For population genetics paleo-genetics investigation, once the DNA sequences have been generated, the categorization and labelling of skeletal remains into “populations” is as methodologically crucial as it is for any population genetics investigation, as exemplified and discussed throughout this Chapter. This information stems primarily from archeological work and *cannot* be filled-in anew by paleo-geneticists alone.

This is precisely where major problems of categorizations emerge in the practice of paleo-genetics, with some strong analogies with the problems previously described between cultural anthropology and human population genetics as well as novel issues.

Indeed, paleo-geneticists tag the skeletal material they investigate most often based on categories provided to them directly by archaeologists or based on archaeological collection databases and metadata associated with the remains. Ultimately, they label their samples with a “population tag”, preferably further informed with an “archaeological date”, but not always so. This “population tag” is based on archaeological work of an extremely complex nature very rarely explicitly discussed in paleo-genetics work, and often apparently mis-understood by geneticists, very unfortunately. As a result, except for more recent paleo-genetics articles making a significant effort to integrate archeological knowledge at the root of their investigation in sincere interdisciplinary efforts, a substantial amount of the population-genetics paleo-genetics investigations are conducted in a way that may be strongly at odds with archaeology, albeit recklessly feeding on this discipline.

In my views, archaeologists integrate multiple knowledge brought from varied disciplines or subdisciplines such as geo-chronology, stratigraphy, sedimentology, and paleo-palynology, art-history, ethnology and material-culture studies, biological anthropology and thanatology, etc. They do so in order to propose a complex meta-constructed knowledge about the archeological sites and objects they investigate, and about the societies that produced them.

They build “archaeological cultures” based on i) a single precisely defined *archaeological criterion* (or a very limited number of such criteria), such as a particular ceramic manufacture, ii) observed throughout sites at a *relatively reduced geographical scale* (regional), and, iii), spanning *relatively short periods of time* (seldom more than one thousand years). For a random instance, the “Corded Ware culture” refers to an archeological category of sites and practices based on a specific ceramic style and manufacture that is found between roughly 3000 and 2000 years before the common era from North-Central Europe to Central Asia. Most importantly, note that it is very frequent that two different archeological cultures, coexisting in time and space, are, respectively, defined based on an archaeological criterion of a very different nature. Some may rely on ceramic manufacture while another may stem from shared specific funerary practices. Therefore, “archaeological cultures” can overlap in time and space, or not, and be produced by biological individuals from different societies, or not, or in biological genealogical relationships with one another, or not.

Once such criterion “archaeological culture” is built, and relatively consensually agreed upon within the archaeologist community, more in deep analyses of archaeological sites inform said “culture” by identifying other sets of archaeological phenomena and practices more or less variable among sites within the culture and not necessary to build the initial categorization. This is how, for instance, funerary practices may vary largely across sites within culture, and even be structured spatially and/or temporally, without re-defining the culture initially defined on another criterion than funerary practices.

In this context, archaeologists may talk about an “archaeological population” most often when historical linguistic records further inform the archaeological site directly or indirectly; hence several intense debates as to whether certain recent pre-historic archaeological cultures should be considered as populations or not.
Therefore, they explicitly add another stringent criterion for such categorization into a population compared to the categorization into an archaeological culture.

Next, archaeologists build “archaeological periods” corresponding to much less specific archaeological phenomenon (such as significant changes in lithic industries between the “Mesolithic period”, literally the “middle stone period”, and the “Neolithic period”, literally the “new stone period”, or metal industry such as the shift from the “Bronze Age” to the “Iron Age”), found at massive geographical scales, spanning much larger periods of time, and relatively less variable across sites and within a period. Importantly, as a consequence of such categorization process, the same archeological period often does not span the same absolute chronological dates in the different regions where it is identified; e.g. the “Bronze Age” or the “Neolithic” do not have the same dates and durations, respectively, in different regions. Furthermore, there may be temporal periods during these “archaeological periods” in certain geographic areas, where no “archaeological cultures” have been defined and recorded albeit archaeological sites have been found and investigated.

Finally, archaeologists and biological anthropologists often further characterize given archaeological periods, cultures, or populations with specific features about the ways of life of the individuals who produced said cultures. For example, among many others, an archaeological site categorized as ancient Mesolithic is often being considered as the product of a hunting-gathering way of life, while, for Neolithic sites, their producers are sometimes characterized as agriculturalists or herders depending on varied archaeological markers such as the presence of remains from domesticated farmed crops or animals. Note, however, that once such way of life has been characterized for certain sites in a given archaeological culture, it may be applied to all other sites in this culture, even in the absence of the same explicit markers locally, *de facto* conducting a dialectical induction without formally testing it and thus possibly wrongly reducing the presumed cultural variation within said archaeological culture.

Most importantly in this context, archaeological cultures were produced by individuals and groups of individuals that indeed existed, but for whom we do not necessarily have skeletal remains. For instance, in certain Celtic archaeological populations, individuals were not buried but most often cremated, leaving little occurrences of human skeletal remains within given sites associated with otherwise rich material cultures and archeological material remains at the origins of the “Celtic” labelling of said sites. Furthermore, and in all cases, even when skeletal remains are associated with cultural artifacts and funerary practices, it is perhaps probable but cannot be formally and scientifically verified that said skeletal remains pertained to an individual having directly participated in the production of this culture, as opposed to a recent migrant conjecturally buried here.

Based on such elaborations, archaeologists may propose models and hypotheses about the varied processes involved in archaeological cultures' or populations' emergences, expansions, diffusions, and disappearances over time and space. Intuitively, the archaeological scientific dialectics resulting in naming an archeological culture, population, period, or, simply, phenomena or trait, from varied information extracted from an archaeological site, may be seen as analogous to the linguistics dialectics building a “Language” from observed communication practices as explained in **section 1.2** above<fnref n="32" />. Indeed, an archaeological culture, population, or period is not a simple object directly observable with our own senses, nor stemming from complex manipulations borrowed from experimental Popperian sciences only; an archaeological culture, an archaeological population, and an archeological period are, in fact, complex

<footnote n="32">³² with all academic cautions needed when doing such analogy.</footnote>
disciplinary interpretations, each non-necessarily overlapping, which are all the subject of extensive
discussions and debates within the scientific discipline.

Therefore, archaeological categories are, by their very construction, nowhere close to the population-
genetics' definition of a population, i.e. a group of individuals more likely to reproduce with one another
than they are with other groups of individuals.

Nevertheless, paleo-geneticists often tend to use, blindly, these archeological labels as population tags for the DNA they extracted and sequenced from skeletal remain. They thus de facto assimilate sets of DNA sequences within an archaeological culture or population or period often independently of the sometimes very large temporal scales the original remains spanned, and further associate these *de novo* paleo-genetics “populations” with sets of ways-of-life practices frequently investigated by human population geneticists such as “agricultural”, “hunter-gatherer”, “farmer”, “herder”, etc. Once this is done, they then investigate these groups of DNA sequences with the same paradigms used to investigate “populations” in population genetics. Based on their DNA sequences, they calculate allelic and haplotypic frequencies across these false populations but real sets of biological individuals, and infer their origins and migration and admixture histories across time and space.

Expectedly at that point, paleo-geneticists often synthesize their results and discussions using these borrowed and altered “population” labels and associated traits in ways that are very often inappropriate as they end up mixing geographical criteria, archeological cultures, populations and/or periods names, absolute chronological dating, and presumed or archaeologically substantiated ways of life...

As an illustrative example, which I find to be representative of many other famous published articles in
paleo-genetics, one can read in an article published in Nature in 2015 and already cited more than 700 times
(Allentoft et al. 2015):

“Abstract:

The **Bronze Age** of Eurasia (around 3000–1000 BC) was a period of major cultural changes. However, there is debate about whether these changes resulted from the circulation of ideas or from human migrations, potentially also facilitating the spread of languages and certain phenotypic traits. We investigated this by using new, improved methods to sequence low-coverage genomes from 101 **ancient humans** from across Eurasia. We show that the **Bronze Age** was a highly dynamic period involving large-scale **population migrations and replacements**, responsible for shaping major parts of present-day demographic structure in both **Europe** and **Asia**. Our findings are consistent with the hypothesized spread of **Indo-European languages** during the **Early Bronze Age**. We also demonstrate that **light skin pigmentation** in **Europeans** was already present at **high frequency** in the **Bronze Age**, but not **lactose tolerance**, indicating a more recent **onset of positive selection on lactose tolerance** than previously thought.”

Which therefore readily refers to:

- archaeological periods (in **bright red**),

- geographical regions (in **dark blue**),

- archaeological dating (in **bright green**),

- linguistics (in **orange**),

- intertwined with purely paleo-genetics information (in **purple**)
- and a population-genetics’ biological definition of “a population” and of “an individual” (in **black**), probably, as the way they use these lexical terms do not fit the above definition of an archaeological population.

After the body of the article deploys, the last concluding paragraph reads:

“Implications:

It has been debated for decades if the major cultural changes that **occurred during** the **Bronze Age** resulted from the circulation of **people** or ideas and whether the expansion of **Indo-European languages** was concomitant with these shifts or **occurred with the** earlier spread of agriculture. Our findings show that these transformations involved migrations, but of a different nature than previously suggested: the **Yamnaya/Afanasievo** movement was directional into **Central Asia** and the **Altai-Sayan region** and probably without much **local infiltration**, whereas the resulting **Corded Ware culture** in **Europe** was the result of admixture with the local **Neolithic people**. The enigmatic **Sintashta culture** near the **Urals** bears genetic resemblance to **Corded Ware** and was therefore likely to be an **eastward migration** into **Asia**. As this **culture** spread towards **Altai** it evolved into the **Andronovo culture** (Fig. 1.), which was then **gradually admixed** and replaced by **East Asian peoples** that appear in the **later cultures** (Mezhovskaya and Karasuk). Our analyses support that migrations during the **Early Bronze Age** is a probable scenario for the spread of **Indo-European languages**, in line with reconstructions based on some archaeological and **historical linguistic data**. In the light of our results, the existence of the **Afanasievo culture** near **Altai** around 3000 bc could also provide an explanation for the mysterious presence of one of the **oldest Indo-European languages**, **Tocharian** in the **Tarim basin** in **China**. It seems plausible that **Afanasievo**, with their **genetic western (Yamnaya) origin**, spoke an **Indo-European language** and could have introduced this **southward** to **Xinjiang** and **Tarim**. Importantly, however, although our results support a correspondence between **cultural changes**, migrations, and **linguistic patterns**, we caution that such relationships cannot always be expected but must be demonstrated case by case.”

Which therefore refers to:

- archaeological periods (in **bright red**),

- archaeological cultures (in **dark red**),

- geographical regions (in **dark blue**),

- archaeological dating (in **bright green**),

- ways of life (in **dark green**)

- historical linguistics (in **orange**),

- intertwined with **paleo-genetics** and **population genetics** inference results (in **purple**)

- and a population-genetics’ biological definition of “a population” and of “an individual” (in **black**), probably, as the way they use these lexical terms do not fit the above definition of an archaeological population.

Despite the academic conditional tense rigorously used and the important final provision, the mixing of categories from very different disciplines and with very different definitions here proposed is not discussed. Furthermore, the archaeological cultures and periods here used as genetic population labels are
not themselves discussed -- this is probably left by paleo-geneticists for archaeologists to discuss in the
future... Symmetrically, the implications for population genetics of the archaeological categorizations here
used are not discussed, and this is probably left by paleo-geneticists to anthropological geneticists and
population geneticists to discuss in the future...

As a result of the collision of complex categories from different disciplines that are seldom explained and even less discussed, as an anthropological geneticist and as explained throughout this chapter, I have honestly a hard time to understand “who are they talking about and who are they conducting their population genetics inferences on?”, not without substantial efforts of re-reading and disentangling categories often outside my areas of expertise. Furthermore, I honestly understand that some archaeologists and biological anthropologists feel that their work and discipline are mutilated by paleo-geneticists (Callaway 2018)...

As a final anecdote, a famous archaeologist that I only briefly encountered at conferences and that knew I was very sensitive about issues of categorization in human population genetics research, directly contacted me to convince me to write with him a rebuttal of a very recently published paleo-genetics paper. He wanted to re-analyze and re-interpret the paleo-genetics data after more careful categorization of samples. He did so the day after the publication of the paper in *Nature*. And he was a co-author of this paleo-genetics paper he wanted to refute the day after its publication<fnref n="33" />...

Ultimately, I find the same categorization pitfalls with paleo-genetics as I did with human population geneticists. Both communities apply and use population labels drawn from other disciplinary productions without sufficient caution nor discussion. Technically, as previously said iteratively above, I am not immune to these issues myself, I have done such mistakes myself in previous publications and will probably find myself doing them again in the future... Without excuses, one has to recognize that those are very complex and difficult problems in practice, both for the collaborative and interdisciplinary scientific work itself, as well as, pragmatically, when it comes down to mimetic publication opportunism and editorial constraints in a challenging academic world...

1.6.b. *Is there really a paleo-genetics revolution, or at least its' possibility, in paleo-anthropology and archaeology?*

I believe that it is possible that, for paleo-anthropology, the development of paleo-genetics indeed represents a scientific revolution, at least an embryo of revolution as of today. Indeed, in the future, the genetic determination of complex anthropometrical and phenotypic traits of interests and their evolution over time in interaction with environmental and developmental constrains will possibly be unraveled by human quantitative and population genetics (it is the explicit goal of countless researchers and projects since the birth of human genetics). In turn and expanding these findings to the study of ancient remains, paleo-anthropology will then be able to build synthetic and mechanistic models of morphological transmission with changes through time anchored on evolutionary genetics mechanisms. Such knowledge and models will thus integrate paleo-anthropology and paleo-genomics to fundamentally reform the former discipline and associated scientific practices, as they currently only rely on their own descriptive ad hoc

<footnote n="33">³³ It also denotes the very ambiguous relationship that some archaeologists have with paleo-geneticists in the challenging academic times we experience, here at odds with deontology of research practice: one does not put his/her name on an article he/she fundamentally disagrees with... For the record, I refused to work on his rebuttal project.</footnote>
models which lack most detailed knowledge about underlying molecular, cellular, and biological
development mechanisms.

For instance, the classical models of morphological evolution from “robust” to “gracile” forms are
currently *ad hoc* and exclusively based on descriptive investigation of bone-records. They remain actively
largely debated and regularly revisited in paleo-anthropology. I believe that they cannot reach a scientific
consensus as they cannot explicit the underlying environmental and biological plasticity and evolutionary
biology mechanisms needed to generalize a synthetic theory of human morphological evolution rooted in
the synthetic theory of evolution. Paleo-genetics could thus indeed revolutionize paleo-anthropology,
provided that human genetics indeed provide the needed understanding of the genetic and environmental
determination of complex morphological traits, which still very largely remains to be discovered today (e.g.
with the genetic determination of adult non-pathologic height in **Chapter 2**, introduced above in **section
1.1.c**). Furthermore, note that while paleo-genetics may revolutionize paleo-anthropology as a whole, not
all paleo-anthropologists are directly, in practice, concerned by paleo-genetics. Indeed, it is not yet possible
for paleo-genetics to investigate completely fossilized skeletal material: DNA is an organic molecule and
its extraction and sequencing require that skeletal remains still comprise organic matter.

Conversely, I believe that paleo-genetics provides novel very interesting tools for archaeologists
without fundamentally changing their disciplinary paradigms and scientific questioning. Instead, it seems
to me that these novel genetics disciplines offer, to archaeologists, sets of novel technical means to address
long-standing questions and formally test certain aspects of long-standing hypotheses that could not be
addressed in numerous pre-historical and historical contexts. To some extent, from my perspective, this
“non-revolution” may nevertheless be as important to these fields than the “non-revolution” brought,
starting in the 1940’s and still ongoing today, by the deployment of isotopic characterization for
archaeological purposes<fnref n="34" />. In other words, without being a revolution (at least in the radical sense I employ
here), paleo-genetics might represent a “very very important” milestone in the long history of
archaeological disciplines...

Indeed, paleo-genetics approaches can provide, and have already provided in numerous instances, key
information to archaeologists about, among existing examples, the determination of biological sex (in
particular when bio-anthropometrical approaches are inoperable or inconclusive, and/or when only social
gender can be assessed by archaeologists), the genealogical biological relationships among remains (in the
lack of explicit such records which would, in any case, only provide familial genealogical information
rather than biological genealogies), and more generally about genetic migrations and admixture histories,
as provided by phylogenetics and population genetics demographic inference approaches.

Thus, with paleo-genetics in the archaeological tool-box, it becomes possible for archaeologists to formally test hypotheses about the links between genealogical and social structures and organizations in the past, including biologically familial or non-familial funerary practices. Furthermore, it can allow to formally test whether past cultural diffusions where accompanied, or not, by demic migrations and/or population admixture. Note importantly here, that this latter point is of major interest to virtually any anthropological geneticists, but of major interest to some archaeologists only.

<footnote n="34">³⁴ Indeed, it seems to me that this latter technological development, derived from fundamental and applied quantum physics, did not change the fundamental paradigms underlying paleo-anthropological and archaeological scientific questioning, but nevertheless provided means to inform archaeological sites about numerous aspects and hypotheses that were largely out of reach of researchers before. They involve, but are not limited to, absolute dating beyond classical relative dating using geo-chronology and sedimentology, understanding human biological and skeletal development, reconstructing past alimentation, past migrations, and, in general, past relationships between humans and their environments.</footnote>
Indeed, archaeologists are often interested in the diversity of past cultural practices, the conditions and processes underlying their emergence, expansion, diffusion, and disappearance, whether they are accompanied by reproduction events leaving genes behind or not. Therefore, when past cultural representations and practices themselves are the objects of study, answering anthropological genetics questions about genetic migrations and admixture is often of very limited interest, if not completely anecdotal. This is the case for numerous archaeologists in practice, including those who otherwise may be interested in the other types of information brought by paleo-geneticists, such as determining biological gender as exemplified above.

Finally, while I do not believe that paleo-genetics represents a fundamental and radical revolution for archaeology, I also believe that it is true that the expansion of paleo-genetics, whether of interest or not to archaeologists, already influenced changes in the technical practices of this discipline at the source of the skeletal material investigated by paleo-geneticists. In particular, archaeologists are now almost all implementing protocols trying to limit human-DNA contamination of the skeletal remains they discover in the field or investigate in collections; and if they do not implement them systematically enough as per paleo-geneticists, they are at least less and less oblivious of these novel practices. Furthermore, they try to implement novel constrains for remains' preservation in collection environments, in order to ensure specifically a better conservation of ancient-DNA for future requests even when not interested in paleo-genetics studies themselves. However, I believe that these technical changes do not fundamentally change archaeological paradigms, methods and aims.

### 1.6.c. "The interdisciplinary requirement" for human population genetics and paleo-anthropologists

In this context, one can see that there is a fundamental asymmetry in the interdisciplinary relationships between paleo-genetics and archaeology: paleo-geneticists imperatively need archeologists as primary providers of skeletal remains and associated information, their object of study, while archaeologists do not always require inputs from paleo-geneticists in their disciplinary practice. This is to some extent similarly asymmetrical between anthropological geneticists and cultural anthropologists or linguists, as explained earlier in this Chapter.

I believe it is important, in such pluri-disciplinary work, to recognize and acknowledge the contours of these asymmetries, as not all projects require true inter-disciplinary integration and their massive level of investment from either discipline to understand each other. In all cases, for pluri-disciplinary asymmetric projects as well as for inter-disciplinary integrated projects, there is a massive need for exchanges and dialogue between disciplines, relying on the efforts made by all parties to truly try to understand and accept the other paradigms, constraints, and focus of interest. It is only then that trust can be gained by both parties, and productive scientific work conducted; a trust that it seems has largely been lost between paleo-geneticists and archaeologists, in part for the varied reasons explained in this section, in turn resulting in defiance if not rupture between research practitioners from either disciplinary field.

