The hidden laws that pervade complex biological and social phenomena

Team lead: Geoffrey West, Distinguished Professor, Science Board, Science Steering Committee, and Past President, Santa Fe Institute

The primary aim of this research program is to construct a quantitative, predictive, mechanistic unifying theory, based on underlying mathematizable principles, for the structure, dynamics, and growth of social organizations such as cities, companies, and biological communities. This is clearly a fundamental scientific challenge as the planet urbanizes at an exponential rate. Two hundred years ago the U.S. was predominantly agricultural with barely 4% of its people living in cities, whereas today it is climbing toward 80%; more than half of the world’s population is now urbanized and this will likely reach 80% by 2050 (U.N.-Habitat 2010). Because cities are the centers of innovation, power, and wealth creation, as well as sources of crime, pollution, and disease (entropy production), the future of humanity is inextricably linked to the fate of cities (Jacobs 1984, Bairoch 1988, Glaeser 2010, Florida 2003, 2008).

More generally, our scientific puzzle is to understand how increasingly complex social systems, which have evolved only over the past 10,000 years, can continue to coexist with the “natural” biological world, which evolved, and has persisted, over billions of years (West 2010). Cities and companies, as consumers of energy and resources, and producers of artifacts and information, have often been compared to organisms and ecosystems (witness phrases like “urban metabolism,” the “DNA of a company,” or the “ecology of the market place”).

Are these only qualitative metaphors, or is there quantitative and predictive substance in the implication that social organizations are extensions of biology, satisfying similar principles and constraints? Are the structures and dynamics that evolved with human socialization fundamentally different from those in biology? Is New York a very large whale and Microsoft an enormous beehive? Why then do almost all cities persist, whereas all companies, even the most powerful and seemingly invincible, die? Can we develop a theory to predict the approximate future trajectory of San Francisco and Nairobi and the longevity of Google? (Bettencourt & West, 2010).

Cities and companies, like life itself, are quintessential multi-dimensional complex adaptive systems whose emergent properties act over many spatio-temporal scales (Mitchell 2008, Batty 2005). The continuing challenge of adaptability, evolvability, and growth requires that these systems are scalable: the same generic underlying dynamical and organizational principles operate at multiple spatio-temporal scales, and this has led to an extraordinary resilience. The process of life covers more than 30 orders of magnitude in mass ranging from the molecules of metabolism (energy) and the genetic code (information) up through microbes and mammals to ecosystems and social organizations. Characteristic time scales vary by over 5 orders of magnitude: a bacterium can operate at 10-13 watts and live for an hour, whereas a human metabolizes at 90 watts and can live for a century. A city can use 10 billion watts and live “forever.” Over this immense spectrum of size, life uses basically the same fundamental constituents and processes to create an amazing variety of forms, functions, and dynamical behaviors.

Scalability plays a pivotal conceptual role in developing our theoretical framework. A central hypothesis is that scaling is a phenomenological manifestation of the dynamics and geometry of the multiple emergent infrastructural and social network systems that mechanistically maintain cities, companies and organisms. Scaling as a manifestation of underlying dynamics and structure has been instrumental in gaining deeper insights into problems across the entire spectrum of science and technology (West 1988, Barenblatt 2003). Phase transitions, chaos, the discovery of quarks, the unification of fundamental forces, and the evolution of the universe from the big bang are but a few of the more significant examples where scaling has illuminated important universal principles or structure.

Despite their amazing diversity and complexity, living systems manifest an extraordinary simplicity and universality in how key structural and dynamical processes scale across an immense range of energy and size from cells through multi-cellular organisms to cities and companies. For example, in biology, almost all physiological characteristics, traits, and life history events, Y(M), scale with body mass, M, as simple power laws: Y(M)=Y0Mb whose exponents, b, are approximate simple multiples of ¼ (Schmidt-Nielsen 1984, Calder 1984). Metabolic rate of both individual organisms and social insect communities scale as M3/4. Almost all time-scales (e.g., life-spans, growth, evolutionary, and diffusion rates) and sizes (e.g., genome lengths, tree heights, RNA densities) typically scale with similar quarter power exponents. This universality and simplicity strongly suggests that, despite the stochasticity inherent in natural selection, fundamental constraints underlie much of the coarse-grained generic structure and organization of living systems (West and Brown, 2005, West et al 1997 and 1999).

