Regular rates of popular culture change reflect random copying

Almost by definition, “popular culture” reflects the effects of most people imitating those around them. At the same time, trends and fashions are constantly changing, with future outcomes potentially irrational and nearly impossible to predict. A simple null model, which captures these seemingly conflicting tendencies of conformity and change, involves the random copying of cultural variants between individuals, with occasional innovation. Here, we show that the random-copying model predicts a continual flux of initially obscure new ideas (analogous to mutations) becoming highly popular by chance alone, such that the turnover rate on a list of most popular variants depends on the list size and the amount of innovation but not on population size. We also present evidence for remarkably regular turnover on “pop charts”—including the most popular music, first names, and dog breeds in 20th-century United States—which fits this expectation. By predicting parametric effects on the turnover of popular fashion, the random-copying model provides an additional means of characterizing collective copying behavior in culture evolution.     

An Experimental Test of the Accumulated Copying Error Model of Cultural Mutation for Acheulean Handaxe Size

Archaeologists interested in explaining changes in artifact morphology over long time periods have found it useful to create models in which the only source of change is random and unintentional copying error, or ‘cultural mutation’. These models can be used as null hypotheses against which to detect non-random processes such as cultural selection or biased transmission. One proposed cultural mutation model is the accumulated copying error model, where individuals attempt to copy the size of another individual''s artifact exactly but make small random errors due to physiological limits on the accuracy of their perception. Here, we first derive the model within an explicit mathematical framework, generating the predictions that multiple independently-evolving artifact chains should diverge over time such that their between-chain variance increases while the mean artifact size remains constant. We then present the first experimental test of this model in which 200 participants, split into 20 transmission chains, were asked to faithfully copy the size of the previous participant''s handaxe image on an iPad. The experimental findings supported the model''s prediction that between-chain variance should increase over time and did so in a manner quantitatively in line with the model. However, when the initial size of the image that the participants resized was larger than the size of the image they were copying, subjects tended to increase the size of the image, resulting in the mean size increasing rather than staying constant. This suggests that items of material culture formed by reductive vs. additive processes may mutate differently when individuals attempt to replicate faithfully the size of previously-produced artifacts. Finally, we show that a dataset of 2601 Acheulean handaxes shows less variation than predicted given our empirically measured copying error variance, suggesting that other processes counteracted the variation in handaxe size generated by perceptual cultural mutation.     

Random drift and culture change

We show that the frequency distributions of cultural variants, in three different real-world examples--first names, archaeological pottery and applications for technology patents--follow power laws that can be explained by a simple model of random drift. We conclude that cultural and economic choices often reflect a decision process that is value-neutral; this result has far-reaching testable implications for social-science research.     

Biases in cultural transmission shape the turnover of popular traits

The neutral model of cultural evolution, which assumes that copying is unbiased, provides precise predictions regarding frequency distributions of traits and the turnover within a popularity-ranked list. Here we study turnover in ranked lists and identify where the turnover departs from neutral model predictions to detect transmission biases in three different domains: color terms usage in English language 20th century books, popularity of early (1880–1930) and recent (1960–2010) USA baby names, and musical preferences of users of the Web site Last.fm. To help characterize the type of transmission bias, we modify the neutral model to include a content-based bias and two context-based biases (conformity and anti-conformity). How these modified models match real data helps us to infer, from population scale observations, when cultural transmission is biased, and, to some extent, what kind of biases are operating at individual level.     

Random copying,frequency-dependent copying and culture change

Previous evolutionary analyses of human culture have found that a simple model of random copying, analogous to neutral genetic drift, can generate the distinct power-law frequency distribution of cultural traits that is typical of various real-world cultural datasets, such as first names, patent citations and prehistoric pottery types. Here, we use agent-based simulations to explore the effects of frequency-dependent copying (e.g., conformity and anti-conformity) on this power-law distribution. We find that when traits are actively selected on the basis of their frequency, then the power-law distribution is severely disrupted. Conformity generates a “winner-takes-all” distribution in which popular traits dominate, while anti-conformity generates a “humped” distribution in which traits of intermediate frequency are favoured. However, a more passive frequency-dependent “trimming”, in which traits are selectively ignored on the basis of their frequency, generates reasonable approximations to the power-law distribution. This frequency-dependent trimming may therefore be difficult to distinguish from genuine random copying using population-level data alone. Implications for the study of both human and nonhuman culture are discussed.     

