[Paper Review] The Build-Up of Diversity in Complex Ecosystems

Andrea Tacchella, Riccardo Di Clemente+2 more|arXiv (Cornell University)|Sep 12, 2016

Economic and Technological Innovation18 references5 citations

TL;DR

This paper proposes that the build-up of diversity in complex ecosystems—observed as diversity explosions and nested interaction patterns—arises from a probabilistic mechanism driven by extreme heterogeneity in the 'usefulness' of fundamental building blocks. Using a maximally entropic tripartite network model, it shows that a scale-free (power-law) distribution of usefulness reproduces real-world stylized facts in biological, economic, and technological systems with high accuracy, unlike exponential or uniform distributions.

ABSTRACT

Diversity is a fundamental feature of ecosystems, even when the concept of ecosystem is extended to sociology or economics. Diversity can be intended as the count of different items, animals, or, more generally, interactions. There are two classes of stylized facts that emerge when diversity is taken into account. The first are Diversity explosions: evolutionary radiations in biology, or the process of escaping 'Poverty Traps' in economics are two well known examples. The second is nestedness: entities with a very diverse set of interactions are the only ones that interact with more specialized ones. In a single sentence: specialists interact with generalists. Nestedness is observed in a variety of bipartite networks of interactions: Biogeographic, macroeconomic and mutualistic to name a few. This indicates that entities diversify following a pattern. Since they appear in such very different systems, these two stylized facts point out that the build up of diversity is driven by a fundamental probabilistic mechanism, and here we sketch its minimal features. We show how the contraction of a random tripartite network, which is maximally entropic in all its degree distributions but one, can reproduce stylized facts of real data with great accuracy which is qualitatively lost when that degree distribution is changed. We base our reasoning on the combinatoric picture that the nodes on one layer of these bipartite networks can be described as combinations of a number of fundamental building blocks. The stylized facts of diversity that we observe in real systems can be explained with an extreme heterogeneity (a scale-free distribution) in the number of meaningful combinations in which each building block is involved. We show that if the usefulness of the building blocks has a scale-free distribution, then maximally entropic baskets of building blocks will give rise to very rich behaviors.

Motivation & Objective

• To explain the emergence of two universal stylized facts in complex systems: diversity explosions and nested interaction patterns.
• To investigate whether a common probabilistic mechanism underlies diversity build-up across disparate domains such as biology, economics, and sociology.
• To determine the role of 'usefulness'—a measure of how often a building block is involved in meaningful combinations—in shaping system-level diversity and complexity.
• To test whether a power-law distribution of usefulness is necessary to reproduce empirical data on nestedness and ubiquity in real-world networks.
• To develop a minimal, entropic model of tripartite networks that captures the essential features of real ecosystemic diversity dynamics.

Proposed method

• Construct a tripartite network model with three layers: collectors (e.g., species, countries), building blocks (e.g., traits, technologies), and combinations (e.g., interactions, products).
• Impose maximum entropy on all degree distributions except one: the distribution of 'usefulness'—the number of combinations a building block participates in.
• Use combinatorics to model how collectors form baskets of building blocks, with diversity determined by the number of unique combinations they access.
• Simulate the system under different distributions of usefulness (power-law, exponential, uniform) and compare resulting matrices of complexity and ubiquity to real data.
• Analyze the fitness-diversification relationship to identify 'Poverty Traps' and regime shifts in system dynamics.
• Validate model predictions against empirical data from 59 plant-pollinator networks and global economic datasets.

Experimental results

Research questions

• RQ1 What underlying mechanism explains the co-occurrence of diversity explosions and nestedness across diverse complex systems?
• RQ2 How does the distribution of 'usefulness'—the number of meaningful combinations a building block participates in—affect the emergence of real-world network structures?
• RQ3 Why does a power-law distribution of usefulness reproduce empirical data better than exponential or uniform distributions?
• RQ4 What role does fitness play in determining the return on increased complexity in diverse systems?
• RQ5 Can a minimal, entropic model of tripartite networks reproduce the key stylized facts of real ecosystems without fine-tuning?

Key findings

• A power-law distribution of usefulness in building blocks produces a qualitative match with real-world data in terms of ubiquity versus complexity ranking, outperforming exponential and uniform distributions.
• The model reproduces the 'Poverty Trap' regime, where low-fitness collectors gain little diversity from increased complexity, and a high-fitness regime where gains are substantial, mirroring real economic and biological data.
• The dynamics of diversity build-up show a sharp transition between regimes only when usefulness follows a fat-tailed (power-law) distribution, not when it is exponential.
• Empirical data from 59 plant-pollinator networks show a clear distinction between ubiquity and complexity, a pattern only explainable by a fat-tailed distribution of usefulness.
• The model’s predictions align closely with real-world data in both macroeconomic (country-product) and biological (pollinator-plant) networks, suggesting a universal mechanism.
• Genetic variant frequencies in human populations and technological code frequencies in patents both exhibit scale-free distributions, supporting the biological and technological plausibility of the model.