To restore this trust and elaborate and conduct future productive projects between paleo-genetics and archaeology, time spent in dialogue is of the essence. It is however a major challenge as both disciplines work at different speed. Nevertheless, I think paleo-geneticists need to devote much more time speaking with archaeologists and trying to better understand their disciplinary paradigms, for the sake of their projects and that of the future advances that they can bring to either field. This comment is also valid for human population geneticists, cultural anthropologists and linguists, as I think I have shown throughout the
previous sections. Frank Alvarez-Pereyre named his seminal book on interdisciplinary work “*L’Exigence interdisciplinaire*” (2003); I think the population genetics disciplines need to embrace this “*exigence*” in their much-needed relationships with other disciplines.

Ultimately, investigating ancient DNA, modern DNA, and human evolution is, very obviously by definition, of major interest to paleo-geneticists, anthropological geneticists, and human population geneticists. However, these academic communities should often realize that their findings, major as well as minor, may not speak to other disciplines as eloquently as they presume. Indeed, while cultural anthropologists and archaeologists are always, respectively, interested in any knowledge acquired on material and/or cultures they explore, it is crucial to understand that their respective paradigms and methods participate to elaborate their objects of study, as for any scientific discipline and as in genetics. This may sound trivial, but has deep consequences that I think are far too often overlooked, or at least not enough actively mobilized in results' interpretations and discussions. Indeed, each one of these disciplines, while all focusing on the same human individuals or groups, and the symbolic or material cultures they perhaps perform and produce, in fact talk about different “populations”.

Geneticists reconstruct the genetic diversity of populations, and sometimes try to reconstruct the history of genetic evolution of groups of DNA sequences carried by biological individuals. Linguists reconstruct the linguistic diversity of populations, that is the diversity of Languages or of manners of performing languages among biological individuals or groups of individuals, sometimes (but not always) trying to reconstruct the history of changes of these different objects. Ethnologists reconstruct the diversity of cultural practices performed by biological individuals and groups of individuals, and sometimes (but not always) try to understand their dynamics and possibly changes over time. Archaeologists reconstruct the diversity of past cultural practices necessarily performed at the time by biological individuals, but not necessarily focusing on said individual performances, and try to reconstruct the history of cultural changes and diffusions, not necessarily interested in the biological individuals involved in these processes *per se*.

All these disciplines use as a central object of study and interpretation the “population” or “group”. However, these terms are very often defined very differently, which introduces, almost systematically in my experience, major mis-understanding during cross disciplinary talk, in turn irremediably impairing fruitful scientific interdisciplinarity<fnref n="35" />. A “linguistic population”, an “archaeological population”, an “ethnological population”, and a “genetic population” represent very different populations, which may ideally refer to the exact same group of biological individuals, but which very rarely, if ever, do so as they in fact involve very different categorization construction processes.

I hope that I have convincingly illustrated this fact in this chapter, which finally leads me to propose that any such interdisciplinary, or pluri-disciplinary, endeavor should imperatively start with a precise and extended discussion to try to explicit for each discipline and each study-case: “*What is the human population under study?*”. First, it is, I believe, a scientific necessity to build a truly interdisciplinary project by building a common object of study. Second, when and if such object is impossible to conjure due to impossible reconciliation of definitions, addressing this question would at least allow to investigate the different aspects of an object, only similar in appearances and in the lexicon, from different pluri-disciplinary perspectives.

<footnote n="35">³⁵ Note that, the problem of not making explicit the definition of what is named “a population” also sometimes lead to major misunderstanding in within-disciplinary talk, however less frequent and dramatic I think, as the common disciplinary jargon and largely shared paradigms often allows easier understanding despite polysemy.</footnote>
Ultimately, the History of Humans is composite and complex, each discipline can bring different insights exploring different facets of this kaleidoscopic object from different perspectives. I think that these facets do not necessarily always have to tell the exact same story or to “always be reconciled”, they altogether exist, whether different or analogous.
# Chapter 2

Admixture in the demographic history and biological evolution of Central African “Pygmy” and neighboring “non-Pygmy” populations
<figure><img src="image_14.png" /><figcaption>Breakfast in Mbonde
Pays Tikar, Région Centre, Cameroun, 2011
©Paul Verdu</figcaption></figure>
**Chapter 2. Admixture in the demographic history and biological evolution of Central African “Pygmy” and neighboring “non-Pygmy” populations**

***Important warning repeated from Chapter 1.1.b:***

“Throughout my work, I have explicitly decided to keep the ambiguous “Pygmy” label (and its counterpart “non-Pygmy”) for naming the groups of individuals based on the criteria of categorization defined in **Chapter 1.1**. It is important to emphasize here that whether it is relevant to continue to use this label is still an ongoing debate in the cultural and biological anthropology communities; a debate to which I have myself participated. A practical problem of using this somehow archaic term is due to the fact, that, in some parts of Central Africa, the word “pygmy” itself is used derogatorily by non-Pygmy neighbors. However, I also found it to be ambivalent in the field. Indeed, certain Pygmy groups or individuals choose to claim this name in front of outsiders, governmental or non-governmental, to emphasize their socio-cultural particularity and advocate, in their local power play, against the socio-economic discriminations they suffer from their neighbors. Finally, at least one tentative “re-naming” of the four historical Cameroonian “Pygmy” populations (the Bezan, the Baka, the Ba.Ghieli, and the Ba.Koya), into the “Quatre B” (the “four Bs”) by Cameroonian civil society in the 2000’s, also resulted in this new label being used derogatorily as well...

In this complex context, I decided to first define precisely in my publications the categorization criteria used for grouping individuals into the binary category explained throughout this chapter, and decided to keep the word “Pygmy” as a label, making almost always sure to mention the potential derogatory usage of the term. I decided to use the original historical term for two reasons: as an exogenous term from ancient Greek, I believe it is more prone to ask the naïve reader the question “who are we talking about?”, which I think is essential for reflexive critical thinking about the results and study design, as explained throughout this dissertation. Second, I do it in reference to the history of anthropology, and to the work of my giant predecessors.

However, as long as criteria of categorization are maintained, I really have no problems whatsoever to use another “label”, as this will not change anything to the population genetics statistical descriptions and inferences performed, nor their discussions based on said criteria. We just haven’t found a consensus on a name, yet. Human population geneticists often prefer to transform the “Pygmy” and “non-Pygmy” categories into “Rainforest Hunter Gatherers” and “Agriculturalists”, as I did myself in certain collaborative publications. I believe this is very far from ideal and, in fact, even more problematic than the classical exogenous and literary “Pygmy” and “non-Pygmy”. Indeed, this particular denomination for genetics research formally essentializes ways-of-life and economic practices and strictly separates them albeit, as explained above, the Central African context is not as strictly dichotomic regarding these cultural traits, far from it. Furthermore, this essentialization, as it is highly meaningful for anthropological geneticists and human population geneticists, might be in fact misleading in that it oversimplifies hypotheses and the methods used to test them into a “case-control” approach that may inevitably fail to capture a known more complex reality of human adaptation to varying ways-of-life.

For all these reasons, and bearing all these warnings in mind, I will henceforth keep using the “Pygmy” and “non-Pygmy” labels throughout this dissertation, in the hopes that readers understand that this is never, in my mouth, used derogatorily.”
I detailed in **Chapter 1-section 1.1** the genesis, fundamental questions, and sampling protocols that presided my research endeavors since the beginning of my PhD, and until now, concerning the reconstruction, from genetic data, of the genetic history and evolution of Central African populations categorized in “Pygmy” and “non-Pygmy” populations based on historical and cultural criteria. In this **Chapter 2**, I will summarize and discuss several previous publications reporting the key-results we obtained over the years concerning this project.

As mentioned previously, the socio-historical construction of the “Pygmy” category in Western cultures resulted in more than 20 populations throughout the Congo Basin being labelled as such by Europeans. Cultural anthropologists and ethnologists during the 20th century showed that numerous cultural criteria could be informed to group these populations into a single category and used the historical word “Pygmy” to designate this super-group of populations differing from all other neighboring populations categorized into the mirror group “non-Pygmyes”. We also saw in this **Chapter 1-section 1.1** that anthropologists and ethnologists could not determine whether these populations had a common biological origin or not, as such question is often beyond their focus of interest, and contradictory in essence with their disciplinary paradigms and methodological means.

However, for biologists, such question is of interest to better understand human evolution and the patterns of genetic diversity observed today within and among populations in the region. In this context, the historical and widely-spread use of the blanket-term Pygmy resulted for numerous biologists in *de facto* considering these historical Pygmy populations as sharing a common origin more recent than the common origin shared between them and neighboring non-Pygmy populations, albeit without formally testing this hypothesis. Furthermore, archaeological work extensively showed the ancient occupation of the Congo Basin for the last 60,000 years at least (Phillipson 2005). However, due in part to the overall lack of ancient human remains in the acidic soils of the rainforest and to methodological limitations inherent to the discipline (see **section 1.6**), they could not link the archaeological occupation of the region with either Pygmy or non-Pygmy extant populations. Furthermore, the lack of knowledge about extensive previous anthropological and ethnological work among population geneticists also widely led to believe that Pygmy populations lived genetically isolated from geographically neighboring populations, without formally testing such prejudice. In this context, it is essential to better understand the demographic and migratory genetic history of these populations before one can even hope to identify the genetic determination and evolutionary history of phenotypic differences across populations and groups of populations in the region.

First (**section 2.1**), we described genetic diversity patterns obtained for numerous populations throughout the Congo Basin, categorized in Pygmies and non-Pygmy neighbors based on numerous cultural criteria.

Second (**section 2.2**), we formally tested whether Pygmy populations shared a common or an independent origin with neighboring non-Pygmy populations.

Third (**section 2.3**), we reconstructed the influence of complex socio-cultural behavior regarding inter-community marriages on genetic diversity patterns, effective populations sizes, and asymmetric gender-biased admixture patterns.

Fourth (**section 2.4**), we synthesize here these fundamental results about the demographic history of the Congo Basin peopling in a schematic way.

Fifth (**section 2.5**), we synthesize our work about the genetic evolution and adaptation signatures in Congo Basin populations, with a specific focus on the genetic determination of non-pathological adult height differentiation across individuals and populations.
Finally (section 2.6), we propose ongoing and future perspectives about investigating the “Neutral” demographic history of Central African extant populations.

<figure><img src="image_15.png" /><figcaption>Figure F2.1.a.</figcaption></figure>

<table><thead><tr><th>Population Name</th><th>Code</th><th>Country</th><th>Linguistic Family (Guthrie 1971)</th><th>Sampling</th></tr></thead><tbody><tr><td>Bezan</td><td>BEZ</td><td>Cameroon</td><td>Bantoid Non-Bantu, Tikar</td><td>P. Verdu</td></tr><tr><td>Kola</td><td>KOL</td><td>Cameroon</td><td>Bantu, A80</td><td>A. Froment</td></tr><tr><td>Central Baka</td><td>CBK</td><td>Cameroon</td><td>Adamawa-Ubangian, Gbanzili-Sere, Ngbaka</td><td>A. Froment, P. Verdu</td></tr><tr><td>Eastern Baka</td><td>EBK</td><td>Cameroon</td><td>Adamawa-Ubangian, Gbanzili-Sere, Ngbaka</td><td>A. Froment</td></tr><tr><td>Southern Baka</td><td>SBK</td><td>Cameroon</td><td>Adamawa-Ubangian, Gbanzili-Sere, Ngbaka</td><td>A. Froment, P. Verdu</td></tr><tr><td>Gabonese Baka</td><td>GBK</td><td>Gabon</td><td>Adamawa-Ubangian, Gbanzili-Sere, Ngbaka</td><td>J-M Hombert, L. Van Der Veen</td></tr><tr><td>Koya</td><td>KOY</td><td>Gabon</td><td>Bantu, B20</td><td>S. Le Bomin</td></tr><tr><td>Central Bongo</td><td>CBG</td><td>Gabon</td><td>Bantu, B30</td><td>P. Verdu, S. Le Bomin</td></tr><tr><td>Eastern Bongo</td><td>EBG</td><td>Gabon</td><td>Bantu, B70</td><td>P. Verdu, S. Le Bomin</td></tr><tr><td>Southern Bongo</td><td>SBG</td><td>Gabon</td><td>Bantu, B30-B50</td><td>P. Verdu, S. Le Bomin</td></tr><tr><td>Aka</td><td>AKA</td><td>CAR</td><td>Bantu, C10</td><td>B. Hewlett</td></tr><tr><td>Baka</td><td>BIK</td><td>CAR</td><td>Bantu C10</td><td>L.L. Cavalli-Sforza, B. Hewlett</td></tr><tr><td>Nyoro</td><td>NSU</td><td>Uganda</td><td>Sudanic, Mangbetu-Efe</td><td>P. Verdu, M.F. Mifumi</td></tr><tr><td>Meut</td><td>MBU</td><td>DRC</td><td>nd</td><td>L.L. Cavalli-Sforza, B. Hewlett</td></tr><tr><td>Twa</td><td>TWA</td><td>Uganda</td><td>nd</td><td>G.H. Perry, L. Barreiro</td></tr><tr><td>Tikar</td><td>TIK</td><td>Cameroon</td><td>Bantoide Non-Bantu, Tikar</td><td>P. Verdu</td></tr><tr><td>Ewendo</td><td>EWD</td><td>Cameroon</td><td>Bantu, A70</td><td>A. Froment</td></tr><tr><td>Nzime</td><td>NZI</td><td>Cameroon</td><td>Bantu, A80</td><td>A. Froment, P. Verdu</td></tr><tr><td>BGD</td><td>BGD</td><td>Cameroon</td><td>Adamawa-Ubangian, Bangandu, Gbaya</td><td>A. Froment</td></tr><tr><td>Bangandu</td><td>BND</td><td>Cameroon</td><td>Bantu, A80</td><td>A. Froment</td></tr><tr><td>Noumba</td><td>NGB</td><td>Cameroon</td><td>Bantu, A70</td><td>A. Froment</td></tr><tr><td>Fang</td><td>CFG</td><td>Cameroon</td><td>Bantu, A70</td><td>A. Froment</td></tr><tr><td>Fang</td><td>GFG</td><td>Gabon</td><td>Bantu, A70</td><td>J-M Hombert, L. Van Der Veen</td></tr><tr><td>Akele (Bongomol)</td><td>AKL</td><td>Gabon</td><td>Bantu, B20</td><td>S. Le Bomin</td></tr><tr><td>Kola</td><td>KOT</td><td>Gabon</td><td>Bantu, B20</td><td>J-M Hombert, L. Van Der Veen</td></tr><tr><td>Teke</td><td>TEK</td><td>Gabon</td><td>Bantu, B70</td><td>J-M Hombert, L. Van Der Veen</td></tr><tr><td>Nzeo</td><td>NZE</td><td>Gabon</td><td>Bantu, B50</td><td>J-M Hombert, L. Van Der Veen</td></tr><tr><td>Tiging</td><td>TSG</td><td>Gabon</td><td>Bantu, B30</td><td>J-M Hombert, L. Van Der Veen</td></tr><tr><td>Kopio</td><td>KJO</td><td>Uganda</td><td>Bantu, D30</td><td>J-M Hombert, L. Van Der Veen</td></tr><tr><td>Kiga</td><td>KIG</td><td>Uganda</td><td>nd</td><td>G.H. Perry, L. Barreiro</td></tr></tbody></table>

Population samples used in genetic analyses in Chapter 2 see detailed Materials and Methods in references cited therein. See Chapter 1.1 for sampling and anthropological categorization procedures in Pygmies and non-Pygmyes based on complex cultural criteria only.

Figures and tables adapted from previous publications: Verdu P et al. *Current Biology* 2009 and Verdu P. *in Hunter-Gatherers from the Congo Basin*, B. Hewlett Eds 2014.
**2.1. Genetic variation patterns among Central African populations with respect to different anthropological categories**

After several years of DNA and anthropological data sampling throughout Central Africa conducted by myself and other colleagues (see **Chapter 1.1** above), we investigated, first between 2006 and 2009, autosomal microsatellite variation for 28 tetranucleotide markers dispersed throughout the genome (and thus genetically independent with very low Linkage Disequilibrium), that I genotyped for more than 800 individuals (**Figure 2.1**), with help from Myriam Georges at the nascent<fnref n="36" /> molecular laboratory of the UMR7206 at the time of my PhD (Verdu 2009; Verdu et al. 2009).

As for any statistical analysis project, one first has to describe statistically the data, before trying to infer the mechanisms (genetic evolution in our case) that gave birth to the observed pattern. Note importantly, however, that inference and evolutionary hypotheses testing should imperatively be formally elaborated so as to avoid circularity and double-use of the data (Devezer et al. 2021). In particular, any population genetics statistical testing should be careful not to test hypotheses circularly based on observed genetic patterns.

In our case, individuals and populations could be categorized in “Pygmies” and “non-Pygmy neighbors” based on numerous cultural criteria described extensively in **Chapter 1.1**, without using genetic or phenotypic criteria such as adult standing height. Alternatively, we could also categorize individuals and populations linguistically based on Guthrie (1967) categorizations of Central African languages, a primary interest of ethnologists in the initial interdisciplinary project I was part of. We therefore set out to investigate genetic variation patterns within and across populations and groups of populations using classical hierarchized or un-hierarchized AMOVA approaches (Excoffier et al. 1992), in order to evaluate how cultural anthropology categories translated into genetic variation distribution, or not.

We first considered only genetically family unrelated individuals at the 2^nd^ genealogical degree (within and across populations), and focusing on roughly 600 individuals born in at relatively small geographical scale in the Western part of the Congo Basin only (**Figure 2.1.a left panel**), from 21 populations that could be categorized in nine “Pygmy” and 12 neighboring “non-Pygmy” populations. We found that a significant proportion of the total genetic variation differentiated across the 21 populations overall (un-hierarchized AMOVA, F\_ST = 0.013, 10,000 permutation p < 0.001). Furthermore, we found that the nine populations categorized as Pygmies a priori where considerably more differentiated (F\_ST = 0.019, 10,000 permutation p < 0.001), than, separately also in un-hierarchized AMOVA, the 12 neighboring non-Pygmy populations (F\_ST = 0.004, 10,000 permutation p < 0.001). Interestingly, we found a much smaller proportion of the total variance explained by linguistic categories as we found a non-significant F\_CT = 0.0025 (10,000 permutation p = 0.042) in a hierarchized AMOVA grouping all 21 populations into 7 linguistic groups (**Figure 2.1.a left panel colors**), without distinction in Pygmies and non-Pygmies.

Furthermore, investigating pairwise-FST values (Weir and Cockerham 1984) across all pairs of 21 populations, and setting non-significant (10,000 permutations) such values to 0, we found that all Pygmy populations where significantly differentiated from one another except the two South Cameroon Baka SBK and CBK populations. Conversely, we found that 68.2% of pairwise FST values across non-Pygmy populations were not significant. **Figure 2.1.b** shows Principal Coordinates Analyses (PCoA) projections

<footnote n="36">³⁶ The molecular lab had been built prior to my PhD in the Musée de l'Homme by Dr. Patricia Balaresque under the supervision of Pr Evelyne Heyer and, together with Myriam Georges, we inaugurated the first DNA extractions and PCRs conducted herein in 2006.</footnote>
of this population-pairwise *F*<sub>ST</sub> matrix further visually illustrating that most genetic variation in our dataset was accounted for by major differentiation across “Pygmy”-labelled populations and that, conversely, non-Pygmy populations were much more closely resembling one another. In these plots, the greatest genetic differentiation between pairs of populations on average along the first PCoA axis occured between, roughly, the four Baka Pygmy populations and the group of non-Pygmy populations, while the second and third PCoA axes both distinguished populations labelled as Pygmies. Importantly here, note that some Pygmy populations, such as the Gabonese Bongo populations, were more resembling non-Pygmy, and that other populations such as the Kola and the Bezan were found at intermediate distances between the Baka and the Bongo along the first PCoA axis. It is important to note in this context that pairwise-*F*<sub>ST</sub> patterns here observed did not stem from vast differentiation in loci’s average heterozygosities (Nei 1978) between Pygmy and non-Pygmy populations (*He* = 0.736 *SD* = 0.012 across 9 populations in Pygmies, and *He* = 0.741 *SD* = 0.007 across 12 neighboring non-Pygmy populations, Wilcoxon two-sided rank sum test *p* = 0.30), albeit these latter results further showed greater *He* variation across Pygmy populations than across non-Pygmy neighbors. Finally, as expected from the linguistic AMOVA, we see no correlation between population genetic differentiation patterns and linguistic groupings: linguistic categories do not translate into genetic variation differentiation across populations in Western Central Africa.

