=Paper=
{{Paper
|id=Vol-3290/long_paper3261
|storemode=property
|title=Lost Manuscripts and Extinct Texts: A Dynamic Model of Cultural Transmission
|pdfUrl=https://ceur-ws.org/Vol-3290/long_paper3261.pdf
|volume=Vol-3290
|authors=Jean-Baptiste Camps,Julien Randon-Furling
|dblpUrl=https://dblp.org/rec/conf/chr/CampsR22
}}
==Lost Manuscripts and Extinct Texts: A Dynamic Model of Cultural Transmission==
https://ceur-ws.org/Vol-3290/long_paper3261.pdf
Lost Manuscripts and Extinct Texts:
A Dynamic Model of Cultural Transmission
Jean-Baptiste Camps1,2,∗,† , Julien Randon-Furling3,4,∗,†
1
Venice Center for Digital and Public Humanities, Univ. Ca’ Foscari, Fondamenta Malcanton 5449, Venezia, 30123,
Italy
2
Centre Jean-Mabillon, École nationale des chartes, Paris Sciences & Lettres, 65 rue de Richelieu, Paris, 75002, France
3
Centre Borelli, Univ. Paris-Saclay, ENS Paris-Saclay, CNRS, SSA, INSERM, 91190, Gif-sur-Yvette, France
4
SAMM, FP2M (FR2036), Université Paris-1 Panthéon-Sorbonne, CNRS, Paris, 75013, France
Abstract
How did written works evolve, disappear or survive down through the ages? In this paper, we propose a
uni昀椀ed, formal framework for two fundamental questions in the study of the transmission of texts: how
much was lost or preserved from all works of the past, and why do their genealogies (their “phylogenetic
trees”) present the very peculiar shapes that we observe or, more precisely, reconstruct? We argue here
that these questions share similarities to those encountered in evolutionary biology, and can be described
in terms of “genetic” dri昀琀 and “natural” selection. Through agent-based models, we show that such
properties as have been observed by philologists since the 1800s can be simulated, and confronted to
data gathered for ancient and medieval texts across Europe, in order to obtain plausible estimations of
the number of works and manuscripts that existed and were lost.
Keywords
agent-based models, stochastic models, loss of cultural artefacts, text transmission, stemmatology
1. Introduction
How much do we preserve of the written knowledge, science [18] and culture of the past? And
how representative is what we know compared to what existed? Such fundamental questions
depend on the process through which texts were distributed materially.
Before the advent of the printing press, written texts were circulated in manuscript form. In
order to make the text available, the author would dictate it to a secretary, or write a dra昀琀 on
wax tablets, papyrus, parchment or, eventually, paper, and this original, authorial manuscript
would then have to be copied manually by a scribe in the form of a new manuscript, and then
circulated. Copies could then be used to create more manuscripts, again by manual copying,
perhaps by other scribes in other regions at a later date. During this process, successive mod-
i昀椀cations were introduced in the text, either by error or intentionally, to make the text more
CHR 2022: Computational Humanities Research Conference, December 12 – 14, 2022, Antwerp, Belgium
∗
Corresponding author.
†
These authors contributed equally.
£ jean-baptiste.camps@chartes.psl.eu (J. Camps); julien.randon-furling@cantab.net (J. Randon-Furling)
ç https://github.com/Jean-Baptiste-Camps/ (J. Camps)
ȉ 0000-0003-0385-7037 (J. Camps); 0000-0001-9497-2297 (J. Randon-Furling)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
198
suited to its intended audience. These alterations in the written sequence that forms the text
could then be transmitted by a given manuscript to its “descendants”. Wear and tear, accidents,
fashions caused the destruction of some manuscripts, while others enjoyed the long life of li-
brary preservation. In the end, knowledge was lost and some texts went extinct, while other
texts gained traction or were eventually preserved for future generations.
