Neutral Diversity in Experimentally Nested Populations 

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A fixed collection of species

Slowly, Science distanced itself from the goal of mapping similarities in nature in order to unveil its secrets. The new reductionist paradigm, illustrated by the obviousness criterion of Descartes, is rooted in the idea that natural systems must be separated in parts that are small enough to be understood simply (Legay, 1997).
The emergence of the concept of the species at the end of the 17th cen-tury constitutes a true paradigm shift, in which heredity plays a central role. For the first time, living beings are not categorised by their shape but their descent, regardless of differences between stages of life (for instance larvae or imago) or individual variations. This classification method stems from the observations of naturalists such as Ray (1686). It gained universal adoption as part of the Linnean system of classification (Linné, 1735).
The Linnean system extends beyond life as it still distinguishes between minerals, plants and animals. Indeed, for Buffon (1829), the frontier between the living and non-living is fuzzy: it is possible to “climb down by seamless steps from the most perfect of creatures to the most shapeless matter, from the most well-organised animals to the most crude of minerals”. However, common characteristics of life start to emerge: “A species is nothing else than a constant succession of similar individuals, that reproduce themselves, and it is clear that this term should only apply to vegetals and animals [and it is by mistake that it was used for minerals]” (Buffon, 1882). Nonetheless, mechanisms of heredity are still out of reach. Buffon imagines an “internal mould” that constrains not only the external form —as the moulds commonly used in casting— but that would also determine internal structure of indi-viduals (Buffon, 1882) but he cannot provide any insight in its mechanism of action.
On the subject of variation, individuals differences from the ideal mould of the species are mostly considered as punctual defects without consequence (Buffon, 1882). It is recognised that some variations are heritable, and possi-bly stabilised by artificial selection (Maupertuis, 1754). However, generation of new species by this mechanism is rejected (Buffon, 1882). Since transfor-mations of species are not yet deployed on the long term to explain the origin of life’s diversity, biology in the 18th century can be qualified as resolutely fixist (Jacob, 1970).
Allégorie de la Science, (Buffon (1829), Gallica/BnF)

