Formalising Evolutionary Theory

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Jun 18, 2014 - 11 See David and Samadi (2000), Rosenberg (1994), Rosenberg and ..... Definition Let there be two organisms a and b, aRB if a and b have ...
Preprint version of : Barberousse A., Samadi S, (2015) Formalising Evolutionary Theory. In: Handbook of Evolution Thinking in the Sciences (eds Heams T, Huneman P, Lecointre G, Silberstein M), pp. 229-246. Springer, Dordrecht, Heidelberg, New York, London. DOI 10.1007/978-94-017-9014-7_11 Sarah Samadi Muséum National d’Histoire Naturelle, Paris, France e-mail: [email protected]; https://sites.google.com/site/samadisarah/ Anouk Barberousse History and Philosophy of Science, Lille University, Lille, France e-mail: [email protected]; http://stl.recherche.univ-lille3.fr/ sitespersonnels/barberousse/accueilbarberousse.html

Chapter 11

Formalising Evolutionary Theory Anouk Barberousse and Sarah Samadi

Abstract We propose a formalization of the principles of evolutionary theory as it is currently used in empirical research, in order to enlighten its explanatory resources. We deliberately adopt a minimalist methodology and refuse to include any notion that would not be entirely clear in our formulation. We discuss a few existing formulations and what we see as the touchstone of any formulation of evolutionary theory at the beginning of the twenty-first century: Lenski’s experiments on Escherichia coli. We show the conceptual benefits we draw from our formalization.

According to most evolutionary biologists and philosophers of biology, the theory of evolution provides theoretical foundations, as well as conceptual unity, to all other domains of biology. On the one hand, all biological phenomena are partly explained by evolutionary theory, which implies that the other biological domains are interdependent; on the other hand, the meaning of sentences contained in other biological disciplines partly depends on the principles of evolutionary theory. The claim that evolutionary theory is the key to all biology is sometimes considered overestimated by biologists outside of evolutionary biology. However, it is just a fact that all organisms and biological processes have been produced by the evolutionary history of our planet. Can we infer from this fact that all these processes are explainable by the same set of principles? Yes, if evolutionary history is governed by a number of small, easily expressible principles. If this is the case, all biology is based on evolutionary theory. Some thinkers, including Popper, have suggested that evolutionary theory (reduced to the 1 principle of natural selection by Popper 1974) is devoid of empirical content because it covers

everything that is or has been alive, without exception. Their argument is that it is impossible to discover any unexpected truth by studying how selection operates because absolutely all biological phenomena have been subjected to natural selection. Others, like Smart (1963), think that the living world, characterised by irreversible processes2 that cannot be reproduced, is too complex to be subject to any general laws. He thus claims that the words “evolutionary theory” are unfair, for, according to him, no relatively simple explanation of any biological phenomenon can ever be proposed. For all that, the development of evolutionary theory since 1859 has demonstrated extensively that it can provide us with precise explanations of many phenomena and allow for the formulation of empirically testable hypotheses. Many biologists’ everyday practice, especially in population genetics, systematics, ecology, and in some domains of developmental biology, is wholly shaped by evolutionary theory and would be meaningless outside of it. Evolutionary theory thus drives and gives structure to empirical research in these domains. Despite their importance, the principles of evolutionary theory have seldom been explicitly formulated, even by those using 3 them on an everyday basis. It is well known that since the neo-Darwinian synthesis in the 1930–1940s, evolutionary theory has be submitted to many important changes, mainly due to the progressive inclusion of genetic drift4 and, more recently, developmental biology. These changes have been integrated within empirical research, but no one has yet proposed an explicit formulation of evolutionary theory as it is actually used today, even though some recent attempts are worth mentioning, like Maynard-Smith (1987, 1988, 1991), MaynardSmith and Szathmáry (1995), Szathmáry and Maynard-Smith (1995, 1997).5 Our own proposal significantly differs from the latter in rejecting the use of the information concept. We claim such attempts are susceptible to conceptual clarification. Examining what is evolutionary theory today will certainly allow some recurrent, conceptual problems affecting the most theoretical aspects of biology – as well as its practical aspects – to be discarded. Let us quote the articulation of developmental biology and evolutionary biology , or evo-devo,6

1 The empirical content of a theory is what it enables us to say about the world, in contrast to definitions, for instance, which determine the words’ meanings but do not relate to the world. A theory that is devoid of empirical content only affords logical facts, but does not capture anything of the outside world. 2 A process is irreversible when it is impossible to survey the (abstract) trajectory back, from its final to its initial state. Thermodynamic phenomena are paradigmatic examples of irreversible phenomena: when an ice cube has melted in a glass of water, it is impossible to restore it identically. 3 The neo-Darwinian synthesis has unified Darwin’s theory and Mendelian genetics. Darwin knew nothing of the mechanisms of heredity, which have been brought to light from the re-discovery of Mendel’s laws onwards. The neo-Darwinian synthesis incorporates these mechanisms into Darwin’s theory. 4 Genetic drift is the stochastic process of sampling applied to the offspring of a population of organisms at a given time, as well as to their genes. It is a purely random sampling process explaining that only certain organisms reproduce; as a result only certain genes are transmitted from one generation to the next. 5 Other attempts include Williams (1966), Lewontin (1970), Gould (2002).