<figure><img src="image_16.png" /><figcaption>Figure F2.1.b.</figcaption></figure>

Principle Coordinates Analyses based on
population pairwise *F*<sub>ST</sub> (Weir and
Cockerham 1984) calculated for 28
independent autosomal tetranucleotide
microsatellites. Population categorization in
Pygmies and non-Pygmies are based on
numerous historical and cultural criteria
without considering phenotypic information
(see Chapter 1.1).

*Top panel* was previously published in
Verdu et al. *Current Biology* (2009).

**Bottom panel** is the same genetic
differentiation PCoA projection colored in
linguistic affiliations instead. Note that this
latter panel was, in essence, originally
published in a slightly different analysis in
Verdu and Destro-Bisol *Human Biology*
2012.

Colors and population labels can be found in
Figure F2.1.a above.

<figure><img src="image_17.png" /></figure>
Finally (Figure 2.1.c), note that these results could be qualitatively expanded at the scale of the entire Congo Basin when considering three additional Aka Pygmy populations (BIA, AKA, AKM) from Central African Republic, Mbuti (MBU) Pygmies from Eastern Democratic Republic of Congo, and Nsua Efe (NSU) Pygmies from Western Uganda (see Map in Figure 2.1.a right panel). Importantly, considering interindividual pairwise Allele Sharing Dissimilarity (Bowcock et al. 1994) calculated from 153,798 autosomal SNPs in another, later (Pemberton, Verdu et al. 2018), study using an overlapping sample set, rather than the microsatellite markers used above, we found very similar patterns, also consistently found in other studies considering neutral short sequences dispersed across the genome (Patin et al. 2009), or whole exome sequences (Lopez et al. 2018, 2019). Note, here, that not only certain Pygmy populations are genetically more resembling non-Pygmy groups, but this result expands to inter-individual genetic variation where some Pygmy individuals resemble more some non-Pygmy individuals, even at reduced geographical scales in Western Central Africa only.

<figure><img src="image_18.png" /><figcaption>**Figure F2.1.c.**</figcaption></figure>

*Top panels:* Multi-Dimensional Scaling based on population pairwise *F*<sub>ST</sub> (Weir and Cockerham 1984) calculated for 28 independent autosomal tetranucleotide microsatellites, data here re-analyzed based on previous analyses in Verdu P. PhD Thesis (Université Pierre et Marie Curie – MNHN, Paris, France, 2009).

*Bottom panel:* Multi-Dimensional Scaling based on individual pairwise Allele Sharing Dissimilarities (Bowcock et al. 1994) calculated using 153,798 autosomal SNPs genome-wide from Pemberton, Verdu et al. *Human Genetics* 2018.

Population categorization in Pygmies and non-Pygmyes are based on numerous historical and cultural criteria without considering phenotypic information (see Chapter 1.1).
We then further explored inter-individual genetic variation using STRUCTURE unsupervised Bayesian clustering algorithms (Pritchard et al. 2000; Falush et al. 2003), whether using autosomal microsatellites or SNPs, and found interesting patterns of shared genetic resemblance across groups of individuals (Figure 2.1.d). Indeed, in all cases, this powerful MCMC-based clustering algorithm systematically found that individuals categorized *a posteriori*<fnref n="37" /> as Pygmies had, on average, higher levels of genotypes' membership to one (red) virtual genetic cluster, while non-Pygmy individuals *a posteriori* clustered more substantially to the alternative (blue) cluster. However, and most importantly, neither red nor blue clusters were represented close to 100% in large groups of individuals. Instead, a substantial amount of blue can be found in all individuals categorized as Pygmies, and a substantial amount of red can be found in all individuals categorized as non-Pygmies. Furthermore, while membership to the red cluster is relatively low and little variable across individuals within each non-Pygmy-labelled population, the amount of blue in most Pygmy individuals is substantially higher on average; and, interestingly, on average variable across the various Pygmy populations: Baka Pygmies have on average lower genetic memberships to the blue cluster while Bongo Pygmies have on average much higher such memberships. This pattern would be expected in the case of asymmetric and heterogeneous admixture across Pygmy and neighboring non-Pygmy populations, where Pygmy populations would be more introgressed by the non-Pygmy gene-pool than the opposite, and where each Pygmy population would be introgressed to a different extent on average. However, such apparent STRUCTURE patterns could also be explained by other scenarios where each Pygmy population would have diverged from their neighboring non-Pygmy population at different times in the recent past and experienced different genetic drift since then. Therefore, whether such patterns stem from differential admixture or differential origins and drift remained, at that point of our descriptions of autosomal genetic patterns, to be assessed.

<figure><img src="image_19.png" /><figcaption>Figure F2.1.d.</figcaption></figure>

Top panel: STRUCTURE analysis obtained for 28 autosomal tetranucleotide markers genotyped in 607 individuals from Western Central Africa only (Figure F2.1.a right panel), previously published in Verdu et al. *Current Biology* 2009.

Bottom panel: STRUCTURE analysis obtained for 40,424 independent (low LD) genome-wide SNPs genotyped in 406 individuals from Western to Eastern Central Africa only (Figure F2.1.a left panel), previously published in Pemberton, Verdu et al. *Human Genetics* 2018.

Each individual is represented by a single vertical line divided into 2 colors (red and blue) corresponding to the relative proportion of genotypes assigned to either virtual cluster inferred for *K*=2 with this software based only on allele frequencies calculated across all individuals.

Population categorization in Pygmies (labelled in red) and non-Pygmies (labelled in blue) are based on numerous historical and cultural criteria without considering phenotypic information (see Chapter 1.1).

<footnote n="37">³⁷ As a reminder, note that unsupervised clustering methods implemented in STRUCTURE (Pritchard et al. 2000; Falush et al. 2003) or ADMIXTURE (Alexander et al. 2009), do not consider population information in their analyses, but only inter-individual genetic resemblances. Individuals in these analyses are grouped *a posteriori* into pre-categorized populations each with a given label but this information does not participate in the obtained results themselves.</footnote>
Altogether, our results based on autosomal data and those of our collaborators as well as those of other independent research groups, indicated since our initial work in 2009 that

1. Pygmy populations are more differentiated from one another than non-Pygmy populations; with Eastern Nsua and Mbuti Pygmies being highly differentiated from Western Baka and Aka, and all other Western Congo Basin Pygmy populations being at intermediate distances between these two groups of populations, on average.

2. Non-Pygmy individuals and populations are highly resembling one another, even at the scale of the entire Congo Basin.

3. Importantly, some Pygmy populations are much more genetically resembling non-Pygmy populations than others, such as the three Bongo populations from Southern Gabon.

4. Linguistics categories are un-informative about genetic differentiation across populations throughout the Congo Basin.

5. Considering inter-individual genetic differentiation, there are signals of possible admixture between Pygmy and non-Pygmy groups of populations, i) largely asymmetrical with more non-Pygmy admixture within Pygmy groups than the opposite, and, ii), heterogeneous in intensity across Pygmy groups. Such complex admixture patterns are nevertheless only indicated in our analyses and should be further formally tested as the observed patterns could alternatively stem from other evolutionary mechanisms.

Therefore, as a result of these descriptive analyses, we can conclude that the Pygmy/non-Pygmy binary categorization of Congo Basin individuals based on numerous historical and cultural criteria translates into extensive average genetic differentiation between groups of individuals sampled from the two categories respectively. Nevertheless, this binary categorization system hides tremendous genetic variation as certain Pygmy individuals and populations are resembling non-Pygmy individuals and populations, while others are much more distant genetically. Furthermore, we found tremendous genetic variation across populations within the Pygmy category, and much more genetically homogeneous non-Pygmy populations, even at the scale of the entire Congo Basin. If this result advocates for a common recent origin of all populations labelled as non-Pygmyes, the single term Pygmy *de facto* hides tremendous genetic variation further questioning the possible common origins of all populations categorized as such during history. Altogether, genetic differentiation results within the group of Pygmy populations echoes the vast cultural diversity recorded by ethnologists and cultural anthropologists across historical Pygmy groups throughout the Congo Basin as well as at more regional scales (Verdu et al. 2009, 2012; Verdu 2014, 2016).

Finally, note that, as an answer to one of the core questions brought by ethnologists about linguistic diversity throughout the Congo Basin, linguistic resemblance among populations does not predict genetic resemblance among individuals and populations (Verdu and Destro-Bisol 2012). This is due to the fact that Pygmy populations most often speak a language closely related to that of certain non-Pygmy immediate neighboring populations and, since Pygmy populations on average substantially differ genetically from these neighbors, there is no correlation between genetic patterns and linguistic diversity locally in the Congo Basin. This would further suggest that, unlike in numerous other worldwide populations but also far from exceptional among *Homo sapiens* populations, while language differences necessarily participate to identity construction in Central African societies, they do not translate into marital and reproductive preferences or segregation between groups.
## 2.2. Reconstructing the origins of Central African Pygmy and neighboring non-Pygmy populations using Approximate Bayesian Computations

In this complex anthropo-genetic context, we set out to formally test *i*) whether Pygmy populations had a more recent common origin together than their common origin with non-Pygmy populations or, alternatively, if each Pygmy population had an independent genetic origin from one another. Furthermore, *ii*) we aimed to test formally whether asymmetrical and heterogeneous admixture occurred between the two groups of populations, or not, in order to explain the observed genetic patterns (see also introduction in Chapter 1.1).

### 2.2.a Briefly introducing Approximate Bayesian Computation statistical inference

Inferring highly complex evolutionary histories from genetic data is not trivial using classical maximum likelihood phylogenetic approaches. Indeed, first, classical such approaches cannot accommodate at the same time numerous population samples with branch-specific changes in effective population sizes and possible gene exchanges, via migration or admixture events, across all pairs of populations throughout history. Such models are often too complex for simply writing the likelihood to be maximized, and even if possible, maximizing this likelihood in a convergent way can be extremely challenging computationally, if not simply out of reach (Foll et al. 2015; Ni et al. 2019). Furthermore, maximum-likelihood approaches' performances to fit a given model to a genetic dataset are, in essence, hard to hierarchize when comparing highly complex models with different numbers and classes of parameters (divergence times, admixture events, effective population size changes), in particular across models performing, *a posteriori*, reasonably similarly to fit the data (Alexander et al. 2009; Gravel 2012). These fundamental limitations of maximum-likelihood approaches were structural when I started the formal reconstruction of the evolutionary history of Central African populations in 2007, and they still remain largely challenging today, even if massive computational and methodological improvements have been achieved since then concerning this specific class of population genetics inference methods.

In this context, a novel statistical inference approach, born in 1997 and rapidly expanding in population genetics at the beginning of the 2000's, seemed promising to investigate the above questions of interest: Approximate Bayesian Computation (Tavaré et al. 1997; Pritchard et al. 1999; Beaumont et al. 2002). As ABC represents a class of inference methods at the core of my research endeavors (see also Chapters 4 and 5), I briefly synthetically explain below how ABC works (note that I provide a schematic representation in Chapter 4):

1. Simulate genetic data under a variety of highly complex genetic scenarios (or models) in competition and assumed a priori to explain the data, by drawing model-parameter values for each simulation in prior distributions set explicitly by the user. This thus result in a vector of parameter value corresponding to a vector of simulated genetic data, for each simulation under each competing scenario.

2. For each simulation separately, calculate a set of summary-statistics thought a priori to be informative about the model-parameters of interest. For instance, population genetics theory classically predicts that genetic differentiation $F_{ST}$ (Weir and Cockerham 1984) between pairs of populations is related to drift parameters (effective population sizes and mutation rates), as well as divergence times and migrations. We can thus use $F_{ST}$ a priori for estimating these parameters with ABC. This step results in a vector of
parameter values for a given simulation associated with a vector of summary statistics calculated on the
obtained simulated genetic data, for each simulation under each competing scenario.

3. Calculate the exact same set of summary statistics on the observed real data (thus only once).

4. ABC allows to formally determine which competing scenario produces simulations for which pseudo
observed genetic data produced summary statistics closest to the real observed ones. Several such ABC
methods for scenario-choice have been produced and rely on simple rejection (a. calculate
multidimensional Euclidean distances between the vector or observed summary statistics and the vectors
of summary statistics calculated separately for each simulated data; b. define a threshold value of
proximity and retain all simulations within a shorter distance than the chosen threshold, c. evaluate the
proportion of simulations obtained from each scenario, respectively, for this subset of “closest”
simulations); or more complex, accurate, and powerful approaches, such as logistic or local linear
regressions (Beaumont et al. 2002), or machine-learning Random Forest or Neural Network more
recently (Csilléry et al. 2012; Pudlo et al. 2016).

5. Under the winning scenario identified in procedure 4. ABC allows to estimate the posterior distribution of model-parameters producing simulations for which summary statistics are closest to the observed ones. Based only on simulations from a single scenario, this procedure, again, identifies the closest sets of simulations to the observed data and uses rejection, regression, or machine learning approaches (among others) on the vectors of parameter values used originally for each simulation to estimate posterior distributions for each original or composite parameter in the model.

Therefore, ABC can be used, in principle, to infer the parameters of the models that best mimic the observed
data for evolutionary scenarios of arbitrary complexity, provided that one can simulate efficiently enough
data to cover the (often large) parameter space and calculate informative summary statistics<fnref n="38" />. In practice,
ABC is often limited by the dimensionality of the parameter space that can be hard to explore thoroughly
even with very large numbers of simulations, and by the informativeness of statistics that may render certain
parameters in the models identifiable while others not (Sisson et al. 2018). More conceptually, ABC has an
obvious limitation: one only tests the models that one can think of. Indeed, ABC does not allow to explore
unspecified possibilities in the realm of evolutionary scenarios. Rather, ABC allows formally testing
hypotheses in the form of clearly defined competing scenarios, with associated prior parameter-distributions
set by the user, thought a priori to be underlying the observed data. This nevertheless represents, to my
personal views, an ideal framework for most my research endeavors. Indeed, I admit that I am not after the
“truth” (which I believe is inaccessible in the case of evolutionary genetic history, at least yet). I am rather
interested in comparing the possible influence of different scenarios, all oversimplifying the “real” history,
on the observed genetic patterns, within the population genetics paradigm of the synthetic neo-Darwinian
theory of evolution (Estoup et al. 2018).

Finally, and importantly, note that while more simple models can also be inferred from genetic data
with ABC, if a model can be reasonably treated via likelihood-maximization procedures, there is no reason
to conduct instead a full-blown ABC inference. Despite ABC practicality and, I think, intuitive dialectics,
it is far less mathematically elegant and philosophically grounded. As its’ name reminds the user, ABC
relies on a strong approximation, namely approximating the real data by a set of summary statistics
calculated on the real data, and cannot therefore be preferred to methods allowing directly to infer the
parameters of evolutionary models from the observed genetic data, when possible.

<footnote n="38">³⁸ Note that this is why ABC is now often used beyond population genetics, in economy for instance, and why we further developed ABC for linguistic inferences during Valentin Houzeau’s PhD that I co-supervised with Frédéric Austerlitz (see **Chapter 5**).</footnote>
It is important for me to acknowledge here that I initially acquired knowledge and skills in ABC inferences mostly thanks to Dr. Arnaud Estoup from the CBGP lab in Montpellier. He kindly and patiently hosted me for several trips to his lab between 2007 and 2008, in order for me to learn and conduct the ABC scenario-choice and posterior parameter estimation procedures adapted to my Central African project. We did so, using the first beta version, not released at the time, of a massive software package that Dr. Estoup and colleagues had developed and that is still extensively used in the population genetics community, Do It Yourself ABC (Cornuet et al. 2008), and that allowed us to do all of the above with a single integrated computational tool. Our work on Central African human populations published in early 2009 represents one of the very first application of ABC approaches to human genetic data. Since then, we have worked on several occasions with Dr. Estoup who developed specific novel ABC tools with help from me, as well as published a book chapter in the main ABC text-book edited by Beaumont et al. and released in 2018 (Estoup et al. 2019).

### 2.2.b Approximate Bayesian Computation inferences in practice in Central Africa

Based on these premises, we elaborated (Verdu et al. 2009) eight competing scenarios (different versions of the two most complex scenarios shown in **Figure 2.2.a** below), for explaining the evolutionary history underlying the observed genetic data that we previously described for 28 autosomal tetranucleotide microsatellites genotyped for more than 600 individuals from the Western part of the Congo Basin (see **previous section 2.1** and **Figures 2.1.a-d**).

Four competing scenarios considered a topology where the various populations categorized as Pygmies based on cultural criteria share a common ancestry preceded by the common ancestry between the ancestral Pygmy lineage and the lineage giving birth to the non-Pygmy neighboring populations. Four other scenarios considered that each Pygmy population derive from the gene-pool that give birth to non-Pygmy populations independently, and potentially at different times.

All eight scenarios considered possible admixture events occurring between the Pygmy and non-Pygmy lineages: both after and before the common origin of Pygmy populations in the four “common origin” scenarios, and two separate admixture events occurring at any time along each Pygmy population lineage after it’s divergence from the non-Pygmy lineage, for the four “independent origins” scenarios. In four scenarios (two with common origins and two with independent origins of Pygmy populations), admixture intensity could take values, independently for each such event, randomly between 0.1% and 99.9%; meaning that, for 99.9% admixture, the gene-pool of the targeted Pygmy population would be almost completely replaced by that of the non-Pygmy lineage, while 0.1% meant that virtually no admixture occurred at this event. Conversely, in the four remaining scenarios, we set all admixture rates to be equal to zero in all simulations, in order to simulate genetic data that did not experience admixture under these scenarios. Comparing both sets of scenarios would allow us to formally test if admixture was involved during the evolutionary history of our populations or if genetic patterns could be satisfactorily explained without this phenomenon, whichever the common or independent topology.
<figure><img src="image_20.png" /><figcaption>Table T2.2.a.
Model-parameters prior distributions.</figcaption></figure>

<table><thead><tr><th>Common Origin scenarios</th><th>Description</th><th>Prior Distribution</th><th>Condition</th></tr></thead><tbody><tr><td>N<sub>1</sub> (Baka)</td><td>Effective pop size</td><td>Uniform[10-10,000]</td><td></td></tr><tr><td>N<sub>2</sub> (Bezan)</td><td>Effective pop size</td><td>Uniform[10-10,000]</td><td></td></tr><tr><td>N<sub>3</sub> (Kola)</td><td>Effective pop size</td><td>Uniform[10-10,000]</td><td></td></tr><tr><td>N<sub>4</sub> (Koya)</td><td>Effective pop size</td><td>Uniform[10-10,000]</td><td></td></tr><tr><td>N<sub>np</sub> (Non-Pygmyes)</td><td>Effective pop size</td><td>Uniform[10-100,000]</td><td></td></tr><tr><td>N<sub>Ap</sub> (Ancestral Pygmy)</td><td>Effective pop size</td><td>Uniform[10-10,000]</td><td></td></tr><tr><td>N<sub>A</sub> (Ancestral population)</td><td>Effective pop size</td><td>Uniform[10-10,000]</td><td></td></tr><tr><td>t<sub>rr</sub></td><td>Admixture time</td><td>LogUniform[1-5,000]</td><td>trr&lt;tp</td></tr><tr><td>t<sub>p</sub></td><td>Divergence time</td><td>Uniform[1-5,000]</td><td>trr&lt;tp</td></tr><tr><td>t<sub>ra</sub></td><td>Admixture time</td><td>Uniform[1-5,000]</td><td>tp&lt;tra</td></tr><tr><td>t<sub>pnp</sub></td><td>Divergence time</td><td>Uniform[1-10,000]</td><td>tra&lt;tpnp</td></tr><tr><td>t<sub>A</sub></td><td>Time of change in Ne</td><td>Uniform[1-10,000]</td><td></td></tr><tr><td>r<sub>r1</sub></td><td>Admixture rate</td><td>Uniform[0-1]</td><td></td></tr><tr><td>r<sub>r2</sub></td><td>Admixture rate</td><td>Uniform[0-1]</td><td></td></tr><tr><td>r<sub>r3</sub></td><td>Admixture rate</td><td>Uniform[0-1]</td><td></td></tr><tr><td>r<sub>r4</sub></td><td>Admixture rate</td><td>Uniform[0-1]</td><td></td></tr><tr><td>r<sub>r5</sub></td><td>Admixture rate</td><td>Uniform[0-1]</td><td></td></tr><tr><td>r<sub>r6</sub></td><td>Admixture rate</td><td>Uniform[0-1]</td><td></td></tr><tr><td>r<sub>a</sub></td><td>Admixture rate</td><td>Uniform[0-1]</td><td></td></tr><tr><td>μ</td><td>28 Mutation rate param.</td><td>Uniform[10<sup>-4</sup>-10<sup>-3</sup>]</td><td></td></tr><tr><td>ρ</td><td>28 Mutation rate param.</td><td>Uniform[0.1-0.3]</td><td></td></tr></tbody></table>

