The dynamics of nestedness predicts the evolution of industrial ecosystems

Abstract

In economic systems, the mix of products that countries make or export has been shown to be a strong leading indicator of economic growth. Hence, methods to characterize and predict the structure of the network connecting countries to the products that they export are relevant for understanding the dynamics of economic development. Here we study the presence and absence of industries in international and domestic economies and show that these networks are significantly nested. This means that the less filled rows and columns of these networks' adjacency matrices tend to be subsets of the fuller rows and columns. Moreover, we show that their nestedness remains constant over time and that it is sustained by both, a bias for industries that deviate from the networks' nestedness to disappear, and a bias for the industries that are missing according to nestedness to appear. This makes the appearance and disappearance of individual industries in each location predictable. We interpret the high level of nestedness observed in these networks in the context of the neutral model of development introduced by Hidalgo and Hausmann (2009). We show that the model can reproduce the high level of nestedness observed in these networks only when we assume a high level of heterogeneity in the distribution of capabilities available in countries and required by products. In the context of the neutral model, this implies that the high level of nestedness observed in these economic networks emerges as a combination of both, the complementarity of inputs and heterogeneity in the number of capabilities available in countries and required by products. The stability of nestedness in industrial ecosystems, and the predictability implied by it, demonstrates the importance of the study of network properties in the evolution of economic networks.

Figure 1. The nestedness of international and domestic economies.

a Country-product network for the year 2000. b Municipality-industry network for the year 2005. c Bascompte et al. null model for the matrix shown in a. d Bascompte et al. null model for the matrix presented in b. In a–d red lines indicate the diversity of a location and the ubiquity of an industry (see full text for details). e Evolution of the density, or fill, of the country-product network between 1985 and 2009. f Evolution of the NODF of the country-product network between 1985 and 2009 (green), its corresponding Bascompte et al. null model (blue, upper and lower lines indicate 95% conf. intervals), and that of a matrix that started identical to that for 1985, but that was evolved by considering an equal number of appearances and disappearances than in the original data (red, upper and lower lines indicate 95% conf. interval). g Same as f but for the municipality-industry network (see SM for results with Atmar and Patterson's temperature metric).

Figure 2. Nestedness predicts appearing and disappearing industries.

a The country-product network for the year 1993 is shown in grey. Green dots show the location of industries that were observed to appear between 1993 and 2000. b Same as a, but with the industries that disappeared in that period shown in Orange. c The municipality-industry network is shown in grey and green dots show the location of industries that were observed to appear between 2005 and 2008. d Same as c, but with the industries that disappeared in that period shown in Orange. e–h Deviance residuals of the regression presented in (1) applied to the presences-absences shown in a–d. i–l ROC curves summarizing the ability of the deviance residuals shown in e–h, to predict the appearances and disappearances highlighted in a–d.

Figure 3. Predicting appearances and disappearances using nestedness.

a Number of appearances for every pair of years in the country-product network. b Number of disappearances for every pair of years for the country-product network. c Accuracy of the predictions for each pair of years measured using the Area Under the ROC Curve (AUC). d Average number of appearances and disappearances for the Chilean data (error bar smaller than symbol). e Average accuracy of the predictions for the municipality-industry network. Error bars indicate 99% confidence intervals. f Distribution for the distance to the diversity-ubiquity line obtained for the observed appearances and for an equal number of random appearances. g Same as f but for disappearances. h Same as f, but for the municipality-industry network. i Same as h but for disappearances.

Figure 4. Modeling nestedness.

a Illustration of the binomial model. From left to right; C_ca, P_pa and the resulting M_cp. b Illustration of the uniform model. From left to right C_ca, P_pa and the resulting M_cp. c NODF as a function of matrix fill for the country-product network (green), the uniform model (orange), the binomial model (red), and the Bascompte et al null model (blue).