or even eco-evo-devo,7the meaning and implications of the “Central Dogma of Molecular Biology”8andthe fate of genetic reductionism,9or the definition of especially difficult conceptslike those of fitness or species,10 as we shall show. Our starting point is that evolutionary theory is as good a scientific theory asaccepted physical theories11and that the form it currently takes deserves explicitformulation. We thereby oppose both Smart (1963) and Beatty (1981) who considerthat biology cannot claim to be as theoretical as physics. Smart goes as far ascomparing biologists with radio engineers who are content to record the world’s diversity. We also oppose those claiming that evolutionary theory can be reduced to“the sciences of evolution”, like Sober (1993) Evolutionary theory is important because evolution is always in the background. Evolutionary theory is related to the rest of biology the way the study of history is related to much of the social sciences. Nothing can be understood ahistorically. I leave it to the reader to consider whether more can be said about evolutionary theory’s centrality than the modest view identified here. Evolutionary theory is the most historical subject in the biological science, in the sense that its problems possess the longest time scales. (Sober 1993: 6–7)

Our aim is to show that it is possible to formalise the principles of evolutionary theory as it is currently used in empirical research, in order to bring to light what its explanatory resources are. We deliberately adopt a minimalist methodology: we refuse to include any notion that would not be entirely clear in our formulation. We begin with the discussion of a few existing formulations, after which we briefly present what we see as the touchstone of any formulation of evolutionary theory at the beginning of the twenty-first century: Lenski’s experiments on Escherichia coli. We then propose our own formalisation as well as the conceptual benefits we draw from it

6 The evo-devo research programme has tried, from the 1990s onwards, to push evolutionary theory further in order to achieve a new synthesis, including developmental biology (See Amundson 2005, and G. Balavoine’s, Chap. 21, in this volume). 7 Some, like Gilbert (2001), have proposed adding ecology to this new synthesis. 8 According to the “Central Dogma of Molecular Biology” stated by Francis Crick in 1958, the DNA molecule is the bearer of genetic information on the basis of which (i) the DNA molecule can replicate, (ii) it can produce RNA through transcription, (iii) it allows for protein synthesis through traduction, proteins being the living cell’s building blocks. The “Dogma” (which is actually a scientific hypothesis) is sometimes summarised as “one gene one protein” but this slogan has lost much of its plausibility today. 9 According to genetic reductionism, every aspect of functional biology can be explained by genetic code and the transcription and traduction mechanisms. Complete genome sequencing programmes in the 1990s and 2000s have shown that their functioning complexity largely exceeds this ideal view. On the words “genetic reductionism”, see Gayon (2009). 10 See Samadi’s and Barberousse’s chapter on species in, Chap. 8, this volume. 11 See David and Samadi (2000), Rosenberg (1994), Rosenberg and McShea (2007).

1 Existing Formulations of Evolutionary Theory The aim of any formalisation is to show precisely what the theory is able to explain, and how. The common assumption (whilst not always written) is that the theory has to explain two sets of phenomena: the organisms’ adaptations and the transformations undergone by biological diversity over time. Whereas the first goal was more important in the nineteenth century, today biologists focus on the second. The first formalisation of evolutionary theory was proposed by Williams (published 1973 but circulated before). It was published in 1973, but the manuscript was completed at the end of the 1960s. It was taken up by Lewontin (1970) and is summarised in Appendix 1. It should first be noted that in this formalisation, natural selection is the only sampling mechanism applied to heritable variations that explain biological diversity. As a result, the notion of fitness, the definition of which is still debated,12 plays a central role in this formalisation. Since Lewontin’s paper, most attempts at making the principles of evolutionary theory explicit consider that selection is the main evolutionary mechanism (despite Gould’s and Lewontin’s 1979 caveat13). Therefore, the fitness concept is also central in these attempts (cf. for instance Brandon 1990), despite the interpretative problems it raises. The interpretative problems raised by the fitness concept have made up a large part of the philosophy of biology research up to now (for a survey, see Brandon 2008). Here are some of these problems. – Should Darwin’s original metaphor, that the fittest organisms to survive and reproduce in a given environment have more offspring, be maintained in the fitness concept? To put it differently, should the fitness concept be defined by the properties of individual organisms that make them better armed than others in the same environment? When a positive answer is given to these questions, the corresponding fitness concept is the folk or ecological concept, derived from the common sense of “fit”. In this sense, the fitness of an organism seems to play a causal role in its capacity to survive and reproduce. How is this capacity to be defined? In order to define it rigorously, it is first necessary to identify the properties of an organism that allow it to interact in a more efficient way than others with its environment; however, this seems a very difficult task, as too many candidates come to mind. – By contrast, in population genetics, all ecological connotations have been discarded. The fitness of an organism is defined as the probability to having such-or-such number of offspring. Some claim that this definition amounts to giving up an important 12 See for instance Ariew and Lewontin (2004), as well as Beatty and Mills (1979), Brandon (1990), Godfrey-Smith and Lewontin (1993), Matten and Ariew (2002), Millstein (2002), Singh et al. (2001), Walsh, Lewens and Ariew (2002), Bouchard and Rosenberg (2004), Rosenberg and Bouchard (2005), Brandon (2006), Abrams (2007). 13 In this famous paper, Gould and Lewontin indicate how inadequate adaptationism is as a scientific project. Adaptationism is the temptation to see adaptations everywhere, even in characters that are perhaps simple by-products of natural selection, or that have fixed only because of drift (See note 4). Considering that every character is adaptive, in the sense that it has been positively selected, amounts to being blind to the other evolutionary mechanisms.

