arXiv subjects

Christopher P. Kempes

Publications and source records attributed to Christopher P. Kempes.

31 records · Page 2Linked to original sources

arXiv2022

Scaling laws and a general theory for the growth of public companies

Publicly traded companies are fundamental units of contemporary economies and markets and are important mechanisms through which humans interact with their environments. Understanding the general properties that underlie the processes of their growth has long been of interest, yet fundamental debates about the effects of firm size on growth have persisted. Here we develop a scaling framework that focuses on company size as the critical feature determining a variety of tradeoffs, and use this to reveal novel systematic behavior across the diversity of publicly-traded companies. Using a large database of 31,553 US companies over nearly 70 years, and 3,160 Chinese companies over 24 year, we show how the dynamics of companies expressed as scaling relationships leads to a quantitative, analytic theory for their growth. This theory produces several predictions that are in good agreement with data for both the US and China, whose markets have strikingly different histories and underlying structures. In both cases sales scale sublinearly with assets and exhibit nearly identical exponents leading, surprisingly and nontrivially, to assets that grow as a power law in time rather than exponentially, as often assumed. On the other hand, liabilities scale linearly in the US (exponent of $1.0$) but superlinearly in China (exponent of $1.09$). We show that such small differences in scaling exponents can have a significant impact on the character and long-term evolution of growth trajectories. These results illustrate that while companies are part of a larger class of growth phenomena driven by incomes and costs that scale with size, they are unique in that they grow following a temporal power-function which sets them apart from organisms, cities, nations, and markets, whose growth over time is often exponential.

physics.soc-ph↗

arXiv2022

Super-linear Scaling Behavior for Electric Vehicle Chargers and Road Map to Addressing the Infrastructure Gap

Enabling widespread electric vehicle (EV) adoption requires substantial build-out of charging infrastructure in the coming decade. We formulate the charging infrastructure needs as a scaling analysis problem and use it to estimate the EV infrastructure needs of the US at a county-level resolution. Surprisingly, we find that the current EV infrastructure deployment scales super-linearly with population, deviating from the sub-linear scaling of gasoline stations and other infrastructure. We discuss how this demonstrates the infancy of EV station abundance compared to other mature transportation infrastructures. By considering the power delivery of existing gasoline stations, and appropriate EV efficiencies, we estimate the EV infrastructure gap at the county level, providing a road map for future EV infrastructure expansion. Our reliance on scaling analysis allows us to make a unique forecast in this domain.

econ.EM↗

arXiv2021

Scaling of Urban Income Inequality in the United States

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 analyzing 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 analyze 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.

physics.soc-ph↗

arXiv2020

Paradox resolved: The allometric scaling of cancer risk across species

Understanding the cross-species behavior of cancer is important for uncovering fundamental mechanisms of carcinogenesis, and for translating results of model systems between species. One of the most famous interspecific considerations of cancer is Peto's paradox, which asserts that organisms with vastly different body mass are expected to have a vastly different degree of cancer risk, a pattern that is not observed empirically. Here we show that this observation is not a paradox at all but follows naturally from the interspecific scaling of metabolic rates across mammalian body size. We connect metabolic allometry to evolutionary models of cancer development in tissues to show that waiting time to cancer scales with body mass in a similar way as normal organism lifespan does. Thus, the expectation across mammals is that lifetime cancer risk is invariant with body mass. Peto's observation is therefore not a paradox, but the natural expectation from interspecific scaling of metabolism and physiology. These allometric patterns have theoretical implications for understanding life span evolution, and practical implications for using smaller animals as model systems for human cancer.

q-bio.OT↗

arXiv2020

Generalized Stoichiometry and Biogeochemistry for Astrobiological Applications

A central need in the field of astrobiology is generalized perspectives on life that make it possible to differentiate abiotic and biotic chemical systems. A key component of many past and future astrobiological measurements is the elemental ratio of various samples. Classic work on Earth's oceans has shown that life displays a striking regularity in the ratio of elements as originally characterized by Redfield. The body of work since the original observations has connected this ratio with basic ecological dynamics and cell physiology, while also documenting the range of elemental ratios found in a variety of environments. Several key questions remain in considering how to best apply this knowledge to astrobiological contexts: How can the observed variation of the elemental ratios be more formally systematized using basic biological physiology and ecological or environmental dynamics? How can these elemental ratios be generalized beyond the life that we have observed on our own planet? Here we expand recently developed generalized physiological models to create a simple framework for predicting the variation of elemental ratios found in various environments. We then discuss further generalizing the physiology for astrobiological applications. Much of our theoretical treatment is designed for in situ measurements applicable to future planetary missions. We imagine scenarios where three measurements can be made - particle/cell sizes, particle/cell stoichiometry, and fluid or environmental stoichiometry - and develop our theory in connection with these often deployed measurements.

