distributions of the conservation score.</caption>
<figure><img src="image_8.png" /><figcaption>Figure 4: Positions of divergent regions with respect to coding genes. The values are Jaccard indices, *i.e.* the size of the intersection of the regions with the considered annotation, divided by the union. The size of up/downstream regions is set to 1kb.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>(a) Conservation score on the *FLC* locus. Each bar is the average score on 10bp. The gene contains four alternative transcripts, named AT5G10140.1 to AT5G10140.4. Exons are figured with yellow boxed, and introns with lines. The gene is on the minus strand, the first exon is thus on the right, and the last exon is on the left.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>(b) Pangenome graph of the locus. Nodes in black are tra-
versed by the reference genome. Nodes in red are the exons
of the gene. The upper-right arm is the 5' end of the gene,
and the bottom-left arm is its 3' end. Gray nodes clearly
show non-reference variations, which match the drop of con-
servation in the 3'-most intron.</figcaption></figure>

<caption>Figure 5: Detail on the *FLC* gene.</caption>