<figure><img src="image_21.png" /></figure>

<table><caption>Figure F2.2.a.</caption><thead><tr><th>Independent Origins scenarios</th><th>Description</th><th>Prior Distribution</th><th>Condition</th></tr></thead><tbody><tr><td>N<sub>1</sub> (Baka)</td><td>Effective pop size</td><td>Uniform[10-10,000]</td><td></td></tr><tr><td>Na<sub>1</sub> (Baka)</td><td>Effective pop size</td><td>Uniform[10-10,000]</td><td></td></tr><tr><td>N<sub>2</sub> (Bezan)</td><td>Effective pop size</td><td>Uniform[10-10,000]</td><td></td></tr><tr><td>Na<sub>2</sub> (Baka)</td><td>Effective pop size</td><td>Uniform[10-10,000]</td><td></td></tr><tr><td>N<sub>3</sub> (Kola)</td><td>Effective pop size</td><td>Uniform[10-10,000]</td><td></td></tr><tr><td>Na<sub>3</sub> (Baka)</td><td>Effective pop size</td><td>Uniform[10-10,000]</td><td></td></tr><tr><td>N<sub>4</sub> (Koya)</td><td>Effective pop size</td><td>Uniform[10-10,000]</td><td></td></tr><tr><td>N<sub>np</sub> (Non-Pygmyes)</td><td>Effective pop size</td><td>Uniform[10-100,000]</td><td></td></tr><tr><td>N<sub>A</sub> (Ancestral population)</td><td>Effective pop size</td><td>Uniform[10-10,000]</td><td></td></tr><tr><td>t<sub>rr(1-4)</sub></td><td>4 Admixture times</td><td>LogUniform[1-5,000]</td><td>trr&lt;tra</td></tr><tr><td>t<sub>ra(1-4)</sub></td><td>4 Admixture times</td><td>Uniform[1-5,000]</td><td>trr&lt;tra</td></tr><tr><td>t<sub>pnp(1-4)</sub></td><td>4 Divergence times</td><td>Uniform[1-10,000]</td><td>tra&lt;tpnp</td></tr><tr><td>t<sub>A</sub></td><td>Time of change in Ne</td><td>Uniform[1-10,000]</td><td></td></tr><tr><td>r<sub>r(1-4)</sub></td><td>4 Admixture rates</td><td>Uniform[0-1]</td><td></td></tr><tr><td>r<sub>a(1-4)</sub></td><td>4 Admixture rates</td><td>Uniform[0-1]</td><td></td></tr><tr><td>μ</td><td>28 Mutation rate param.</td><td>Uniform[10<sup>-4</sup>-10<sup>-3</sup>]</td><td></td></tr><tr><td>ρ</td><td>28 Mutation rate param.</td><td>Uniform[0.1-0.3]</td><td></td></tr></tbody></table>

Two competing scenarios for ABC scenario-choice and posterior parameter inferences. Model parameters' prior distributions are indicated in the adjacent Table T2.2.a.

Model descriptions can be found in text.

Alternative scenarios are described above and can be found in detail and schematically represented in Verdu et al. *Current Biology* 2009 Supplementary Materials.

Figure originally published in Verdu et al. *Current Biology* 2009.
Finally, four scenarios comprised the possibility of an instantaneous expansion of effective population size at any time in the history of the non-Pygmy lineage, while the four other scenarios did not comprise such possibility and the effective population size of the non-Pygmy population remained constant throughout history. This was introduced in our models as numerous previous archaeological, linguistic and genetic works investigated the demographic and genetic expansion of non-Pygmy Bantu-speaking populations. The ill called “Bantu-expansion”<fnref n="39" /> was reported to have started at least 5000 years ago with the emergence of agriculture in the region and the concomitant spread of Bantu-speaking populations from Western Cameroon into the rest of Central, Eastern and Southern Africa (e.g. Vansina 1995; Phillipson 2005).

We thus wanted to formally test this hypothesis to find if such scenario *a posterior* best explained our
data, or if such scenarios were un-identifiable with our data. Note that for all eight scenarios, Pygmy
lineages can each independently punctually change effective population size when diverging from the non-
Pygmy lineage or among themselves.

Note that in this initial work, we did not consider the evolutionary history of non-Pygmy neighbors
and pooled altogether our samples in a single “population”. This simplification was rendered possible as
our descriptive analyses showed that, with our data, these populations were barely distinguishable in a first
place. As ABC relies on summary statistics informativeness, we already knew that our data was insufficient
to capture the evolutionary history of the diverse non-Pygmy populations; a question nevertheless of major
interest and which we addressed with vastly more extensive data in other, later, papers produced by Pr.
Lluis Quintana-Murci and Dr. Etienne Patin (Pasteur Institute), and their colleagues, to which we had the
chance to contribute (see a summary in **section 2.5** below). Similarly, the four Baka Pygmy populations
highly resembled one-another and were pooled in a single “Baka” population in these analyses for very
similar reasons. Finally, note that the two Bongo Pygmy populations highly resembled non-Pygmy
neighbors in our descriptive analyses. We thus designed specific treatments for these populations and whose
technics will not be detailed here, but such specificities can be found in extenso in the original 2009 *Current
Biology* article.

For each eight scenarios, we performed 500,000 separate simulations drawing parameter values in
prior distributions (see **Figure F2.2.a** and associated **Table T2.2.a**), using the classical coalescent
backward-in-time simulator implemented in DIY ABC. For each 4 million simulations separately, we
calculated, using DIY ABC, 35 different summary statistics, considering within-population statistics such
as average Heterozygosities (Nei 1978) or average number of different microsatellite alleles and their
variances across loci, as well as statistics calculated between pairs of populations such as *F*<sub>ST</sub> (Weir and
Cockerham 1984) and Goldstein's pairwise molecular distance (δμ)<sup>2</sup> (Goldstein 1995).

We used regression ABC scenario-choice procedures and found that a scenario of common origins of
all Western Central African Pygmy populations presented in the top panel of **Figure F2.2.a** largely best
explained our data with ABC posterior-probability superior to 95%. Importantly, note that all other
scenarios largely failed to best explain the observed summary statistics, with a low type 2 error of wrongly
choosing a given scenario *a priori* using in turn 1000 random simulations under each scenario as pseudo-
observed data for ABC scenario-choice (0.042 on average ranging from 0.000 to 0.090 across scenarios).
Moreover, we found that to best explain the data, the winning scenario had to incorporate a possible increase

<footnote n="39">³⁹ Another illustration of how shortening concepts to be used as labels may introduce categorization issues, the linguistic category here transforming surreptitiously into a population name or identifier and subsequent demographic processes attached to its’ prejudiced history, although no Bantu population exist as this linguistic category spans local populations speaking more than 300 languages throughout half of one of the largest continents worldwide.</footnote>
in effective size occurring at some point in the non-Pygmy lineage. Finally, scenarios where admixture events were set to intensities of 0 throughout the history of Central African populations largely lost ABC scenario-choice with respect to the observed data. In other words, ancient and more recent admixture need to occur in our scenarios in order to best mimic the observed data. Finally, note that we obtained highly similar results for our treatments involving the two Bongo Pygmy populations (see Verdu et al. 2009 Supplementary materials), hence pointing to their common origin with all other Central African Pygmy populations despite their high levels of genetic resemblance with non-Pygmy neighbors.

Based on this winning scenario, we then used regression ABC to estimate, *a posteriori*, the distributions of each model-parameters used for the 1% simulations that produced vectors of summary-statistics closest to our observed data (Figure F2.2.b). Altogether, numerous parameters could be inferred satisfactorily as they substantially departed *a posteriori* from the prior distribution of parameter values used for simulating data as their 95% Credibility Intervals were relatively narrow.

This was the case for effective population size parameters that indicated that all Pygmy populations did not substantially changed sizes since their common ancestral population. Conversely, our results advocated for a strong increase in effective size in the non-Pygmy lineage.

Furthermore, not only our results qualitatively indicated the need for admixture to have occurred in the evolutionary history of Pygmy and neighboring non-Pygmy populations, but we estimated that admixture was heterogeneous with Bongo populations being much more admixed than Baka populations for instance.

Concerning divergence times, our results strongly supported a very recent common origin for all Western Central African Pygmy populations between 2,600 years before present (95% CI: 725–34,275) and 3,500 YBP (95% CI: 870–41,139) considering a generation time of 25 years or 30 years and based on the modal posterior point estimate for this parameter<fnref n="40" />.

Such recent and apparently strong isolation across populations sometimes not very distant geographically was somewhat unexpected in particular for hunter-gatherer populations often reported to have vast exploration ranges and extensive mobility. Thus, we investigated further at an extremely local scale for the three Cameroonian Baka populations in our sample sets, patterns of Isolation-By-Distance following Rousset et al. (1997) methods. In brief, Pr. Rousset and colleagues demonstrated that, at very reduced geographical scale, the slope of the linear correlation between interindividual genetic differentiation and logarithmic geographic distances among individuals (birthplaces in our case) was inversely proportional to effective dispersal in the population (namely the relative distance between an individual birthplace and that of both his/her parents).

<footnote n="40">⁴⁰ Note that the prior distribution for this parameter has a mode (due to constraints on time parameters it is not Uniform albeit drawn from a Uniform distribution) of 9,775 YBP and a 95% CI between 2,050 and 90,875 YBP considering a generation time of 25 years.</footnote>
<caption>Figure F2.2.b.</caption>

ABC estimations of the posterior distribution of four model-parameters under the winning scenario of common origin of Western Central African Pygmy populations, with and expansion of non-Pygmy effective population sizes and possible ancient and recent admixture events across lineages.

In all posterior distribution panels, the distribution of parameters used a priori to perform simulations is given in dashed black line while the parameters' posterior distributions are colored and correspond to parameters shown in the schematic scenario figure (on the left) by a black box. Intuitively in ABC, we consider that our data and summary statistics withhold identifiable information about model parameters when the estimated posterior distribution substantially departs from their respective priors and when 95% Credibility Intervals are relatively small. In this context, note here that, as an example, while our data seem to withhold substantial information for posterior estimation of the tp parameter, the posterior estimate of tpnp is only indicative of this parameter as 95% CI is wide.

Figure derived from results presented in a table
format in Verdu et al. *Current Biology* 2009.

<figure><img src="image_22.png" /></figure>
As our anthropological field-work yielded such detailed birthplace information at a very local scale, we applied this method and found, surprisingly, that Baka Pygmies had very reduced effective dispersal ranging between roughly 12 and 65 km² (Verdu et al. 2010; Verdu 2012). In other words, we found that Baka Pygmies, despite extensive exploration ranges and mobility in their environment for social, ritual, or economic reasons, nevertheless were born very close to where their biological parents were born. Furthermore, note that this result is in fact highly conservative, as any change in reproductive behavior in space or data collection mistakes would instantaneously erase this IBD pattern here observed. Note (unpublished results) that we obtained very similar results in the Bezan Pygmies, but not in the Kola albeit the latter were known to have experienced population displacements in the 1980s due to the construction of a pipeline likely having resulted in breaking the IBD signal at the following generation that we sampled.

Altogether such reduced effective dispersal could explain the reproductive isolation among Pygmy populations even at reduced geographical scale and despite large exploration range. Nevertheless, we still do not know since when such dispersal behavior exists in this population, which would need to be assessed in order to propose this mechanism as having contributed to the ABC inferred divergence history here identified.

Finally, despite relatively low information in our observed data, our results provided indications that the more ancient divergence between the ancestral Pygmy population and the lineage that gave birth to non-Pygmy neighbors occurred between 60,000 and 90,000 years ago, albeit, again, with large 95% CI.

Despite these positive results, several parameters could not be well estimated although they contributed to scenario-choice and thus behaved similarly as nuisance-parameters. This was the case for admixture times that were not satisfactorily inferred *a posteriori*, either the most recent time or the more ancient admixture time. Finally, although admixture intensities could be relatively well estimated in most cases, the posterior distribution for the ancient admixture estimate was seldom departing from its’ prior. These results show either that we lacked information in our data to satisfactorily identify these important parameters, and/or that scenarios oversimplifications here considered (e.g. a single admixture event in the past over a very large period of evolution), probably mis-fitted the data, although not considering any such events would result in even poorer fit to the data. This may also lead to relatively discrepant results between our inferences and our initial descriptive analyses, for certain aspects. For instance, if STRUCTURE results can be interpreted as due to admixture events as suggested by our ABC results, then we obtain certain ABC posterior estimates, for instance for the Baka, that are higher than what can be inferred from STRUCTURE results. This could be due to constraints on the parameter space for oversimplified scenarios with a single divergence time for all Pygmy populations that could possibly need to be compensated for some populations by a trade-off on posterior estimates of other parameters such as drift and/or admixture intensities. Ultimately, this advocates for further complexifying models which may then hit the dimensionality wall as we will have a hard time thoroughly and evenly explore very large spaces of parameters, as well as be strongly limited in all cases by the lack of information inherent to our very modest marker set used at the time.

Finally, we synthesized our findings from this work and beyond about the neutral demographic history of Central African peopling in a schematic way in **section 2.4** below.
**2.3. Complex sex-biased admixture processes between Central African Pygmy and neighboring non-Pygmy populations inferred with Approximate Bayesian Computations**

We deployed the same dialectics and inference methodology described above more specifically to investigate admixture processes across Central African populations. Indeed, our previous results established that heterogeneous and largely asymmetrical admixture was at play between Central African populations categorized as Pygmies based on numerous historical and cultural criteria, and the neighboring non-Pygmy populations with whom they share complex socio-economic relationships locally. Importantly, these findings were at odds with the common Western mis-representation of Hunter-Gatherer Pygmy populations living hidden remotely in the heart of the equatorial rainforest, and thus thought to be genetically isolated from their neighbors. Again, as detailed in introduction in **Chapter 1.1**, ethnologists had repeatedly highlighted that this prejudice was indeed a prejudice extremely far from the reality of numerous and complex socio-cultural and economic interactions between Pygmies and neighboring non-Pygmyes, as well as the diversity of such relationships across pairs of populations throughout the Congo Basin.

In this context, a review of the ethnographic literature, exchanges with ethnologists including shared experiences on the field in Central Africa, and relatively intense training in cultural anthropology methods and approaches allowed me to further disentangle the socio-cultural behaviors at play between these communities, which allowed us to propose population genetics expectations based on different sociological scenarios regarding intermarriages and reproduction.

As a summary (Kazadi 1981; Bahuchet 1992a; Bahuchet and Guillaume 1992; Joiris 2003; Hewlett 2014; Verdu 2014), complex socio-cultural relationships between Pygmies and neighboring non-Pygmyes locally include complex socio-marital and reproductive behavior relationships. Pygmy communities are very often strongly discriminated against by their socio-economically dominant non-Pygmy neighbors, both in reality and in self-reported endogenous discourses and representations. It is very common that non-Pygmy communities represent Pygmy communities as barely human in a classical racist way, where the other-than-self shows cultural differences which are then rendered innate and further hierarchized as lower than self. As a consequence, for non-Pygmyes, marriage with a Pygmy individual is often socially detrimental and reported to be largely avoided. However, both endogenous representations and their prevalence in realized behaviors are more complex (Figure F2.3.a).

In fact, Central African populations mostly report patrilocal philopatry practices, which is to say that brides move, after marriage, to live close to their husbands' family, against a bride-compensation paid by the husband's family to the bride's family. In addition to socio-economic discriminations against Pygmies, this result in marriages between a Pygmy male and a neighboring non-Pygmy female being highly improbable and strongly detrimental for the non-Pygmy bride and her family. Beyond this endogenous representation, very few such marriages have been reported in the literature and I only witnessed it in a single instance across all my fieldworks. In other words, this endogenous representation and socio-cultural norm seems to be indeed normative and highly prevalent.

However, in this context, marriages between a Pygmy female and a non-Pygmy male are more often tolerated, as I also witnessed. Indeed, several contexts may favor such marriages as, for instance, the frequent case of an economically poor non-Pygmy male unable to pay bride- compensations within his community, who will possibly have more opportunities to find a Pygmy female for marriage as bride-compensations to be paid would likely be much less expensive. Another example emerges when a non-
Pygmy male wishes to establish a beneficiary alliance with a specific Pygmy family renowned for their hunting skills and/or medical and magical knowledge of the forest<fnref n="41" />.

<figure><img src="image_23.png" /><figcaption>Figure F2.3.a.</figcaption></figure>

Part 1 of the schematic representation of spouse and offspring mobility in intermarriages between Pygmies and non-Pygmyes base on ethnographic investigations. Photographs ©Paul Verdu, Gabon and Uganda, 2006-2007.

Therefore, in the patrilocal context, the Pygmy bride moves to her non-Pygmy in-laws and give birth to admixed children within the non-Pygmy community. As illustrated above, this should result in genetic patterns opposite to what we observed and inferred in our data, with substantial amounts of “red” into the “blue”, and much lesser “blue” into the “red” ... Further investigating ethnographically, we noticed that these marriages almost systematically end up in a divorce within five years, mostly due to the strong discriminations experienced by the Pygmy female in the non-Pygmy community. Beware, divorces occur frequently in either community separately, but these specific inter-community marriages seem to always rapidly fail. As a consequence of the divorce, or in the case of the non-Pygmy husband’s death, the Pygmy female returns to her community of origin together with her children also discriminated against in the non-Pygmy community (Figure 2.3.b).

Altogether, such purely socio-cultural process would result in substantial asymmetric genetic admixture from the non-Pygmy gene-pool into the Pygmy gene-pool, with a relatively much lower gene-flow from Pygmies into non-Pygmyes that would correspond to exception to this reported socio-cultural behavior. Finally, note that illegitimate children between Pygmy females and non-Pygmy males, whether due to dramatic abuses or simply extra-marital reproductive events, would result in the same genetic patterns. Such scenario, albeit complex, would thus satisfactorily explain the observed genetic patterns and previous ABC inference results based on autosomes only.

<footnote n="41">⁴¹ Note that Pygmy females are often attributed a fantastic fertility in the equatorial forest region where secondary infertilities are frequent. This myth, never formally demonstrated, may result in increased sexual abuses against Pygmy females, but was rarely presented as a reason for marriage in my investigations. I am still not sure how this representation about fertility is prevalent and normatively influencing reproductive behaviors across communities.</footnote>
<figure><img src="image_24.png" /><figcaption>Figure F2.3.b.</figcaption></figure>

Part 2 of the schematic representation of spouse and offspring mobility in intermarriages between Pygmies and non-Pygmy base on ethnographic investigations.
Photographs ©Paul Verdu, Gabon and Uganda, 2006-2007.

Finally, how do we explain, under this framework, variation in introgression intensities across the various Pygmy groups throughout the Congo Basin? We observed qualitative variation across pairs of community in levels of discriminations against Pygmies reported by either the Pygmy victims and their non-Pygmy abusers. As a consequence, certain Pygmy communities, such as some Bongo groups, seem to be relatively more socially integrated with neighboring non-Pygmy than others, such as the Koya or the Baka for instances who are strongly discriminated against. Ultimately, the apparent strength in discrimination against Pygmies locally seem to qualitatively predict relatively well the observed intensity of genetic introgressions.