These universal quarter power scaling laws follow mathematically from generic underlying principles that constrain the dynamics and geometry of distribution networks that sustain organisms. Highly complex self-sustaining structures, whether cells, organisms, ecosystems, cities, or corporations require close integration of enormous numbers of constituent units, or agents, that need efficient servicing. This is accomplished via optimized space-filling, fractal-like, branching networks whose constraints are independent of specific organismic design. These ideas lead mathematically to a general quantitative, predictive framework that captures many essential features of diverse biological systems, including the cardiovascular and respiratory systems, forest communities, ontogenetic growth, cancer, aging and death, sleep, cell size, and evolutionary rates (Gillooly et al 2001, 2002, 2005, West et al 2002).

Because these networks determine rates at which energy and resources are delivered to functional terminal units (e.g., cells), they set the pace of all physiological processes including life history events. Theory predicts that characteristic times such as life spans, turnover times, and times to maturity scale as M1-b ~ M1/4, whereas rates such as heart and evolutionary rates, scale as Mb-1 ~ M-1/4, all in agreement with data. Furthermore, since metabolic rate per unit mass (effectively, cellular metabolic rate) decreases as M-1/4, larger organisms systematically consume less energy per second to support the same unit mass of tissue. Thus, the pace of biological life is dominated by economies of scale and systematically slows down with increasing size of the organism (Brown et al 2004).

Remarkably, cities and companies also manifest “universal” power law scaling, and this discovery provides a major motivation for this program (Kuhnert et al 2006, Bettencourt et al 2007a&b, 2008, 2009, 2010, Bettencourt & West 2010). These scaling regularities were revealed in previous work from an analysis of worldwide datasets which showed that the scaling exponents take on approximately the same value, whether measured in the U.S., China, Japan, Europe, or Latin America at any time and for a wide range of metrics. For cities, all socio-economic metrics, such as wages, wealth, the number of patents, violent crime and educational institutions, scale with population size with a common exponent b ~ 1.15 (> 1, “superlinear” scaling), whereas all infrastructural metrics, such as length of roads, electrical cables, and number of gas stations, scale with b ~ 0.85 (< 1, “sublinear” scaling). Thus, on a per capita basis, socio-economic quantities, whether wages, crime or patents, systematically increase to the same degree as city size increases; and, to the same degree, there are increasing savings from economies of scale in all infrastructural quantities. Put slightly differently, this says that, if city size is doubled, whether from 20,000 to 40,000 or from 2M to 4M, then, on average, wages, wealth, the number of patents, violent crime and educational institutions all increase by approximately the same degree (by about 15%)!

A major component of this project is to develop a network theory of urban social interaction based on underlying principles that transcend particularities of individual cities and specific activities with the goal of deriving mathematically the approximately 15% deviation from linearity in the scaling exponents and to understand what fundamental socio-economic parameters determine its value. It will extend the network framework successfully developed in the biological context to social organizations. Minimizing losses and dissipation, whether social, informational or energetic, to maximize competitive advantage via optimized distribution networks is clearly relevant for cities and companies. The classic Lagrange formalism used in biology for addressing constrained optimization problems will also be used here.

We will investigate the generic mathematical structure and dynamics of social networks within organizations and their role in facilitating continuous multiplicative innovation and wealth creation. Our goal is to develop a quantitative theory for how the geometric, topological and dynamical properties of energy, resource, and infrastructural networks integrate with those of information, innovation and wealth creation networks. We will explore in what way, and to what extent, successful organizational structures have evolved towards joint optimization of energy and information distributions (see project 1) and how economies of scale associated with infrastructure (and therefore with energetic and material needs) interface and integrate with networks associated with information, creativity, innovation, and wealth creation (see project 3). We will investigate what, if any, optimization principles are at work; is wealth creation, as represented by income distribution, maximized or is it innovation as represented, for example, by the number of patents produced? These questions will be addressed integrating powerful techniques of theoretical physics, including the language of field theory, the renormalization group, information theory, statistical physics and thermodynamics with more traditional social science methodology; world-wide datasets, case studies, model building and computer simulations will test and refine theory (Brock & Durlauf 2001, Mas-Collel et al 1995, Barro and Sala-i-Matin 2003, Romer 1986, Arbesman et al 2009).