In textual studies and philology, since the development of the “common errors” methods
from the 19th century onward [48, 24], the analysis of text alterations allows philologists to
reconstruct relations between the surviving copies of a given work (so-called witnesses), and
to represent them as a tree-like graph, called a stemma codicum (昀椀g. 1). This reconstructive
process is not entirely di昀昀erent from the methods used by biologists to reconstruct the links
between existing or extinct species, based on their shared characteristics that are supposed to
derive from a common ancestry, and to represent it as a phylogenetic tree. Methods from this
biological sub昀椀eld, known as cladistics, have even sometimes been directly applied to texts,
with controversial results [3, 31, 47, 36, 26]. These trees represent the result of an enquiry
into the relationships between the surviving witnesses, together with the hypothetical lost
nodes that can be deduced from them. To arrive at it, researchers have to study the variants
— more precisely, common innovations or errors (i.e., mutations) — observed in the text of the
surviving witnesses (昀椀g. 1, A). The reconstructed tree will show only what can be deduced from
surviving witnesses: the witnesses themselves, and as many hypothetical nodes as are needed
to explain their relationships (昀椀g. 1, B). While it may be the case with more recent works that
all nodes are known and the graph represents the full transmission of the text — for instance
with the genealogy of printed editions (昀椀g. 1, C) —, most of the time the tree represents only a
(potentially very small) subset of what existed (昀椀g. 1, D).
A long standing observation, not yet fully understood, about the structure of the recon-
structed trees was made by the French philologist Joseph Bédier, almost a century ago, in 1928
[6]. He observed that most trees reconstructed by philologists show a root bifurcation (a root
with outdegree 2): in most reconstructions, the original (or the lowest common ancestor, called
the archetype) had two, and only two, direct descendants, preventing an accurate reconstruc-
tion of the original text by majority principle (e.g., two witnesses vs one).1 Instead of searching
an explanation for such data in the dynamics of text transmission, he interpreted this “forest
of bi昀椀d trees” as the result of a methodological 昀氀aw or an unconscious bias. Indeed, the main
goal of establishing textual genealogies was, at that time, perceived to be the “mechanical”
reconstruction of the original text (or, at least, of the archetype), and the elimination of the
personal judgement of the philologist in the choice of the original variant in the places were
several readings were in competition. But, for this to be possible at the top of the genealogy,
it is necessary to be able to proceed by majority principle (e.g., for three direct descendants,
1
It is to be noted that this bias for bifurcation in stemmata is di昀昀erent from the systematic bifurcations that appear
in many linguistic trees or biological phylogenies, in which the process of divergence of two lineages at a given
point in time is represented as a bifurcation. For true multifurcations (or pitchforks) to happen, it would need the
simultaneous divergence of three lineages. These true multifurcations, called hard polytomies, are di昀케cult to spot
or verify, and subsequently rare in phylogenetic trees. Moreover, they can only appear in very speci昀椀c evolutionary
contexts, notably in cases of rapid simultaneous radiations of lineages: for instance, tectonic upli昀琀 may have
abruptly fragmented the habitat of the lizard genus Liolaemus between simultaneously isolated populations, and,
in combination with rapid climate change in temperature, caused the rapid divergence of several lineages of the
cold blooded and temperature-sensitive lizards [39].
199
Figure 1: From the real tree to the reconstruction. A an artificial example of the transmission of a
very short text and its plausible reconstruction, where circles depict extant manuscripts, rectangles lost
ones), and gray, nodes that are recoverable when reconstructing the tree; B another artificial example,
where the distribution of lost manuscripts causes the loss of a whole branch, and where, consequently,
the last common ancestor is not the original (root), but a lower witness (archetype); C the observed
phylogeny of the successive editions of Fortunio, Regole grammaticali della volgar lingua (1516) [44, 23];
D the reconstructed phylogeny (stemma) of the Old French Song of Roland [45]; E the reconstructed
phylogeny of the Anglo-French Guy de Warewic (Ewert, 1932), showing many cases of lateral transmis-
sion (“contamination”) in dashed lines, and even one instance of lateral transmission from outside the
200outline of a lost branch (cf. [28]).
tree; F the same tree, but including (box shape) the
the variant present in two of them will be selected over the one in single occurrence). Yet,
Bédier observed, philologists tended to establish genealogies with only two direct descendants
(or even, to revise existing genealogies with three direct descendants to reduce them to two),
regaining control over the selection of reading and abolishing the ‘mechanical’ choice. For
this reason, he advocated to stop reconstructing the original, and use only the genealogy to
select the ‘best’ witness (the closest to the original) and transcribe it in a conservative fashion,
limiting modi昀椀cations or corrections. This spurred a century long debate and caused, between
‘bédierists’ and supporters of the genealogical method, a long lasting methodological schism
that remains to be fully resolved [1, 20].