A set of evasive living particles

In the 18th century, advances in physics and chemistry open the path for an in-depth exploration of natural phenomena such as respiration and digestion (Lavoisier, 1862). Vaucanson (1738) presents to the Académie des Sciences, an automaton of a duck that “eats, drinks, digests and empty its bowels”. Even though it illustrates how the phenomenon of life could be imitated by machines, the artificial duck is first and foremost a feat of mechanical engineering. The author himself admits that the artificial digestion does not “produce new blood” or participate in the upkeep of the organism. If the engineering metaphors are successful in addressing physiology problems, they are vastly under-equipped to tackle the problems of reproduction and heredity. This epistemological blind spot is jarring, as aptly summarised by Fontenelle (1912): “You say that beasts are machines as well as watches ? But put a dog-machine and a bitch-machine next to each other, and it could result a third small machine. In contrast, two watches would be next to each other all their life without ever producing a third watch.”
Two main theories govern the generation of living beings at the time: preformation, and preexistence. Preexistence is the idea that all germs have been created concurrently with the creation of the world. Preformation is the complementary idea that all future beings already exist as germs, nested within the germs of the previous generation, and are just growing (Jacob, 1970). However, those notions bring contradictions that cannot be solved.
Preexistence theory is riddled with contradictions that are aptly pointed out by the scientists of the 18th century. First, hybrids like the mule are trou-blesome, because they suppose the blending of preexisting animalcules. The regrowth of limbs observed in some species is a second contradictory point: it implies that individuals are either preformed with “spare parts”, or borrow them from their descent. Finally, using simple mathematical arguments, it can be shown that preformation of several generations would quickly require nesting of individuals to absurdly small scales (Buffon, 1884).
Beyond recognition of the identity of the species, that ensures the univer-sal recurrence of the same shape, a systematic exploration of the heredity of variants starts to take place. For instance, simple statistics show that observ-ing several polydactyls people within the same family would be an extremely uncommon event if this particular defect was distributed uniformly in the population: it must be hereditary (Maupertuis, 1756).
One of the main problems is the physical support of heredity. There is no way to distinguish the support of heritable traits from the traits them-selves. Several mechanisms are proposed. For instance, the theory of “living particles” postulates that organisms are composed of elements with a mem-ory. Those elements are transmitted by the seeds and, remembering their position in the parent, will re-assemble in the same way within the offspring. The living particles are supposed to come from all over the parent organism, and are often not distinct from the particles actually composing the body: the information of the shape is not decoupled from the shape itself. At the same time though, Maupertuis (1754) inspired by comparison with political systems, postulates different classes of particles with one dedicated to the maintenance of the memory while others have a purely functional role.
At the end of the 18th century, the separation between inert and living ob-jects is acted. “In order to really know what constitute life,” writes Lamarck (1809), “we have to, first of all, carefully consider the differences between in-organic materials and living bodies.” He then enumerates nine properties: he first points out the individuality of organisms. Birth and development from a germ coming from a similar individual constitute his eighth point, and the death of organism the ninth.
An ability to change through long periods of time intellectual life to incorporate the evolutionary world view”, after cosmolgy (with the nebular hypothesis for the formation of planets, formulated by Kant in 1786 and formalised by Laplace in 1796), geology (with the principle of uni-formitarism which implies that general laws apply over long periods of times, attributed to Hutton in 1785 and popularised by Lyell in 1830), thermody-namics (with Carnot in 1824 and Thomson in 1851) and linguistics (with the idea that languages have been developed rather than created, which was the dominant view in 1857 according to Spencer). In natural sciences, the influ-ence of geological studies cannot be understated, even more so that they were coherently fitting in with the early transformist theories, as for instance pro-posed by Lamarck (Mayr, 1991). Darwin himself wrote that Lyell’s Principles “altered the whole tone of one’s mind” (Ameisen, 2008).
Darwin’s magnum opus about the common descent with modification (Darwin, 1872) closes with the outline of the characteristics of all living organ-isms that will become the Darwinian properties: “growth with reproduction”, “inheritance” and “variability”.
Darwin’s own vision of heredity changes dramatically during his lifetime (Mayr, 1991). In 1868, he proposes the provisional hypothesis of pangenesis, which accounts for both heredity and development (Darwin, 1968). In a manner reminiscent of the living-particles theories from the previous century, Darwin postulates the existence of gemmules. Gemmules are self-dividing particles, produced by cells and that can, under the right conditions, develop into a cell of the same kind as its producer. Gemmules are collected from all parts of the body to form the sexual elements. Once again, development is explained by the affinity of particular gemmules to particular types of cells. Heredity of acquired traits is possible. However, the theory of pangenesis is quickly disproved by blood transfusion experiments (Galton, 1871). Later, the first statistical theory of heredity is established by Galton (1894).
Even the scale of the unit of life changes during the 19th century: cell theory gives to cells the status of the smallest unit presenting all characteris-tics of life. This is in contrast with the purely structural vision of cells that can be found earlier (for instance in Lamarck (1809)). From this moment on, multicellular organisms can be considered as collectives of interacting cells: every “so-called individual represents a kind of social arrangement of parts”, writes Virchow (1863) in his lectures about cell phathologies, “an ar-rangement of a social kind, in which a number of individual existences are mutually dependant.”
By the end of the 19th century, neo-Darwinist thought came to question the inheritance of acquired traits (Mayr, 1991). At the center of this rebuttal, a growing body of evidence shows the separation of germinal and somatic lines. This theory leaves no room for cytological mechanisms explaining the transmission of characters from soma to germ (Weismann, 1892).

