Transmission and Survival of Iberian Patristic Texts (3rd–5th Centuries)

Anthology of Computers and the Humanities, Vol. 1 Transmission and Survival of Iberian Patristic Texts (3rd–5th Centuries) Émilie Guidi1, Théo Moins1, Jean-Baptiste Camps1 1École nationale des chartes, Université PSL, Paris, France Abstract This paper analyses the textual transmission of the Church Fathers from the Iberian Peninsula. The corpus is characterised by formal (prose, verse) and generic (sermons, letters, chronicles, epics) heterogeneity. Our computational analyses reveal two contrasting transmission dynamics: prose texts are more numerous but are transmitted by fewer witnesses, sometimes only via their inclusion in medieval collections. Poetic texts, fewer in number, have generated a higher number of witnesses, likely due to their integration in large literary projects. We model these dynamics using two approaches: probabilistic unseen species models, which estimate an upper bound of text and witness survival rates and indicate low corpus diversity and evenness; and stochastic birth-death models, which explore cultural evolutionary patterns in text and witness populations. Results suggest a text survival rate below 67% (potentially closer to 20%) and a manuscript survival rate below 10% (possibly under 1%). Notably, these estimates diverge from prior findings for Medieval French literature, where unseen species and birth-death models yielded similar results. This discrepancy suggests that diachrony – specifically, the broader chronological range of the patristic corpus – plays a key role in shaping transmission outcomes. Our findings also highlight limitations of the birthdeath model, particularly in accounting for highly successful texts and in temporal variations in production/destruction rates. Keywords: Unseen Species, Agent-Based Modelling, Birth-and-Death Process, Cultural Transmission, Philology, Patristics 1 Introduction 1.1 Computational methods for textual transmisssion In the field of textual history, textual transmission designates the way a text is disseminated and preserved through the copy of material artefacts like manuscripts. This process of transmission is neither linear nor static; it follows an evolutionary dynamic marked by processes of dissemination, selection, variation and extinction. Books are first produced – for instance, in the case of patristic texts we envision here, manuscripts are usually copied in scriptorial workshops linked to libraries or monastic schools, where scribes copy them with a view to preserving them [1]. Their diffusion, whether immediate or spread over the long term, depends on a number of factors, in particular the decision to reproduce certain texts rather than others. Liturgical manuscripts and the major texts of the Fathers of the Church were widely copied. Texts from Classical and Late Antiquity were also favoured, as they were often used in schools to teach reading and rhetoric. Some manuscripts disappeared, whether for human or natural reasons (gradual loss of interest in a work, library fires, wars, etc.), while others were reused, prolonging their existence in new contexts. The manuscript tradition thus reflects different uses and intentions at different times. It evolves, transforms and adapts according to chance and to the needs and views that societies have of texts. Émilie Guidi, Théo Moins, and Jean-Baptiste Camps. “Transmission and Survival of Iberian Patristic Texts (3rd–5th Centuries).” In: Proceedings of Conference XXX, ed. by Editor1 Editor2. Vol. 1. Anthology of Computers and the Humanities. 2025, 1–1. https://doi.org/00000/00000. ©2025 by the authors. Licensed under Creative Commons Attribution 4.0 International (CC BY 4.0). 1 Traditional manuscript sciences have long been the principal tools used to describe a textual tradition. Palaeography focuses on the evolution of scripts, while codicology focuses on the material aspects of manuscripts. Philology, which notably includes ecdotics and textual criticism, concentrates on the linguistic and literary study of texts, sometimes attempting to reconstruct earlier versions, or even lost versions, of them [19]. In particular, textual criticism aims to examine the variants present in the different witnesses, organise them in a genealogical perspective, and restore the earliest accessible form of a text based on the available evidence. While these disciplines can help to recover certain aspects of a lost manuscript tradition, they are nevertheless unable to grasp the tradition in its entirety. This is precisely where new approaches come into play, made possible by the development of computational humanities. Recent years have seen the emergence of computational methods applied to the study of textual transmission, with the aim of modelling the dynamics of loss and survival. Two main approaches have emerged. The first, developed as part of the Forgotten Books project [16], applies models of unseen species derived from ecology to manuscript traditions, from a probabilistic perspective. The second, carried out by the ERC-LostMA project [3], uses stochastic processes of the birth-and-death type, coupled with computer simulations, in the direction pioneered by the work of Weitzman [23] and Cisne [7]. 