explanatory role for fitness (in its ecological sense), which is to explain the success of the relationship between an organism and its environment (cf. Bouchard 2006; Bouchard and Rosenberg 2004; and Bouchard’s chapter in this volume). Giving up this explanatory role amounts to losing the possibility of achieving causal explanations in evolutionary biology. – Another problem is that it is unclear whether fitness (in the population genetics sense) is a property of individual organisms or an averaged property within a population. Giving fitness a central place in evolutionary theory is thus opening Pandora’s box. We will therefore adopt a minimalist definition of fitness, thus avoiding the above-mentioned problems. Another striking feature of Lewontin’s, and other formalisations of evolutionary theory, is that the explanatory processes they introduce (like those explaining the origin of variation or heritability) are never described in probabilistic terms. Now, since Williams’ and Lewontin’s work, the neutralist theory14 (Kimura 1983), widely accepted by evolutionary biologists, has provided the representation of evolutionary processes with a probabilistic dimension. Taking the probabilistic character of evolutionary processes seriously by representing them with the help of probabilistic laws15 is the best way to express the explanatory resources of evolutionary theory precisely. When emphasising the probabilistic aspect of evolutionary processes, one is bound to deny the popular view that populations are submitted to evolutionary “forces”, like selection, mutations, drift, and migrations (this view is adopted by Sober 1993). The force metaphor, even though it allows for a comparison between evolutionary theory and Newtonian mechanics, is misleading. Drift, for instance, is just a sampling process and cannot be compared to the action of any force. We shall show in the following that this is also true of selection. Finally, let us emphasise that the role of historical and geographical contingency16 is not fully appreciated in Lewontin’s formalisation as he only expresses hypotheses about the effects of different environments. It is, however, commonly acknowledged17 that large parts of the history of life on Earth have been determined by purely contingent events. For sure, it is extremely difficult to include contingent elements within a scientific theory: we are not used to considering theories in which contingent events play any explanatory role

In the 1960s Kimura showed that some genetic mutations are neutral with respect to natural selection. This means that some phenotypic characters evolve without having any effect on organisms’ fitness. This is due to the random sampling which occurs during reproduction. Kimura’s is a mathematical, probabilistic theory, relying on diffusion models. 15 Many biologists and philosophers of biology have denied that there are any laws of evolution. In the following, we show that the notion of natural law applies equally to physics and to biology. 16 We call “historical and geographical contingency” the set of events depending on the position of an organism or a population in space and time and capable of influencing its fate. Climate, geological era, mountains, etc. are thus elements upon which the evolutionary history of an organism is contingent. 17 See for instance Gould 1989. In contrast, some consider that self-organisation principles impose such constraints on organisms that their evolution is less contingent on contextual elements (See Kauffman 1993). 14

