# One tree to Yule them all? Reflexions on intertextuality and text transmission

Jean-Baptiste Camps, Kelly Christensen, Ulysse Godreau, Théo Moins

► To cite this version:

Jean-Baptiste Camps, Kelly Christensen, Ulysse Godreau, Théo Moins. One tree to Yule them all? Reflexions on intertextuality and text transmission. Digital Humanities 2025, Lisbon, Jul 2025, Lisbon, Portugal. 2025. [hal-05531280](https://hal HAL Id: hal-05531280)

Submitted on 28 Feb 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
# One tree to Yule them all? Reflexions on intertextuality and text transmission

Jean-Baptiste Camps¹, Kelly Christensen¹, Ulysse Godreau¹, and
Théo Moins¹

¹École nationale des chartes, Université PSL, France

## 1 Introduction

Text transmission is the process through which a text is disseminated and preserved dynamically through successive reproductions in one or several media (oral or written; manuscript, print or digital). It typically involves modifications, especially when the chain of transmission of a text moves substantially across time, space and cultural contexts, switches between media of transmission or types of reproduction (from paraphrase or citation to copy in full).

A typical case of text transmission is the dissemination of literary works in Antiquity and the Middle Ages. In this process, scribes generally use an existing material copy of a text to produce a new one, inducing innovations that can be intentional (e.g. translation, prosification, rewriting) or not (e.g. copy errors). Philologists use a genealogical tree (*stemma codicum*) to represent the relations between the surviving copies, and their shared ancestries based on shared innovations.

The relation between a model (exemplar) and its copy can be construed as a specific subtype of intertextuality, i.e. the interrelation between texts in general. Yet, the genealogies seldom represent the relations between all versions of a work, including translations and rewriting, or similar types of derivation, and they even more rarely include other types of intextextual relations (such as inspiration, paraphrase,...), even if there are counter-examples to be found (Aubreton, 1968; Bédier, 1902; Treutler, 1880). Consequently, stemmata represent texts as independent entities, each having its own single root (the authorial manuscript or the latest common ancestor of the surviving copies). This is a strong difference with phylogenetics, in which all species are ultimately united in a single tree of life, going back to the last universal common ancestor of all life on earth (LUCA).

The underlying assumption of independence – a conscious simplification made mostly for practical reasons – is not without creating taxonomic difficulties. There is no universally accepted definition in philology as to when two versions, linked by intertextual relations, constitute only two redactions of the same text or two distinct texts. For instance, should the assonanced version of the Song of Roland (Segre, 1971) be considered a different text than the rhymed version? Should the Middle Welsh translation (or even its descendants) be considered a witness to the French?
Theoretic as this question may seem, it has very concrete implications, for instance in terms of counting surviving (and estimating lost) copies of historical texts. Recent research has attempted to create a dynamic model of text transmission, using a stochastic birth and death model, and has shown results that aligned with existing data in terms of tree topology and of median age and surviving number of documents, allowing inferences on the number of lost works and documents, on a case study of medieval French chivalric narratives (Camps & Randon-Furling, 2022). Created using established philological concepts, this model considered all root nodes (of texts) to be independent.

Even though correspondence between the model and historical data was shown to be close, we have noticed discrepancies regarding the distribution of witnesses (i.e. surviving copies) per text. Could a model that additionally includes the notion of ‘speciation’ yield results that give a better representation of historical data, confirming the importance of intertextual relations beyond typical copy? In this context, speciation may be understood as representing the creation of a new text, through derivation from an existing witness of the parent text, and could stand for cases such as translation, rewriting, prosification, or even the writing of prequels or sequels.

For the present study, we build upon the following definitions (Christensen & Camps, 2025):

**work** a story, e.g. Perceval and the Grail

**text** an expression of the story, in a given language and form, for instance Chrétien de Troyes' *Conte du graal*; Wolfram von Eschenbach's *Parzival*; or the anonymous *Perceval en prose*

**witness** a manifestation of the text, through a given copy, for instance, Guyot of Provins' copy of Chrétien's *Conte du graal*, preserved in a physical document.

Yet, even with these specific definitions, used in our research, the level of generality of the model we are going to use make it fit to describe various types of derivation and applicable to other taxonomies.

# 2 Materials and methods

## 2.1 Datasets

We compiled sets of texts and their witnesses from data published in the Forgotten Books research project (Kestemont et al., 2022) as well as the Jonas (Section romane, 2024) and Handschriftencensus (Busch & Wolf, 2024) databases. It is to be noted that, since those datasets preexisted, we do not control the criteria used to define and distinguish texts. Instead, each database rest upon cumulative philological scholarship in their respective domains.