Based on these expectations, we set out to formally investigate patterns of sex-specific admixture and formally test different scenarios, using the same ABC dialectics and methodology as explained in the previous section (and which we will not further detail here).

Together with Master students Viola Grugni and Noémie Becker which I supervised, and again with the crucial technical support from Myriam Georges, we generated microsatellite data on our samples for the X-chromosome, for the non-recombining portion of the Y chromosome, as well as HVR-1 mitochondrial sequences (Verdu et al. 2013). This provided us with sex-specific genetic data which could be incorporated explicitly in the novel version of DIY ABC that Dr. Estoup and colleagues released in 2011. We therefore set out to evaluate, for each chromosomal compartment separately, ABC posterior parameter distributions specifically concerning male and female effective population sizes as well as male and female-mediated gene-flows in each Pygmy population, by considering simplified versions of the winning model previously identified, restricted to only three populations: two Pygmy populations and a single non-Pygmy sample merging the two neighboring populations. After extensive simulations specific to each population-samples trio for each chromosomal compartment separately, we conducted ABC posterior parameter
inferences for all pairs of Pygmy populations in our dataset (and associated neighboring non-Pygmy populations), and synthesized results obtained for each Pygmy population separately (Verdu et al. 2013).

Our ABC posterior parameter inferences showed that the complex sex-specific scenarios proposed by ethnographic work was indeed compatible with the observed genetic data. For compelling instances in addition to other results not discussed here, **Figure F2.3.c** shows that levels of female-mediated mitochondrial DNA admixture in each Pygmy population separately were always extremely low. In contrast, levels of male-mediated introgression via the Y-chromosome were always much higher. Finally, and most interestingly, while our hypothesis about the prevalence of discriminations influencing the absolute levels of observed genetic admixture still held, we found here that, in fact, the Pygmy communities most discriminated against also exhibited the strongest sex-biased admixture patterns. In interaction with reduced effective population sizes in Pygmy populations, this resulted in the extreme case of the Koya Pygmies, strongly discriminated against by their non-Pygmy immediate neighbors, where virtually non-Pygmy mitochondrial DNA are found, and where, conversely, Y-chromosome variation seem to have been replaced almost completely by that of the non-Pygmy neighbors. Finally, while we were unable at the time to investigate admixture patterns in non-Pygmy populations with our modest microsatellite dataset, further work conducted by Dr. Patin and Quintana-Murci and their team to which we could collaborate, identified, using genome-wide data for hundreds of thousands of SNP markers, that the low levels of Pygmy introgression into the non-Pygmy gene-pool was, conversely, largely female mediated rather than male mediated, as expected with the above complex socio-cultural scenario.

<figure><img src="image_25.png" /><figcaption>Figure F2.3.c.</figcaption></figure>

ABC estimations of the posterior distribution of admixture introgression rates from non-Pygmy neighboring populations into each Pygmy population, based on Y-chromosome microsatellites and mitochondrial DNA HVR-1 sequences. Figure is simplified from Verdu et al. *Molecular Biology and Evolution* 2013.
**2.4. A synthesis of anthropological genetics perspectives on the neutral demographic history of Central African peopling in the framework of the Pygmy/non-Pygmy complex categorization**

In schematic **Figure 2.4.a** below, we synthesized the descriptive and inference results described above (Sections 2.1 – 2.3), and further explored in other publications following the seminal works of Cavalli-Sforza et al. (1986) and Destro-Bisol et al. (2004), and our first formal testing for the origins and admixture history of Central African populations in the complex historical and cultural binary categorization of populations into Pygmies and non-Pygmyes as detailed in **Chapter 1.1**. Furthermore, we reproduced below the schematic figure (**Figure F2.4.b**) previously published in Verdu et al. (2013) and specifically focusing on the influence of sex-specific socio-cultural behavior on admixture and effective population sizes patterns in Central African populations.

Altogether, interdisciplinary data collections between population genetics and cultural anthropology allowed obtaining diverse types of genetic data from numerous populations extensively described anthropologically and categorized as Pygmies and neighboring non-Pygmyes based on numerous cultural criteria (and no phenotypic criteria). Using these data and population genetics hypotheses carefully translated from ethnological and linguistic previous questioning, anthropological geneticists could show that populations gathered under the blanket term “Pygmy” today in Central Africa show genetic patterns consistent with a common, shared, genetic origin more recent than their common origin with the ancestral non-Pygmy lineage. More specifically, we found an ancient divergence between ancestral Pygmy and non-Pygmy lineages between 70,000 and 130,000 years ago<fnref n="42" />, for reasons that remain, to my knowledge, unelucidated and rarely hypothesized.

Then, more recently some 25,000 years ago, Eastern and Western Congo Basin Pygmy populations seem to have diverged. It has been hypothesized that such reproductive isolation might have been due to a fragmentation of the rainforest environment at this time in this region. However, we do not know where the ancestral Pygmy populations lived, nor whether such forest fragmentation indeed resulted in population fragmentations, in particular since Pygmy populations live in different environments today.

Finally, we unveiled the very recent divergence across the various Western Central African Pygmy populations during the last 5000 to 3000 years, concomitant with the last climatic crisis and forest areas reductions in the region, and also contemporary with the expansion of agriculture accompanied by demic migrations of non-Pygmy populations throughout the Congo Basin. Furthermore, we found that Pygmy and non-Pygmy neighboring populations are admixed as a result of complex sex-specific asymmetric and heterogeneous admixture process in the context of patrilocality and social discriminations against Pygmies. Given the importance of these complex sociocultural behaviors to explain admixture patterns today, it may be plausible that the expansion of agricultural non-Pygmy populations was accompanied by profound socio-cultural changes for Western Pygmy populations possibly triggering the fragmentation of the ancestral genetic population. Then, we showed that differential admixture strongly drove the genetic differentiation across Pygmies, in addition to different effects of genetic drift.

<footnote n="42">⁴² Remember that population genetics do not estimate times in years, but in coalescent events, mutation rates, and generation times. Translating this evolutionary-genetics time into years necessarily suffers several profound approximations that can be discussed albeit some of these key approximations do not stem from population genetics but from other disciplines such as functional genetics or demography.</footnote>
<figure><img src="image_26.png" /><figcaption>Figure F2.4.a.</figcaption></figure>

Synthetic schematic representation of the genetic peopling history of Central African populations as inferred by anthropological genetics and human population genetics methods from observed, extant, genetic and
anthropological data. Note that the "Pygmy" and "non-Pygmy" populations' categorization labels rely on numerous historical and cultural categorization criteria characterized and discussed in Chapter 1.1.

This figure is largely updated from a previous similar attempt published in Verdu P (2014) in "*Hunter-Gatherers of the Congo Basin: Culture, History and Biology of African Pygmies*", Ed. Barry S. Hewlett, Transaction Pub.
Moreover, our inferences of sex-specific effective population sizes variation across Central African populations echoed a very long-standing debate in the cultural and biological anthropology community. Indeed (Figure F2.4.b), we found that populations categorized as Pygmies throughout the Congo Basin often had sex-specific effective population sizes (estimated taking into account admixture with neighboring non-Pygmies) that fitted expected patterns under matrilocal philopatric marriage behaviors. Indeed, in matrilocal populations, where males move to live close to their in-laws after marriage, we expect high genetic variation across male genetic lineages within and across populations, and relatively lower genetic variation across female genetic lineages; which is what we find for Central African Pygmy populations. The opposite genetic patterns are expected in patrilocal populations, this latter pattern being observed within and across non-Pygmy populations. However, today, both Pygmy and non-Pygmy populations report exclusively patrilocal philopatric practices in marriages within populations (Verdu et al. 2013).

In this context, it was hypothesized by cultural and biological anthropologists in a seminal work “*Man the Hunter*” (DeVore and Lee 1968), that patrilocal behaviors emerged with agriculture and that hunter-gatherer human populations were likely matrilocal before their transition to agriculture. While our results may support such hypothesis, where hunter-gatherer Pygmies still retained genetic signatures of past matrilocal practices, I strongly believe that our population genetics inferences are inconclusive about this particular question, largely out of reach, in fact, of our paradigms and methods. Indeed, other alternative scenarios are equally probable and other mechanisms are likely to be at play to explain the observed patterns. For instance, the complex sex-specific admixture processes here observed could be sufficient, if they have been ongoing for reasonably long, to explain the matrilocal genetic signature here observed despite Pygmy populations practicing patrilocality. In this case, genetic patterns today reflect this former history, and genetic signatures from philopatric practices in a more remote past are irremediably lost for genetics inferences. Furthermore, from a cultural anthropology perspective, while Pygmy populations report practicing patrilocality, numerous other socio-cultural rules may apply to make this simplistic endogenous speech not as prevalent in Pygmy populations than in non-Pygmies. Finally, note that all three possibilities are not mutually exclusive… In all cases, future work will be needed, but it is plausible that it will never be possible to address this question with extant genetic data alone, and without the insights of ancient DNA data from the region, which are crucially lacking, still (Verdu et al. 2013; Verdu and Austerlitz 2015).
<figure><img src="image_27.png" /><figcaption>**Figure F2.4.b.**</figcaption></figure>

Synthetic schematic representation of sex-specific effective population sizes, migrations and admixture within and across groups of Pygmy and non-Pygmy populations in Central Africa as inferred by anthropological genetics and human population genetics methods based on observed extant genetic data.

Note that the “Pygmy” and “non-Pygmy” populations’ categorization labels rely on numerous historical and cultural categorization criteria characterized and discussed in Chapter 1.1.
A black and white version of this exact figure was previously published in Verdu et al. *Molecular Biology and Evolution* 2013.
In this context, numerous questions remain to be assessed for further elucidating the genetic history of Central African peopling. For instance<fnref n="43" />, the admixture process itself remains to be dated and better understood, despite one of our early attempts to do so (Patin et al. 2014). Indeed, it is still debated in the anthropology community whether the complex socio-cultural relationships observed today between communities existed before the European colonization of the region, or not. Furthermore, recent seminal work about the demographic expansion of Bantu-speaking populations throughout the Congo Basin further question whether admixture processes emerged synchronically with the first encounters or whether they occurred only later after substantial societal changes for both groups of ancestral populations. More technically, we proposed in 2013 that sex-specific *cultural* transmission of the reproductive success varied across Pygmy and non-Pygmy populations throughout the Congo Basin, echoing previous propositions across human populations with different lifestyles (Blum et al. 2006). This has not been tested yet, and most, if not all, previous inference approaches were conducted under random matting assumptions; and, therefore, may be strongly biased. However, in general, a major difficulty for further investigating the evolutionary history of Central African populations remain the difficult access to extended datasets from the region. For instance, little is known today about the demographic history of Eastern Central African Pygmy populations, largely under-represented in studies and only recently investigated by ourselves, Pr. Luis Barbosa Barreiro (University of Chicago), and Pr. George H. Perry (Pennsylvania State University), and their respective teams (Perry et al. 2014). Most crucially, detailed anthropological information about the same individuals sampled for DNA is imperative, as I hope to have demonstrated here, and further renders the challenge... challenging. Furthermore, remember that population demographic census sizes are small throughout the Congo Basin and in particular in Pygmy populations. I thus fear that we may never reach sufficient sample sizes to achieve the statistical power needed to disentangle complex evolutionary forces having shaped the genetic diversity patterns observed today.

Finally, I hope to have illustrated here how interdisciplinary work between cultural anthropology and population genetics, rooted in joint field-work and extensive exchanges and discussions, can be fruitful for anthropological genetics and human population genetics. In return, I often published cross-disciplinary articles reporting these findings and discussions directly to the cultural anthropology community (Verdu 2012, 2014, 2016, 2019; Verdu and Austerlitz 2015; Perry and Verdu 2017). I would like to stress here that this is a substantial work in itself. Diffusing population genetics methods and paradigms is, I believe, essential for other non-experimental and non-biological disciplines to better understand what can and what cannot be said based on genetics results, as well as which novel questions population geneticists indeed bring to cultural anthropologists, and which questions are beyond the reach of population genetics. This has massively helped me to foster novel research projects and collaborations over the years, thus, in practice, illustrating the richness of such interdisciplinary approach. Again, the genetic history of a population is only one of its many histories, and while it is tempting to draw analogies across disciplines, they all have to be considered as hypothetical and further tested with the specific scientific methods deployed by either discipline, even in none experimental sciences.

Beyond its self-interest, reconstructing the neutral demographic history of Central African populations was absolutely crucial for better understanding the evolutionary history of these populations and identifying genomic signature of differential natural selection processes having shaped, or not, observed genetic variation at the root of phenotypic differences, as we will briefly overview in the following section.

<footnote n="43">⁴³ See also **Section 2.6** for ongoing perspectives on other key questions.</footnote>
**2.5. Admixture as a major force driving phenotypic diversity and evolutionary trajectories of Central African populations: what about height?**

Identifying the genetic factors determining non-pathologic phenotypic variation across individuals and populations rely classically in comparing allelic frequencies within and across groups of individuals categorized based on the phenotype of interest, similarly to the case-control approach extensively deployed in medical genetics. The goal is thus to identify correlations between given mutations and phenotypic variation providing candidate mutations further explored by functional genetics (real biology) to establish, or reject, a causality linking genotypes to the observed traits, and decipher the biological and bio-chemistry mechanisms from genotype to phenotype. In the statistical framework of association studies, the evolutionary history of mutations is not strictly necessary to identify them. However, the statistical testing itself relies on comparing allelic frequencies across groups of individuals, and sample stratification and cryptic genetic structure may strongly reduce the power needed to identify candidate mutations, and may dramatically increase rates of false-positive discovery, therefore rendering the whole investigation futile. It is thus crucial for bio-statisticians involved in association studies, and aiming at identifying the genetic determination of phenotypic traits, to consider subtle genetic patterns within and across studied groups, themselves the product of the evolutionary and demographic histories of the individuals.

Furthermore, identifying mutations whose distribution within and across populations and associated frequencies have been targeted by natural selection processes also heavily relies on knowledge of the neutral evolutionary history of humans. Indeed, human population geneticists looking for signatures of differential natural selection processes across human populations formally need to demonstrate that observed allelic frequencies cannot be obtained by just flipping a coin, a.k.a. by “sole” neutral demographic and drift processes. In this context, our work about the demographic reconstruction of neutral genetic variation patterns across Central African populations was also essential to further investigate possible different evolution across populations. Indeed, what about non-pathologic adult standing height genetic determination and evolution across shorter Pygmies and taller non-Pygmyes?

I hereby honestly reckon that I personally lack interest in working myself to identify the genetic determination of phenotypic variation in humans and its' evolutionary relevance... I am, unsurprisingly at that point of this document, vastly more interested in deciphering neutral evolutionary mechanisms. As a consequence, most of my work revolves around demographic inference from genetic data rather than exploring natural selection processes in humans. Nevertheless, I also reckon, and know from extensive experience, that "determining the genetic basis and evolutionary relevance of the short adult height of Central African Pygmies" is perhaps the essential question that drew the interest of Western evolutionary biologists to investigate these populations for more than a hundred years (see **Chapter 1.1**); which subsequently and incidentally allowed me to work...

Indeed, numerous anthropological biology hypotheses have been proposed to explain the observed shorter stature of Pygmy populations in Central Africa (Froment 1993; Perry and Dominy 2009; Becker et al. 2010, 2011). Evolutionary hypotheses proposed that it was:

i) a thermoregulatory adaptation to the hot and humid environment of the equatorial rainforest, or

ii) a morpho-mechanical adaptation to hunting and gathering efficiently in a dense environment, or

iii) a physiological adaptation to irregular and low availability of hunting and gathering nutritional produces in a diluted environment, or

iv) the by-product of an immunity adaptation to a highly challenging epidemiological environment, or
v) the by-product of an earlier onset of reproduction as an adaptation to high mortality rates triggered by both the hunting and gathering lifestyle and the challenging infectious environment, or, finally, vi) a combination of these hypotheses.

Conversely, numerous other anthropologists simply refused the evolutionary explanation to the reduced Central African Pygmy height, and rather considered this observed phenotypic trait as due to phenotypic plasticity resulting from high infection rates and insufficient nutritional intakes experienced by individuals during growth, but not adaptive on evolutionary scales in any ways.

Altogether, the debate has been raging since the 1950s at least, as the overall lack of demographic, epidemiological, and anthropological data from Central Africa never allowed to formally test these varied hypotheses satisfactorily. In fact, the heritability of the “pygmy phenotype” was not even assessed due to lack of data. Beyond the lack of data for formal testing, anthropologists had nevertheless gathered sufficient data to show the tremendous variation in adult height across the various Pygmy populations throughout the Congo Basin, a variation that was never explicitly explained in the previously proposed evolutionary hypotheses, and thus impaired their plausibility in a first place. Nevertheless, these hypotheses slowly transformed, over the years, into scientific known facts in the eyes of the non-specialized audience as well as in the eyes of numerous scientists.

In this context, and despite my relative lack of enthusiasm to dig into these very difficult questions, Pr. Evelyne Heyer and my student at the time Dr. Noémie Becker incited me to investigate the genetic determination of Pygmies' height. Our initial Central African dataset comprised extensive non-pathological adult height data, that I participated to collect on the field, and often associated with DNA samples from several Pygmy and some non-Pygmy populations categorized as such based only on cultural criteria. We initially only had microsatellite data for these individuals which rendered association studies impossible. However, Dr. Becker had the intuition that it might be worth to compare our phenotypic data with one major aspect of genetic variation across individuals and populations identified in our previous work: admixture levels (Verdu et al. 2009). I reckon I really did not think this could work, but I was wrong... Indeed, we found that individual standing and sitting height variation in Western Central African individuals categorized as Pygmies based on cultural criteria only, significantly strongly positively correlated with individual levels of admixture from the non-Pygmy gene-pool (Figure F2.5). In other words, the more a Western Central African Pygmy individual was genetically resembling the non-Pygmy gene-pool, the taller he or she was, on average (Becker, Verdu et al. 2011). To our knowledge, this was the first indirect proof that height differences between Pygmies and non-Pygmy were reflected in neutral genetic differentiation patterns, a single step beyond the possibility of a genetic determination of height differences evolutionarily relevant. Indeed, several other research teams replicated the result since, and we extended it at the genome-wide scale using tens of thousands of independent SNPs genotyped throughout the genome of Pygmy and non-Pygmy neighbors throughout the entire Congo Basin (Pemberton, Verdu et al. 2018).

Most importantly to my views, identifying that phenotypic differences significantly correlated with neutral admixture patterns had one essential dialectical consequence. It empirically showed that, beyond the elusive genetic determination of the “pygmy phenotype” chased by biological anthropologists, it might be much more productive for population geneticists to investigate the genetic determination of height differences between Pygmies and non-Pygmyes based on cultural criteria. Indeed, the focus had been almost exclusively set on explaining why Pygmies were shorter, and virtually never on why non-Pygmyes were
taller. Instead, our results showed the link between height differences and genetic admixture patterns, rather
than either phenotype taken separately<fnref n="44" />.

<figure><img src="image_28.png" /><figcaption>Figure F2.5.</figcaption></figure>

Positive correlation between individual height and individual levels of genetic resemblance with the non-Pygmy gene-pool.
Figure previously published in Becker, Verdu et al. *American Journal of Physical Anthropology* 2011
Note that the “Pygmy” and “non-Pygmy” populations’ categorization labels rely on numerous historical and cultural categorization
criteria, without considering height, characterized and discussed in Chapter 1.1.

Based on these results, Pr Barreiro and Pr Perry conducted the first full-blown association study on
novel anthropometrical and genetic data they had gathered in the Ba.Twa Pygmies from Southwest Uganda
and in their non-Pygmy neighbors, the Ba.Konjo. Most importantly, they used an admixture-mapping
approach, taking-into-account the genomic admixture structure of individuals and increased their power to
identify mutations potentially involved in height-differences determination between groups of populations
(Perry et al. 2014). Importantly, they did not identify the same genomic regions associated with height
differences between the few pairs of Pygmy and non-Pygmy populations they investigated in the West and,
respectively, in the East of the Congo Basin. Furthermore, they showed that either candidate mutations had
changed in frequency more rapidly than expected under neutrality. They thus concluded that natural
selection was at play for determining height differences across Pygmy and non-Pygmy populations, but that

<footnote n="44">⁴⁴ As a side note, this conceptual angle further echoes the ethnological approach of Frederik Barth that I favored in my anthropological genetics work; and approach interested in studying ethnic groups from the perspective of the dynamic boundaries they share rather than on a putative cultural nucleus defining them separately (see **Chapter 1**).</footnote>
different regions were the target of such evolution in different Congo Basin population. Hence, they advocated for convergent evolution of this trait after the divergence of Eastern and Western Pygmy populations, rather than a common origin of the genetic determination of height differences throughout the Congo Basin acquired in the ancestral Pygmy population.

