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FROM DNA TO ECONOMICS: ANALOGY IN ECONOBIOLOGY.

1. Introduction

The last economic crisis generated a lot of debates and questions about the ability of economists to deal with economic complexity. Roughly speaking, complexity can be associated with the formation/emergence of macro-structure (system) and how this macro-level influences the micro-interacting elements causing it. Though complexity is difficult to model and measure, several frameworks (biology, statistical physics etc.) recently emerged to deal with this kind of environment. In this challenging context for the economic theory, can economic theory benefit from these new advances in the other fields like physics or biology? One can observe new modelling practices with the emergence of new fields such as econophysics or econobiology. The former deals with the extension of statistical physics to economics and finance while the latter refers to the application of biological reasoning/reasoning to economics. Econophysics became a quite popular field in the recent literature (Jovanovic and Schinckus, 2017) whereas econobiology is still under-investigated. The objective of this article is to offer a reflexive perspective on this sub-field.

Extending biological reasoning to economic/financial sphere implies an implicit analogy between the two fields. This article aims at clarifying the kind of analogies that justifies this movement. By definition, an analogy is a comparison between two objects/systems that have similarities. Analogies play a key role in scientific practices: several authors have emphasized their pedagogical utility (Hodstrater, 2001; Weisberg, 2016) while others have detailed their heuristic role in the aid of discovery (Bartha, 2013; Bailer-Jones, 2009). In the context of the development of econobiology, which is characterized by an extension of biological reasoning outside of its borders, the issue of scientific analogy became particularly interesting. What are these similarities that paved the way for an analogical comparison between a biological system and an economic one? More precisely, I will investigate how an extension of a biological reasoning to economics might be justified through a formal analogy. In this context, it is important to understand the role of analogies and what is meaningful in this new field called "econobiology."

The first part of this paper will define what econobiology is by presenting an example of the modelling practices used in this field. Afterwards, this article will investigate the way such extension of a biological reasoning can used in economics/finance. Precisely, I will detail the kind of analogy used by scholars when they associate a biological system to an economic one.

2. Econobiology

Zeidan and Richardson (2010: 12) explained that "econobiology take its lessons from biological complexity models." More precisely, econobiology draws its modelling practices from the analysis of evolutionary processes (Rosser, 2010). Scholars involved in this field view the stylized facts in economics as emergent properties of complex systems that they try to characterize through biological complexity models (Mertzanis, 2014). This new area of knowledge must be distinguished from what is called "bioeconomics" (Clark, 1990) that refers to the use of economic models/tools to characterize the dynamics of biological systems. (1) In other words, econo-biology imports concepts and tools from biology to characterize evolutionary economic systems while bioeconomics refers to the opposite approach consisting in using economic concepts to describe biological systems. A good example of econobiology modelling practices can be found in "Anomalous fluctuations in the dynamics of complex systems: from DNA and physiology to econophysics" (Stanley et al., 1996). This section presents this paper in more detail and shows how authors used reasoning from biology for describing the dynamics of companies' growth rates. As the abstract of the paper notes, the authors aimed to export biological reasoning into other disciplinary contexts. Precisely, they wanted to: "discuss examples of complex systems composed by many interacting subsystems. [...] These includes the one-dimensional sequence of base pairs in DNA, the sequence of flight time of the large seabird Wandering Albatross and the annual fluctuations in the growth rate of business firms" (Stanley et al., 1996: 302).

How can DNA, seabirds and business growth rates be related? How (and why) can scholars model these different phenomena within the same conceptual framework? The major idea connecting these complex phenomena refers to the existence of anomalous fluctuations in their dynamics. According to Stanley et al. (1996), these anomalous changes indicate analogies in the underlying mechanism in totally different systems. Concretely, the authors focused on correlations between the anomalous variations in the sequence of DNA, sea birds movements and the sales fluctuations of firms. Such statistical analysis aims at identifying common patterns in these complex large fluctuations. Stanley et al. (1996) began their argument by studying the anomalous variations in the DNA walks (frequency of each pairing nucleotide couple changes). After having observed the existence of anomalous fluctuations, the authors gave a visual representation of how nucleotides couple each other. Here is an illustration of such visualization:

This graph shows three levels of visualization (linear, discontinuous and continuous) of different kinds of nucleotides (characterized by three levels of colours: white, dark grey and light grey). What is important here is the evolution of the DNA where the movement of the nucleotides can move either up (u(i) = +1) or down (u(i)=-1) for each step of the walk. In other words, positive fluctuations (going up on the graph above) corresponds to what geneticists call a "purine-pyrimidine" pair, while negative fluctuations (going down on the graph above) refers to a "hydrogen bond" pair. Starting from this visualization of these DNA walks (Figure 1), the authors wrote: "Such DNA landscapes naturally motivate a quantification of these fluctuations by calculating the 'net displacement' of the walker after l steps, which is the sum of the unit steps u(i) for each step i" (Stanley et al., 1996: 309, my italics). From this perspective, the dynamics of the DNA sequence after i steps can be considered as a sum where the trajectory (l) can be expressed as follows:

[mathematical expression not reproducible] (1)

Where l refers to the DNA displacement (movement) and i is the number of steps. Another important indicator in this walk is given by the root mean square fluctuation about the average of the displacement (l). Statistically, this quantity can be estimated with the following relation:

[mathematical expression not reproducible] (2)

where the [DELTA]y (l) is defined by y ([l.sub.0] + l) - y([l.sub.0]) and the bars indicate the average over all positions (1) in the gene. This quantity informs us about the average sequence in the dynamics of the DNA sequences. What Stanley et al. (1996) wanted to describe is the anomalous fluctuations around this average (i.e. dispersion) and they observed that the statistical distribution of these variations follows a power law taking the following form:

F(l)~ [l.sup.[alpha]] (3)

with the critical exponent [alpha]< 2 (implying that the variable follows a stable Levy process). Visually, that means that the coding of the DNA sequences behaviour is linear on a log-log plot of f(l) as the following graph shows:

This diagram indicates a power law in the relative dispersion (RD) of fluctuations after i steps. One can observe that these fluctuations evolve in line with a power law according to which every step generates a variation that is exponentially related to the previous one. This formal structure is clarified by Stanley et al. (1996) when they assume the existence of only two kinds of nucleotides (say a and b), each of them can be represented by a step up or a step down in the DNA sequences. After k steps, the dynamics will generate a sequence of [2.sup.k] nucleotides, whose total excess of a nucleotides over the b ones is given by the following relationship:

[mathematical expression not reproducible] (4)

Schematically, this process can be summarized by the figure following on which each tree-like structure can be associated with a step in the dynamics of the DNA sequences.

This graph is important in the reasoning because it shows the long-range correlations that result from the fact that all nucleotides are descendent from a common origin. So statistically speaking, the move (l) decays exponentially with a factor k and acts therefore as a power law. This pattern of power law has a long story in biology since several scientists observed that linearity in their observations. Kleiber (1932) and Brody (1945), for example, also identified this linear relationship in their biological observations by finding that the metabolic rate of various animals had a linear function of their body mass

Stanley et al. (1996) deal with unrelated phenomena, which they describe through the same conceptual framework. After having characterized the evolution of the DNA sequences, the authors used the same analogy to describe the fluctuations of annual growth rates for firms by showing that the dynamics of sales generate the same statistical situation as the one observed for the DNA walks. Using public data published by American companies, the authors worked on the standard deviation of the annual fluctuations of sales [sigma] ([S.sub.0]) (and number of employees), which they presented as a function of the initial value of sales (initial number of employees) [S.sub.0]. Observing the evolution of this variable, they noticed that "the remarkable linearity of the [sigma] ([S.sub.0] vs [S.sub.0] function on a log-log scale over many orders of magnitude may indicate some universal law of economics that is applicable for small companies [...] as for giants of size" (Stanley et al., 1996: 311). This power law discovered by the authors takes the following form:

This diagram shows a power law dependence between the standard deviation [sigma] ([S.sub.0]) of sales and the initial level of sales ([S.sub.0]) as expressed in the following relationship:

[sigma] ([S.sub.0]) ~ [S.sub.0.sup.[alpha]] (5)

where [alpha] is empirically estimated at 0.82. This power law characterizes the evolution of sales, which increases by following a self-similar pattern. The authors assumed that this evolution has its origin in the internal structure of each firm. In so doing, they considered that the evolution of sales (or the employee number) results from N independent units (sales), which can be computed as follows:

[mathematical expression not reproducible] (6)

where the unit sales [[epsilon].sub.i] have an average of [epsilon] = [S.sub.0]/N and an annual variation u(i) independent of [S.sub.0]. In this context, the annual change in sales can be estimated by:

[mathematical expression not reproducible] (7)

The familiarity of this equation with the statistical description of the DNA sequence walk (see eq. 1) caught the attention of Stanley et al. (1996) who wrote that the evolution of sales for companies and the DNA sequence walks can be explained through the same conceptual framework: "Remarkably, the hierarchical structure of the company can be mapped exactly onto the diagram of the DNA mutations" Stanley et al. (1996: 312). Visually, we have: [10.sup.2]

Stanley et al. (1996, p. 312) described this diagram as follows: "Each level of the firm hierarchy corresponds to one generation of repeat family and each modification of the head decision by the lower level management corresponds to a mutation. Note that the [sigma] ([S.sub.0]) for firm sales is exactly F(l) for DNA sequences" [see the similarity between eq. 4 and eq. 6 for an illustration of these words].