Bédier’s initial observation has been replicated, with estimates of the proportion of root
bifurcation varying, from Bédier’s 95.5%, to somewhat lower estimates ranging from 70% to
83% [46, 16, 25]. Yet, some have argued that the prevalence of root bifurcation could be an
explainable feature of manuscript transmission of texts as it reached us. Tentative explanations
include combinatorial estimations of the proportion of root bifurcation for a given number
of witnesses, under the assumption that all con昀椀gurations are equally likely [34, 16, 29], or
consider the e昀昀ects of decimation (i.e., manuscript loss) [22], for instance by applying a uniform
loss probability to static preexisting trees [23] or by calculating a node speci昀椀c loss probability
to simulated trees [27]. Even if it generated little follow-ups, there have also been rare attempts
of using birth and death process for exploring the dynamics of manuscript transmission [51,
52].
The abundance of roots – and more generally nodes [25] – with out-degree 2, is not the
only property that can be observed in many stemmas. The asymmetry between branches (cf.
昀椀g. 1, C and D), the presence or not of lateral transmission (generally called “contamination”;
昀椀g. 1, E) are other properties worthy of investigations, as well as those that can indicate that
the tree made from extant witnesses represents only a small portion of the original tradition
(i.e., lateral transmission from outside the tree; root identi昀椀able not with the original but with
a later manuscript; 昀椀g. 1, F). It is reasonable to assume that some of these properties re昀氀ect
the dynamics of manuscript transmission, while others keep trace of important destruction,
decimating manuscripts and removing even full branches. For the texts, this can be seen as an
evolutionary process, where two antagonist tendencies are at work: the apparition of textual
variants in individuals, causing the increase of diversity in the tradition, and the extinction of
full branches, causing some variants to prevail upon others and so reducing diversity.
Here again, these observations can be put in perspective with problems occurring in evo-
lutionary biology, where, too, two antagonists tendencies are at work, mutation and 昀椀xation,
either by dri昀琀 or natural selection, in a context where processes of speciation and extinction
are strongly linked and where extant species represent only a small subset of the species that
have existed [55]. In both cases, survival might be the exception and extinction the rule, be it
by “bad genes or bad luck”, a process that can be seen in terms of gambler’s paradox [43, 14]: a
gambler starts playing a game, in which, at each discrete step, he or she has a chance of loosing,
let say 50%; even if the game is fair, a昀琀er a su昀케cient number of random steps, the inevitable
and only possible 昀椀nal outcome is ruin (extinction). If the gambler has a winning streak at the
beginning, ruin might be signi昀椀cantly delayed, but, very o昀琀en, ruin will happen immediately.
Basic processes of reproduction and destruction create complex shapes in the trees, from
which one might want to deduce whether they can be fully explained by random process akin to
201
genetic dri昀琀, or if di昀昀erences in selective values are to be suspected. In other terms, going back
to textual traditions, if cultural context, through literary taste, canon or fashion for instance,
creates a form of evolutionary pressure on textual traditions. Any insights gained on this
question would have an applicability beyond the question of the transmission of antique and
medieval texts, because it seems that similar dynamics are at work in the di昀昀usion of content
in other medium, including print [23] or even the web [2], and have been observed in areas
such as the cognitive evolution of scienti昀椀c 昀椀elds and the dynamics of scienti昀椀c memes [7, 17].