Following this major work, we generated genome-wide SNP data in the much larger sample set that we had, but with much lower numbers of SNPs due to financial constraints (genotyping chips were really more expensive ten years ago). Our association study incorporating interindividual genetic differentiation and admixture patterns identified possible genomic regions and groups of mutations involved in height differences determination, further expanding the already vast list of genetic mutations possibly involved in non-pathologic height variation determination in humans in general. However, we could not produce convincing results as to natural selection signatures at these loci, in the face of the fundamental lack of power due to the high levels of genetic stratification and admixture across Central African populations investigated with too small a number of genetic markers (Pemberton, Verdu et al. 2018).

In this context, the team of Pr. Quintana-Murci and Dr. Patin set out, implicating us in their projects, to generate more data on our samples, and scanned differential natural selection signatures throughout the genomes of Central African Pygmy and non-Pygmy neighbors, without aiming at a particular phenotype, and, most importantly, taking-into-account explicitly the neutral demographic history of the investigated populations. This approach yielded tremendous novel insights into the evolutionary history of Central African populations in general, and further fed the debate about height differences' evolutionary relevance in particular.

In very brief, in a work led by Dr. Marie Lopez, PhD student in the Quintana-Murci lab at the time, we showed that the frequency of deleterious mutations and the efficiency of negative natural selection to sweep them was rather equivalent in Pygmies and non-Pygmy neighbors, based on whole-exome sequences. This was rather surprising: we expected genetic-load to be increased in Pygmy populations compared to their neighbors, as the formers did not experience effective size growth and even underwent recent bottlenecks (see previous sections in this chapter and **Figure 2.4.a** above). However, our results comparing Pygmies and non-Pygmies, taking-into-account explicit demographic “neutral” models of evolution for these populations via extensive simulations, showed that admixture from non-Pygmy neighbors effectively counter-balanced the accumulation of deleterious mutations in Pygmy populations (Lopez et al. 2018).

Furthermore, Dr. Lopez further showed in another important work that natural selection occurring after admixture from non-Pygmies into Pygmy populations maintained genetic variation acquired by this mechanism, further contributing to the genetic adaptation of Pygmies to their local environment, in particular with respect to immunity related pathways (Lopez et al. 2017). Importantly, in this paper, we further found strong signals of polygenic adaptation directly targeting genes and mutations previously shown to be involved in morphological traits and height. In turn, the large pleiotropy of these genomic variants resulted in a signal of adaptation for other pathways including life-history traits and the reduction of reproductive age. This result thus rejected the previous anthropological biology hypothesis stating that height phenotypes would be, instead of what we found, the indirect by-product of adaptation to high mortality rates assumed to be favoring an earlier onset of reproduction.

Finally, we showed that non-Pygmy populations had also benefited from the low levels of admixture from their Pygmy neighbors (Patin et al. 2017). Indeed, in another seminal article led by Dr. Patin and Pr. Quintana-Murci, we identified strong signatures of positive natural selection targeting immunity-related mutations in regions of the genomes of non-Pygmies particularly enriched in admixed segments from Pygmies compared to the rest of the genome and to expectations under neutral demographic models
incorporating admixture events as previously reconstructed. This result further showed the importance of admixture in natural selection processes, positive or negative, as a determinant force driving human evolution and possible adaptation to local environments.

Altogether, while the exact biological and bio-chemical mechanisms underlying non-pathologic phenotypic differences, including adult height differences, across Pygmy and non-Pygmy populations are still largely un-elucidated, anthropological genetics and population genetics’ work demonstrated over the past 15 years the evolutionary relevance of these phenotypic differences in general and of height-differences in particular, and showed the importance of admixture processes in having shaped them throughout the Congo Basin.
**2.6. Ongoing and future perspectives about the evolutionary history of Central African populations**

After more than 15 years of intense population genetics work on the evolutionary history of Central African populations, numerous fascinating questions remain to be addressed, some of which I investigate myself. As illustrated throughout this Chapter, ancient and recent admixture processes have played a key role in the genetic evolution of all human populations settling the Congo Basin today. However, while we acquired detailed knowledge about recent admixture processes, ancient admixture histories are still largely misunderstood (Figure F2.4.a). Indeed, while we know that we need to consider possible gene-flow exchanges in the remote past across ancestral lineages to explain the genetic diversity patterns observed today, we do not know when did they happen, between which ancestral populations, and how much gene-flow did they involve.

As a matter of fact, the question of ancient population structure and migration in the African continent as a whole is a very “hot” topic today in the human population genetics community (Schlebusch and Jakobsson 2018; Ragsdale and Gravel 2019; Bergström et al. 2021). The first essential question about ancient admixture in Africa stems from the past ten years’ discoveries of admixture events between the *Homo sapiens* lineage and other, now extinct, Neanderthal or Denisovan “archaic” hominid species, dated several tens of thousands of years ago in different regions of the world. Indeed, by comparing modern *Homo sapiens* genomes with newly generated ancient genomes from various Neanderthal samples in Europe, or Denisovan remains in Central Asia, population geneticists identified portions of non-African populations’ genomes originated from these other species, thus settling the fundamental debate of the existence of such events among paleo-anthropologists. In the lack of ancient remains clearly attributed to another species than *Homo sapiens* since its’ emergence some 300,000 years ago on the African continent, and in the lack of ancient genomes older than several thousands of years in Sub-Saharan Africa in general, it is extremely difficult to rule out that certain highly diverging portions of the genomes of extant African populations may derive from analogous ancient admixture events; a challenge that several research labs have taken.

Furthermore, the classical paleo-anthropological view of a single ancestral *Homo sapiens* population emerged in East Africa has long-lived. Paleo-anthropologists continuously revisit their models in the light of new discoveries and currently form a view of *Homo sapiens* emergence from numerous proto *Homo sapiens* from different regions of the continent in interaction with one another over long periods of time having eventually given birth to *Homo sapiens*. Population geneticists have also considered, for a long time now, that the speciation event for our species was likely rather a long, complex, and regionally sub-structured process, rather than a unique “Adam and Eve” event. Thus, two competing scenarios are explored today by populations geneticists at the root of genetic diversity patterns observed today in Africa (Ragsdale et al. 2022). The first model considers that *Homo sapiens* evolution in Africa in a remote past occurred in a tree-like manner, with sub-populations isolated for long periods of time after their respective divergences, with low levels of genetic migrations among them until much more recently. The second model considers rather a complex network of geographically separated populations nevertheless regularly exchanging genes over long periods of time followed by more recent geographic and cultural isolation until further gene exchanges in a much more recent past. These two views are, in fact, philosophically divergent as the former considers a somewhat classical isolation with possible migration Wright-Fisher island-model (Fisher 1922; Wright 1931) for the evolution of *Homo sapiens*, while the latter considers instead a continuous network of genetic movements in a “population” only defined by its contours rather than demes. It is from this ancestral
“meta-population” that the lineages ancestral to the extant populations would have emerged, those we investigate throughout the continent and at the root of all human genetic diversity worldwide.

I do not yet explore the fundamental questions detailed above first about ancient “archaic” admixture in African populations. Indeed, I think that without any reference of very ancient (> 10,000 years old) African genomes from unquestionably non-*Homo sapiens* remains as defined by paleo-anthropologists, such endeavors, while extremely interesting conceptually and methodologically, will be unable to convincingly bring new knowledge about the subject.

However, I currently extensively work with Pr. Mattias Jakobsson and Pr. Carina Schlebusch from Uppsala University, to reconstruct ancient admixture histories among *Homo sapiens* populations in Africa since the last 300,000 years. We conduct model-based inferences across numerous Central African and Austral African novel high-quality whole-genome sequences to address several nested questions. Namely, we investigate several possible tree-like topologies having given birth to observed genomic diversities and further try to distinguish whether ancient migration models, with recurring constant gene-flow over large periods of time, better fit the observed data than admixture models, where ancient admixture events occurred more punctually, all models taking-into-account the known much more recent gene-flow events described in our previous studies. This ongoing work was conducted mainly by Dr. Gwenna Breton during her PhD co-mentored by us three, and is currently being prepared for publication (Breton et al. 2020).

Beyond these fundamental questions about deciphering the influence of ancient admixture and migration events across ancestral African populations, as stated in **section 2.4** above, the recent history of admixture across Central African populations remains to be better understood. Indeed, our initial attempt at reconstructing the admixture history between Pygmies and non-Pygmies showed that these events occurred no earlier than 1000 years before present. However, the methods we used at the time could only consider over-simplistic models of admixture, and our results would be more accurately described as: “if admixture occurred at a single point in time in the history of Pygmy and non-Pygmy populations, then it would take at most 1000 years since then to obtain the genetic patterns that we observed today”; which is unsatisfactory when the question to address is rather “when and how did admixture events occurred in Central Africa”… In this context, the following chapters **3** and **4** recapitulate most of the theoretical and methodological research I have developed until today to build the population genetics tools which would allow us to reconstruct complex admixture histories from genetic data; which we will apply to the Central African context in a proximal future.

Finally, investigating the evolutionary history of natural selection’s influence on genetic diversity patterns in Central Africa still represents a substantial amount of my research endeavors in collaboration mainly with Pr. Quintana-Murci and Dr. Etienne Patin’s team, as well as with Pr. Zachary Szpiech (Pennsylvania State University). For this purpose, we have collected anew more than 400 DNA samples from four Cameroonian populations (2 “Pygmies” and 2 neighboring “non-Pygmies”), together with more than 20 anthropometric measurements and several basic physiological data for each volunteer participant. This project started in 2015 with Dr. Pemberton and initially funded by a national Canadian grant that we had obtained as co-PIs. Since then, my colleague completely retired academic research, and I am now in the process of rebuilding the project and securing funding to thoroughly investigate this unique novel data.
# Chapitre 3

A general theoretical framework for
investigating complex admixture histories
<figure><img src="image_29.png" /></figure>

Ribeira Grande de Santo Antão at dusk.
Santo Antão, Cabo Verde, 2016
©Paul Verdu
**Chapter 3. A general theoretical framework for investigating complex admixture histories**

During my PhD, I showed how complex socio-cultural behaviors shaped genetic diversity patterns in Central Africa, and, in particular, how admixture processes were deeply determined by these cultural forces. It was then clear to me that I wanted to further investigate complex admixture processes in human populations. My goal was to understand how the history of complex sociocultural relationships within and between communities triggered, or not, genetic admixture events; leaving a signature, or not, in genetic diversity patterns across human populations. This would also allow me to understand how complex admixture processes themselves acted to shape human genetic evolution.

In this context, I was very interested in studying the influence of recent socio-cultural changes on admixture processes in-turn having influenced genetic diversity patterns during the history of European colonization since the 15th century and the Trans-Atlantic Slave Trade (TAST). My initial, spontaneous, questions were: When did admixture between enslaved and non-enslaved communities started in the various colonial empires? Did the expansion of the Plantation Economy in the 17th century and the concomitant establishment of strong socio-marital segregation between communities throughout colonial empires, as enacted in the *Code Noir* or the *Sistema de Castas* for instances, modify admixture processes? Did the abolition of the TAST, during the first half of the 19th Century, change admixture processes? Did the abolition of slavery, during the second half of the 19th century, change admixture processes? Did the end of racial segregation and extensive voluntary migrations, in the second half of the 20th century, modify admixture processes?

In other words, I aimed at using observed genetic data in admixed populations descending from enslaved-Africans since the 15th century to reconstruct when did admixture events occur and how did they occur (intensity and duration), compare the obtained genetic results with major known historical processes, and determine which such processes had possibly influenced admixture patterns, and which did not translate in the book of our genetic evolution.

On these premises, I investigated the methodological tools available at the time in 2008 to the population genetics community for inferring complex admixture histories from genetic data. As explained briefly in **Chapter 1.2.a** above, admixture in general, and admixture among enslaved-African descendants in the Americas in particular, had been the focus of countless theoretical, methodological, and data-analyses investigations in population genetics since at least the 1930's, when the first statistical formalization of expected allelic frequencies in admixed populations was proposed (Bernstein 1931).

**Section 3.1** presents the classical population-genetics statistical framework for investigating admixture and migration processes from genetic data. **Section 3.2** then presents our general mechanistic admixture model. In **section 3.3**, we show how the distribution of admixture fractions in the admixed population may be informative about the underlying parameters of historical admixture models. **Section 3.4** then briefly presents our latest developments about the sex-specific generalization of our mechanistic admixture model. Finally, in **Section 3.5**, we present ongoing perspectives about theoretical investigations of complex admixture models.
**3.1. Classical mechanistic models of admixture**

Classically in population genetics, admixture is defined as a punctual exchange of genes between previously genetically isolated populations resulting in a novel “admixed” population. In this admixed population, allelic frequencies are expected to be a simple linear combination of allelic frequencies in the source populations, respectively, proportional to the relative contribution of each source to the gene-pool of the novel admixed population. Alternatively, classical migration models between two populations, or demes, as in Wright and Fisher’s island-models (Fisher 1922; Wright 1931), involved recurrent and constant exchanges of genes between otherwise genetically isolated populations over entire periods of time, resulting also in allelic frequencies in the receiver population being linear combinations of allelic frequencies in the receiver and source populations (Figure F3.1 below). Classical models of admixture thus considered a single founding admixture event (or pulse) over the entire history of the admixed populations, and migration models considered recurrent constant gene-flows over entire evolutionary periods (Long 1991).

<figure><img src="image_30.png" /><figcaption>**Figure F3.1.**
Classical models of admixture and migration. Adapted from Bernstein (1931), and Long (1991).
*F*<sub>1</sub>(A), *F*<sub>2</sub>(A), and *F*<sub>adm.</sub>(A) represent, the frequency of allele A in Source population 1, Source population 2, and the Admixed population after the founding admixture event, respectively.
*s*<sub>1</sub>, *s*<sub>2</sub>, and *h* are in [0,1] with *s*<sub>1</sub> + *s*<sub>2</sub>=1 or *s*<sub>2</sub> + *h* = 1 respectively.</figcaption></figure>

I was surprised to discover that virtually all the literature about admixture and genetic migration since
then considered simple mechanistic models very marginally differing<fnref n="45" /> from the original models of the
founders of the discipline. Until the 2005’s, it was as if the entire population genetics community
fundamentally agreed that admixture and genetic migration were major mechanisms of biological evolution
of all species, including humans, but were satisfied by the performances of over-simplistic such models for
their daily research, and despite perfectly admitting that these models were often not realistic at all. Indeed,
we have countless examples, in both humans and non-human species, for which we expect gene-flows to
have occurred at several points in time, or even during relatively short periods of time, and varying in

<footnote n="45">⁴⁵ For instance, asymmetric admixture and migration models where rapidly proposed as in **Figure F3.1**, but migration itself remained a constant recurrent process, and admixture remained a punctual event.</footnote>
intensity from either source populations and in time. Such likely more realistic models were thus impossible
to approach with classical models considering a single event of admixture or constant migrations over time.
I was under the impression, then, that population geneticists mostly pragmatically preferred to primarily
investigate genetic evolution within trees of isolated lineages, each under drift and mutation and natural
selection, and admixture and migration were “just” a supplementary layer of complexity, often only
considered as a necessary nuisance to the tree-like evolution, and only sometimes considered as the process
of interest. From my very reduced experience at the time, it rather intuitively seemed to me that all
populations may be practically seen by population geneticists as non-admixed, but just take a look and you
will inevitably always actually find complex admixture histories...

Numerous, elegant, efficient, and sometimes sophisticated statistical methods had been developed, and
are still developed, to identify admixture and estimate it in observed genetic data (Cavalli-Sforza and
Bodmer 1971; Chakraborty and Weiss 1988; Long 1991; Bertorelle and Excoffier 1998; Pritchard et al.
2000; Tang et al. 2005). To do so, one does not, strictly speaking, need to explicit the underlying
mechanistic model of admixture, whether complex or simple. Indeed, these statistical methods ultimately
aim at estimating the parameters of the linear combination of allelic frequencies from the sources in the
observed admixed population (Figure F3.1), rather than at disentangling when and how admixture and
migration occurred to produce, in the observed data, said admixture patterns.

Therefore, researchers over the years had sometimes punctually implemented more complex
mechanistic models for their specific statistical needs without generalizing nor thoroughly investigating
them, but most of the community interested in admixture inference to determine when and how did
admixture occur still relied on simplistic mechanistic approaches to admixture.

In this context, it became clear to me that I would need to build some complex mechanistic models
from scratch in order to be able to apply them to observed genetic data to address my specific questions of
interest. However, despite me not being afraid of mathematics and probabilities, at least as long as they
were not too complex, I had no empirical experience in mathematical formalization nor theoretical
population genetics. I therefore set out to look for a post-doctoral contract in order to fill this gap with this
project, and had the chance and luxury to interest Pr. Noah A. Rosenberg at the University of Michigan (at
the time) who enthusiastically proposed to me a position to pursue this endeavor with him (Verdu and
Rosenberg 2011).
**3.2. A general mechanistic model for admixture histories**

Despite my detailed specific questions about the TAST, I wanted to investigate a sufficiently flexible
general model possibly of interest to other problematics and other diploid and sexually-reproducing species.
Also, for my first theoretical work, I was afraid of having to treat the mathematics of continuous-in-time
genetic models and therefore, right from the beginning, decided to opt for discrete-in-time models without
possible overlapping generations. While this initial constraint was strongly reducing the array of possible
applications of my model, it was nevertheless of interest to numerous cases and, in any case, represented a
reasonable starting point. I therefore proposed the general model described schematically in **Figure F3.2.a**.

The first founding element of the model was how to define the admixed population itself (Verdu and Rosenberg 2011). Indeed, should the admixed population be composed only of genetically admixed individuals? Or should it be composed of individuals among which admixture was possible but not necessary? As explained in **Chapter 1.2.a** above, this was a categorization choice fundamentally influencing both the range of applicability of the model and how the model would be treated mathematically and probabilistically. Here, I chose to be comprehensive, which also incidentally made the model more general and easier to treat analytically: I decided to define the admixed population as a population where admixture could potentially occur, but may or may not occur. In other words, imagine an un-inhabited island at time 0, where and when two or more previously isolated populations disembark. Admixture between members of these source populations is then possible and may or may not occur. Under such definition, we expect *a priori* that admixture fractions from either source populations should be between 0 and 1, at each generation after the initial disembarkation.

<figure><img src="image_31.png" /><figcaption>Figure F3.2.a.</figcaption></figure>

General mechanistic model for admixture histories of hybrid populations.
Figure published as is in Fortes-Lima, Laurent et al. *Molecular Ecology Resources* 2021, where it
was re-drawn from its initial conception in Verdu and Rosenberg *Genetics* 2011.
We define the parameters of the general model in **Figure3.2.a** as follows:

- $g$ in [0..G], is the discrete number of generations since the founding of the admixed population at "time" 0 and until generation G. The duration of the evolutionary process here considered, whether admixture occurs or not, is thus G generations.

- $s_{i,g}$ in [0,1], is the parental contribution of source population $i$ in [1..M] to the admixed population at generation $g$.

- $h_g$ in [0,1], is the parental contribution of the admixed (hybrid) population to itself at generation $g$.

- Note that, henceforth, we often call $s_{i,g}$ and $h_g$ the “admixture parameters” at generation $g$.