for the current philosophical conceptions of scientific explanation, which result from the study of physical theories, rely on natural regularities as their main explanatory factors. Physical theories are thus of no help in this enterprise. It is, however, necessary to complete it, unless very important explanatory factors are left out. In a previous paper,18 we have proposed a basic formulation of evolutionary theory as it is currently used by evolutionary biologists. We rely on it in the present paper. • The origin of diversity among organisms is mutation taken in a broad sense as referring to any modification of an organism’s characters that is transmitted to its offspring via reproduction. The canonical example of mutation is the substitution of one nucleotide for another in a DNA molecule. Another mutation type is chromosomal rearrangement. • The sorting of offspring-leaving organisms is caused by two processes. The first is Darwinian natural selection, i.e. that certain organisms are more efficient than others in reproducing (they are more fit). The second is drift, i.e. that with each generation a random sampling of offspring producing organisms occurs. It is important to keep in mind that both natural selection and drift are sampling processes, the former being directed fitness and the latter random. The action of natural selection and drift is context-dependent. The geographical location of organisms, the associated ecological conditions (biotic and abiotic), and the evolutionary history of their ancestors are elements of the relevant context. Together with inheritance, they determine both which organisms interact and the nature of their interactions. However, spatiotemporal context cannot by itself provide genuine causal explanations of the pattern displayed by the history of life on Earth. Such explanations are provided by probabilistic laws describing the effects of evolutionary forces. (Samadi and Barberousse 2006, 511)

2 Richard Lenski’s Experiments An important feature of the above basic formulation is that it corresponds exactly to the empirical content of Lenski’s experimental work. With his team, he has been elaborating an experimental setup of in vitro evolution for more than 20 years. The aims of these sets of experiments are: (i) to study the dynamics of change within populations of E. coli in the course of evolution, (ii) to assess the repeatability of events occurring in the course of evolution, (iii) to establish correspondences between phenotypic and genomic change. We claim that the formalisation of evolutionary theory as it is used today should match and explain the results of Lenski’s experiments because these results play the same role for the current theory as the observations Darwin collected (especially about artificial

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Samadi and Barberousse (2006). See also our other, Chap. 8, in this volume.

selection) played for his own theory. Our main argument is that Lenski’s experimental setup possesses all the features of a good empirical model of evolution19 for E. coli is a very wellknown model organism, reproducing rapidly and easily in perfectly controllable and measurable conditions. Therefore, Lenski’s experimental setup is ideally suited to checking different formulations of evolutionary theory. Even though Lenski never makes which formulation of evolutionary theory he relies on explicit, his aim is clearly to investigate the role of natural selection and the features of mutations with the help of the standard models of population genetics within an empirical model (vs. in abstracto). As he wishes to test the various ways natural selection can act, he has created a specific context in which genetic drift has been minimised due to the large size of laboratory-produced populations. The populations’ size also provides adequate conditions to the investigation of the mutation processes (see Appendix 2). Whereas it is fiercely debated how fitness is to be measured, Lenski’s experimental setup makes use of a simple, uncontroversial measure: the relative fitness of two clones is measured by the difference between their offspring’s number when they are both put in the same, controlled environment and compete therein. Because the stems are strictly clonal20 as all recombinations21 are avoided, the competition between stems is pure and the fitness measure is simple. As no recombination occurs, it is also possible to genetically trace the competing clones. In order to measure the evolution of fitness within a lineage, Lenski makes use of the resurrection process that is possible when the bacteria are mixed with glycerol and frozen within liquid nitrogen. By keeping up replicates of the stem at different steps of the experiments, he can not only measure the evolution of fitness within a lineage but also among replicates within an experiment (see Appendix 3). Lenski’s concept of relative fitness answers our minimalist requirement for it is less theory laden than the other fitness concepts that are commonly used. Even though Lenski does not state any explicit formulation of evolutionary theory as he uses it, we believe that the fitness concept probably plays a lesser role for him than for Lewontin. What Lenski does, however, is to explicitly test the predictions of population genetic models.

3 Evolutionary Theory Today: Toward Formalisation The traditional purpose of evolutionary theory is to explain the diversity as well as the adaptations of organisms during the history of life. As mentioned above, we add the explanation of the numerous results Lenski obtained with his experimental setup to this task. We define “model organism” and “empirical model” in Appendix 2. A strictly clonal stem is a set of bacteria coming from the same ancestor, thus all possessing the same genes. 21 Recombination is the process of gene exchange either during reproduction or through horizontal gene transfer occurring through physical contact. A recombination event suppresses strict clonality in a bacteria lineage coming from the same [lineage]. 19 20