1.2 Contributions The main objective of our work is to apply these recent approaches to patristic texts produced in the Iberian Peninsula between the mid-3rd century and the mid-5th century. This textual tradition is still unexplored with such methods, which has so far concentrated on ancient texts [23], medieval scientific manuscripts [7], or chivalric narratives [16]. Studying the transmission of a corpus in this pivotal period between Classical Antiquity and the Middle Ages from this perspective remains therefore unprecedented. We can wonder whether this corpus follows similar patterns of transmission and loss than those previously studied, or if the difference in the length of the period envisioned, and the mode of transmission and reception of those texts (particularly confronted with vernacular fictional literature studied in previous projects) will be revealed through computational analysis. This study aims to model the transmission of the patristic tradition in the Iberian Peninsula by estimating the survival and disappearance rates of texts and manuscript witnesses. It also examines whether distinct dynamics emerge in the processes of conservation, diffusion, and extinction depending on textual form, particularly between prose and poetry. For this purpose, we will employ probabilistic models, especially those of unseen species [16], as well as stochastic processes [3]. The approach relies on the creation of a new database recording all known manuscript sources of the Iberian patristic tradition of texts originating between the 3rd and the 5th century. It also proposes the application, for the first time, of computational methods to this corpus, which involves adapting the existing computational models to the specific features of Late Antiquity, in order to better account for the dynamics specific to this period. 2 Material 2.1 Data collection The constitution of the corpus involved manual data collection, consisting of an inventory of the texts of the Church Fathers active in the Iberian Peninsula between the 3rd and 5th centuries, as well as the identifiable manuscript witnesses that transmitted them. The selection focused exclusively on the direct tradition, including both preserved manuscripts (complete or fragmentary) and those whose existence is attested despite their loss (fire, war, etc.), but not the derived works. This corpus 2 covers the geographical area of the Iberian Peninsula, corresponding to the territories of presentday Spain and Portugal. This choice is particularly relevant because the tradition from this period is well documented and has recently been the subject of critical editions [see 8]. It is delimited chronologically by the Councils of Nicaea (325) and Chalcedon (451), in accordance with the boundaries established by the Clavis Patrum Latinorum [12]. Authors of Late Antiquity (6th-7th centuries) have been deliberately excluded, since many of their texts have not yet been reliably edited or their manuscript tradition studied in depth. The identification of texts and authors was done mainly on the basis of the Clavis Patrum Latinorum [12] [henceforth CPL], supplemented by the Traditio Patrum, Scriptores Hispaniae [8]. Authors were selected who were either of Iberian origin or who were active in the region. Texts attributed with certainty, but also those described as dubia or spuria1, were included, as long as their author’s origin was recognised as Iberian. Two anonymous texts have also been included (CPL, 789 and 373a), their production context being located on the Iberian peninsula. Indirect tradition has been deliberately excluded from our study. In our corpus, it manifests itself in a variety of forms. Some texts are taken up, summarised or adapted in other works. This is particularly true of the Chronicle of Hydace, an epitome of which is incorporated into later compositions such as the Historia Gothorum, Wandalorum et Suevorum (CPL 1204) by Isidore of Seville, or the Pseudo-Fredegarius. This phenomenon also applies to poetry, where texts such as those by Prudentius served as models or were taken up in intertextual chains, notably involving Arator’s Apostolic History, Corippus’ Johannides or, more recently, Milon de Saint-Amand’s De Sobrietate. A second case that is also excluded is that of recensions, as shown by the example of Montanus of Toledo, whose Epistulae (CPL, 1094) circulated within the Collectio Hispana. The latter itself gave rise to derivative versions, such as the Hispana