A complex system

The 20th century opens with the rediscovery of Mendel’s laws of inheritance and constitute the final nail in the coffin of the theory of blending inher-itance. These organism-level observations are rapidly correlated with the movements of chromosomes during meiosis and fecundation. Observations of the segregation of both traits and chromosomes in Drosophila firmly establish chromosomes as the physical support for heredity (Morgan, 1915).
The first quarter of 20th century offers also statistical refinements for the analysis of heredity, with the spreading of the Analysis of Variance. More than a technical improvement, those methods pioneered by Fisher constitute a true epidemiological shift. For the first time, it is indicated clearly that there may exists many factors influencing a character, even though the scientist can affect only a handful. The other factors are not ignored in the analysis but considered as “uncontrolled”. This is the beginning of complex systems thinking, in clear contrast with the previous criterion of evidence (Legay, 1997). In addition, Fisher is at the centre of the reductionist approach of evolution, that defines evolution purely in terms of the dynamics of genes frequency (Mayr, 1991).
Before the middle of the century, the idea that the gene is a molecule is commonplace. At the meantime, the veil is slowly lifted on the physical mech-anisms of variation: the spontaneous nature of mutations is demonstrated in bacteria by the fluctuation test (Luria and Delbrück, 1943). This constitutes the proof that the source of biological variation is largely independent of the selective process. Additionally, decisive experiments with X-ray-induced mu-tatagenesis place the gene-molecule size at about a thousand atoms, and hint at it being a kind of “aperiodic cristal” (Schrödinger, 1944), or, rather, an aperiodic polymer. Finally, the discovery of the molecular structure of DNA (Watson and Crick, 1953b) and, shortly after, the discovery of the genetic code mark the beginning of the molecular genetics era.
By the middle of the 20th century, the modern evolutionary synthesis unifies the fields of genetics, systematics and palaeontology that used to be separated. Heredity and variation play a central role in this unified view. The synthesis cements and diffuses within the scientific community the concepts of genotype and phenotype, the idea that the source of variation is spontaneous mutations, that heredity is not blending and does not concern acquired traits (Mayr, 1991).

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A vehicle for information

The years following the synthesis (from 50s to 70s) see the reaffirmation of the individual as the object of selection (Mayr, 1991). However, naïve individual-centred approaches have the shortcoming of not being able to predict, or ex-plain, neither cooperative behaviours nor control of inter-individual conflict. In a seminal article, Hamilton (1964) puts forward the concept of inclusive fitness, a quantity that aims to correct for social context and take into ac-count the harm and benefits caused by the focal individual on its neighbours, proportionally to their relatedness. Concurrently, Maynard Smith and Price (1973) introduce evolutionary game theory as a method to solve the prob-lem of restraint in animal conflict. These developments participate in the effort of distinguishing what kind of entities might be subject to evolution by natural selection, and operate a much-needed clarification of the possible mechanisms of evolution: the « good-of-the-species » cannot (as seen in Wynne-Edwards (1962)) be invoked as the evolutionary cause for a behaviour or a trait. This does not disqualify the plurality of levels of organisation to play a role in evolution, but their Darwinian nature has to be justified (May-nard Smith et al., 1993). In 1966, Williams (2018) states that “only by a theory of between-group selection could we achieve a scientific explanation of group-related adaptation.” He classifies mechanisms by their effect on the individual level (named organic) or beyond (named biotic). Finally, he con-cludes that biotic selection, if possible in theory, is not potent enough to be significant in most natural situations and famously states “Group-related adaptation do not, in fact, exist.”
The 70s mark a turning point in the study of what constitutes the unit of evolution. Lewontin (1970) puts forward the modern formalisation of the set of properties that are necessary for evolution by natural selection: phenotypic variation, differential fitness and heritable fitness. He decouples those neces-sary properties from the mechanisms of heredity. Natural selection is expected if these properties are verified, had they arosen from “Mendelian, cytoplasmic or cultural inheritance”. Pioneered by Williams (2018), and popularised by Dawkins’ widely influential Selfish Gene (Dawkins, 1976), the gene-centered view of evolution postulates that the gene is the only entity that really fits the definition of a unit of evolution. All in all, if the 18th century saw liv-ing beings as machines made of pumps and furnaces, the metaphor favoured by the 20th century is the one of information and programme, encoded in genes. As a prime example, Monod (1970) distinguishes two properties of living systems: reproductive invariance, (i.e., information transmitted across generations) and structural teleonomy (i.e., the apparent purposefulness of living beings to fulfil the programme of invariant reproduction).