By “parental contribution of source population $i$ to the admixed population”, or “by the admixed population to itself”, at generation $g$, we mean the proportion of biological parents coming from either source population, or the admixed population itself, having given birth to all individuals in the admixed population at generation $g$. In other words, pick a random individual in the admixed population at generation $g$, he/she has a probability $s_{i,g}$ (between 0 and 1) of having exactly one of his/her parent originating from source population $i$ at the previous generation, and a probability $h_g$ (between 0 and 1) of having exactly one parent from the admixed population itself at the previous generation. With such definitions, at each generation, all $s_{i,g}$ and $h_g$ sum to one.

This general model heavily differed from classical mechanistic models in that it could consider varying gene-flow at each generation from the same source as well as possibly different sources contributing to the gene-pool of the admixed population over time. Furthermore, defined as such, our model encompassed all classical admixture and migration models for particular values of model parameters. For instance, for constant values over time of the genetic contribution from a given source (for all values of $g$ in [0..G] and for a given $i$ in [1..M], $s_{i,g} = s_{i,g+1}$), and all other parameters set to 0 (for all values of $g$ in [0..G] and whichever $j$ in [1..M] different from $i$, $s_{j,g} = 0$), this general model formally becomes the classical unidirectional migration model from Long (1991) described in **Figure F3.1** above. Similarly, if only two source populations contribute to the gene pool of the admixed population synchronically at generation $g$ summing source contributions to 1, and all other admixture parameters from all other sources at all subsequent generations are set to 0, this comes down to the classical admixture model with two-source populations founding the admixed population at generation $g$.

Most importantly, I was obviously not the first one to have had thought off such intuitive, but complex, model for mechanistic histories of admixture. I much later found out, in fact while writing my paper, that this model had been proposed and investigated by Ewens and Spielman in 1995. However, these authors had not investigated this model for historical inference from genetic data, but rather to benchmark the influence of population subdivision and gene-flow on transmission disequilibrium tests (TDT). Similarly, note that it had been used once since, to my knowledge, by Guo et al. (2005) to examine linkage-disequilibrium statistics, and again not for developing demographic inferences nor to investigate the influence of the admixture process itself on the genetic evolution of admixed populations<fnref n="46" />.

Ideally, I would use genetic data to infer all admixture parameters at each generation; a somewhat utopic goal intuitively. However, I thought that genetic information might help identify at least some of

<footnote n="46">⁴⁶ Note that I was relieved after feverishly reading and re-reading these papers, thinking that all my work was in fact redundant before even submitted to a journal... I was then told by Pr Rosenberg and other colleagues versed in theoretical population genetics, that this very often happened in math: someone had sometimes thought about it before you. Fortunately, they also taught me that it was also rarely an issue as different points of views and formulations by different researchers on a given problem were also of major interest to researchers in theoretical mathematicised disciplines, even if the model was no longer as novel as I initially arrogantly thought...</footnote>
these parameters therefore allowing me to, a posteriori, compare results with expectations from historical data.

As a perfect illustration of my proposed research on genetic admixture in societies from the TAST-era, and further echoing **Chapter 1's** thesis about categories and categorization processes, the *Sistema de Castas* in Hispanic Americas (Ramos Pérez and Díaz-Trechuelo López Spínola 1992) in the 17th and 18th century defined social categories and accompanying segregation systems following a genealogical model recapitulated incompletely in the general admixture model here proposed.

As exemplified in the painting from the 18th century Mexico reproduced below (Figure F3.2.b): individuals were assigned to a named category of the society based on the origins of their parents (from either source or admixed populations in our model above), over no less than the sixteen previous generations, and with different possible source populations across continents: Europe/Spain ("Español/a", beware, see next), Sub-Saharan Africa ("Negro/a"), North Africa ("Moro/a"), or the Americas ("Indio/a"). However, compared to our model, far from all reproductive possibilities are evenly considered (not to say the least in this racist system...), as, for instances:

i) no categories are reported in this painting for admixed individuals between "Sub-Saharan Africa" and "America",

ii) some categories confusingly use the same name over generations across different origins of the parents, as for instance certain types of marriages over several generations produce offspring with a name similar to that of one of the source population: "Español" designated either a Spanish person from Spain, the offspring of Spanish parents in the Americas, or the offspring of a "Castizo" with an "Española", knowing that the "Castizo" is himself the offspring of a "Meztiso" with an "Española", and the "Meztiso" himself the offspring of an "Español" with an "India" from the Americas...

iii) note that reproduction events considered in this system are heavily sex-biased. For instance, while marriages with females from Sub-Saharan Africa ("Negra") or North Africa ("Mora") exist in this painting, there are no reports of marriages between males from either region...

This perfectly illustrated the type of questions I was interested in and why I needed a complete general mechanistic model of admixture to formally test them: how effectively did this highly complex social categorization and segregation system (which designated categories of admixed offspring with specific names over at least 16 generations!), translated, or not, in genetic admixture patterns observed in descendant populations today? Where the "missing categories" also missing in observed genetic admixture patterns? If yes, this would have meant that the system was highly prevalent and normative for all reproductive events which strictly conformed to it over many generations. If not, that would have highlighted a discrepancy between endogenous representations, social norms, and the realized behaviors of individuals, which would in-turn need to be explained by other social mechanisms allowing for the transgression of the norm.
<figure><img src="image_32.png" /><figcaption>Figure F3.2.b.</figcaption></figure>

Painting of the Sistema de Castas "a cuadretes", 18th century.
Museo Nacional del Virreinato, Tepotzotlán, Mexico.
https://commons.wikimedia.org/w/index.php?curid=4642698
### 3.3. Distribution of admixture fractions across individuals in the admixed population

Now that we had the general mechanistic model, which quantity of interest did we want to investigate under it? My previous investigations of admixture patterns in Central Africa (Chapter 2), had shown that variation of genetic admixture patterns across populations reflected socio-cultural behaviors regarding inter-marriages. I therefore thought to investigate how the parameters of our general admixture model influenced the distribution of admixture fractions across individuals within the admixed population. As numerous population genetics methods already existed to estimate individual admixture fractions from observed allelic frequencies in the admixed and the source populations, we could then, in principle, use this observed distribution to infer the parameters of the complex history of admixture that had given birth to our observations.

We therefore decided to define $H_{i,g}$, the probability for a random locus in a random individual in the admixed population at generation $g$ to have ultimately originated from source population $i$ (Verdu and Rosenberg 2011).

Thus, for a random individual in the admixed population at generation $g$, if we consider an infinite mutation model, then $H_{i,g}$ is the proportion of the genome of this individual ultimately deriving from source population $i$. In this framework, the density of probabilities of $H_{i,g}$ would represent the distribution of admixture fractions from population $i$ at generation $g$ in the admixed population; and all the moments of $H_{i,g}$ would fully describe this distribution; with the expectation, $E[H_{i,g}]$ being the mean admixture from source population $i$ in the admixed population at generation $g$, the variance $V[H_{i,g}]=E[H_{i,g}^2]-(E[H_{i,g}])^2$ would be the inter-individual variance of admixture fractions from source $i$ at generation $g$, and so on for all the higher moments of the distribution of $H_{i,g}$.

With the definitions of our general model, we could easily write a recursion relation to calculate $H_{i,g}$, for any one source population $i$, as a function of all model parameters based on all possible pairs of parents for a random individual in the admixed population, denoted $Y$, at the previous generation (see Verdu and Rosenberg 2011 Supplementary materials p.2):

“For the first generation ($g = 1$), for any mutually distinct values of $i, j$, and $l$ between 1 and $m$, we have

$$H_{i,1} = \begin{cases} 1 & \text{if } Y = S_i S_i, \text{ with } P[Y = S_i S_i] = s_{i,0}^2 \\ \frac{1}{2} & \text{if } Y = S_i S_j, \text{ with } P[Y = S_i S_j] = 2s_{i,0}s_{j,0} \\ 0 & \text{if } Y = S_j S_j, \text{ with } P[Y = S_j S_j] = s_{j,0}^2 \\ 0 & \text{if } Y = S_j S_i, \text{ with } P[Y = S_j S_i] = 2s_{j,0}s_{i,0}. \end{cases} \quad (S1)$$

For all subsequent generations ($g \ge 2$), we have
$$
H_{i,g} = \begin{cases}
1 & \text{if } Y = S_i S_i, \text{ with } P[Y = S_i S_i] = s_{i,g-1}^2 \\
\frac{H_{i,g-1} + 1}{2} & \text{if } Y = S_i H, \text{ with } P[Y = S_i H] = 2s_{i,g-1} h_{g-1} \\
\frac{1}{2} & \text{if } Y = S_i S_j, \text{ with } P[Y = S_i S_j] = 2s_{i,g-1} s_{j,g-1} \\
\frac{H_{i,g-1}^{(1)} + H_{i,g-1}^{(2)}}{2} & \text{if } Y = HH, \text{ with } P[Y = HH] = h_{g-1}^2 \\
\frac{H_{i,g-1}}{2} & \text{if } Y = S_j H, \text{ with } P[Y = S_j H] = 2s_{j,g-1} h_{g-1} \\
0 & \text{if } Y = S_j S_j, \text{ with } P[Y = S_j S_j] = s_{j,g-1}^2 \\
0 & \text{if } Y = S_j S_i, \text{ with } P[Y = S_j S_i] = 2s_{j,g-1} s_{i,g-1}.
\end{cases} \quad (S2)
$$

Here, $H_{i,g-1}^{(1)}$ and $H_{i,g-1}^{(2)}$ are fractions of ancestry from source population $S_i$ for the two parents of a hybrid individual at generation $g$ with $Y = HH$. We use the superscripts (1) and (2) only to indicate that $H_{i,g-1}^{(1)}$ and $H_{i,g-1}^{(2)}$ are independent and identically distributed (IID) random variables, so that if an individual in population H at generation $g$ has two parents from H, the admixture fraction is distributed as the mean of the admixture fractions for two IID random individuals from H in the previous generation.”

From there, using the law of total expectations and the binomial theorem, we derived recursion relations for all *k*-moments of the distribution of admixture fractions from one source population *i* at generation *g* (see Verdu and Rosenberg 2011 Supplementary materials p.5):

"For *g* = 1, we have for *k* ≥ 1 and any *i* from 1 to *m*,

$$
E[H_{i,1}^k] = s_{i,0}^2 + \frac{s_{i,0}}{2^{k-1}} \sum_{\substack{j=1 \\ j \neq i}}^{m} s_{j,0}. \qquad (S9)
$$

For $g \ge 2$, we have

$$
\begin{equation}
\begin{split}
E[H_{i,g}^k] = {}& s_{i,g-1}^2 + \frac{s_{i,g-1} h_{g-1}}{2^{k-1}} \sum_{r=0}^{k} \binom{k}{r} E[H_{i,g-1}^r] \\
& + \frac{s_{i,g-1}}{2^{k-1}} \sum_{\substack{j=1 \\ j \neq i}}^{m} s_{j,g-1} \\
& + \frac{h_{g-1}^2}{2^k} \left( \sum_{r=0}^{k} \binom{k}{r} E[H_{i,g-1}^r] E[H_{i,g-1}^{k-r}] \right) \\
& + \left( \frac{h_{g-1}}{2^{k-1}} \sum_{\substack{j=1 \\ j \neq i}}^{m} s_{j,g-1} \right) E[H_{i,g-1}^k].
\end{split}
\tag{S10}\]
$$
From here, and without further re-doing here the whole previous publication, we could analytically solve,
or numerically compute, these recursions to show numerous things detailed in our initial 2011 publication
and following published developments.

For the simplest example, under the classical admixture scenario with two source populations founding
the admixed population at time 0, and then no longer further contributing to the admixed population (Figure
F3.3.a), the above equations simplify to give us, for all g > 0, E[H₁,g]= s₁,₀; meaning that the average
admixture fraction across individuals in the admixed population from source population 1, should reflect
the initial contribution of source population 1 to the gene-pool of the admixed population under this simple
model.

Furthermore, under the same model, we could solve the second moment to then obtain, for all g > 0,
the variance V[H₁,g] = s₁,₀(1-s₁,₀) / 2g, therefore a function of the funding admixture parameter and time since
that event.

Therefore, if admixture occurred in such a way in an observed population today (a single event back
g+1 generations since the DNA sampling), by estimating the distribution of individual admixture fraction
from one of the source population from genetic data, calculating simply it's mean (M) and variance (V)
would directly give us (within all the fundamental assumptions, and thus limitations, of our general model
described above), its initial intensity (s₁,₀ = M) and when did the admixture event occurred with g= (ln[M(1-
M)] - lnV)/ln2 (see **Figure F3.3.a** below).

More generally, we hereby showed that, theoretically, the shape of the distribution of admixture
fractions across individuals within the hybrid population, its observed range and estimated mean, variance,
kurtosis, skewness, etc, carried substantial information about all the parameters of the underlying highly
complex admixture process that had given birth to our observations. Furthermore, different distributions of
admixture proportions from a given source population between different target admixed population would
reflect different admixture histories experienced respectively.
<figure><img src="image_33.png" /></figure>

$$E[H_{1,g}] = s_{1,0}.$$

$$V[H_{1,g}] = \frac{s_{1,0}(1 - s_{1,0})}{2g}.$$

$$g = \frac{\ln[M(1-M)] - \ln V}{\ln 2}.$$

$g = 1$

$P(H_{1,g})$

$s_{1,0} = s_{2,0} = 0.5$

$s_1 = s_2 = 0$

$s_{1,0} = 0.7 \ ; \ s_{2,0} = 0.3$

$s_1 = s_2 = 0$

$g = 2$

$P(H_{1,g})$

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>

...

<figure><img src="image_36.png" /></figure>

<figure><img src="image_37.png" /></figure>

...

...

$g = 5$

$P(H_{1,g})$

<figure><img src="image_38.png" /></figure>

<figure><img src="image_39.png" /></figure>

...

...

$g = 10$

$P(H_{1,g})$

<figure><img src="image_40.png" /></figure>

<figure><img src="image_41.png" /></figure>

$H_{1,g}$

$H_{1,g}$

<caption>Figure F3.3.a.</caption>

Examples of the density distribution of the admixture fractions $H_{i,g}$ from one of the source populations ($i = 1$) in the simplest version of Verdu and Rosenberg (2011) general mechanistic model of admixture presented in the top-left panel, over 10 generations after the founding admixture event. One can see that, over time, the variance of admixture fractions in the admixed population diminishes while the mean remains constant in such simple classical admixture models.

See Verdu and Rosenberg (2011) equations 3-5 for the analytical expression of $P(H_{1,g})$ under any two-population version of the general mechanistic model presented in Figure F3.2.a.
All this theoretical ambition was challenged, in practice, by a simple fact, beyond the inherent simplifying assumptions of the model for representing “reality”. Can we estimate the distribution of admixture fractions, even in an ideal pseudo-observed population, with sufficient accuracy to identify the parameters of the underlying complex admixture history model in a first place?

With Pr. Erkan O. Buzbas (University of Idaho), at the time a post-doctorate fellow in Pr. Rosenberg lab, we set out, schematically, to evaluate when past admixture parameters of a complex admixture model would cease to be identifiable from the distribution of admixture fractions in the admixed population (Buzbas and Verdu 2018). We considered two two-source-populations versions of our general model: one with a single period of recurring constant admixture, and the other with two consecutive periods of recurring constant admixture, with different constant admixture parameters, respectively. First, we found analytically that, for any model with constant recurring admixture, admixture fractions estimated from diagnostic bi-allelic markers (whose alleles discriminated between the two source populations), inevitably would reach a stationary distribution, and would do so rather rapidly as a function of the precision of our estimations of admixture fractions, within 50 generations at most. This fundamental result is numerically illustrated in **Figure F3.3.b** below, reproduced and adapted from Figure 2 in Buzbas and Verdu (2018).

Second, we found that, when this stationarity would be achieved, model parameters from the preceding period of admixture as well as the duration of the second period of admixture would irremediably be un-identifiable only from the admixture patterns observed in the admixed population (see Figure 5 in Buzbas and Verdu 2018).

These results demonstrated what could be intuitively appreciated from the results of our analytical developments of the general model of complex admixture histories (e.g. **Figure F3.3a**). First, admixture fractions in the admixed population rapidly reach stationarity when the admixture process is recurrent and constant over time. Importantly, note that, a model with a single founding pulse of admixture without subsequent admixture falls into this definition: after the pulse of admixture, the model is a recurrent constant admixture model of intensity 0 from either source. Second, once this stationarity is achieved, observed admixture fractions are only informative about the intensity of this recurring admixture process, and no longer informative about its duration. Finally, when stationarity is achieved, all other older admixture processes having preceded the last period of admixture experienced by the population, are irremediably impossible to infer from admixture fractions only. Thus, while admixture fractions inherently carry extensive information about the underlying complex admixture process, model parameters may still be un-identifiable.

In practice, this meant that a relatively recent admixture process could completely obliterate the signatures in the distribution of admixture fractions inherited from the process having occurred before, and it could do so as a function of the duration of the last process ongoing until sampling in the admixed population. The limit would be 50 generations of no admixture until sampling which would only leave the footprint of the intensity of the last admixture pulse in the admixture fraction and not even how old was this last event, but could also be much more rapidly un-identifiable if the distribution of admixture fractions were not accurately estimated.
<figure><img src="image_42.png" /><figcaption>**Figure F3.3.b.**</figcaption></figure>

Time to convergence to the stationary distribution of admixture fractions under the model described in the top-left panel: after a founding pulse of admixture, the admixed population experiences recurring constant admixture from both source populations until sampling in generation *t*.

Time to convergence increases with the much larger contribution of the admixed population to itself over time (h~1), and with estimation precision of admixture fractions. Note that for low precision estimates (10⁻¹), convergence to stationarity is achieved within a few generations for relatively low values of *h* (~10%), thus for historical models where the admixed population is largely founded anew at each generation.

Reproduced and adapted from Figure 2 in Buzbas and Verdu *Theoretical Population Biology* 2018.

<figure><img src="image_43.png" /></figure>

<figure><img src="image_44.png" /><figcaption>III.</figcaption></figure>

<table><thead><tr><th rowspan="2"></th><th colspan="8">Precision</th></tr><tr><th>10<sup>-1</sup></th><th>10<sup>-2</sup></th><th>10<sup>-3</sup></th><th>10<sup>-4</sup></th><th>10<sup>-5</sup></th><th>10<sup>-10</sup></th><th>10<sup>-12</sup></th><th>10<sup>-16</sup></th></tr></thead><tbody><tr><th>h</th><td>0.09</td><td>2</td><td>3</td><td>3</td><td>4</td><td>6</td><td>9</td><td>11</td><td>13</td></tr><tr><th></th><td>0.19</td><td>2</td><td>3</td><td>4</td><td>5</td><td>7</td><td>12</td><td>14</td><td>16</td></tr><tr><th></th><td>0.29</td><td>2</td><td>4</td><td>5</td><td>6</td><td>13</td><td>14</td><td>17</td><td>19</td></tr><tr><th></th><td>0.39</td><td>3</td><td>4</td><td>5</td><td>7</td><td>15</td><td>17</td><td>19</td><td>22</td></tr><tr><th></th><td>0.49</td><td>3</td><td>4</td><td>6</td><td>8</td><td>17</td><td>19</td><td>22</td><td>27</td></tr><tr><th></th><td>0.59</td><td>2</td><td>4</td><td>6</td><td>8</td><td>19</td><td>21</td><td>25</td><td>29</td></tr><tr><th></th><td>0.69</td><td>2</td><td>4</td><td>7</td><td>9</td><td>22</td><td>24</td><td>28</td><td>34</td></tr><tr><th></th><td>0.79</td><td>2</td><td>4</td><td>7</td><td>9</td><td>24</td><td>27</td><td>32</td><td>39</td></tr><tr><th></th><td>0.89</td><td>2</td><td>4</td><td>7</td><td>10</td><td>27</td><td>30</td><td>35</td><td>42</td></tr><tr><th></th><td>0.99</td><td>1</td><td>2</td><td>6</td><td>9</td><td>28</td><td>32</td><td>38</td><td>46</td></tr></tbody></table>
**3.4. A sex-specific version of the general mechanistic admixture model**

With Dr Amy Goldberg (Duke University), a master student under my supervision for one year at Pr. Rosenberg lab, we developed our general admixture model to encompass explicitly sex-specific contributions from either source populations to the gene-pool of the admixed population, as well as that of the admixed population to itself, over time (Figure F3.4.a). Indeed, admixture process often occur in a sex-biased manner in humans and non-human species (e.g. Verdu et al. 2013, see Chapter 2), and we wanted to investigate how such processes may influence the distribution of admixture fractions over time. Furthermore, this development would allow us to investigate expected admixture fractions from different types of chromosomal compartments, namely autosomes, X-chromosome, Y-chromosome, and mitochondrial DNA, separately, to further gain information on the underlying complex admixture process from comparisons among autosomal and sex-specific genetic data (Goldberg et al. 2014).