Our main reason to do so is that the setup generates a set of purified evolutionary situations whose outcomes are easier to predict than natural situations, at least if one can use a wellformulated theory. In addition, the purified evolutionary situations are close, in several aspects, to those obtained in artificial life, a domain to which Lenski has also contributed. It seems therefore fair to claim that the aim of Lenski’s experiments is to reveal the features of life in general, if they are well described by evolutionary theory. According to this perspective, the purpose of the formalisation we aim at is to distinguish two aspects within the theory: first, the general aspects that are true for all possible life, and second, the aspects that are contingent on the fact that the only life we know about is terrestrial life. The latter are precisely the ones we call “contingent”. We propose formalisations of (i) the common descent principle, (ii) the principles of mutation, selection, and drift, and (iii) the role of spatio-temporal context. We have to emphasise that the following is only a provisional attempt to formalise evolution. First of all, it is necessary to define the theory’s domain: it is constituted by the global genealogical network, that is, the set of all organisms that are linked to one another by descent relationships. It seems reasonable to assume that there is only one such genealogical network on Earth today: it is constituted by all past, present, and future organisms living on Earth. The assumption that this genealogical network is unique on Earth does not seem too bold. Even though it is possible, or even likely, that other networks have appeared during the history of Earth, or are even appearing today, both their small size and the ubiquity22 of the main network we know on Earth explain that it is impossible that they compete with the latter and are doomed to become extinct. Within a genealogical network, each organism is related to at least one other organism by a reproduction relationship we call R in the following. Definition Let there be two organisms a and b, aRB if a and b have common direct offspring. This means that a or b, or both, have transmitted, within finite time, some material substrate to one or more other organisms. The material substrate may be modified; it provides the offspring with the capacity to reproduce. This general definition of the reproduction relationship allows us to formalise different reproduction modes that are common in earthly organisms: • {aRb} ↑€Ø and ∀ c {c/cRa or cRb}€ = €Ø represents strictly monogamic biparental reproduction; • {aRb} ↑€Ø and ∀ b {b/bRa}}€= €Ø represents strictly clonal reproduction; • {aRb} ↑€Ø and {aRc}}€= €Ø represents biparental, polygamic reproduction.

In order to represent other modalities, it is possible to generalise relation R so that it can take any (finite) number of organisms as relata. Within this approach, an organism is a material system coming from the instantiation of relation R at the preceding generation. We emphasise that the definition of R depends on the existence of a material substrate belonging to the organisms of the preceding 22

The genealogical network we know on Earth has conquered all possible spaces.

generation and being transmitted to offspring. R is thus not an abstract relationship, but rather a transmission relationship. It is very important to evolutionary theory because it allows for the definition of the genealogical network that constitutes its domain. From the point of view of observation, an organism can be characterised as an autonomous physical system23 capable of reproduction with possible modifications. Reproduction means the production of another organism, also capable of reproduction. For instance, a bacterium is an organism in contrast to both a DNA molecule and a virus, because the DNA molecule cannot reproduce (but it can copied) and a virus cannot autonomously reproduce. The existence of an organism can be visualised as a trajectory in space and time. This allows us to express an important constraint: only organisms whose trajectories intersect can be relata of relation R. The possibility for two organisms to be related by relation R is thus contingent upon the spatio-temporal context they live it. Its role cannot be overestimated. Moreover, as the reproduction process is not instantaneous, successive generations of organisms exist. This aspect provides the living domain with one of its major properties: historicity. We then define an organism’s reproductive success by the size of the network it generates: because the fitness concept encounters so many difficulties, we propose replacing it with the univocal notion of reproductive success. We represent the reproductive success of an organism by a discrete random variable S whose components represent what is called “selection” and “drift” when the population scale is considered. S(a) is thus simply the number of organism a ‘s offspring. It can vary randomly due to mutations and contingent interactions between a and its environment. S(a) is defined within a given environment: to put it in other words, environment is a parameter in the definition of S(a). Random variable S is first composed of purely stochastic elements, which, at the population scale, are described by drift effects; second, of an element representing the evolutionary inheritance of a (the definition will be partly recursive); third, an element representing the effects of mutations. Here are our hypotheses about the factors determining the reproductive success of an organism within its environment: – Let ai be a node of the genealogical network whose parents are ai−1 and aĄ i−1 (ai−1 can be identical to aĄ i−1). – f is a function of the reproductive success of ai’s parents, the contingent features of ai’s life, ai’s mutations relative to ai−1 and aĄ i−1. – Ei = g(V(ai), Ep (ai), Eb (ai)), where g is a function of the genealogical neighbourhood of ai V(ai), that is the organisms belonging to the same fragment of the genealogical network, of the physical environment Ep (ai), and of the biological environment Eb (ai) constituted by contemporaneous organisms living in ai’s physical environment. – d(ai) is a discrete random variable representing the effects of contingent events.

The required notion of autonomy is difficult to define rigorously. This difficulty also affects the notion of organism. There is some theoretical work left to do here. However, there are numerous cases where the intuitive notion of organism applies.