Considering the duality (flying or sitting on the water) of sea birds' behaviour, the authors extended their conceptual framework to the description of sea birds' migration by quantifying their behaviour with the help of an electronic recording device that was placed on the legs of several birds. By emphasizing macro-statistical patterns, econobiology does not focus on the individual description of micro-elements composing the system but rather on the organicist nature of economic systems. Such way of modelling implies an implicit analogy between economic and biological systems. The following section investigates further this analogical dimension.

3. Analogies in Econobiology

An important literature exists for distinguishing analogical and metaphorical models (Hesse 1953, 1964; Hutten, 1954; Miller, 1996; Bradie, 1998; Bailer-Jones, 2002). Metaphorical models refer to a linguistic statement that has been transferred from one domain of application, where it commonly understood, to another domain in which it is unusual; whereas analogical models instead characterize statements that describe relational information through a transfer of a mathematical framework from one domain to another. In other words, metaphor is a simple descriptive comparison between two relevant domains (Bailer-Jones, 2009), while analogies are more likely to be mathematically formulated since they deal with similar dynamics, relations or processes observed in different domains - from this perspective, the extension of the Ising model by econophysicists in finance can be perceived as an analogical model. Roughly speaking, analogies are based on the understanding of something in terms of something else that is well understood and familiar. However, as Bailer-Jones (2009: 117) explained: "Being familiar does not equate with being understood, but familiarity can be a factor in understanding. This is also not to suggest that understanding can be reduced to the use of analogy, but having organized information in one domain (source) of exploration satisfactorily can help to make connections to and achieve the same in another domain (target). The aim is to apply the same pattern assumptions of structural relationship in both source and the target domains."

In their seminal article, Stanley et al. (1996: 316) wrote, "The analogy between economics and DNA walks is sufficiently strong that a similar story might evolve." It is worth emphasizing that the authors wrote the word "might," showing therefore their deflationary perspective on the use of power law as a form in which the mind can grasp the complex nature of the phenomenon. Statistical distributions are well-known for their broad applicability and there are countless examples of the same mathematics being applicable in disparate disciplines. (2) What is special in the case of econobiology actually refers to the implicit assumption associated with these power laws in biology: the idea that variables involved in the dynamics evolve simultaneously by keeping a scaling property (i.e. proportional relationship). Kleiber (1932) and Brody (1945) were the first to suggest that this kind of self-organized pattern could rule biological systems. By extending this assumption to economics, scholars in econobiology enhance the idea that economic systems could also be governed by self-organized patterns. This point is quite new from a (mainstream) economist's point of view. (3)

In this context, the real question is to know if this power law can really help to understand economic/financial phenomena. As mentioned earlier, scholars assume as an analogy between the source domain (biological systems) and the target domain (economic/financial systems). This reasoning can be summarized through a tabular representation found in Hesse (1966):

Hesse (1966) suggested clarifying the known similarities and observational ones to better understand the role of analogy in science. In accordance with this suggestion, I propose in the Table 1 above, where the horizontal relations are the relations of similarity in the mapping of the source and target domains, and the vertical relations are those between the objects and properties within each domain. What is interesting to emphasize here is the way of listing the horizontal similarities, because scholars involved in econobiology and economists might agree on these aspects. However, the kind of conclusions one can draw from these characteristics would be totally different: while the former consider that the emergence of a power law is an indication of complexity (Hughes, 1999); the latter who use another statistical lens simply do not see this power law. (4) As Bartha (2013: 6) noticed, the "manner in which we list similarities and differences, the nature of the correspondences between domains: these things are left unspecified [in Hesse's works]." Extending an earlier discussion on an analogy introduced by Keynes (1921), Hesse (1966) distinguished three kinds of analogies: negative, positive and neutral analogies. The former refers to relations that we know to be different between the two domains; the second one concerns the known (and acceptable) similarities and the latter characterizes what we do not know or what was not known before the association between the source and the target domains. In this sense, a negative analogy between biological systems and economic/financial ones could refer to the fact that in opposition with the former, the latter is composed of micro elements in economic/financial systems that have a human and social consciousness. The horizontal (known) similarities mentioned in the table above illustrate positive analogies, and the observational similarities could be seen as a neutral analogy in a sense that this similarity was neither assumed nor expected in the analogical association of the two domains. On this point, Frigg and Hartmann (2012: 14) wrote that "neutral analogies play an important role in scientific research because they give rise to questions and suggest new hypotheses." In this occurrence, we can summarize the aforementioned table as follows:

In this analogical reasoning, scholars consider that the statement according to which the dynamics of an economic/financial system follows a power law is plausible because of certain known similarities in biological systems that generate this kind of dynamics. Of course such analogical extension requires a particular interpretation of the "plausibility criteria" evoked above. Hesse (1966: 87) explained that this plausibility must be "acceptable in a scientific sense" and she added that "a tendency to co-occurrence" is an essential requirement for a good analogical association. In the case of econobiology, scholars explicitly associate this plausibility with the statistical patterns they observe in economic/financial data. From biologists' perspective, the fact that power laws are regularly observed in empirical data and that these patterns can be explained mathematically appear to be an acceptable scientific reason for considering the plausibility evoked above. In other words, for scholars involved in econobiology, this "co-occurrence" of power law in the source and target domains takes the form of a formal analogy.

Hesse (1966) distinguishes between two categories of analogies: formal ones and material ones. When the analogous refers to material entities (material analogy), the association between two domains is mainly based on the sameness or resemblance of common properties. These similarities being observable, the three levels of analogy evoked above are always present, but the negative one appears to be more obvious (Mellor, 1968). For instance, Earth and Mars are both celestial bodies, (approximately) spherical, have moons and orbit the sun (positive analogy) but the observability of these common properties also makes obvious their differences: the absence of water/atmosphere on Mars, the distance between these two bodies and the sun, the periodicity of their respective circumvolution, etc. When two systems are related by formal analogy, they are both interpreted through the same mathematical framework. Very often, this kind of analogy concerns a situation in which the dynamics between certain ingredients within one domain are perceived as identical (or comparable) to the relations between elements of another domain (Bailer-Jones, 2009: 57). According to Mellor (1968) and Falkenhainer et al. (1989), when the analogy between two domains refers to relations or dynamics, then, although the negative analogy is still present, it is less important, since only the formal evolution of the domain is taken as a formal analogy focusing therefore on the movement of elements rather than their resemblances.

4. Conclusion

The last economic crisis generated a lot of debates and questions about the ability of economists to deal with economic complexity. Econobiology offers an alternative conceptual framework inspired by complexity studies for a better understanding of economic systems. A complexity-based thinking will attempt to use/to combine these new perspectives in the elaboration a new conceptual framework for recentring economics on different key themes which appear to characterize the contemporary evolution of economic systems: the importance of coordination and interactions between agents as a generator of slow emerging events and latent self-organization. This kind of methodology focuses on change rather than statics, on macroscopic patterns rather than causal individual events and it provides an organicist perspective of economic systems (rather than a reductionist approach as usually adopted by the economic mainstream). The last financial crisis showed the growing holistic nature of economic systems that are more and more interrelated. In such context, a strictly reductionist approach (as it is implemented in the economic mainstream) might not be appropriate anymore. It is worth mentioning that a recent document published by OECD (2016) recommended/promoted a complexity-based approach in economics with two major implications for policymakers: predictability and explanation (i.e. providing an alternative way of describing economic systems).

NOTES

(1.) This field deals with topics such as the dynamics of fish populations (Gradmont, 1998); the predatory-prey dynamics between insects, birds and trees in the forest (Ludwig et al., 1978) or differential games applied to the exhaustion of a fishery (Hernandez-Flores et al., 2018). For further information about bioeconomics, see Sundar (2011) or check the website of the Journal of Bioeconomics: https://link.springer.com/journal/10818

(2.) I thank the reviewers for inviting me to nuance this aspect. This point is especially true for the use of power laws that have been "observed" in many different phenomena (see Newman, 2005) for further details on the applicability of power laws.

(3.) Of course, economists know and use power laws but they use these tools as descriptive framework without necessary drawing conclusion from the scaling properties of these laws (for more information about the use of power laws by economists, see Gabaix 2009, or Akdere and Schinckus, 2017). In the same vein, some economists working on Hayekian approach of economics are aware about self-organized patterns but their level of analysis is quite rhetorical and not analytical (for further information about Hayek and the use of power laws, see Schinckus, 2017).

(4.) See Jovanovic and Schinckus (2017) for further details on this aspect.

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CHRISTOPHE SCHINCKUS

christophe.schinckus@rmit.edu.vn

RMIT University Vietnam

Received 24 January 2018 * Received in revised form 1 March 2018

Accepted 2 March 2018 * Available online 25 March 2018

doi:10.22381/RCP1720183
Table 1 Similarities between biological and economic/financial systems

Biological systems                  Economic/financial systems

Known similarities
Interacting elements                Interacting agents
High number of micro components     High number of individual agents
Complex micro interactions          Complex micro behaviours
Observational similarity
Dynamics following a power law      Dynamics following a power law
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Date:Jan 1, 2018
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