Despite their dramatically disparate sizes, the different datasets demonstrate a similar imbalance in the number of surviving witnesses per text: most texts have less than five witnesses, a small minority have dozens of extant copies. At the same time, the probability of having a hundred witnesses is not negligible, see Figure 1. This suggest a heavy-tailed, Pareto-like behaviour for the distribution of witnesses per text, which is a pervasive property in cultural diffusion phenomena (Bentley, Hahn, & Shennan, 2004; Newman, 2005; Pinto, Lopes, & Machado, 2012).
<table><caption>Table 1: Number of texts and witnesses for the three data sources.</caption><thead><tr><th>Source</th><th>Texts</th><th>Witnesses</th></tr></thead><tbody><tr><td>Forgotten Books</td><td>776</td><td>3,587</td></tr><tr><td>Jonas</td><td>24,514</td><td>73,150</td></tr><tr><td>Handschriftencensus</td><td>6,201</td><td>36,893</td></tr></tbody></table>

<figure><img src="image_2.png" /><figcaption>Figure 1: Distribution of witnesses per text for the three data sources (in log scale). The linear tendency of the curves suggests a heavy-tail behavior, rather than an exponential one as the simple birth-death model produces. The artificial dataset (in yellow), generated with known parameters, is one of those used for validation (see Figure 3).</figcaption></figure>

## 2.2 From birth-and-death processes to Yule's model

Several attempts have been made at modelling manuscript traditions by stochastic processes since the seminal work of Weitzman in the 1980s (Camps & Randon-Furling, 2022; Cisne, 2005; Weitzman, 1987). These approaches, up to differences in corpora of interest and implementation, including time variations of the parameters of the dynamics, essentially consist in describing text transmission by a birth-and-death process accounting for the continuous creation of new manuscripts, modelled as independent agents, copied from their predecessors with probability $\lambda$ per individual manuscript and unit time, along with their destruction and loss happening with rate $\mu$.

Although these models have been quite successful at reproducing several features of known textual traditions, they predict an exponentially decreasing distribution of the number of extant witnesses per text, incompatible with empirical data (see Figure 1).

Interestingly, the first historical attempt at modelling evolutionary dynamics in
biology through stochastic processes (Yule, 1925) also aimed at understanding the power law distribution of species per genus. In addition to the simple birth-and-death dynamics, Yule process introduces a *speciation event* with rate $\gamma$ by which a new agent -representing a species- is created, belonging to a new class -representing a genus. The large time distribution of surviving individuals per class is then known to follow the *Yule-Simon* distribution, with asymptotic power-law behaviour.

In our approach we model simultaneously the creation of independent traditions, appearing with rate $\Lambda$ as a single living agent, and the internal process of speciation within traditions with rate $\gamma$. This implies adding two additional parameters to the birth-and-death model, resulting in the parameter set $\theta = (\Lambda, \lambda, \mu, \gamma)$.

<table><caption>Table 2: Main hyperparameters and parameters of the model. The values for ($T_{\text{act}}$, $T_{\text{inact}}$, $K$, $N_0$) are the one used for estimations. The intervals for ($\Lambda, \lambda, \mu, \gamma$) define the initial search space for each parameter in our inference procedure.</caption><thead><tr><th></th><th>Definition</th><th>Values</th></tr></thead><tbody><tr><td>$T_{\text{act}}$</td><td>Duration of the active phase (n. time steps)</td><td>1000</td></tr><tr><td>$T_{\text{inact}}$</td><td>Duration of the inactive phase (n. time steps)</td><td>1000</td></tr><tr><td>$K$</td><td>Tradition's maximum population size</td><td>500000</td></tr><tr><td>$N_0$</td><td>Initial number of traditions</td><td>1</td></tr><tr><td>$\Lambda$</td><td>Average number of new traditions per time step (root birth rate)</td><td>[0,1]</td></tr><tr><td>$\lambda$</td><td>Probability of a witness being copied (node birth rate)</td><td>[0,0.05]</td></tr><tr><td>$\mu$</td><td>Probability of a witness being destroyed (node death rate)</td><td>[0,0.01]</td></tr><tr><td>$\gamma$</td><td>Probability of a new witness to manifest a new derived text (speciation rate)</td><td>[0,0.01]</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>Figure 2: Example of a tree generated by the model. The tree stands for a single *work*, but the nodes are distributed in different *text versions* that arise through speciation events, and are shown here in different colours</figcaption></figure>

## 2.3 Likelihood-free inference for Yule's parameter

The obtained process introduces significant complexity to the inference problem: in addition to the four parameter to infer, several additional hyperparameters must be provided for the simulation (see Table 2): a number of active (and inactive, when there is only deaths) time steps which defines the time scale in which we operate, and a theoretical maximum population $K$ and an initial number of traditions $N_0$ to control the generation of new individuals. The interaction between these parameters and hyperparameters produces complex tree structures through time, making the likelihood function analytically intractable.