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– m(ai) is a discrete random variable representing the effects of mutations. m describes the variation of reproductive success of organism ai as due to some of its mutations. SEi (ai), the reproductive success of organism ai within environment Ei, is defined as follows: S Ei ( a i )= f ( SEi ( a i −1 ) , SEi ( a’i −1 ) , d ( a i ) , m ( a i ) ) By decomposing S(a) in such a way, we formalise the principles of evolutionary theory by making explicit the way the factors which are commonly called “genetic drift”, “natural selection”, “mutation”, and “environment” determine an organism’s reproductive success within its environment. The next step will be to show how population-genetic models follow from this formalisation. In order to assess the validity and relevance of our formalisation, we apply it to the results of Lenski’s experiments. As the main experiment takes place within a constant environment, we have E0 = E1 = … = Ei. As reproduction is strictly clonal, there is one unique parent ai−1. Given the populations’ size, the purely stochastic component (genetic drift) can be neglected. Reproductive success is thus given by: SE 0 ( ai )= f (SE 1 ( ai −1 ) , m ( ai )) In these circumstances, the experiment shows that SE0(ai) is an increasing, asymptotical function. The other experiments can be formalised in the same way in order to study the behaviour of S under given conditions.

4 Theoretical and Conceptual Advantages Our formulation differs from Maynard-Smith and Szathmáry’s in an important way: we consider the nature of the material substrate that is transmitted during reproduction as indifferent (whether it is carbon-based or silicium-based does not have any impact from a theoretical point of view). It is thus unnecessary to mention this nature within the theory. The only important element from a theoretical point of view is that the transmitted material substrate, whatever it is, is what makes the building up of another organism possible. Modifications may occur. On Earth, the current material substrate is made of DNA molecules, but it seems that this state of affairs is relatively recent. Other possibilities may be conceived, some of which have perhaps been instantiated somewhere on Earth. That DNA is the main material substrate transmitted is just a contingent outcome of the history of life. This is due to the particular chemical composition of Earth during its pre-biotic history and the first steps of the history of life. In the same way, the number of transmitted genes or the way they are transmitted (vertically or horizontally) are contingent properties of the reproduction relationship. They do not have to appear in any general enough formulation of evolutionary theory.

As a result, the so-called “dogma of molecular biology”, far from being a dogma, is probably the outcome of a series of contingent events during the history of life. By emphasizing that the transmitted substrate is material, we move away from the views of evolutionary theory in which information plays a major role (cf. Appendix 2). We believe that we are better off without this notion than with it because of the many conceptual problems it raises. We also abstain from using the concept of gene, thus moving away from the lengthy discussions relative to its problematic character.24 Another consequence of this choice is that it allows us to be clear about the place of bacteria within the genealogical network. Some, relying on the search for molecular phylogenies, express doubts about the hypothesis that it is possible to reconstruct a unique tree of life, especially at the beginning of its history (see, e.g., Woese 2000; Doolittle and Bapteste 2007). Reconstructing phylogenies from genes indeed leads to hardly readable results about the deepest nodes of the network. It is thus very difficult to obtain a unique tree from molecular phylogenies. We reply that as soon as one leaves the “gene’s point of view” to adopt, as we do, the “organism’s point of view”, the difficulties fade away. When representing the history of life by a genealogical network of organisms vs. genes, one avoids the various biases introduced by molecular phylogenies and, at the same time, one better understands their origin. As a matter of fact, gene trees and organism trees do not overlap. Far from being a reason for favouring gene trees over organism trees, this is simply explainable by the frequency of horizontal gene transfers25 among unicellular organisms. The aim of gene phylogenies is thus to reconstruct degrees of parenthood rather than genealogies. As a result, gene phylogenies do not tell the history of organism with enough precision. Within our formulation of evolutionary theory, the notion of natural selection becomes a metaphor, for the action of selection is represented by a mathematical function: namely a random variable (from a mathematical point of view, random variables are functions randomly associating values to their arguments). It is thus possible to get rid of every unwanted assumption about what is selected for or against, in complete agreement with Lewontin’s enterprise, who emphasised that selection occurs even in situations where the resources are unbounded, that is, where the organisms do not compete for resources. The principle of selection thus becomes more general and loses all its undesirable features. Like in Lenski’s work, the fitness concept is reduced to a simpler notion. In our formulation, the fitness difference between two organisms is simply the difference between the sizes of the genealogical networks they generate. It is thus useless to postulate a richer fitness concept, of which the size of the network would only be the measure (in the same way that it was useless to postulate the existence of the ether which was supposed to fill up space in the framework of relativistic mechanics, as shown by Einstein in 1905).

See Keller (2000), Morange (1998), Moss (2003). A horizontal gene transfer is the transmission of parts of the DNA molecules from one bacterium to another through simple contact, independent of any reproduction event. By contrast, vertical gene transfer occurs during reproduction. Whereas in multicellular organisms, reproduction and gene transmission occur together, it is different in bacteria, in which these two processes are distinct. This explains why it is so difficult to build up phylogenetic trees based on genetic data. 24 25

