Developing a predictive science of the biosphere requires the integration of scientific cultures.

Increasing the speed of scientific progress is urgently needed to address the many challenges associated with the biosphere in the Anthropocene. Consequently, the critical question becomes: How can science most rapidly progress to address large, complex global problems? We suggest that the lag in the development of a more predictive science of the biosphere is not only because the biosphere is so much more complex, or because we do not have enough data, or are not doing enough experiments, but, in large part, because of unresolved tension between the three dominant scientific cultures that pervade the research community. We introduce and explain the concept of the three scientific cultures and present a novel analysis of their characteristics, supported by examples and a formal mathematical definition/representation of what this means and implies. The three cultures operate, to varying degrees, across all of science. However, within the biosciences, and in contrast to some of the other sciences, they remain relatively more separated, and their lack of integration has hindered their potential power and insight. Our solution to accelerating a broader, predictive science of the biosphere is to enhance integration of scientific cultures. The process of integration-Scientific Transculturalism-recognizes that the push for interdisciplinary research, in general, is just not enough. Unless these cultures of science are formally appreciated and their thinking iteratively integrated into scientific discovery and advancement, there will continue to be numerous significant challenges that will increasingly limit forecasting and prediction efforts.

Idea engines: Unifying innovation & obsolescence from markets & genetic evolution to science.

Innovation and obsolescence describe dynamics of ever-churning and adapting social and biological systems, concepts that encompass field-specific formulations. We formalize the connection with a reduced model of the dynamics of the "space of the possible" (e.g., technologies, mutations, theories) to which agents (e.g., firms, organisms, scientists) couple as they grow, die, and replicate. We predict three regimes: The space is finite, ever growing, or a Schumpeterian dystopia in which obsolescence drives the system to collapse. We reveal a critical boundary at which the space of the possible fluctuates dramatically in size, displaying recurrent periods of minimal and of veritable diversity. When the space is finite, corresponding to physically realizable systems, we find surprising structure. This structure predicts a taxonomy for the density of agents near and away from the innovative frontier that we compare with distributions of firm productivity, COVID diversity, and citation rates for scientific publications. Our minimal model derived from first principles aligns with empirical examples, implying a follow-the-leader dynamic in firm cost efficiency and biological evolution, whereas scientific progress reflects consensus that waits on old ideas to go obsolete. Our theory introduces a fresh and empirically testable framework for unifying innovation and obsolescence across fields.

A general theory for temperature dependence in biology.

At present, there is no simple, first principles-based, and general model for quantitatively describing the full range of observed biological temperature responses. Here we derive a general theory for temperature dependence in biology based on Eyring-Evans-Polanyi's theory for chemical reaction rates. Assuming only that the conformational entropy of molecules changes with temperature, we derive a theory for the temperature dependence of enzyme reaction rates which takes the form of an exponential function modified by a power law and that describes the characteristic asymmetric curved temperature response. Based on a few additional principles, our model can be used to predict the temperature response above the enzyme level, thus spanning quantum to classical scales. Our theory provides an analytical description for the shape of temperature response curves and demonstrates its generality by showing the convergence of all temperature dependence responses onto universal relationships-a universal data collapse-under appropriate normalization and by identifying a general optimal temperature, around 25 ∘C, characterizing all temperature response curves. The model provides a good fit to empirical data for a wide variety of biological rates, times, and steady-state quantities, from molecular to ecological scales and across multiple taxonomic groups (from viruses to mammals). This theory provides a simple framework to understand and predict the impact of temperature on biological quantities based on the first principles of thermodynamics, bridging quantum to classical scales.

Systematic shifts in scaling behavior based on organizational strategy in universities.

To build better theories of cities, companies, and other social institutions such as universities, requires that we understand the tradeoffs and complementarities that exist between their core functions, and that we understand bounds to their growth. Scaling theory has been a powerful tool for addressing such questions in diverse physical, biological and urban systems, revealing systematic quantitative regularities between size and function. Here we apply scaling theory to the social sciences, taking a synoptic view of an entire class of institutions. The United States higher education system serves as an ideal case study, since it includes over 5,800 institutions with shared broad objectives, but ranges in strategy from vocational training to the production of novel research, contains public, nonprofit and for-profit models, and spans sizes from 10 to roughly 100,000 enrolled students. We show that, like organisms, ecosystems and cities, universities and colleges scale in a surprisingly systematic fashion following simple power-law behavior. Comparing seven commonly accepted sectors of higher education organizations, we find distinct regimes of scaling between a school's total enrollment and its expenditures, revenues, graduation rates and economic added value. Our results quantify how each sector leverages specific economies of scale to address distinct priorities. Taken together, the scaling of features within a sector along with the shifts in scaling across sectors implies that there are generic mechanisms and constraints shared by all sectors, which lead to tradeoffs between their different societal functions and roles. We highlight the strong complementarity between public and private research universities, and community and state colleges, that all display superlinear returns to scale. In contrast to the scaling of biological systems, our results highlight that much of the observed scaling behavior is modulated by the particular strategies of organizations rather than an immutable set of constraints.