Gallica. Excluding indirect tradition and recensions thus allows us to focus on the corpus proper and the diversity of its textual forms, both in prose and versified form. On the prose side, we find a wide variety of genres: letters and treatises, writings related to preaching such as sermons and homilies, texts of confession of faith such as credo, foundational texts such as ecclesiastical canons, as well as historiographical texts including historical chronicles. It is worth highlighting a specific feature of the transmission of the texts in our corpus: Late Antique texts circulated in the form of collections [22], structured according to thematic or generic coherence. Some texts owe their preservation to their inclusion in homilies, others to their inclusion in canonical collections. Still others have been preserved as part of vast doctrinally-oriented collections, notably on themes such as Priscillianism and other theological controversies. The Ancients did very little theorising on literary genres, a fact that is particularly evident in prose, which contains many hybrid work, such as the “lettres-traités”, that blend correspondence and morale treatise. The text De similitudine carnis peccati (CPL, 567) by the priest Eutrope is a representative example as it’s a letter addressed to Caesaria, a pious woman, combining the personal form of an epistolary exchange with a structured theological argument on the nature of Christ and the incarnation. On the poetic side, the corpus includes verse texts ranging from relatively short poems covering a variety of themes such as panegyric, lyrical, satiric, and didactic pieces, to large-scale works such as epics, which are represented by major figures like Prudentius and Juvencus. 2.2 Corpus analysis Applying these criteria, we assembled a corpus of M= 1159 manuscripts corresponding to T= 67 texts by 37 different authors. The oldest manuscripts date from the 6th century, while we set the 15th century as the upper limit, since in our tradition manuscripts later than the 15th century 1Works considered dubia are those whose attribution is questioned, and works considered spuria are those whose attribution has been recognised as false. 3 (a) Abundance data distribution for prose and poetry. (b) Singletons f1, doubletons f2, number of texts Tand number of manuscript witnesses Mfor each part of the corpus. Genre f1f2T M Poetry 3 1 6 365 Prose 16 4 61 794 Total 19 5 67 1159 (c) Evenness profiles for prose and poetry texts across orders q Figure 1: Abundance and evenness comparison for prose and poetic texts. are often copies based on printed editions, whereas we are primarily interested in witnesses of the manuscript tradition itself. Their provenance spans the whole of Europe. The dataset is illustrated in Figure 1, and highlights a marked contrast between the two genres. Prose exhibits a significantly greater richness, with 61 distinct texts identified, compared to only 6 for poetry. However, despite this disparity in textual diversity, poetry shows a remarkably high total abundance (M= 365 poetry manuscripts), concentrated in a small number of works. In contrast, the 61 prose texts collectively amount to a total abundance of M= 794, see Figure 1b. This disproportionate distribution indicates a strong transmission dynamic for a small number of poetic texts, reflecting their cultural or literary prominence in our corpus. To further characterize this distribution, we plot in Figure 1c diversity profiles based on the parameter q, which controls the sensitivity to dominant versus rare elements: at q= 0, diversity corresponds to richness (number of distinct texts), while higher values of qprogressively emphasize the most abundant texts. Evenness, derived from these profiles, measures how equitably transmission is distributed across texts, with values near 1 indicating balanced distribution and lower values reflecting concentration around a few dominant works. As shown in Figure 1c, the evenness profiles reveal a marked difference between prose and poetry texts. Across all orders q, the curve corresponding to poetry declines more rapidly and reaches significantly lower values than that of prose. This steep drop, observable even at low values of q, indicates a strong concentration of transmission around a few highly 4 dominant poetic works, to the detriment of the rest of the corpus. In contrast, the prose curve follows a more gradual slope and maintains higher evenness values, suggesting a more balanced distribution among the various texts. How can we explain and model the fact that poetic texts, though fewer in number, were widely transmitted and frequently copied? In particular, how does this specific behaviour influence our analyses of text survival? A first response would be to make two separate studies for poetry and prose, but the small number of poetry samples forces us