Data on cases as di昀昀erent as the songs of the Medieval Occitan troubadours from southern
France or the incunabula editions printed in Renaissance Italy outline the same Pareto-like
world, where a large number of texts are kept only in a single or handful of documents, while
a limited number of “successful” texts are kept in a large number of copies (昀椀g. 2, A and B),
where most authors are known only for one or two texts, while a very limited number of writers
can have dozens of texts preserved (昀椀g. 2, C and D)… Such a process is also apparent in the
constitution of a literary canon of a limited number of authors and texts. This ‘canonization’
can be seen has a progressive loss of diversity, where an ever shrinking number of authors and
texts take on an ever growing share of the circulated documents (昀椀g. 2, E and F). But is this
due to chance or to a selective process?
In fact, some properties as were just mentioned for textual traditions have some pendants in
evolutionary models, concerning for instance the very unequal distribution of descendants [19],
the varying patterns of biodiversity varying in time and space, studied in macroecology and
biogeography [10, 42] and the dynamics of speciation and extinction that manifest themselves
in the shape of phylogenies and the loss of branches from the tree of life [35, 55]. For this
reason, there are inspiration and resources to be found in the study of mathematical properties
of evolutionary trees, regarding the establishment of a null-model [8].
Can we gain some insight on what existed, what was lost, and the driving forces between
extinction or survival of texts — by dri昀琀 or selection? In order to do so, we need a better
understanding of the dynamical processes of manuscript transmission.
2. An agent-based model of a stochastic process
In this paper we present a selection of the 昀椀rst results obtained with a stochastic model for
the transmission of manuscripts in the Middle Ages. Following Weitzman [51, 52], we use so-
called birth-and-death processes. These are random processes introduced in probability theory
to describe, among other things, simple population dynamics and genealogies. For the simplest
versions of theses processes, it is possible to derive analytically (i.e. with mathematical formu-
lae) certain quantities of interest: the expected number of individuals (here for us, manuscripts)
still present at a time �㕡, the extinction probability, the survival probability,… But also, quanti-
ties of particular interest in the context of manuscript genealogies: the probability that the
latest common ancestor (lca) be an archetype rather than the original, or the probability of
root bi昀椀dity for the reconstructed stemma. Here we favour a numerical approach, that allows
us to explore more complicated variants of a birth-and-death process through an agent-based
computer simulation. The agents correspond to manuscripts, and during each time step of the
simulation each agent has a probability �㔆 of being copied (i.e., ‘giving birth’ to one copy) and
202
Figure 2: A Pareto-like world with diminishing diversity. A distribution of witnesses per
troubadour text; B distribution of the extant copies per work for incunabula printed in Italy; C dis-
tribution of texts per author for troubadours and D incunabula; E Shannon diversity, Generations as
sites, texts as species, witnesses as individuals; F number of texts and witnesses per author.
a probability �㔇 of disappearing. Following Cisne, we limit the increase rate of the population
by letting the birth rate �㔆 depend on the size of the population at the previous step �㕘�㕡−1 :
�㔾
�㔆�㕡 = �㔆 , (1)
�㕘�㕡−1
where �㔾 is a theoretical upper bound on the maximum possible size of the manuscript popula-
tion extant at any given time during the period under consideration.
203
Each simulation starts with a single agent (the original manuscript), at �㕡 = 0. At the 昀椀rst step,
this agent has a probability of being copied (birth rate �㔆) and a probability of being destroyed
(death rate �㔇), both between 0 and 1. If an agent is destroyed, it ceases to be able to give birth,
but, as long as this hasn’t happened, it can still be copied at each time step (according to �㔆). If all
agents are destroyed, and the tradition extinct, the simulation stops. Otherwise, it keeps going
for a 昀椀xed number of active steps (e.g. 1000) and, optionally, a 昀椀xed number of inactive steps
(e.g. 1000), were manuscripts can no longer be copied (�㔆 becomes 0) but can still be destroyed,
re昀氀ecting the long period where, a昀琀er the Middle Ages, the texts were no longer copied, but
manuscripts were still subject to destruction.
In the Cisne-type model, where a population limit �㔾 is used, �㔆 is adjusted at step �㕡 according
to the total active population and the value of �㔾 (eq. 1). This limit �㔾 is the theoretical maximum
number of copies of a given work that could exist simultaneously at any time step, and it re昀氀ects
the maximum capacity of the book market, before being saturated by copies of a text. It is
similar to the notion of the carrying capacity of an ecosystem, i.e. the maximum number of
individuals from a given species that an ecosystem can support, given the availability of food,
water or habitat.