Scaling of urban income inequality in the USA.

Urban scaling analysis, the study of how aggregated urban features vary with the population of an urban area, provides a promising framework for discovering commonalities across cities and uncovering dynamics shared by cities across time and space. Here, we use the urban scaling framework to study an important, but under-explored feature in this community-income inequality. We propose a new method to study the scaling of income distributions by analysing total income scaling in population percentiles. We show that income in the least wealthy decile (10%) scales close to linearly with city population, while income in the most wealthy decile scale with a significantly superlinear exponent. In contrast to the superlinear scaling of total income with city population, this decile scaling illustrates that the benefits of larger cities are increasingly unequally distributed. For the poorest income deciles, cities have no positive effect over the null expectation of a linear increase. We repeat our analysis after adjusting income by housing cost, and find similar results. We then further analyse the shapes of income distributions. First, we find that mean, variance, skewness and kurtosis of income distributions all increase with city size. Second, the Kullback-Leibler divergence between a city's income distribution and that of the largest city decreases with city population, suggesting the overall shape of income distribution shifts with city population. As most urban scaling theories consider densifying interactions within cities as the fundamental process leading to the superlinear increase of many features, our results suggest this effect is only seen in the upper deciles of the cities. Our finding encourages future work to consider heterogeneous models of interactions to form a more coherent understanding of urban scaling.

The universal visitation law of human mobility.

Human mobility impacts many aspects of a city, from its spatial structure1-3 to its response to an epidemic4-7. It is also ultimately key to social interactions8, innovation9,10 and productivity11. However, our quantitative understanding of the aggregate movements of individuals remains incomplete. Existing models-such as the gravity law12,13 or the radiation model14-concentrate on the purely spatial dependence of mobility flows and do not capture the varying frequencies of recurrent visits to the same locations. Here we reveal a simple and robust scaling law that captures the temporal and spatial spectrum of population movement on the basis of large-scale mobility data from diverse cities around the globe. According to this law, the number of visitors to any location decreases as the inverse square of the product of their visiting frequency and travel distance. We further show that the spatio-temporal flows to different locations give rise to prominent spatial clusters with an area distribution that follows Zipf's law15. Finally, we build an individual mobility model based on exploration and preferential return to provide a mechanistic explanation for the discovered scaling law and the emerging spatial structure. Our findings corroborate long-standing conjectures in human geography (such as central place theory16 and Weber's theory of emergent optimality10) and allow for predictions of recurrent flows, providing a basis for applications in urban planning, traffic engineering and the mitigation of epidemic diseases.

Growth, death, and resource competition in sessile organisms.

Population-level scaling in ecological systems arises from individual growth and death with competitive constraints. We build on a minimal dynamical model of metabolic growth where the tension between individual growth and mortality determines population size distribution. We then separately include resource competition based on shared capture area. By varying rates of growth, death, and competitive attrition, we connect regular and random spatial patterns across sessile organisms from forests to ants, termites, and fairy circles. Then, we consider transient temporal dynamics in the context of asymmetric competition, such as canopy shading or large colony dominance, whose effects primarily weaken the smaller of two competitors. When such competition couples slow timescales of growth to fast competitive death, it generates population shocks and demographic oscillations similar to those observed in forest data. Our minimal quantitative theory unifies spatiotemporal patterns across sessile organisms through local competition mediated by the laws of metabolic growth, which in turn, are the result of long-term evolutionary dynamics.

Unraveling why we sleep: Quantitative analysis reveals abrupt transition from neural reorganization to repair in early development.

Sleep serves disparate functions, most notably neural repair, metabolite clearance and circuit reorganization. Yet the relative importance remains hotly debated. Here, we create a novel mechanistic framework for understanding and predicting how sleep changes during ontogeny and across phylogeny. We use this theory to quantitatively distinguish between sleep used for neural reorganization versus repair. Our findings reveal an abrupt transition, between 2 and 3 years of age in humans. Specifically, our results show that differences in sleep across phylogeny and during late ontogeny (after 2 or 3 years in humans) are primarily due to sleep functioning for repair or clearance, while changes in sleep during early ontogeny (before 2 or 3 years) primarily support neural reorganization and learning. Moreover, our analysis shows that neuroplastic reorganization occurs primarily in REM sleep but not in NREM. This developmental transition suggests a complex interplay between developmental and evolutionary constraints on sleep.

The ecological and evolutionary energetics of hunter-gatherer residential mobility.