q-bio.QM↗

arXiv2020

Dynamics of 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 include resource competition based on shared capture area separately. By varying relative 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 that primarily weakens the smaller of two competitors such as canopy shading or large colony dominance. When such competition couples slow timescales of growth with fast competitive death, it generates population shock waves similar to those observed in forest demographic data. Our minimal quantitative theory unifies spatiotemporal patterns across sessile organisms through local competition mediated by the laws of metabolic growth which in turn result from long-term evolutionary dynamics.

q-bio.PE↗

arXiv2019

The Scalability, Efficiency and Complexity of Universities and Colleges: A New Lens for Assessing the Higher Educational System

The growing need for affordable and accessible higher education is a major global challenge for the 21st century. Consequently, there is a need to develop a deeper understanding of the functionality and taxonomy of universities and colleges and, in particular, how their various characteristics change with size. Scaling has been a powerful tool for revealing systematic regularities in systems across a range of topics from physics and biology to cities, and for understanding the underlying principles of their organization and growth. Here, we apply this framework to institutions of higher learning in the United States and show that, like organisms, ecosystems and cities, they scale in a surprisingly systematic fashion following simple power law behavior. We analyze the entire spectrum encompassing 5,802 institutions ranging from large research universities to small professional schools, organized in seven commonly used sectors, which reveal distinct regimes of institutional scaling behavior. Metrics include variation in expenditures, revenues, graduation rates and estimated economic added value, expressed as functions of total enrollment, our fundamental measure of size. Our results quantify how each regime of institution leverages specific economies of scale to address distinct priorities. Taken together, the scaling of features within a sector and 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 particularly highlight the strong complementarity between public and private research universities, and community and state colleges, four sectors that display superlinear returns to scale.

cs.CY↗

arXiv2019

Scaling of the risk landscape drives optimal life history strategies and the evolution of grazing

Consumers face numerous risks that can be minimized by incorporating different life-history strategies. How much and when a consumer adds to its energetic reserves or invests in reproduction are key behavioral and physiological adaptations that structure much of how organisms interact. Here we develop a theoretical framework that explicitly accounts for stochastic fluctuations of an individual consumer's energetic reserves while foraging and reproducing on a landscape with resources that range from uniformly distributed to highly clustered. First, we show that optimal life-history strategies vary in response to changes in the mean productivity of the resource landscape, where depleted environments promote reproduction at lower energetic states, greater investment in each reproduction event, and smaller litter sizes. We then show that if resource variance scales with body size due to landscape clustering, consumers that forage for clustered foods are susceptible to strong Allee effects, increasing extinction risk. Finally, we show that the proposed relationship between consumer body size, resource clustering, and Allee effect-induced population instability offers key ecological insights into the evolution of large-bodied grazing herbivores from small-bodied browsing ancestors.

q-bio.PE↗

arXiv2017

The dynamics of starvation and recovery

The eco-evolutionary dynamics of species are fundamentally linked to the energetic constraints of its constituent individuals. Of particular importance is the interplay between reproduction and the dynamics of starvation and recovery. To elucidate this interplay, we introduce a nutritional state-structured model that incorporates two classes of consumer: nutritionally replete, reproducing consumers, and undernourished, non-reproducing consumers. We obtain strong constraints on starvation and recovery rates by deriving allometric scaling relationships and find that population dynamics are typically driven to a steady state. Moreover, these rates fall within a 'refuge' in parameter space, where the probability of population extinction is minimized. We also show that our model provides a natural framework to predict maximum mammalian body size by determining the relative stability of an otherwise homogeneous population to a competing population with altered percent body fat. This framework provides a principled mechanism for a selective driver of Cope's rule.

q-bio.PE↗

arXiv2017

The thermodynamic efficiency of computations made in cells across the range of life