for now to study only the prose texts for the rest of the study. Results on the entire corpus (prose and poetry) are also given and discussed in Appendix D. 3 Methods 3.1 Unseen Species Model Recent research demonstrated that the statistical diversity estimators, traditionally commonly used - among other fields - in ecology, can also be successfully applied to cultural heritage [16]. The non-parametric methods, such as unseen species models, make it possible to estimate total richness (i.e., the total number of species, or texts in our case) and diversity of a population, by integrating unobserved elements, and correct the bias induced by the frequent presence of rare species, a major characteristic of our corpus. In particular, the Forgotten Book project applied several estimators to a corpus of European medieval chivalric narratives, in several languages, thanks to which the authors were able to estimate a minimal number of unseen (i.e. lost) texts and manuscript witnesses [16]. The methods they introduced to the field of philology were made available in the Copia Python package, that has also since been enriched with additional estimators [15]. We choose three estimators used in Forgotten Books [16]: Chao1 [5], iChao1 [6] and Jackknife [2]. The Chao1 estimator provides a minimum bound on the original richness based on texts preserved in one or two witnesses (singletons and doubletons), while iChao1 refines this estimate by also including texts present three or four times, thus reducing the risk of underestimation. This approach is particularly well-suited to our corpus, in which 40% of the texts (27 in total) are transmitted by only a very small number of witnesses (one to four witnesses). The Jackknife estimator stands out for its ability to take into account the heterogeneity of the distribution of texts, which is crucial in a corpus where a small number of widely distributed texts, such as Prudentius texts that total almost 300 witnesses, coexist with others that are extremely rare. Unlike Chao1 and iChao1, which rely mainly on the frequency of the rarest texts, Jackknife uses a systematic resampling mechanism that exploits all the frequencies of appearance, providing a nuanced estimate of the original richness2. In order to estimate the minimum number of witnesses that would need to be observed in order to register all the unobserved texts in the Iberian patristic tradition, we used the estimator Minimum Additional Sampling [16], included in Copia, that was used to estimate the survival rates for documents preserving romances and heroic narratives in different linguistic traditions [16]. This estimator allows us to estimate how many additional witnesses would be required for an extended sample to contain at least one occurrence of each original text. It is based on the dynamics of singletons when the sample is enlarged: those already present in the initial sample versus those newly discovered. On the basis of these richness estimators, we also estimated the survival rate of texts and witnesses: to do this, we converted the estimates of textual and witness richness into survival proportions, by relating the estimated richness to the richness actually observed. We then generated 2Although the ACE estimator is available in the Copia package [15], we do not consider this method here as it requires an arbitrary abundance threshold corresponding to the upper limit for considering a species as rare, and complicates comparison between estimations made on different corpora, that could require the use of different thresholds. Similarly, Egghe’s estimator [11], also implemented in Copia but initially designed for printed corpora with a known number of print runs, is not relevant to a manuscript tradition. 5 density curves by resampling using the bootstrap method, making it possible to visualise the variability of the survival rates for each estimator selected (see below, Figure 8 and Figure 9). 3.2 Modelling the dynamics of text transmission Alternatively, one can consider a dynamic approach by simulating the temporal evolution of both text and witness populations, in order to reconstruct the evolutionary processes that led to the formation of our current corpus. The real-world dynamics of transmission or extinction of texts were probably influenced by a multiplicity of factors, be they extrinsic (fires, wars, economic crises, etc.) or intrinsic (different fitness of the texts or the witnesses, reception and reader interest, etc.). From the modelling perspective, the core transmission dynamic reduces to a new text appearing with an original witness (the authorial manuscript), and witnesses that can be copied and/or destroyed in time. For each text, this implies two outcomes: survival if there is more copy than destruction, or disappearance. A primary method for modelling involves employing a birth-death process