Residential mobility is a key aspect of hunter-gatherer foraging economies and therefore is an issue of central importance in hunter-gatherer studies. Hunter-gatherers vary widely in annual rates of residential mobility. Understanding the sources of this variation has long been of interest to anthropologists and archeologists. The vast majority of hunter-gatherers who are dependent on terrestrial plants and animals move camp multiple times a year because local foraging patches become depleted and food, material, and social resources are heterogeneously distributed through time and space. In some environments, particularly along coasts, where resources are abundant and predictable, hunter-gatherers often become effectively sedentary. But even in these special cases, a central question is how these societies have maintained viable foraging economies while reducing residential mobility to near zero.

Scaling and universality in urban economic diversification.

Understanding cities is central to addressing major global challenges from climate change to economic resilience. Although increasingly perceived as fundamental socio-economic units, the detailed fabric of urban economic activities is only recently accessible to comprehensive analyses with the availability of large datasets. Here, we study abundances of business categories across US metropolitan statistical areas, and provide a framework for measuring the intrinsic diversity of economic activities that transcends scales of the classification scheme. A universal structure common to all cities is revealed, manifesting self-similarity in internal economic structure as well as aggregated metrics (GDP, patents, crime). We present a simple mathematical derivation of the universality, and provide a model, together with its economic implications of open-ended diversity created by urbanization, for understanding the observed empirical distribution. Given the universal distribution, scaling analyses for individual business categories enable us to determine their relative abundances as a function of city size. These results shed light on the processes of economic differentiation with scale, suggesting a general structure for the growth of national economies as integrated urban systems.

The mortality of companies.

The firm is a fundamental economic unit of contemporary human societies. Studies on the general quantitative and statistical character of firms have produced mixed results regarding their lifespans and mortality. We examine a comprehensive database of more than 25 000 publicly traded North American companies, from 1950 to 2009, to derive the statistics of firm lifespans. Based on detailed survival analysis, we show that the mortality of publicly traded companies manifests an approximately constant hazard rate over long periods of observation. This regularity indicates that mortality rates are independent of a company's age. We show that the typical half-life of a publicly traded company is about a decade, regardless of business sector. Our results shed new light on the dynamics of births and deaths of publicly traded companies and identify some of the necessary ingredients of a general theory of firms.

The dynamics of mergers and acquisitions: ancestry as the seminal determinant.

Understanding the fundamental mechanisms behind the complex landscape of corporate mergers and acquisitions is of crucial importance to economies across the world. Adapting ideas from the fields of complexity and evolutionary dynamics to analyse business ecosystems, we show here that ancestry, i.e. the cumulative sum of historical mergers across all ancestors, is the key characteristic to company mergers and acquisitions. We verify this by comparing an agent-based model to an extensive range of business data, covering the period from the 1830s to the present day and a range of industries and geographies. This seemingly universal mechanism leads to imbalanced business ecosystems, with the emergence of a few very large, but sluggish 'too big to fail' entities, and very small, niche entities, thereby creating a paradigm where a configuration akin to effective oligopoly or monopoly is a likely outcome for free market systems.

A theoretical physicist's journey into biology: from quarks and strings to cells and whales.

Biology will almost certainly be the predominant science of the twenty-first century but, for it to become successfully so, it will need to embrace some of the quantitative, analytic, predictive culture that has made physics so successful. This includes the search for underlying principles, systemic thinking at all scales, the development of coarse-grained models, and closer ongoing collaboration between theorists and experimentalists. This article presents a personal, slightly provocative, perspective of a theoretical physicist working in close collaboration with biologists at the interface between the physical and biological sciences.

The scaling of human interactions with city size.

The size of cities is known to play a fundamental role in social and economic life. Yet, its relation to the structure of the underlying network of human interactions has not been investigated empirically in detail. In this paper, we map society-wide communication networks to the urban areas of two European countries. We show that both the total number of contacts and the total communication activity grow superlinearly with city population size, according to well-defined scaling relations and resulting from a multiplicative increase that affects most citizens. Perhaps surprisingly, however, the probability that an individual's contacts are also connected with each other remains largely unaffected. These empirical results predict a systematic and scale-invariant acceleration of interaction-based spreading phenomena as cities get bigger, which is numerically confirmed by applying epidemiological models to the studied networks. Our findings should provide a microscopic basis towards understanding the superlinear increase of different socioeconomic quantities with city size, that applies to almost all urban systems and includes, for instance, the creation of new inventions or the prevalence of certain contagious diseases.

Using Fractal Geometry and Universal Growth Curves as Diagnostics for Comparing Tumor Vasculature and Metabolic Rate With Healthy Tissue and for Predicting Responses to Drug Therapies.