Biological organisms must perform computation as they grow, reproduce, and evolve. Moreover, ever since Landauer's bound was proposed it has been known that all computation has some thermodynamic cost -- and that the same computation can be achieved with greater or smaller thermodynamic cost depending on how it is implemented. Accordingly an important issue concerning the evolution of life is assessing the thermodynamic efficiency of the computations performed by organisms. This issue is interesting both from the perspective of how close life has come to maximally efficient computation (presumably under the pressure of natural selection), and from the practical perspective of what efficiencies we might hope that engineered biological computers might achieve, especially in comparison with current computational systems. Here we show that the computational efficiency of translation, defined as free energy expended per amino acid operation, outperforms the best supercomputers by several orders of magnitude, and is only about an order of magnitude worse than the Landauer bound. However this efficiency depends strongly on the size and architecture of the cell in question. In particular, we show that the {\it useful} efficiency of an amino acid operation, defined as the bulk energy per amino acid polymerization, decreases for increasing bacterial size and converges to the polymerization cost of the ribosome. This cost of the largest bacteria does not change in cells as we progress through the major evolutionary shifts to both single and multicellular eukaryotes. However, the rates of total computation per unit mass are nonmonotonic in bacteria with increasing cell size, and also change across different biological architectures including the shift from unicellular to multicellular eukaryotes.

q-bio.OT↗

arXiv2017

On the records

World record setting has long attracted public interest and scientific investigation. Extremal records summarize the limits of the space explored by a process, and the historical progression of a record sheds light on the underlying dynamics of the process. Existing analyses of prediction, statistical properties, and ultimate limits of record progressions have focused on particular domains. However, a broad perspective on how record progressions vary across different spheres of activity needs further development. Here we employ cross-cutting metrics to compare records across a variety of domains, including sports, games, biological evolution, and technological development. We find that these domains exhibit characteristic statistical signatures in terms of rates of improvement, "burstiness" of record-breaking time series, and the acceleration of the record breaking process. Specifically, sports and games exhibit the slowest rate of improvement and a wide range of rates of "burstiness." Technology improves at a much faster rate and, unlike other domains, tends to show acceleration in records. Many biological and technological processes are characterized by constant rates of improvement, showing less burstiness than sports and games. It is important to understand how these statistical properties of record progression emerge from the underlying dynamics. Towards this end, we conduct a detailed analysis of a particular record-setting event: elite marathon running. In this domain, we find that studying record-setting data alone can obscure many of the structural properties of the underlying process. The marathon study also illustrates how some of the standard statistical assumptions underlying record progression models may be inappropriate or commonly violated in real-world datasets.

physics.soc-ph↗

arXiv2017

Dynamics of beneficial epidemics

Pathogens can spread epidemically through populations. Beneficial contagions, such as viruses that enhance host survival or technological innovations that improve quality of life, also have the potential to spread epidemically. How do the dynamics of beneficial biological and social epidemics differ from those of detrimental epidemics? We investigate this question using three theoretical approaches. First, in the context of population genetics, we show that a horizontally-transmissible element that increases fitness, such as viral DNA, spreads superexponentially through a population, more quickly than a beneficial mutation. Second, in the context of behavioral epidemiology, we show that infections that cause increased connectivity lead to superexponential fixation in the population. Third, in the context of dynamic social networks, we find that preferences for increased global infection accelerate spread and produce superexponential fixation, but preferences for local assortativity halt epidemics by disconnecting the infected from the susceptible. We conclude that the dynamics of beneficial biological and social epidemics are characterized by the rapid spread of beneficial elements, which is facilitated in biological systems by horizontal transmission and in social systems by active spreading behavior of infected individuals.

physics.soc-ph↗

arXiv2015

Predicting Whole Forest Structure, Primary Productivity, and Biomass Density From Maximum Tree Size and Resource Limitations

In the face of uncertain biological response to climate change and the many critiques concerning model complexity it is increasingly important to develop predictive mechanistic frameworks that capture the dominant features of ecological communities and their dependencies on environmental factors. This is particularly important for critical global processes such as biomass changes, carbon export, and biogenic climate feedback. Past efforts have successfully understood a broad spectrum of plant and community traits across a range of biological diversity and body size, including tree size distributions and maximum tree height, from mechanical, hydrodynamic, and resource constraints. Recently it was shown that global scaling relationships for net primary productivity are correlated with local meteorology and the overall biomass density within a forest. Along with previous efforts, this highlights the connection between widely observed allometric relationships and predictive ecology. An emerging goal of ecological theory is to gain maximum predictive power with the least number of parameters. Here we show that the explicit dependence of such critical quantities can be systematically predicted knowing just the size of the largest tree. This is supported by data showing that forests converge to our predictions as they mature. Since maximum tree size can be calculated from local meteorology this provides a general framework for predicting the generic structure of forests from local environmental parameters thereby addressing a range of critical Earth-system questions.

q-bio.PE↗