Measuring frequency-dependent selection in culture.

The frequency of a cultural trait can influence its tendency to be copied. We develop a maximum-likelihood method to measure such frequency-dependent selection from time series data, and we apply it to baby names and purebred dog preferences over the past century. The form of negative frequency dependence we infer among names explains their diversity patterns, and it replicates across the United States, France, Norway and the Netherlands. We find different growth rates for male versus female names, attributable to different rates of innovation, whereas biblical names enjoy a genuine selective advantage at all frequencies, which explains their predominance among top names. We show how frequency dependence emerges from a host of underlying selective mechanisms, including a preference for novelty that recapitulates boom-bust fads among dog owners. Our analysis of cultural evolution through frequency-dependent selection provides a quantitative account of social pressures to conform or to be different.

Self-Similar Processes Follow a Power Law in Discrete Logarithmic Space.

Cities, wealth, and earthquakes follow continuous power-law probability distributions such as the Pareto distribution, which are canonically associated with scale-free behavior and self-similarity. However, many self-similar processes manifest as discrete steps that do not produce a continuous scale-free distribution. We construct a discrete power-law distribution that arises naturally from a simple model of hierarchical self-similar processes such as turbulence and vasculature, and we derive the maximum-likelihood estimate (MLE) for its exponent. Our distribution is self-similar, in contrast to previously studied discrete power laws such as the Zipf distribution. We show that the widely used MLE derived from the Pareto distribution leads to inaccurate estimates in systems that lack continuous scale invariance such as branching networks and data subject to logarithmic binning. We apply our MLE to data from bronchial tubes, blood vessels, and earthquakes to produce new estimates of scaling exponents and resolve contradictions among previous studies.

Detecting evolutionary forces in language change.

Both language and genes evolve by transmission over generations with opportunity for differential replication of forms. The understanding that gene frequencies change at random by genetic drift, even in the absence of natural selection, was a seminal advance in evolutionary biology. Stochastic drift must also occur in language as a result of randomness in how linguistic forms are copied between speakers. Here we quantify the strength of selection relative to stochastic drift in language evolution. We use time series derived from large corpora of annotated texts dating from the 12th to 21st centuries to analyse three well-known grammatical changes in English: the regularization of past-tense verbs, the introduction of the periphrastic 'do', and variation in verbal negation. We reject stochastic drift in favour of selection in some cases but not in others. In particular, we infer selection towards the irregular forms of some past-tense verbs, which is likely driven by changing frequencies of rhyming patterns over time. We show that stochastic drift is stronger for rare words, which may explain why rare forms are more prone to replacement than common ones. This work provides a method for testing selective theories of language change against a null model and reveals an underappreciated role for stochasticity in language evolution.

Do Vascular Networks Branch Optimally or Randomly across Spatial Scales?

Modern models that derive allometric relationships between metabolic rate and body mass are based on the architectural design of the cardiovascular system and presume sibling vessels are symmetric in terms of radius, length, flow rate, and pressure. Here, we study the cardiovascular structure of the human head and torso and of a mouse lung based on three-dimensional images processed via our software Angicart. In contrast to modern allometric theories, we find systematic patterns of asymmetry in vascular branching, potentially explaining previously documented mismatches between predictions (power-law or concave curvature) and observed empirical data (convex curvature) for the allometric scaling of metabolic rate. To examine why these systematic asymmetries in vascular branching might arise, we construct a mathematical framework to derive predictions based on local, junction-level optimality principles that have been proposed to be favored in the course of natural selection and development. The two most commonly used principles are material-cost optimizations (construction materials or blood volume) and optimization of efficient flow via minimization of power loss. We show that material-cost optimization solutions match with distributions for asymmetric branching across the whole network but do not match well for individual junctions. Consequently, we also explore random branching that is constrained at scales that range from local (junction-level) to global (whole network). We find that material-cost optimizations are the strongest predictor of vascular branching in the human head and torso, whereas locally or intermediately constrained random branching is comparable to material-cost optimizations for the mouse lung. These differences could be attributable to developmentally-programmed local branching for larger vessels and constrained random branching for smaller vessels.

Assortative mating can impede or facilitate fixation of underdominant alleles.

Underdominant mutations have fixed between divergent species, yet classical models suggest that rare underdominant alleles are purged quickly except in small or subdivided populations. We predict that underdominant alleles that also influence mate choice, such as those affecting coloration patterns visible to mates and predators alike, can fix more readily. We analyze a mechanistic model of positive assortative mating in which individuals have n chances to sample compatible mates. This one-parameter model naturally spans random mating (n=1) and complete assortment (n→∞), yet it produces sexual selection whose strength depends non-monotonically on n. This sexual selection interacts with viability selection to either inhibit or facilitate fixation. As mating opportunities increase, underdominant alleles fix as frequently as neutral mutations, even though sexual selection and underdominance independently each suppress rare alleles. This mechanism allows underdominant alleles to fix in large populations and illustrates how life history can affect evolutionary change.

Testing Foundations of Biological Scaling Theory Using Automated Measurements of Vascular Networks.

Scientists have long sought to understand how vascular networks supply blood and oxygen to cells throughout the body. Recent work focuses on principles that constrain how vessel size changes through branching generations from the aorta to capillaries and uses scaling exponents to quantify these changes. Prominent scaling theories predict that combinations of these exponents explain how metabolic, growth, and other biological rates vary with body size. Nevertheless, direct measurements of individual vessel segments have been limited because existing techniques for measuring vasculature are invasive, time consuming, and technically difficult. We developed software that extracts the length, radius, and connectivity of in vivo vessels from contrast-enhanced 3D Magnetic Resonance Angiography. Using data from 20 human subjects, we calculated scaling exponents by four methods-two derived from local properties of branching junctions and two from whole-network properties. Although these methods are often used interchangeably in the literature, we do not find general agreement between these methods, particularly for vessel lengths. Measurements for length of vessels also diverge from theoretical values, but those for radius show stronger agreement. Our results demonstrate that vascular network models cannot ignore certain complexities of real vascular systems and indicate the need to discover new principles regarding vessel lengths.