Previous work has shown that species interacting in an ecosystem and actors transacting in an economic context may have notable similarities in behavior. However, the specific mechanism that may underlie similarities in nature and human systems has not been analyzed. Building on stochastic food-web models, we propose a parsimonious bipartite-cooperation model that reproduces the key features of mutualistic networks - degree distribution, nestedness and modularity -- for both ecological networks and socio-economic networks. Our analysis uses two diverse networks. Mutually-beneficial interactions between plants and their pollinators, and cooperative economic exchanges between designers and their contractors. We find that these mutualistic networks share a key hierarchical ordering of their members, along with an exponential constraint in the number and type of partners they can cooperate with. We use our model to show that slight changes in the interaction constraints can produce either extremely nested or random structures, revealing that these constraints play a key role in the evolution of mutualistic networks. This could also encourage a new systematic approach to study the functional and structural properties of networks. The surprising correspondence across mutualistic networks suggests their broadly representativeness and their potential role in the productive organization of exchange systems, both ecological and social.
The analogy between ecological and economic systems is not new. Biologists have always being intrigued about the economic aspects of nature [1,2], and economists and sociologists have taken insight from biological systems to shed new light on the factors shaping socio-economic systems. For instance, researchers have adapted biological models that focus on constructs such as niche width, resource partitioning, or specialization and generalization to explain the birth and death rates of organizational populations [3,4]. More recently, multidisciplinary approaches have led to the discovery of significant structural similarities across different network domains, including biological and socio-economic networks [5,6,7]. This has awakened an even more spirited search for common structural properties between ecological and economic networks [8,9], and pointed to a greater need for work on mutually-beneficial interactions across realms.
Cooperation [10,11,12] is a central concept in biological and social studies, and although the evolution of cooperation was initially modeled for homogeneous populations, subsequent work has also included spatial effects [13]. The recent development of simulation models for evolutionary games on graphs [14] and collaborative social networks [15] provides a starting point for addressing the question of how cooperative structures are assembled. In ecology, contemporary research on mutualistic networks provides us with an increasingly detailed picture of the complex set of cooperative interactions between different species in an ecosystem, and demonstrates that purely local interactions can generate highly structured macroscopic patterns of mutually beneficial exchanges [16].
However, despite the increasing interest in cooperative systems, we currently lack models that allow us to connect the cooperative behavior at the level of individuals with emergent global network properties. Furthermore, although cooperation appears as distinctive characteristic at different levels of organization ranging from groups of animals to human society [17], it has been difficult to find empirical evidence showing similar patterns of cooperation shared across these levels. In previous work [18], we have proposed a bipartite-cooperation model (BC model) that can replicate key properties of mutualistic networks. To test the BC model across ecological and socio-economic networks, we have used ten large pollination datasets that have been compiled in the literature, and a unique and extensive, economy -wide dataset of designers and contractors engaged in joint production in the New York City garment industry. In the present paper, we attempt to go beyond showing associations in the assembling principles of these ecological and socio-economic networks to show the effects of different organizing mechanisms on the hierarchical arrangement of these networks. In Sections 2 and 3 we discuss some of the main features of mutually-beneficial interactions in ecological and socio-economic networks respectively. Sections 4, 5 and 6 describe the BC model, the empirical data and the validation of the BC model respectively. Section 7 introduces a further justification of the BC model using empirical data. In Section 8 we use the BC model to study the effects of different organizing mechanisms and interaction constraints on the hierarchical arrangement of empirical networks. Finally, Section 9 summarizes our conclusions and overall findings.
In ecology, mutualistic networks are formed by the mutually-beneficial interactions between populations of different species (e.g. P for plants and A for animals) [16]. Species in class P offer rewards with certain characteristics to attract species in class A. These individual attributes, determined by their own reward traits, may also have evolved to reduce exploitation and favor mutualism [19]. Species in class A foraging for resources can benefit from the rewards offered by a given species in class P if the respective foraging traits (e.g. efficiency, morphology, behavior) and reward traits (e.g. quantity, quality, availability) are complementary [20,21]. External factors such as the environmental context (e.g. population density, geographic variation) attenuate or amplify the value of reward and foraging traits, and impact the number of potential partners that a given species cooperates with [22,23,24]. Furthermore, Rezende et al. [25] have shown that mutualistic networks exhibit hierarchical constraints introduced by phylogenetic relationships between species in the same class, which impact mutualistic interaction patterns by favoring ecological similarity.
Recent work has found key structural properties in mutualistic networks. Mutuallybeneficial interactions between species exhibit broad-scale distributions and a significant presence of asymmetric interactions (i.e. links connecting high-degree to low-degree nodes), which can be the result of mechanisms such as aging, forbid
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