Even though our work is only preliminary, our formalisation unambiguously shows that an organism’s fitness results from the accumulation of all the variations by which its ancestors have been affected. Such an accumulation is contingent in the sense that it does not obey any law, be it deterministic or probabilistic. This is why we choose a random variable to represent reproductive success, in order to emphasise the role of the spatiotemporal context in which an organisms lives and reproduces. The context depends on the position of the organism on the Earth surface, within the Earth history, and within the genealogical network. Each context thus encompasses the entire evolutionary history of the looked-at organism as well as its ancestors’ evolutionary histories. It also encompasses the history of all the interactions between its ancestors and the other organisms living in their own time and place. This enlarged and integrative notion of context allows for explanations of interactions amongst organisms at a given time as well as phenomena of niche construction.26 Our bet is that this new notion of context will allow one to explain most phenomena put forward by Odling-Smee et al. (2003), without introducing any “principle of niche construction” beyond the principle of natural selection within evolutionary theory. Our formulation gives organisms the privileged role of main evolutionary units as selection acts on organisms, not on genes or on groups of organisms.27 However, it makes clear that, when one adopts the “gene’s point of view” (cf. Dawkins 1976, 1982; Dennett 1995), evolutionary theory takes a much simpler form, because the role of environment is significantly reduced. This is why the latter version of evolutionary theory is often the default one. At last, our choice of a unique random variable in the theory (S(a), the reproductive success of organism a), in which we enclose the combined actions of selection, drift and mutations, makes clear why evolutionary explanations so often appeal to contingent events. These play a major role in the fate of organisms; therefore, by accumulation through time, in the fate of populations, of species, and of the entire biosphere. Our way of gathering and unifying the different evolutionary processes thus sheds light on the question of what developmental constraints are. They consist in the elements limiting the action of selection. The fact that developmental processes are generally channelled and rather robust, and depend on a set of genes that are common to many groups, from Drosophila to human beings, is sometimes considered to protect them against selection pressures.28 The genetic mechanisms warranting robustness in development are sometimes called “phylogenetic constraints”, which suggests that they result from regularities governing the fate of lineages; however, they are more likely the outcomes of contingent events, which have generated the Cambrian explosion29 (cf. Davidson et al. 1995). Instead of relying on other types of explanation for developmental constraints, like, for instance, alleged principles of selfOn niche construction, see Pocheville’s, Chap. 26, in this volume. On the notion of group selection, see Huneman’s, Chap. 4, in this volume. 28 See Balavoine’s, Chap. 21, in this volume (Samadi and Barberousse 2006). 29 During the Cambrian era, a huge diversity of new animal body plans appeared in a relatively small period (at the scale of geological times). 26 27

organisation (cf. Kauffman 1993),30 we thus suggest to rely on what contingent events, whose effects accumulate through time, can explain. Moreover, a side-effect of such an accumulation is to make further transformations almost impossible, thus giving the impression that development is submitted to genuine regularities.31 Our approach thus sheds a new light on the evo-devo perspective.

5 Conclusion Our formulation shows that evolutionary theory can account for all aspects of the historicity of the evolution of life, and give it a strong explanatory power. It also establishes that irreversibility and non-repeatability is no obstacle to the theoretical representation of events in the living world, for these events are governed by probabilistic laws, which can explain many observed phenomena. In order to give full-fledged evolutionary explanations, the succession of the relevant contexts has to be put forward, which generally requires hard work. The main advantage of our formulation is to emphasise that the context is itself the result of evolutionary processes, at least partly. This is represented by the partly recursive character of the definition of reproductive success. Let us end our chapter with a comparison. Geology, like biology, tries to explain certain states of affairs by integrative history. However, the objects of geology are fundamentally different from the objects of biology, for the latter are organisms that come to life and reproduce by transmitting their capacity to reproduce. In our formulation, we have tried to take this difference seriously.

Appendices Appendix 1: Formalisation of Evolutionary Theory by Lewontin (1970) Lewontin states three principles of evolution by natural selection in natural populations: (1) Different individuals within populations have different morphologies, physiologies, and behaviours (phenotypical variation).

Kupiec criticises the appeal to self-organisation. It is very likely that the major transitions of evolution (like the appearance of cells, of multicellular organisms, of societies) result from series of events of the same type: mutations occur that, due to environmental change, are especially efficient, and then rapidly propagate so that the way back quickly becomes difficult or even impossible. 30 31

(2)

Different phenotypes have different survival and reproduction rates in different environments (differential fitness). (3) There is a correlation between parents and offspring in their respective contribution to future generations (fitness is heritable).

Lewontin insists that these principles are fairly general: “The generality of the principle of natural selection means that entities, which in nature show up variation, reproduction and heritability can evolve”. For instance, these principles do not involve any specific heredity mechanism: “No particular heredity mechanism is given, but only a correlation between parents and offspring as far as fitness is concerned”. Lewontin also makes the reasons why the differences in contribution rates to the next generation are left unspecified in this formulation clear, and emphasises that it is not necessary to bound resources in order for natural selection to occur.