There is a fundamental characteristic of social networks that is quite distinct from biological and infrastructural ones. In biology, local network properties, such as branch sizes and flows of energy and resources systematically increase in a self-similar fashion from terminal units (capillaries, cells, etc.) up through the network. This generically leads to sub-linear scaling (b < 1) and, consequently, to economies of scale, the slowing of the pace of life and to 1/4-powers, in agreement with data. However, in social networks with a level structure beginning with individuals up through families to increasingly larger working clusters, network variables such as strengths of social interaction and flows of information progressively decrease, generically leading to superlinear scaling (b > 1) and an accelerating pace of life, as observed. Our strategy is to use an optimization principle (such as maximizing interactions, information flow, wealth creation, or possibly minimizing social “friction” and entropy production in information exchange) to construct a Lagrange function which captures the essential dynamics responsible for the geometric multiplicative processes of innovation to calculate the universal exponents b.

The super- or sub-linear nature of scaling has profound consequences for the growth of the system (Bettencourt et al 2007, West et al 2001). Resources are the necessary fuel for growth; in biology, this is metabolism, which scales sublinearly, whereas in cities it is wealth creation derived from innovation, which scales superlinearly. In companies, it might be profits (see below). In any case, we can apportion these into allocations for maintenance and to growth leading to a mathematical growth equation for how the size of the system changes with age. This results in two possible growth scenarios, one determined by the dominance of economies of scale, the other by increasing returns to scale. The former is the situation occurring in biological organisms and social insect communities, which eventually stop growing, reaching a predictable approximately fixed size at maturity. A company may similarly grow to a finite size once it has explored as efficiently as possible its market niche (Chan et al 2003, Penrose 1959, Audretsch et al 2006, Weitzman 1998).

On the other hand, in cities where growth is driven by superlinear scaling, wealth creation and social innovation, growth is unbounded and super-exponential, and does not typically stabilize to an “asymptotic” state. To maintain such growth in the light of resource limitation requires continuous cycles of paradigm-shifting innovations such as those associated with the discovery of iron, steam, coal, computation, and most recently digital technology. Theory suggests, and data support, the idea that continuous growth driven by wealth creation requires such discoveries must occur at an ever-increasing accelerated pace: the time between successive innovations is predicted to systematically and inextricably get shorter and shorter. We will further develop the growth theory by disaggregating resource and maintenance components and use the framework to analyze growth trajectories of cities and companies and investigate to what extent they are dominated by economies of scale versus increasing returns.

We have performed preliminary (unpublished) analyses showing that companies also manifest power law scaling. Several common economic indicators across different business sectors and countries, including net income and total assets, scale with company size. Our results suggest that firms are not like cities, but are much more like organisms in that they are dominated by sub-linear scaling and do not, on average, manifest increasing returns to scale. While revenues and cost of scales scale linearly with number of employees, net profits scale sublinearly. Furthermore, as companies grow, R&D expenses like net profits decrease on a per employee basis, implying that investments in innovation decrease per unit of revenue. This suggests that profit margins asymptotically vanish so that growth decelerates and eventually ceases, potentially putting companies seriously at risk.

A major component of this project is to conduct vigorous analyses of these datasets to verify our preliminary results and conclusions. This will be used to elaborate on the theoretical framework to explore the possibility of constructing a predictive framework for the birth, growth and mortality of companies in terms of failures to appropriate sufficient resources for maintenance and innovation. We will develop formal network models of these processes extending the framework developed for cities to understand the origins of the eventual dominance of economies of scale (driven by administrative requirements) over open-ended increasing returns (driven by innovation).

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