with constant rates [3, 23]: each witness is modelled as an independent agent, from which copies are made with rate λ per unit time and that can be destroyed with rate µ. A recent update applied to Medieval chivalric literature [3] allows parameters λand µto be estimated from observations, in a model with a temporal division into two distinct phases: a period of activity, when texts were actively transmitted and copied in manuscript form, and a period of inactivity when the texts are no longer copied, but witnesses can still be destroyed, and so λis fixed at 0 but not µ(modelling the period after the appearance of the printing press). Obtaining an estimate of λand µallows to deduce an estimate of quantities of interest such as survival rate, extinction probability, topological properties of trees, etc., either by mathematical derivation or by re-simulations of this process with estimated parameters. Yet, our corpus presents a relatively different type of tradition, particularly regarding chronological parameters, since the texts go back to Late Antiquity. Moreover, while the texts were conceived by authors from the Iberian peninsula, during a limited amount of time (the 3rd to 5th centuries), copies continued to be actively produced throughout Europe during the centuries of the Middle Ages. Therefore, some adaptations are needed with respect to the model used by Camps et al. [3], in order to distinguish a period of both texts and witnesses creation, to a period where no new text appear but witnesses keep being reproduced. To overcome these obstacles, we suggest a model of transmission divided into three phases: 1. An innovation phase (201–500): This corresponds to Late Antiquity, when patristic authors were actively producing new texts while existing texts were simultaneously being transmitted through manuscript copying. During this period, new independent texts are created while existing manuscript witnesses continue to be copied and potentially destroyed. This phase is characterized by the two parameter λ(copying rate) and µ(destruction rate), but also by a third one, Λ, for new tree creation per unit time. Λact as an innovation rate, and is not proportional to the average population (contrary to λand µ), but represents the external appearance of a new text. 2. A reproduction phase (501–1450): This corresponds to the medieval period, when patristic texts were no longer being authored but were actively transmitted throughout Europe through manuscript copying, with scribes reproducing existing texts without creating fundamentally new texts. This phase is marked by the cessation of new text creation (Λ = 0), while existing witnesses continue to be copied and destroyed according to rates λand µrespectively. 3. An inactive phase (1451–1700): This phase typically corresponds to the post-medieval period, particularly after the advent of printing, when manuscript copying was largely aban6 doned while existing witnesses remained vulnerable to loss and destruction. During this final period, copying activity ceases (λ= 0), leaving only the destruction rate µactive. Witnesses can still be lost through various factors (wars, fires, material degradation, neglect) but are no longer being reproduced. Time (years) t0t1t2t3 201 501 1451 1700 Innovation Λ, λ, µ > 0 Reproduction λ, µ > 0 Inactive µ>0 Figure 2: Timeline of the three-phase transmission model with active parameters for each period. A diagram of the different periods, along with the definition of the time points ti’s, that mark the start/end times for each phase, is summarised in Figure 2. This model allows an explicit calculation of quantities of interest like the richness or the proportion of surviving texts and witnesses at t3, as a function of the parameters (Λ, λ, µ)and duration of the different phases ti. The various formulas are given in subsection B.1. Parameter estimation for (Λ, λ, µ)from observed data constitutes a classical inverse problem: while we can simulate this kind of process from given parameters, we need to infer parameters from observed data. We employ here Simulation-Based Inference (SBI) [9], which simulates the transmission process across various parameter combinations and learns the mapping between parameters and resulting data to identify the most probable parameters generating our observations. Unlike point estimation methods, this Bayesian framework provides full posterior probability densities p(Λ, λ, µ |data), quantifying uncertainty in parameter estimates and enabling robust statistical inference. Therefore, all the quantities of interest obtained by parameter transformation such as richness will be probabilistic, and so all density of probability will be available for inference, in particular to describe the uncertainty around the estimation (more details in subsection B.2). The method requires defining a prior distribution p(Λ, λ, µ)over parameter space: we use constrained uniform priors that enforce biological constraints (e.g., λ > µ for population growth) and computational limits through a maximum population threshold max_pop to prevent memory overflow during simulation. The inference pipeline, implemented in the simmatree package [17], uses Neural Posterior Estimation [20] to approximate the posterior distribution directly via neural networks.3Model validation is performed through posterior predictive checks, where parameters sampled from the posterior are used to simulate new datasets and compare them with original observations to assess model adequacy (see Appendix C). 