Healthy vasculature exhibits a hierarchical branching structure in which, on average, vessel radius and length change systematically with branching order. In contrast, tumor vasculature exhibits less hierarchy and more variability in its branching patterns. Although differences in vasculature have been highlighted in the literature, there has been very little quantification of these differences. Fractal analysis is a natural tool for comparing tumor and healthy vasculature, especially because it has already been used extensively to model healthy tissue. In this paper, we provide a fractal analysis of existing vascular data, and we present a new mathematical framework for predicting tumor growth trajectories by coupling: (1) the fractal geometric properties of tumor vascular networks, (2) metabolic properties of tumor cells and host vascular systems, and (3) spatial gradients in resources and metabolic states within the tumor. First, we provide a new analysis for how the mean and variation of scaling exponents for ratios of vessel radii and lengths in tumors differ from healthy tissue. Next, we use these characteristic exponents to predict metabolic rates for tumors. Finally, by combining this analysis with general growth equations based on energetics, we derive universal growth curves that enable us to compare tumor and ontogenetic growth. We also extend these growth equations to include necrotic, quiescent, and proliferative cell states and to predict novel growth dynamics that arise when tumors are treated with drugs. Taken together, this mathematical framework will help to anticipate and understand growth trajectories across tumor types and drug treatments.

Urban scaling and the production function for cities.

The factors that account for the differences in the economic productivity of urban areas have remained difficult to measure and identify unambiguously. Here we show that a microscopic derivation of urban scaling relations for economic quantities vs. population, obtained from the consideration of social and infrastructural properties common to all cities, implies an effective model of economic output in the form of a Cobb-Douglas type production function. As a result we derive a new expression for the Total Factor Productivity (TFP) of urban areas, which is the standard measure of economic productivity per unit of aggregate production factors (labor and capital). Using these results we empirically demonstrate that there is a systematic dependence of urban productivity on city population size, resulting from the mismatch between the size dependence of wages and labor, so that in contemporary US cities productivity increases by about 11% with each doubling of their population. Moreover, deviations from the average scale dependence of economic output, capturing the effect of local factors, including history and other local contingencies, also manifest surprising regularities. Although, productivity is maximized by the combination of high wages and low labor input, high productivity cities show invariably high wages and high levels of employment relative to their size expectation. Conversely, low productivity cities show both low wages and employment. These results shed new light on the microscopic processes that underlie urban economic productivity, explain the emergence of effective aggregate urban economic output models in terms of labor and capital inputs and may inform the development of economic theory related to growth.

The importance of quantitative systemic thinking in medicine.

The study and practice of medicine could benefit from an enhanced engagement with the new perspectives provided by the emerging areas of complexity science and systems biology. A more integrated, systemic approach is needed to fully understand the processes of health, disease, and dysfunction, and the many challenges in medical research and education. Integral to this approach is the search for a quantitative, predictive, multilevel, theoretical conceptual framework that both complements the present approaches and stimulates a more integrated research agenda that will lead to novel questions and experimental programmes. As examples, the importance of network structures and scaling laws are discussed for the development of a broad, quantitative, mathematical understanding of issues that are important in health, including ageing and mortality, sleep, growth, circulatory systems, and drug doses. A common theme is the importance of understanding the quantifiable determinants of the baseline scale of life, and developing corresponding parameters that define the average, idealised, healthy individual.

A general model for effects of temperature on ectotherm ontogenetic growth and development.

The temperature size rule (TSR) is the tendency for ectotherms to develop faster but mature at smaller body sizes at higher temperatures. It can be explained by a simple model in which the rate of growth or biomass accumulation and the rate of development have different temperature dependence. The model accounts for both TSR and the less frequently observed reverse-TSR, predicts the fraction of energy allocated to maintenance and synthesis over the course of development, and also predicts that less total energy is expended when developing at warmer temperatures for TSR and vice versa for reverse-TSR. It has important implications for effects of climate change on ectothermic animals.

A quantitative theory of solid tumor growth, metabolic rate and vascularization.

The relationships between cellular, structural and dynamical properties of tumors have traditionally been studied separately. Here, we construct a quantitative, predictive theory of solid tumor growth, metabolic rate, vascularization and necrosis that integrates the relationships between these properties. To accomplish this, we develop a comprehensive theory that describes the interface and integration of the tumor vascular network and resource supply with the cardiovascular system of the host. Our theory enables a quantitative understanding of how cells, tissues, and vascular networks act together across multiple scales by building on recent theoretical advances in modeling both healthy vasculature and the detailed processes of angiogenesis and tumor growth. The theory explicitly relates tumor vascularization and growth to metabolic rate, and yields extensive predictions for tumor properties, including growth rates, metabolic rates, degree of necrosis, blood flow rates and vessel sizes. Besides these quantitative predictions, we explain how growth rates depend on capillary density and metabolic rate, and why similar tumors grow slower and occur less frequently in larger animals, shedding light on Peto's paradox. Various implications for potential therapeutic strategies and further research are discussed.