<figure><img src="image_45.png" /><figcaption>Figure F3.4.a.
Sex-specific two-population version of the general mechanistic model of Verdu and Rosenberg 2011.
Figure reshaped from Figure 1 in Goldberg, Verdu and Rosenberg Genetics 2014</figcaption></figure>

We investigated analytically and numerically the distribution and moments of sex-specific admixture fractions in the admixed population as a function of all model parameters, with the exact same dialectic as in Verdu and Rosenberg 2011. We did so “simply” by explicitly decomposing in our recursions the two parents of a random individual in the admixed population as a male and a female parent, for each source and admixed population at each generation. In brief, we found out that, even for classical simple or recurring
constant admixture processes, the distribution of admixture fractions in the admixed population estimated
from autosomal data was influenced by sex-biased admixture processes. Indeed, we found that a strongly
sex-biased admixture process, with all males from one source population and all females from the other
(for an extreme instance), diminished the variance of the distribution of admixture fractions over time more
rapidly than a more equilibrated sex-specific admixture process, while the mean admixture fraction would
not be affected. For one possible intuitive explanation of the phenomenon: under such strongly sex-biased
admixture process and in particular when the total contributions from the source populations are uneven
(one contributes more than the other), the effective sizes in the source populations from which parents are
drawn are *de facto* reduced, compared to non-sex-biased processes, hence producing admixture patterns
less variable in the admixed population (Goldberg et al. 2014).

This theoretical result was both good and bad news. Inferring complex admixture parameters from
autosomal data only could result in biased estimates, if a sex-biased admixture process in fact occurred. In
other words, in certain parts of the parameter space, a given distribution of admixture fractions estimated
from autosomal data could be obtained with two very different complex admixture models with different
parameters (duration and admixture rates), one sex-biased and the other not. The good news was that the
parameters of complex sex-specific admixture models could be identified by contrasting the distribution of
admixture fractions obtained from the admixed population using, separately, autosomal, X-chromosome,
Y-chromosome, and mitochondrial data; each chromosomal compartment carrying specific information
about the different parameters of the model.
**3.5. Perspectives for theoretical developments of complex admixture histories models investigated with genetic data.**

Numerous developments of this general theoretical framework are of interest for future analytical work investigating the behavior of complex admixture processes influencing genetic diversity patterns. Among others, a major primary interest to me in my future endeavors is to introduce parameters specifically controlling non-random matting processes in the admixed population. Indeed, we considered here only random matting in the admixed population, whether sex-biased or not. However, admixture processes in numerous populations are likely not random.

For instance, hybrid depression in plants can often be due to individual admixture fractions determining different flowering periods across individuals differently admixed, thus preventing matting among individuals with different genomic admixture landscapes. This classical phenetic consequence of admixture in plants would thus be much better modeled by a general model with an assortative matting parameter itself a function of individual admixture fractions (e.g. Escobar et al. 2008).

For another example of primary interest to my research: admixture processes during the TAST are known to have been strongly sex-biased, in particular during the Plantation Economy era (see **Chapter 5**), but were also highly stratified across socio-economic classes during the colonial history of European monarchic empires. Indeed, social norms would also influence (prevent) marriage opportunities among aristocrats, bourgeois, and lower classes, bourgeois and lower classes being more likely to over-represent genetically admixed individuals compared to aristocrats (Berlin 1998; Carreira 2000; Eltis 2002; Eltis and Richardson 2015). Therefore, complex socio-cultural behavior regarding marriages in socially stratified populations may result in non-random matting processes further related to the genetic admixture histories of the admixed population. I am therefore in the process of explicitly parameterizing non-random processes in admixed populations under our general model, and similarly investigate its effect analytically on the distribution of admixture fractions over time; a work still in progress today (see **Chapter 5**).

Finally, an intuitive and very promising development for the novel theoretical framework here developed would be to investigate, under the same general mechanistic model, another quantity of major interest to the investigation of admixture processes: the distribution of length of admixed-chunks from each source populations along the genomes of individuals in the admixed population over time. Indeed, since at least the formalized “junction” theory of Fisher (Baird 2006), introducing the notion of admixed-chunks of chromosomes due to recombination in the genome of admixed individuals, we expect the distribution of length of admixture segments in high-LD along the genome of admixed individuals to bear extensive information about the admixture process and in particular about the time since admixture events. This was thus a very promising development for our theoretical framework... which was brilliantly developed independently from us and published the year after our initial paper by Pr. Simon Gravel (McGill University), a post-doctorate student in a neighboring Stanford lab at the time (Gravel 2012). The fantastic paper from Pr. Gravel deployed the exact same mechanistic model inspired from Ewens and Spielman (1995) as the one we proposed, and derived under it the expected distribution of admixed-chunks lengths from each source populations. Most importantly, Pr. Gravel did not “only” conduct analytical investigations as we did in our paper, but further provided a readily usable algorithm implemented in a software, TRACTS, allowing to infer model parameters deterministically from observed distribution of admixture LD. This, very legitimately, brought extensive attention from the human population genetics community that, since then, has extensively used TRACTS to infer the complex admixture models underlying observed genetic patterns. Despite this immense success, however, similarly to us, Pr. Gravel could not derive closed forms
of the expected distribution of admixed fragments lengths for admixture models encompassing more than
two punctual pulses of admixture. As a consequence, observed data could only be fitted to exponential
curves expected under either single or two-pulse scenarios over the entire admixture history of the admixed
population. As acknowledge and extensively discussed by the authors in methodological papers developing
on Pr. Gravel’s seminal approach, this was a computational limit of these approaches forbidding empirically
to investigate more complex admixture processes possibly underlying the observed data (Gravel 2012;
Hellenthal et al. 2014).

We thus proposed to overcome at least in part this limitation with the novel ABC framework presented
in the following Chapter.
# Chapitre 4

***MetHis:*** a novel Approximate Bayesian
Computation framework for reconstructing
complex admixture histories from genetic
data
<figure><img src="image_46.png" /></figure>

Alto Mira.
Santo Antão, Cabo Verde, 2016
©Paul Verdu
**Chapter 4. *MetHis: a novel Approximate Bayesian Computation framework for reconstructing complex admixture histories from genetic data***

I introduced Approximate Bayesian Computation methods in **Chapter 2.2** above (Tavaré 1997; Pritchard et al. 1999; Beaumont et al. 2002), emphasizing on how flexible and promising these inferences approaches were. Indeed, in principle, models of an arbitrary complexity could be inferred from genetic data with ABC, provided that simulations under said models could be efficiently performed, and provided that summary-statistics would carry identifiable information about the underlying model-parameters. Therefore, as other maximum-likelihood approaches were inherently unable to consider admixture models more complex than two-admixture pulses’ models (see **Chapter 3.5**), I decided to opt for ABC inference using the general model presented in **Chapter 3**.

Indeed, we had shown theoretically that the distribution of admixture fractions in the admixed population carried substantial information about the model-parameters of the underlying complex admixture process (Verdu and Rosenberg 2011). Therefore, as numerous population genetics statistical methods already existed to infer individual admixture fractions from varied source populations in the observed admixed population, we could readily use them to obtain the distribution of admixture fractions observed from genetic data, and use this distribution, or rather the statistics describing it such as its’ mean, quantiles, variance, kurtosis, and skewness, as summary-statistics for ABC inference with our general admixture model. Therefore, I “just” needed to be able to simulate large amounts of realistic genetic data under the general model, calculate summary statistics on each simulation including statistics describing the distribution of admixture fraction in the sampled admixed population, and then use the obtained reference tables of vectors of model parameters used for each simulation associated with the corresponding vector of summary-statistics, to apply existing ABC algorithms to perform ABC scenario-choice and posterior-parameter inferences using observed genetic data (Figure F4).
<figure><img src="image_47.png" /><figcaption>Figure F4.</figcaption></figure>

Schematic general workflow of complex admixture history inference from genetic data using Approximate Bayesian Computation
Freshly recruited in the CNRS in 2012, and appointed to my former lab UMR7206 Eco-anthropology under the direction of Pr. Bahuchet and Pr. Heyer, I set out to fulfill this apparently sound endeavor (Figure F4), but rapidly hit a completely foreseeable wall I had nonetheless not expected: simulating data under the general admixture model we had proposed was not trivial. Indeed, I naïvely thought that I could readily use existing fantastic coalescent-based simulators such as *MS-MS* (Ewing and Hermisson 2010) or *FastSimcoal* (Excoffier and Foll 2011), and simply implement the versions of admixture or migration fitting my complex admixture models. It turned out that, while indeed these simulators can be efficiently adapted to simulate data under the general model, the nature of classical coalescent simulations where not fitting the fundamental definition of our models.

Indeed, classical coalescent approaches reconstruct different genetic pedigrees underlying each observed genetic marker while, in our models, each individual's genome stem from a single genealogical pedigree. As a result, when conducting classical coalescent simulations under the simplest admixture scenario from two source populations, at the first generation after the admixture event, all simulated individuals show the same admixture fraction from one of the source populations, proportional to the intensity of the admixture parameter set for the simulation. We thus do not have individuals with 0%, 100%, or 50% admixture from this source at the first generation, with a mean of the distribution of individual admixture fractions in the admixed population close to $s_{1,0}$, the intensity of the founding admixture event from one of the source populations, as expected in Verdu and Rosenberg 2011 (see Chapter 3). Instead, we obtain all individuals with a proportion of admixture close to $s_{1,0}$ at the generation after the admixture event under the coalescent, as each independent markers are coalescing within this source population with probability $s_{1,0}$, per definition. To convince one-self of this possible caveats, I had the chance to supervise Dr. Marguerite Lapierre, master student at the time, to conduct series of coalescent simulations showing exactly the patterns expected above at odds with the theoretical expectations from our general admixture model.

Therefore, to mimic our general admixture model using existing backward-in-time simulators under the coalescent, we first needed to define pedigrees for each sampled individual in the admixed population, and then conduct coalescent simulations of genetic markers within these pedigrees. Such approach first simulating a full pedigree, and then simulating under the coalescent within this pedigree, had been brilliantly proposed in 2012 by Wakeley et al., to further investigate natural selection processes under the coalescent, for models possibly comprising admixture across populations. However interesting, I was left with the need to first simulate pedigrees, a complex task in itself as I needed to set priors and processes that I barely knew anything about in human populations in general, nor in admixed populations related to the TAST.

In this context, I decided to build my own genetic data simulator under our general mechanistic model of complex admixture histories. I decided to opt for a forward-in-time simulator as only such approach would allow the flexibility that I needed to consider any version of this general model fully parameterizable by the user, and as I thought this would yield the most potential for future developments implementing non-random matting or admixture-related natural selection processes (see section 4.3 below). Furthermore, I would need to design this simulator for performing efficiently under ABC; which meant with parameter-priors easily set by the user, drawing large numbers of vectors of parameter values from these priors readily usable to perform numerous simulations as needed for ABC. In turn, we would need to efficiently calculate summary statistics for each simulation in order to obtain the two reference tables, one for the vectors of parameter values and the other for the corresponding vectors of summary statistics.
**4.1. *MetHis software for simulating data and calculating summary-statistics under the Verdu and Rosenberg 2011 general mechanistic model of complex historical admixture***

After obtaining funding from the French ANR in 2015-2016 for five years, I could hire a post-doctoral student, Dr. Cesar A. Fortes-Lima (University of Uppsala), to start implementing such simulator and conduct an initial proof of concept. Indeed, ABC is an *a posteriori* class of inference method. In practice, this means that, as explained above, once it is determined that ABC can work in principle, then one has to perform the ABC analysis until the end to actually determine whether it has worked in the specific study-case, or not. The good news is that, even if it does not work *a posteriori*, one will be able to determine in details which step of the process failed, and why; whether simulations were unable to mimic the observed data, whether summary-statistics were overall uninformative about model parameters, whether the parameter space was too large producing high-dimensional summary-statistics spaces in which different ABC inference approaches get lost and fail to produce posterior parameter distributions departing from their priors, or else.

Dr. Fortes-Lima managed to build a first pre-alpha version of the software following the algorithm I had designed (below), in Python language. After we had shown that indeed, this could produce genetic data whose behavior were very closely predicted by our analytical expectations under the model, we decided that a full-blown C version of our preliminary software was worth producing for publication to the community. However, after 18 months of post-doctoral contract with me, Dr. Fortes-Lima had another opportunity at Dr. Schlebusch's lab in Uppsala, which I supported him for as it provided him with data analyses opportunities more aligned with his ambitions than the methodological work conducted with me.

As I did not know how to code in C, I started looking for private services possibly interested in translating our initial software into C, and failed to find any for such specific fundamental research endeavor. Fortunately for me, I managed to get Dr. Romain Laurent, Research Engineer in the lab, interested in the project, thanks to our initial proof of concept. I had long known Dr. Laurent, and his skill, enthusiasm and scientific rigor ultimately allowed this project to be completed with success. We have worked extensively together on this project on a daily basis for more than eight months, but I need to emphasize here that he is the one who really built the software's code, and I have only assisted him for general algorithmic and detailed scientific strategic choices and posterior benchmarking and checks, but I did not write the code myself for this software, even if I conducted myself most subsequent ABC inferences.

We thus produced and benchmarked a novel software, called *MetHis*, coupled with existing ABC tools for scenario-choice and posterior-parameter inferences using genetic data, and specifically designed for investigating complex admixture histories (Fortes-Lima, Laurent et al. 2021). While this method and results are extensively described in the resulting publication in *Molecular Ecology Resources* (2021), where interested-readers shall find in a synthetic scientific way all the needed information to re-use our methods and tools, I decided to explain below how and why several choices were made during the process, to better explain its dialectics. I will then very briefly summarize results from the publication. Finally, I will further expand on ongoing methodological implementations, as well as future perspectives for this new set of population genetics tools.
### 4.1.a. Simulating genetic data under the Verdu and Rosenberg 2011 model

As previously said in **Chapter 1** and in **Chapter 3**, I was ultimately interested in reconstructing the complex admixture histories of enslaved-African descendants admixed populations since the 15th century on either side of the Atlantic. Previous extensive human population genetics investigations had shown that, in numerous such populations in the Americas, including the Afro-American communities in the USA, admixture patterns had occurred mainly between European and African continental source populations (e.g. Baharian et al. 2016; Mathias et al. 2016; Micheletti et al. 2020; Fortes-Lima and Verdu 2021).

*How many source populations did we want to consider in our simulations?*

I therefore decided to opt for building our genetic data simulator for the two-source population version of our software. This was a pragmatic choice substantiated by the very definition of our general mechanistic model. Indeed, while M possible source populations for the admixture of an admixed population would have been, in many study-cases, more suitable, it was far easier to start with a two-source population model. Furthermore, in **Chapter 3** we investigated the influence of complex M population admixture models on the distribution of admixture fraction across individuals within the admixed population, but calculated for a single given source population at the time. In other words, while admixture could stem from many sources, we would investigate the history of admixture specific to each source population, separately and in turn. In this framework, a two-source population version of our model could be used sequentially, one source population being the targeted population from which we would reconstruct introgression into the admixed population, and the other source population could, conceptually, embed all other source populations involved in the admixture process (“one minus the targeted source population”). Then another of these populations could be the focus, while the second source population would embed all other remaining sources, including, this time, the first source that we had previously investigated. Therefore, while conceptually not as satisfactory as readily building a simulator for M source populations, the simple two source population models could, in principle, be hijacked for investigating indirectly M source population models, an interesting trade-off knowing the complexity of building, from scratch, a genetic data simulator with numerous possible source populations.

*Which populations in our models did we want to simulate?*

We then decided that our simulator would focus on simulating data in the admixed population over the mechanistic history of admixture from $g = 0$ until the present, when a sample mimicking the observed one would be drawn from the admixed population and used for summary statistics calculation. We thus decided not to simulate the genetic evolution of the source populations during the admixture process, but instead obtain the source population data, either from observed data for recent admixture histories (such as the TAST histories of admixture which only occurred within the roughly last 20 generations until today), or using simulations under a classical coalescent to generate data from isolated source populations that our simulator would then take as input for simulating the admixed population.

*Which type of genetic data did we want to simulate?*

Previous complex admixture histories reconstructed with maximum-likelihood approaches, such as TRACTS (Gravel 2012) or GLOBETROTTER (Hellenthal et al. 2014), required massive amounts of data to operate satisfactorily, as patterns of admixture LD decays had to be estimated along the genomes of admixed individuals. This often required several hundreds of thousands of SNPs, which represent still a
substantial financial investment not easily obtainable even for human genetics investigations, and clearly
out of reach of most non-human species.

We did not need a priori such extensive data to estimate inter-individual distribution of admixture
fractions in the admixed population, from which we hoped to gain sufficient information for parameter
estimation, theoretically. We therefore opted to simulate any number of autosomal independent SNPs
chosen by the user, and then evaluate how our method performed for different absolute amounts of data.
From previous experiences with investigating publicly available SNPs sets in Afro-Americans and putative
source populations from continental Europe and Africa, we evaluated that 100,000 autosomal independent
SNPs were sufficient to obtain estimates of individual admixture fractions from either Africa or Europe that
would not massively change when considering more SNPs (Mathias et al. 2016; Micheletti et al. 2020).

Ultimately, the question “how many markers do you need?” is a non-trivial and circular question a priori. This all depends on how reproductively isolated the populations at the source of admixture have been prior to the admixture event. The closer genetically the two source populations are, the more SNPs one will need to estimate accurately the admixture patterns in the admixed population. Alternatively, the more genetically distant the source populations are, the less markers will be needed to do so.

In this framework, investigating human populations is often much more challenging than other non-
human admixture processes. Indeed, *Homo sapiens* is a very recent species on evolutionary time scales,
and so are divergences across populations, leaving little amounts of time for mutation and drift to
differentiate isolated sub-populations. Therefore, when considering admixture histories between
continental Europe and Sub-Saharan Africa at the time of the TAST, we are working with *F*<sub>ST</sub> values
between the source populations in the order of 0.07-0.10 at the genome-wide scale, a much lower value
than when investigating hybridization histories between populations genetically isolated for tens of
thousands of generations. As a consequence, while investigating human genetic history may sound “easy”
thanks to the wealth of data already accessible, or possibly generated, it is in practice often very hard, as
even such massive amounts of data may be insufficient to distinguish source populations with a very recent
evolutionary history in a first place.

Nevertheless, we did not know a priori how our ABC inferences would perform as a function of the number of genetic markers, and in all cases, numerous non-model species do not have access to genome-wide SNP data<fnref n="47" /> but rather investigate microsatellite markers, as we had investigated in Central Africa (see **Chapter 2**). We therefore decided to build the simulator to allow different types of data to be used. We readily implemented independent autosomal SNPs, and any type of microsatellite data specified by the user and with a General Mutation Model allowing for insertion and deletion, fully parameterized by the user and whose parameter-values could also be drawn from priors for ABC inferences (Fortes-Lima, Laurent et al. 2021).

*How did we simulate individual genetic data under the two-source population version of Verdu and Rosenberg 2011?*

We therefore aimed at simulating independent genetic markers in the admixed population as a function
of model parameters and in a two-source population model. We simply applied a random matting process,
creating random gametes from randomly drawn parents (without selfing) in each source and admixed

<footnote n="47">⁴⁷ Note that is less and less the case with the advances of RAD sequencing and Next Generation Sequencing, now allowing to collect numerous makers from non-model species even lacking well known reference genomes. It is still a financially costly endeavor for the investigation of non-model species requiring extensive amount of highly skilled work in molecular genetics and bio-informatics.</footnote>