Appendix 2: Theories, Laws, Models The words “theory” and “model” have varying uses. In this chapter, what we mean by “theory” is a set of general, explanatory principles about a large domain of empirical phenomena. These principles may be expressed in natural language sentences, and sometimes in formal languages, whenever the employed concepts are precise enough. The principles of a scientific theory are sometimes called “laws”, but this term can also refer to regularities that are consequences of the principles. A scientific law states the regular concomitance or succession of several events. It can be deterministic, in which case the events always occur together, or successively; it can also be probabilistic (or statistical), in which case the events occur together or successively with some probability. This means (at least for the domain we are talking about) that the proportion of cases in which the law is verified relative to the cases in which only one event occurs, approaches the probability appearing in the law. The notion of a probabilistic law is sometimes difficult to grasp, because the notion of a natural law is commonly associated with determinism. However, this is an entirely legitimate notion, for probabilistic laws allow one to make predictions as much as deterministic laws do. Several types of models may be distinguished: • Theoretical models: Within the framework of this chapter, theoretical models are specific interpretations of the theory. For instance, the interpretation of evolutionary theory taking the notion of information as central is a theoretical model of it, because most phenomena are conceived and explained in terms of the transmission of genetic information. We prefer a materialistic interpretation excluding both the notion of information, because it is difficult to define rigorously (cf. Godfrey-Smith and Sterelny 2007), and the notion of “informational molecule” (criticised by Godfrey-Smith 2000; Griffiths 2001; Oyama 2000).

• Mathematical models: They occur in population genetics and are applications of the principles of evolutionary theory to particular situations, usually idealised, in order to make the calculations easier or even simply possible. In all mathematical models there is a tension between two requirements: the requirement of correct representation and the requirement of tractability. The latter may alter the former. • Empirical models: These are real, well-controlled situations, usually built up within laboratories, which exactly correspond to the principles of the theory. • Model organisms: These are real organisms whose genetic and phenotypic properties are both well-known and well-controlled. Certain model organisms, like the vinegar fly Drosophila melanogaster, have been used as such since the 1930s.

Appendix 3: Lenski’s Experimental Setup32 Experimental Conditions Twelve populations each of which has been founded by a unique cell coming from the same ancestor clone on February 15, 1988. Liquid culture, transplanting once a day (6.64 generations per day). Storage in liquid nitrogen every 100th generation (then every 500th) of the 99 % that have not been used in transplanting.

Some Results (1) “Relative fitness” measured as the relative growth rate of two competing clones in a given environment. Fitness increases every second lineage. The increase goes parallel in both lineages. The increase rate of relative fitness has decreased over time. The rhythm is “punctuated”: changes are not gradual but come in successive stages. (2) Phenotypic and genomic evolution The cell size also increases in parallel in all 12 lineages. This evolution is correlated with fitness evolution. The capacity to convert glucose into biomass increases in all lineages. The decrease of the fitness increase rate suggests that an adaptive peak has been reached.

32

See http://myxo.css.msu.edu/index.html and Lenski (2004).

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Anouk Barberousse is professor in history and philosophy of physics at Lille University. Her main fields of research are the philosophy of computer simulation and computer-assisted production of scientific knowledge, the foundations of evolutionary theory and of taxonomy, the role of pictures in scientific investigation. Among her recent publications: • Barberousse, A. with Vorms, M. (2014) “About the warrants of computer-based knowledge”, Synthese, DOI 10.1007/s11229-014-0482-6, Published online 18 June 2014. • “Recurring models and sensitivity to computational constraints”, with Cyrille Imbert, The Monist vol. 97, no. 3 (July, 2014; “Models and Simulations”). • “New Mathematics for Old Physics: The Case of Lattice Fluids”, with Cyrille Imbert, Studies in the History and Philosophy of Modern Physics, 44, 2013, 231–241. • “La taxonomie dans la tourmente”, with Sarah Samadi, Revue d’Anthropologie des Connaissances, 7/2, 2013, 411–431. “What Is the Use of Diagrams in Theoretical Modeling?”, Science in Context/Volume 26/ Special Issue 02/June 2013, pp 345 362, DOI: 10.1017/S0269889713000082, Published online: 30 April 2013. Sarah Samadi is professor at the Muséum National d’Histoire Naturelle (MNHN) in Paris in the “Institut de Systématique, Evolution et Biodiversité” (Head of the Institut, Pr. Philippe Grandcolas). The analysis of the conceptual grounds of systematics and evolutionary biology is an important component of her projects. She also develops empirical projects in the field of species delimitations and of the study of speciation processes. These projects are focusing on organisms from poorly known environments (mainly deep-sea environments, notably seamounts and organic remains sunken on the deep-sea floor) and are developed in the methodological framework of “Integrative Taxonomy”, in which methods in phylogenetics, population genetics and ecology are combined.