Once enough simulations are run for a given set of parameter values, the resulting trees can
be analysed to compute properties such as the rate of survival of traditions, the rate of survival
of agents (manuscripts), the average age of surviving manuscripts, the ratio of bi昀椀dity in the
genealogies (once the genealogy is simpli昀椀ed, e.g. by removing destroyed manuscripts without
descent and more generally destroyed manuscripts that would not appear in a stemma due to
reconstruction rules), the generation of the lowest common ancestor, etc. (Fig. 3).
3. Phase diagrams obtained through computer simulations
In our simulations and our choice of parameter values, we focus here on the transmission of
medieval texts. We ran agent-based simulations of a Cisne-type tradition with a total time
frame of 500 pseudo-years, of which 250 active (with manuscripts being copied and destroyed)
and 250 inactive (with manuscripts being only destroyed). This duration is chosen to match
the time between the development of medieval Western vernacular literatures in the 13th cen-
tury and the Renaissance, and the Renaissance and the progressive advent of modern cultural
heritage curation, from the second half of the 18th century. Each pseudo-year is equivalent to
four time-steps— that is, a time-step in the simulation corresponds roughly to 3 months. This
was derived using an estimate for the time taken to produce an average 200 page manuscript
(though the speed of scribes is known to vary a lot, from 1 to 10 leaves a day) [41]. We chose
�㔾 = 100 000 = 105 , as an order of magnitude (rather than 104 or 106 ) for the total number
of manuscripts in a given tradition that could be extant simultaneously at any one time. This
order of magnitude is a very rough estimate based on human population and our own assump-
tions: the medieval population of countries such as France or Italy was in the 107 range; we
estimate that the maximum saturation of this market for a given book would be reached if
around 1% of the population were to own a copy.
As for the remaining free parameters, namely the base “birth” or copy rate, �㔆, and the “death”
rate �㔇, we explored all possible pairs of values of these parameters within their range (from 0
204
Figure 3: Final state of a simulation (one of 100, for �㔆 = 0.0008, �㔇 = 0.0005 and �㔾 = 105 ), with destroyed
manuscripts in grey, and surviving in orange (le昀琀); stemma-like simplification, with only the necessary
nodes to express the relationships between the surviving witnesses (right). In this case, the generation
of the LCA is 1 (original and LCA are the same), the root is bifid, the survival rate of manuscripts is
approximately 5% ( 985 ). It is to be noted that manuscript 70 is the sole witness of an otherwise fully lost
branch, and that all other are descended from lost manuscript 9, and even, with the exception of 66,
from lost manuscript 24 (6th generation). This type of configuration is also encountered in many real
traditions (see for instance above, fig. 1).
to 1 in theory, but reduced here to 10−4 to 10−3 by 昀椀eld expertise, i.e. rough estimates from
philological knowledge).
It is to be noted, that historical and philological knowledge of loss rates is very scarce and
elusive, but it can still be approached from various angles, such as the collection of data from
ancient library catalogues, inventories, wills, as well as allusions and intertextuality [54, 4, 9].