Several frameworks exist for inference in that case. Among them, Approximate Bayesian Computation (ABC, Sisson, Fan, & Beaumont, 2018) allows us to perform a complete Bayesian analysis without explicitly evaluating the likelihood. Recently, Simulation-Based Inference (SBI, Cranmer, Brehmer, & Louppe, 2020) methods have emerged as powerful alternatives to traditional ABC approaches. These techniques
leverage neural networks to automatically learn the relationship between simulation
outputs and model parameters, effectively constructing an approximation of the pos-
terior distribution of the parameters (Λ, λ, μ, γ). Here, we use a multi-round version
of one methode called Neural Posterior Estimation (NPE). The aim of running several
rounds is to iteratively focus simulations on promising regions of the parameter space,
refining the posterior approximation by concentrating computational resources where
they matter most specifically for each dataset. Some results obtained after 5 rounds
of NPE are presented in Figure 3 on an artificial dataset with known parameters, and
in Table 3 and Figure 4 for our three corpora. While the estimation of the root birth
rate Λ requires further refinement, we recovers the key correlations between λ and
μ identified in previously in Camps and Randon-Furling (2022), while additionally
highlighting distinct regions of interest in the full parameter space (Λ, λ, γ, μ) that
characterise the different manuscript traditions.

<figure><img src="image_4.png" /><figcaption>Figure 3: Parameter estimates for our Yule model (Λ: new tradition rate, λ: copy rate, γ: speci-
ation rate, μ: death rate) using artificial data. Diagonal panels show marginal posterior
distributions for each parameter, while off-diagonal panels show joint distributions between
parameter pairs. Black star markers indicate the true parameter values used to generate
the synthetic dataset, and happens to be inside the inferred zone.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 4: Parameters estimates for our Yule model across the three datasets (Handschriftencensus, Jonas, Forgotten Books). Diagonal panels show marginal posterior distributions for each parameter, while off-diagonal panels show joint distributions between parameter pairs. Point markers indicate the point estimation in Table 3, which is the median estimates for each dataset. The pairwise relationships between $\lambda$, $\gamma$ and $\mu$ reveal strong parameter dependencies, highlighting distinct regions of interest that characterize each corpus’s unique transmission dynamics.</figcaption></figure>

# 3 Discussion

To fully validate the significance of intertextual relationships in manuscript transmission, our investigation must proceed along three complementary axes. First, we need to apply our inference framework across different textual corpora (see Table 1). Second, we must compare the performance of our Yule-based model against other candidates, particularly the simpler birth-death process, using formal model selection techniques. Finally, different algorithm choices should be tested to ensure the robustness of our conclusions. We plan to further investigate in these directions to better represent text transmission. If our current insights are confirmed, the use of Yule’s model may constitute an advancement in the modelling of text transmission, beyond the simple birth-and-death processes already suggested, as a case of cultural drift. From this basis, it will be possible to see if further refinements are necessary, such as the introduction of a process of selection (modelling cultural preferences), or more generally, the use of the very large array of phylogenetic methods currently available
<table><caption>Table 3: Estimations of the four parameters of the Yule model along with their credible intervals at 95%. The values presented here can be visualized along the diagonal of Figure 4.</caption><thead><tr><th></th><th>Forgotten Books</th><th>Handschriftencensus</th><th>Jonas</th></tr></thead><tbody><tr><td>Λ</td><td>7,310<sup>-1</sup> ∈ [1,8.10<sup>-1</sup>, 9,7.10<sup>-1</sup>]</td><td>5,510<sup>-1</sup> ∈ [5,8.10<sup>-2</sup>, 9,510<sup>-1</sup>]</td><td>4,7.10<sup>-1</sup> ∈ [5,9.10<sup>-2</sup>, 9,7.10<sup>-1</sup>]</td></tr><tr><td>λ</td><td>3,710<sup>-3</sup> ∈ [2,8.10<sup>-3</sup>, 4,2.10<sup>-3</sup>]</td><td>8,010<sup>-3</sup> ∈ [5,3.10<sup>-3</sup>, 1,2.10<sup>-2</sup>]</td><td>6,6.10<sup>-3</sup> ∈ [5,7.10<sup>-3</sup>, 8,2.10<sup>-3</sup>]</td></tr><tr><td>μ</td><td>1,6.10<sup>-4</sup> ∈ [1,5.10<sup>-5</sup>, 8,7.10<sup>-4</sup>]</td><td>1,6.10<sup>-3</sup> ∈ [1,7.10<sup>-4</sup>, 4,1.10<sup>-3</sup>]</td><td>5,6.10<sup>-4</sup> ∈ [1,1.10<sup>-4</sup>, 1,3.10<sup>-3</sup>]</td></tr><tr><td>γ</td><td>5,1.10<sup>-4</sup> ∈ [3,5.10<sup>-4</sup>, 8,2.10<sup>-4</sup>]</td><td>6,1.10<sup>-4</sup> ∈ [4,2.10<sup>-4</sup>, 9,6.10<sup>-4</sup>]</td><td>2,1.10<sup>-3</sup> ∈ [1,8.10<sup>-3</sup>, 2,8.10<sup>-3</sup>]</td></tr></tbody></table>

for modelling species diversification (Morlon et al., 2024).

