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his article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright Author's personal copy Physics Letters A 377 (2013) 250–256 Contents lists available at SciVerse ScienceDirect Physics Letters A www.elsevier.com/locate/pla Ecological analysis of world trade ∗ L. Ermann b,a,D.L.Shepelyanskya, a Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, F-31062 Toulouse, France b Departamento de Física Teórica, GIyA, Comisión Nacional de Energía Atómica, Buenos Aires, Argentina article info abstract Article history: Ecological systems have a high complexity combined with stability and rich biodiversity. The analysis Received 22 March 2012 of their properties uses a concept of mutualistic networks and provides a detailed understanding of Received in revised form 28 August 2012 their features being linked to a high nestedness of these networks. Using the United Nations COMTRADE Accepted 31 October 2012 database we show that a similar ecological analysis gives a valuable description of the world trade: Availableonline21November2012 countries and trade products are analogous to plants and pollinators, and the whole trade network Communicated by A.R. Bishop is characterized by a high nestedness typical for ecological networks. Our approach provides new Keywords: mutualistic features of the world trade. Complex networks © 2012 Elsevier B.V. All rights reserved. Nestedness World trade p 1. Introduction of trade transactions Mc,c expressed in USD for a given product (commodity) p from country c to country c in a given year (from Ecological systems are characterized by high complexity and 1962 to 2009). For product classification we use 3-digit Standard biodiversity [1] linked to nonlinear dynamics and chaos emerging International Trade Classification (SITC) Rev. 1 with the number of in the process of their evolution [2,3]. The interactions between products N p = 182. All these products are described in [19] in the species form a complex network whose properties can be analyzed commodity code document SITC Rev. 1. The number of countries by the modern methods of scale-free networks [4–7]. An important = = varies between Nc 164 in 1962 and Nc 227 in 2009. The im- (i) Nc p feature of ecological networks is that they are highly structured, port and export trade matrices are defined as M = M p,c c =1 c,c being very different from randomly interacting species [7,8].Re- (e) Nc p and M = M respectively. We use the dimensionless cently it has been shown that the mutualistic networks between p,c c =1 c ,c (i) = (i) (e) = (e) plants and their pollinators [8–12] are characterized by high nest- matrix elements m M /Mmax and m M /Mmax where = { [ (i) ] [ (e) ]} edness [13–16] which minimizes competition and increases bio- for a given year Mmax max max M p,c , max M p,c .Thedistri- diversity. It is argued [14] that such type of networks appear in bution of matrix elements m(i), m(e) in the plane of indexes p various social contexts such as garment industry [15] and banking and c, ordered by the total amount of import/export in a de- [17,18]. Here we apply a nestedness analysis to the world trade creasing order, is shown in Fig. 1 for years 1968 and 2008 network using the United Nations COMTRADE database [19] for (years 1978, 1988, 1998 are shown in Fig. S-1 of Supporting the years 1962–2009. Our analysis shows that countries and trade Information (SI)). These figures show that globally the distribu- products have relations similar to those of plants and pollinators tions of m(i), m(e) remain stable in time especially in a view of and that the world trade network is characterized by a high nest- 100 times growth of the total trade volume during the period edness typical of ecosystems [14]. This provides new mutualistic 1962–2009. The fluctuations of m(e) are visibly larger compared characteristics for the world trade. to m(i) case since certain products, e.g. petroleum, are exported by only a few countries while it is imported by almost all coun- 2. Results tries. To use the methods of ecological analysis we construct the mu- The mutualistic World Trade Network (WTN) is constructed on tualistic network matrix for import Q (i) and export Q (e) whose the basis of the UN COMTRADE database [19] from the matrix matrix elements take binary value 1 or 0 if corresponding elements m(i) and m(e) are respectively larger or smaller than a certain trade threshold value μ.Thefractionϕ of nonzero matrix ele- Corresponding author. − − * ments varies smoothly in the range 10 6 μ 10 2 (see Fig. S-2 E-mail address: [email protected] (L. Ermann). URLs: http://www.tandar.cnea.gov.ar/~ermann (L. Ermann), of SI) and the further analysis is not really sensitive to the ac- http://www.quantware.ups-tlse.fr/dima (D.L. Shepelyansky). tual μ value inside this broad range. Indeed, the variation of μ in 0375-9601/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physleta.2012.10.056 Author's personal copy L. Ermann, D.L. Shepelyansky / Physics Letters A 377 (2013) 250–256 251 Fig. 1. Normalized import/export WTN matrix elements m(i) and m(e) shown on left/right panels for years 1968 (bottom) and 2008 (top). Each panel represents the (i) (i) (e) (e) dimensionless trade matrix elements m = M /Mmax and m = M /Mmax on a thee-dimensional (3D) plot as a function of indexes of countries and products. Here products/countries (p = 1,...,N p and c = 1,...,Nc ) are ordered in a decreas- ing order of product/country total import or export in a given year. The color is proportional to the amplitude of the matrix element changing from red (for amplitude maximum) to blue (for zero amplitude). Each panel shows the 3D distribution and its projection on 2D plane of countries–products in which the amplitude of matrix elements is shown by the same color as in 3D. (For interpretation of the ref- erences to color in this figure legend, the reader is referred to the web version of this Letter.) −5 −3 the range 10 μ 10 by two orders of magnitude produces a rather restricted variation of ϕ only by a factor two. It is important to note that in contrast to ecological systems [14] the world trade is described by a directed network and hence we characterize the system by two mutualistic matrices Q (i) and Q (e) corresponding to import and export. Using the standard nestedness BINMATNEST algorithm [20] we determine the nestedness parameter η of the WTN and the related nestedness temperature T = 100(1 − η). The algorithm reorders lines and columns of a mutualistic matrix concentrating nonzero elements as much as possible in the top-left corner and thus providing Fig. 2. Nestedness matrices for the plant–animal mutualistic networks on top panels, information about the role of immigration and extinction in an and for the WTN of countries–products on middle and bottom panels. Top-left and top-right panels represent data of ARR1 and WES networks from [12,21].TheWTN ecological system. A high level of nestedness and ordering can be − matrices are computed with the threshold μ = 10 3 and corresponding ϕ ≈ 0.2for reached only for systems with low T . It is argued that the nested years 1968 (bottom) and 2008 (middle) for import (left panels) and export (right architecture of real mutualistic networks increases their biodiver- panels). Red and blue represent unit and zero elements respectively; only lines and sity. columns with nonzero elements are shown. The order of plants–animals, countries– The nestedness matrices generated by the BINMATNEST al- products is given by the nestedness algorithm [20], the perfect nestedness is shown by green curves for the corresponding values of ϕ. (For interpretation of the refer- gorithm [20] are shown in Fig. 2 for ecology networks ARR1 ences to color in this figure legend, the reader is referred to the web version of this (Npl = 84, Nanim = 101, ϕ = 0.043, T = 2.4) and WES (Npl = 207, Letter.) Nanim = 110, ϕ = 0.049, T = 3.2) from [12,21]. Using the same algorithm we generate the nestedness matrices of WTN using the mutualistic matrices for import Q (i) and export Q (e) for the WTN − in years 1968 and 2008 using a fixed typical threshold μ = 10 3 (see Fig.

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