4 Results As mentioned above, both methods will be applied to the prose texts of our Iberian patristic corpus, and results on the entire corpus can be found in Appendix D. Results are given in Figure 3 for text survival rate. The application of unseen species estimators and birth-death modeling to our prose corpus reveals contrasting perspectives on textual loss (Table 1). The unseen species estimators converge on a relatively narrow range for the lower bound of original text richness, with Chao1 suggesting 93 texts, iChao1 indicating 99 texts, and Jackknife estimating 89 texts. These estimates, representing minimum bounds, imply that the 61 observed prose texts constitute at most 67% of the original production (see Figure 3). In contrast, 3The package also offers multi-round refinement to improve estimation accuracy [10, 20]. 7 Table 1: Estimation of textual richness using Chao1, iChao1, Jackknife, and the one from the Birth–Death model, with 95% confidence intervals (CI) for each estimator (prose texts). Estimator Text Richness 95% CI Chao1 93 [64, 173] iChao1 99 [70, 178] Jackknife 89 [70, 108] Birth–Death 313 [220, 338] (a) Bootstrap distribution of text survival rates upper bound for iChao1 estimator. (b) Posterior distribution of text survival rates using the birth–death modelling. Figure 3: Estimations of text survival rates on the prose corpus, using iChao1 and birth–death forest method. the birth-death model yields a substantially higher estimate of 313 texts for the original corpus. This threefold difference between approaches is noteworthy: while unseen species methods suggest an upper bound of 67% survival based on the iChao1 estimator, the birth-death model’s posterior distribution centers around a 20% survival rate (Figure 3). These divergent estimates reflect the different mathematical frameworks underlying each approach—one providing conservative lower bounds, the other attempting to model the full transmission dynamics. Looking at Figure 4 and Figure 5, the disparity between methods becomes even more pronounced when examining manuscript witnesses. The Minimum Additional Sampling approach suggests that current witnesses represent at most 10% of the original manuscript production (Figure 4), but the birth-death model indicates a median survival rate of merely 0.5%, though uncertainty in the model produces a broad distribution extending up to 1.5% (Figure 5). This uncertainty translates into dramatic variation in absolute numbers: the 95% credible interval spans from 37,000 to over 2 million original witnesses, with a median estimate of approximately 160,000 manuscripts. This suggests a variety of possible scenarios that could lead to the same number of surviving witnesses. 5 Discussion The previous results deserve to be discussed both from a methodological and a text historical perspective. From a methodological standpoint, the apparent difference in the estimate provided by unseen species estimators and a birth-death process do not imply, strictly speaking, a contradiction. Since said estimators provide a lower bound to richness (and consequently an upper bound to survival), 8 (a) Species accumulation curve. The purple point represents empirical data, the dashed line is the extrapolation curve, and the purple shaded area illustrates the uncertainty range. (b) Witnesses survival rates. Estimation and variability using the bootstrap procedure. Vertical solid grey line corresponds to the estimate, and dashed lines represent the confidence interval at 95%. Figure 4: Estimated survival rates by bootstrap and witness richness extrapolation for prose corpus (a) Posterior distribution of witness richness. (b) Posterior survival rate of witnesses. Figure 5: Posterior distribution of richness and survival rate for witnesses, using the birth–death forest modelling, for the prose corpus. 