## Supplementary material

Code for the model and for the ABC method will be available at the Github repository of the LostMa project, https://github.com/LostMa-ERC/BayesYule, and archived on Zenodo, https://doi.org/10.5281/zenodo.15350478.

## Acknowledgements

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

Funded by the European Union (ERC, LostMA, 101117408). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.

The authors would like to thank the two reviewers, Wouter Haverals and Stefanie Schneider, for their insightful suggestions. Errors remain our own.

## References

Aubreton, R. (1968). La tradition manuscrite des épi programmes de l’anthologie palatine. *Revue des études anciennes*, 70(1), 32–82.

Bentley, R. A., Hahn, M. W., & Shennan, S. J. (2004). Random drift and culture change. *Proceedings of the Royal Society of London. Series B: Biological Sciences*, 271(1547), 1443–1450.

Busch, N., & Wolf, J. (Eds.). (2024). *Handschriftencensus* [Database]. Retrieved from https://handschriftencensus.de

Bédier, J. (Ed.). (1902). *Thomas d'Angleterre: Le roman de Tristan, poème du XIIe siècle*. Paris, France: Librairie de Firmin Didot et Cie. (ISSN: 0768-4991)

Camps, J.-B., & Randon-Furling, J. (2022). Lost Manuscripts and Extinct Texts: A Dynamic Model of Cultural Transmission. In *Proceedings of the Computational Humanities Research Conference 2022 Antwerp, Belgium, December 12-14, 2022* (pp. 198–214). Retrieved 2022-10-25, from https://ceur-ws.org/Vol-3290/long_paper3261.pdf

Christensen, K., & Camps, J.-B. (2025). Greening your database of literary works: How to avoid reinventing vocabularies, in favor of sustainable, reusable models. In *Digital humanities 2025: Book of abstracts*. Lisbon.

Cisne, J. L. (2005). How science survived: Medieval manuscripts’ ”demography” and classic texts’ extinction. *Science*, 307(5713), 1305-1307. Retrieved
from https://www.science.org/doi/abs/10.1126/science.1104718 doi: 10.1126/science.1104718

Cranmer, K., Brehmer, J., & Louppe, G. (2020). The frontier of simulation-based inference. *Proceedings of the National Academy of Sciences*, 117(48), 30055–30062.

Kestemont, M., Karsdorp, F., de Bruijn, E., Driscoll, M., Kapitan, K. A., Macháin, P., ... Chao, A. (2022). *Forgotten books: supplementary materials (data and code)*. Zenodo. Retrieved from https://doi.org/10.5281/zenodo.5947206 doi: 10.5281/zenodo.5947206

Morlon, H., Andréoletti, J., Barido-Sottani, J., Lambert, S., Perez-Lamarque, B., Quintero, I., ... Veron, P. (2024). Phylogenetic insights into diversification. *Annual Review of Ecology, Evolution, and Systematics*, 55 (Volume 55, 2024), 1-21. Retrieved from https://www.annualreviews.org/content/journals/10.1146/annurev-ecolsys-102722-020508 doi: https://doi.org/10.1146/annurev-ecolsys-102722-020508

Newman, M. E. (2005). Power laws, Pareto distributions and Zipf's law. *Contemporary physics*, 46(5), 323–351.

Pinto, C. M., Lopes, A. M., & Machado, J. T. (2012). A review of power laws in real life phenomena. *Communications in Nonlinear Science and Numerical Simulation*, 17(9), 3558–3578.

Section romane. (2024). *Jonas* (M.-L. Savoye, Ed.) [Database]. Retrieved from https://jonas.irht.cnrs.fr

Segre, C. (Ed.). (1971). *La chanson de Roland* (No. 16). Milano and Napoli: R. Ricciardi.

Sisson, S. A., Fan, Y., & Beaumont, M. (2018). *Handbook of approximate bayesian computation*. CRC press.

Treutler, H. (1880). Die Otinelsage im Mittelalter. *Englische studien*, 5, 97–149. Retrieved from http://archive.org/stream/englischestudien05leipuoft# page/96/mode/2up

Weitzman, M. P. (1987). The evolution of manuscript traditions. *Journal of the Royal Statistical Society. Series A (General)*, 150(4), 287–308.

Yule, G. U. (1925). A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis. *Phil. Trans. R. Soc. Lond. B*, 213, 402–410. doi: https://doi.org/10.1098/rstb.1925.0002