Buringh [9] provides estimates for the Latin West, with a geometric mean of loss around -25%
per century, with variations from -11% in the 9th to -32% in the 14th and 15th centuries (with
local variations between medieval institutions from –3% to –71% per century). The global loss
rate for non-illustrated manuscripts of several well known collections have been estimated
around 93-97% [32, 38, 53, 40]. But there is a potential bias in accounting only for well known
institutional collections, from which some manuscripts are known to have survived: trying to
account for fully lost libraries, Buringh [9] is compelled to revise his estimates higher, to -25%
by century until the 12th, up to -43% in the 15th. For incunabula, using editions whose original
number of print made is known, it is possible to gather loss estimates by counting known sur-
205
viving exemplars in public or private collections: doing so for Venetian incunabula, Trovato
[49] 昀椀nds very variable loss rates according to textual and material typology, from 73% for
the Decretales printed on parchment to 99.3% for more popular chivalrous literature (Orlando
furioso for instance). This shows the importance both of variation in time and space, and of tex-
tual contents and material typology. In some extreme cases, loss can be very close to 100%, for
reasons that may combine the fragility of the document form, lack of consideration for the doc-
uments or large scale historical events such as political instability, invasions or major cultural
changes; examples are provided by cases as di昀昀erent as the Merowingian royal diplomas on pa-
pyrus or the Lombard royal charters [21], the Mayan (pre-colombian) manuscripts or medieval
notarial acts [30]. Production estimates have also been attempted on the basis of the quantity
of sealing wax acquired by a given producer (a chancellery for instance [5]). More founded loss
estimates have also been gathered by counting how many of the acts mentioned in imperial
or royal registers are kept in original or consigned in the archives of the recipients: this gives
a loss rate of originals varying from 80% (acts from the emperor Charles IV in 1360-1361) to
90% for the acts from Louis X of France, increasing to 99% for the judgements rendered by his
Parliament, suggesting here as well a massive e昀昀ect of typological variation [30, 15], resulting
in very strong biases in the body of documents available to us.
For our simulation needs, if we start from Trovato’s estimates (potentially more reliable,
because based on editions whose original number of copies is known), we get a survival rate
whose order of magnitude is between 0.1 and 0.01 (between 10−2 and 10−3 ) in 500 years (2000
steps in our model), in similar ranges as Buringh’s 0.75 in 100 years and those reported by
Holtz and Canteaut; from this we can deduce a step loss rate for a given total survival rate.
For instance, for 1% survival rate, (1 − �㔇)2000 = 0.01, which simpli昀椀es to �㔇 = 0.002. So we
retain values of �㔇 between 10−4 to 10−3 . Given that books could not have been produced order
of magnitudes higher or slower than they were destroyed (or we would be either drown in
medieval manuscripts or keep none), we explore the same range for �㔆. Of course, 昀椀xed rates
are a limitation, and do not yet account for substantial variations in time (such as massive
extinction events, like, e.g., the fall of the Roman empire, the 昀椀re in Alexandria library, the
shi昀琀 from volumen to codex or from caroline to gothic script, etc.).
The space of all possible values is usually called the phase space in physics and other mathe-
matical sciences, and a representation of the value taken by a given observable quantity (eg the
extinction probability) when parameters are varied across the phase space is called the phase
diagram of this quantity. In our simulations, due to limitations in computing power, we were
not yet able to explore full parameter spaces for the models, and limited ourselves to these plau-
sible values, thus not producing complete phase diagrams but instead heat maps representing
a portion of the parameter space.2
We thus produced heat maps for a number of relevant observables, based on the variation
of parameter �㔆 and �㔇 between 10−4 and 10−3 , with �㔾 = 105 (Fig. 4). Note that, since there is a
stochastic component in the model, each heatmap is computed by averaging over the results of
a relatively large number of simulations, here 100 — this means that we produced 100 arti昀椀cial
2
In the future, we plan to extend the explored parameter space for �㔆 and �㔇, using exact computations whenever
analytical solutions are available, and by augmenting the number of simulations, using more computing power
and time. In particular, we will need to explore the impact of the variation of parameter �㔾 for which, for now, we
only used a 昀椀xed initial value.
206
manuscript traditions for each pair (�㔆, �㔇) ∈ [10−4 , 10−3 ], varying values by increments of 10−4 ;
hence each heatmap required 10 000 simulations.
The approach then consists in identifying, within the heat maps, regions in which the values
for the observables are consistent either with measured quantities (as is done in the natural
sciences) or with estimates for these quantities coming from other, independent and altogether
di昀昀erent, models. We have circled in red such regions on the heatmaps in Fig. 4.
The features selected for this comparison re昀氀ect three di昀昀erent aspects of the traditions.