9 Figure 7: Posterior predictive checks on 500 summary statistics, drawn using parameters samples from the posterior distribution, using the prose corpus. Figure 7 presents posterior predictive checks based on 500 simulations drawn from the posterior distribution. These checks evaluate the model’s ability to reproduce key summary statistics of the observed data by comparing the empirical values (shown as vertical lines) with the distribution of values obtained from posterior predictive simulations. The majority of summary statistics show satisfactory agreement between the model predictions and observed data. The model successfully captures the number of texts, witnesses, the maximum and median number of observations per text. This indicates that the three-phase birth-death process provides a reasonable approximation of the core transmission dynamics for prose texts in the Iberian patristic tradition. A small discrepancy emerges in the number of texts with one witness, which suggests that while the birth-death model captures the general transmission patterns, certain aspects of the empirical distribution remain inadequately modelled. D Results on the entire corpus First, applying unseen species estimators to the corpus of patristic texts from the Iberian Peninsula enables us to assess both the minimal number of texts originally produced and an upper bound of the proportion currently preserved. These results (Figure 8) suggest that the initial Iberian patristic tradition comprised at least one hundred distinct texts. The bootstrap method enables an evaluation of the variability in the estimated survival rates. For instance, the density curves resulting from the iChao1 procedure indicate that 66% of the texts have likely survived (Figure 8). This trend suggests that two thirds of the patristic texts produced in the Iberian Peninsula could represent a maximal bound on what has been preserved, thereby moderating the extent of textual loss. To complete this finding, we compare with richness estimation from the stochastic process modelling. Here, contrary to the unseen species results, this estimation is not a lower bound but an estimation of richness supposing a birth–death model. Still, the estimation around 300 stays in the same order of magnitude of all unseen species method, while it remains higher than the highest probable lower of each estimator. Therefore, the results of our modelling do not contradict those of unseen species methods. 16 (a) Bootstrap distribution of text survival rates upper bound for iChao1 estimator. (b) Posterior distribution of text survival rates using the birth–death modelling. Figure 8: Estimations of text survival rates on the entire corpus (poetry and prose), using iChao1 and birth-death method. (a) Species accumulation curve. The green point represents empirical data, the dashed line is the extrapolation curve, and the green shaded area illustrates the uncertainty range. (b) Manuscript witnesses survival rates. Estimation and variability using the bootstrap procedure. Line in red correspond to the estimate, and dashed line represent the confidence interval at 95%. Figure 9: Estimated survival rates by bootstrap and witnesses richness extrapolation on the entire corpus (poetry and prose) 17 (a) Posterior distribution of witness richness. (b) Posterior survival rate of witnesses. Figure 10: Posterior distribution of richness and survival rate for witnesses, using the birth–death forest modelling, for the entire corpus (poetry and prose). For the manuscript witnesses, the application of the Minimum Sampling estimator allowed us to establish a lower bound for the original richness, estimated at approximately 14774 witnesses. The survival rate analysis, based on a bootstrap procedure, indicates a preservation of approximately 10% of the witnesses, with a confidence interval ranging from 4% to 18% (Figure 9b). This result highlights a significant loss in the transmission of witnesses which is greater than that observed for the texts themselves. However, this method may produce by design a lower bound that can be very loose, as it consists in completing the dataset only with the minimum number of samples, itself based on a lower bound of the number of texts. This is illustrated by a significant drop in the survival rate for witnesses for the birth–death method, see Figure 10: the posterior credible interval at 95% for the survival rate of witness is [0.01%,1.52%], which is far from the 10% rate produced by the minimum sample method. However, using the estimations of the stochastic process point of view reveals difficulties in modelling the dynamics of the entire corpus using our stochastic process approach. Indeed, despite a posterior distribution that seems to be refocused on fairly probable parameter values, the posterior predictive checks (Figure 11) show that none of the replications that can be carried out on the basis of these probable parameters provide abundance data with enough one-text witnesses, and a maximum number of one-text witnesses that is also insufficient to be up to Prudentius. 18 Figure 11: Posterior predictive checks on 500 summary statistics, drawn using parameters samples from the posterior distribution, using the entire corpus. 19