A nested structure

The nested organisation of living systems becomes a focus of research in the last part of the 20th century. The endosymbiosis theory for the origin of the eukaryotic cell advocated by Margulis (1970) makes manifest the fact that, even at the cellular level, organisms are the result of the integration of different components that used to have their own individuality. On the other side of the spectrum, the field of sociobiology funded by Wilson (1975b) uses Hamilton’s inclusive fitness to propose an evolutionary theory for social structures.
Jacob (1970) claims that the advances of molecular biology mark, at last, the merging of physiology and natural history: organisation and evolution, molecular mechanisms of heredity and teleonomy can finally be treated in a unified biological framework. As a consequence, the nested organisation of living beings, composed of layers of integrated sub-units (called integrons), becomes a consequence of evolutionary processes. In the following years, the origin of new levels of organisation is treated a general question on its own right, with for instance the work of Buss (1987) on the evolutionary origins of individuality. The concept of major transitions in evolution, formalised in the seminal book of Maynard Smith and Szathmary (1995), applies such ques-tion across scales, from the origin of chromosomes and cells, to multicellular organisms and societies.
Despite its apparent dismissal in the 60s, group selection was the subject of continuous of research until today (Wilson and Wilson, 2007). On the side of theory, multi-level selection extends Darwinian principles to a hierarchical organisation: particles populations nested in a population of collectives (Okasha, 2006). Two kinds of approaches are distinguished: Multi-level se-lection 1 (MLS-1) models focusing on particles, where the group structure of the population is modelled as environment (such as the classic trait-group model of Wilson (1975a)), and Multi-level selection 2 (MLS-2) models where collectives are treated as unit of evolution on their own right. On the side of experiments, a wealth of results confirmed that group-level selection is a potent force in controlled conditions: successful selection at the level of the group was performed on hens to select for non-aggressive behaviour (Hesters et al., 1996). Artificial selection is also possible on whole communities as shown in floor beetles (Goodnight, 1990b,a) with the selection of population size and immigration rates. In microbial communities, experiments selecting for pollutant degradation (Swenson et al., 2000a), selecting plant microbiome for increased biomass (Swenson et al., 2000b) or flowering time (Panke-Buisse et al., 2015) opens new perspectives in microbiome “breeding” (Arias-Sánchez et al., 2019; Xie et al., 2019). In evolutionary microbiology, the influence of population structure on viral restraint (Kerr et al., 2006) and early multicellu-larity (Hammerschmidt et al., 2014; Ratcliff et al., 2012) illustrates how some key phenomena of the history of life can be explained by a nested Darwinian population structure.
Both Darwinian properties and the concept of evolutionary transition in individuality are the product of the long process of formalisation of biological thought. They reflect the current version of a constantly changing framework for the study of the principles organising the living world. This history of-fers an example on the long term dynamics of knowledge itself, with paradigm shifts (Kuhn, 1970) when an explanation emerges and replaces another. Keep-ing this context in mind, the next chapter focuses on a very contemporary view of evolutionary processes, based on mechanistic explanations as well as a quantifiable formalisation of Darwinian properties.

Table of contents :

Introduction 
1 Historical Perspectives 
2 Darwinian Properties 
3 Neutral Diversity in Experimentally Nested Populations 
3.1 Modelling Nested Population Dynamics
3.2 Modelling Neutral Diversity
3.3 Artificial selection of droplets
3.4 Discussion
Appendix
4 Locating Mutations in Collective-level Genealogies 
4.1 The cheat as first propagule hypothesis
4.2 Establishing collective level genealogies
4.3 Survival probability estimation
4.4 Propagating sequencing information to the full genealogy
4.5 Discussion
5 From Particles Traits to Collective-level Demography 
5.1 Evolution of collective survival and reproduction
5.2 Trade-off between survival and reproduction
5.3 Particle dynamics
5.4 Collective Population Dynamics
5.5 Migration between collectives
5.6 Discussion
Appendix
6 An Ecological Recipe for the Evolution of Collective-level Heredity 
6.1 Results
6.2 Discussion
6.3 Stochastic Model
6.4 Lotka-Volterra deterministic particle ecology
Conclusion 
Bibliography 

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