The 昀椀rst group (昀椀g. 4, 昀椀rst row) deals with the survival rate of works of traditions, that are
not directly observable in historical data, but that can be compared with estimates based on
secondary information or on other models [33]; the median 昀椀nal population of surviving tradi-
tions can, on the other hand, be directly observed by counting (known) surviving manuscripts
of real-world texts. The second row deals with age properties of individual manuscripts, that,
in real-world data, are sometimes known (dated manuscripts) or estimated (based on features
of writing style, support, ink, language, etc.). Finally, the third row deals with the structural
properties of the resulting trees, such as the distance between the original and the lowest com-
mon ancestor (archetype), a feature of much interest for existing traditions, as it cannot be
directly observed, but gives an idea on how distant the text accessible to us is from the orig-
inal, and how much of its history is lost). Information concerning the outdegree of the LCA
matches the initial observation of Bédier on the prevalence of bi昀椀dity (root bifurcation), while
the Shannon (biodiversity) index gives an insight into the asymetry of the branches, observable
on real-world stemmata.
These heat maps show that the results obtained through these simulations are internally
consistent in terms of not only population size and survival rates, but also in terms of structural
�㔇
properties of the resulting trees. In particular, the results obtained for a ratio �㔆 between 85
and 67 are surprisingly consistent with the observed properties of some medieval traditions, in
particular those from chivalric narratives in Old French. In particular, values of 0.55 for the
survival of works and 0.05 for the survival of manuscripts (昀椀g. 4), A and B, red squared area,
bottom-right tile) are identical to those provided by Kestemont et al. for Old French chivalric
romances, using unrelated methods from ecodiversity [33]. Yet, for what regards speci昀椀cally
Old French epics, known as chanson de geste – a genre predating the later form of the roman,
and whose circulation and reception considerably di昀昀ers for a long time –, the median 昀椀nal
population of 2 and the third quartile of LCA outdegree of 2 (though, median LCA Shannon
index is 0.69).3 This would lead us to revise Kestemont et al. estimates to 0.22 (instead of 0.55)
for the speci昀椀c survival of Old French epics (chansons de geste) and 0.01 (instead of 0.5) for the
survival of epic manuscripts (a 昀椀gure closer to that observed by Trovato [49] for their later
Italian successors). On the other hand, speci昀椀c values, this time, for (Arthurian and Antique
matters) romans yield a third quartile of LCA outdegree of 3 more coherent with Kestemont
et al. general estimate (median tradition size, according to Martina [37], is 2 – and mean 4.8 –
for the sole romans en vers, similarly to chansons de geste, but is expected to be higher for later
romans en prose).
3
Data about the traditions of the chansons de geste follow Vitale-Brovarone’s [50] and Camps’ [11]. Information on
the shape of stemmata have been computed based on a restriction to chansons de geste and deduplicating of the
collection provided by OpenStemmata [13, 12].
207
Figure 4: Heat maps (phase diagrams) for the simulation of Cisne-like models; first row contains
population size and survival properties, namely A Survival rate of traditions (i.e., trees); B survival
rate of manuscripts (i.e., nodes); C the median final population of surviving witnesses for traditions
with at least one; second row contains data about the age of manuscripts in the simulation, for D all
manuscripts ever created; E extant ones; as well as F the date of the oldest extant manuscript; the third
row concerns structural properties of the trees themselves, F the median distance between the lowest
common ancestor of the surviving manuscripts and the actual root of the original tree; G the third
quartile of the LCA (archetype) out-degree and H and the median Shannon index for the families (the
main branches stemming from the LCA). For each pair of parameter values between 0.0001 and 0.001,
100 simulations were run for 1000 active and 1000 inactive steps. Grey areas correspond to irrelevant
values of the parameters, or unstable regions. The red square shows parameter regions where the
observables computed on the simulated manuscript populations are consistent with observations made
for Medieval French epics or with plausible estimates made using di昀昀erent methods.
The situation is, for the moment (and until further data is acquired) consistent yet deserving
of further inquiry concerning the distribution of age of surviving manuscripts: in the simula-
tion’s red-squared area, the median date of surviving manuscripts would be in the 800’s step
(around 200 years a昀琀er the original) and the median date of the oldest for each tradition in the
150-200 years range. For chansons de geste, the median date of surviving manuscripts would
208
be between 1250 and 1300 [50, 11] – 150 to 200 years a昀琀er the 昀椀rst documents of the genre
itself (the end of the 11th century for the composition of the oldest version of the Roland). For
romans en vers, it is, like the genre itself, slightly o昀昀set in time, with a peak between 1275 and
1325 [37].
4. Discussion
Combining previous inquiries by Weitzman and Cisne with the power of computer simulations
and the methodology of statistical physics, we are able to reproduce the evolutionary process
that underlies the observable data for, at least, some textual traditions such as those from me-
dieval French epics and romances. The results obtained can even corroborate or re昀椀ne results
obtained by unrelated methodologies, such as those recently published by Kestemont et al. [33],
indicating that these relatively simple birth-and-death process have relevancy in philology as
well as they have in Evolutionary Biology for instance. This method then provides us a way
to account both for population dynamics in time, loss or production estimates, as well as the
shape of the stemmata (the phylogenies) of manuscripts, answering the century long Bédier
observation [6], whose lack of solution until now has been at the core of a lasting schism in
philological studies.
Indeed, concerning the problem of bi昀椀dity, initially raised by Bédier, our simulations tend to
show that a ratio of root bi昀椀dity of at least 75% can be coherent with other observable properties
of the textual traditions of Old French texts, such as the 昀椀nal population or even the date of
surviving manuscripts. According to our simulations, it is not necessary to hypothesise any
昀氀aw or bias in the method. In fact, it seems that bi昀椀dity is one of the measurable properties
resulting from the transmission dynamics of manuscript texts.
The range of further investigations opened by this research is considerably large. Models
using individual variable rates of �㔆 and �㔇 could be used to account for phenomenon such as
e昀昀orts of preservation of old and venerable artefacts, or higher selective values of some copies,
or accelerated destruction due to small scale (e.g., burnt libraries), larger scale (e.g., the Disso-
lution of English monasteries, French Wars of Religion,…) or global events (e.g., shi昀琀 in book
types such as from volumen to codex or caroline to gothic scripts, major cultural changes like
the Renaissance, …). Modelling should also include the actual variation of the texts, to re昀氀ect
the introduction of variants (mutations) in some families, and processes of transmission of
inherited variants, as well as lateral transmission.
More generally, once having established this ‘null model’, deviations due to di昀昀erent factors
should be explored, such as higher selective values for some mutations (variants) or individuals,
昀氀uctuations in time and space and the existence of di昀昀erent ‘ecological niches’ (e.g., the Anglo-
Norman public versus the readers of Franco-Italian epics), typological variation in books or
texts, chocks and bottlenecks, etc. The question of the age of surviving manuscripts should
also be explored and accounted for, especially in the light of potential variations of �㔆 and �㔇
in time. For instance, the demand and rate of copy for a given text could be expected to be
highest shortly a昀琀er its initial release, when it is most 昀椀tted to the taste and fashion of the
time, perhaps reinforce itself if the text gets a quick breakthrough, and then decrease with the
passing of years. Similarly, the rate of destruction could vary at a global or local level, as some
209
shocks lead to peaks of destruction or canonicalisation and conservation e昀昀orts lead to lower
rates. Last but not least, the model should account for non standard transmission, in particular
lateral transmission (contamination), a process not uncommon in textual transmission but that
is also encountered in the natural world (e.g., lateral gene transfer).
Finally, coming back to the question of the relative importance of dri昀琀 versus selection, our
current results show that a purely stochastic process can account for many observable prop-
erties of textual transmission, without having to model di昀昀erences in selective value for the
agents. Yet, to fully answer this question, other type of models have to be experimented, im-
plementing di昀昀erent scenario for selection, and then systematically compared to the results
obtained with the current model.
The generality of the models considered here makes them applicable not only to medieval
texts, but to any type of cultural transmission, at least in written form, from manuscript cir-
culation to the elaboration of a canon of works. Further investigations should try to verify it
on the broadest possible range of cases, starting with Western Medieval and Antique texts, but
preferably encompassing cultural productions from very di昀昀erent time periods and continents.
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