How copying affects the amount, evenness and persistence of cultural knowledge: insights from the social learning strategies tournament

Darwinian processes should favour those individuals that deploy the most effective strategies for acquiring information about their environment. We organized a computer-based tournament to investigate which learning strategies would perform well in a changing environment. The most successful strategies relied almost exclusively on social learning (here, learning a behaviour performed by another individual) rather than asocial learning, even when environments were changing rapidly; moreover, successful strategies focused learning effort on periods of environmental change. Here, we use data from tournament simulations to examine how these strategies might affect cultural evolution, as reflected in the amount of culture (i.e. number of cultural traits) in the population, the distribution of cultural traits across individuals, and their persistence through time. We found that high levels of social learning are associated with a larger amount of more persistent knowledge, but a smaller amount of less persistent expressed behaviour, as well as more uneven distributions of behaviour, as individuals concentrated on exploiting a smaller subset of behaviour patterns. Increased rates of environmental change generated increases in the amount and evenness of behaviour. These observations suggest that copying confers on cultural populations an adaptive plasticity, allowing them to respond to changing environments rapidly by drawing on a wider knowledge base.     

NULL MODELS FOR THE NUMBER OF EVOLUTIONARY STEPS IN A CHARACTER ON A PHYLOGENETIC TREE

Random trees and random characters can be used in null models for testing phylogenetic hypothesis. We consider three interpretations of random trees: first, that trees are selected from the set of all possible trees with equal probability; second, that trees are formed by random speciation or coalescence (equivalent); and third, that trees are formed by a series of random partitions of the taxa. We consider two interpretations of random characters: first, that the number of taxa with each state is held constant, but the states are randomly reshuffled among the taxa; and second, that the probability each taxon is assigned a particular state is constant from one taxon to the next. Under null models representing various combinations of randomizations of trees and characters, exact recursion equations are given to calculate the probability distribution of the number of character state changes required by a phylogenetic tree. Possible applications of these probability distributions are discussed. They can be used, for example, to test for a panmictic population structure within a species or to test phylogenetic inertia in a character's evolution. Whether and how a null model incorporates tree randomness makes little difference to the probability distribution in many but not all circumstances. The null model's sense of character randomness appears more critical. The difficult issue of choosing a null model is discussed.     

Predictions of Taylor's power law, density dependence and pink noise from a neutrally modeled time series

There has recently been increasing interest in neutral models of biodiversity and their ability to reproduce the patterns observed in nature, such as species abundance distributions. Here we investigate the ability of a neutral model to predict phenomena observed in single-population time series, a study complementary to most existing work that concentrates on snapshots in time of the whole community. We consider tests for density dependence, the dominant frequencies of population fluctuation (spectral density) and a relationship between the mean and variance of a fluctuating population (Taylor's power law). We simulated an archipelago model of a set of interconnected local communities with variable mortality rate, migration rate, speciation rate, size of local community and number of local communities. Our spectral analysis showed ‘pink noise’: a departure from a standard random walk dynamics in favor of the higher frequency fluctuations which is partly consistent with empirical data. We detected density dependence in local community time series but not in metacommunity time series. The slope of the Taylor's power law in the model was similar to the slopes observed in natural populations, but the fit to the power law was worse. Our observations of pink noise and density dependence can be attributed to the presence of an upper limit to community sizes and to the effect of migration which distorts temporal autocorrelation in local time series. We conclude that some of the phenomena observed in natural time series can emerge from neutral processes, as a result of random zero-sum birth, death and migration. This suggests the neutral model would be a parsimonious null model for future studies of time series data.     

The logic of fashion cycles

Many cultural traits exhibit volatile dynamics, commonly dubbed fashions or fads. Here we show that realistic fashion-like dynamics emerge spontaneously if individuals can copy others' preferences for cultural traits as well as traits themselves. We demonstrate this dynamics in simple mathematical models of the diffusion, and subsequent abandonment, of a single cultural trait which individuals may or may not prefer. We then simulate the coevolution between many cultural traits and the associated preferences, reproducing power-law frequency distributions of cultural traits (most traits are adopted by few individuals for a short time, and very few by many for a long time), as well as correlations between the rate of increase and the rate of decrease of traits (traits that increase rapidly in popularity are also abandoned quickly and vice versa). We also establish that alternative theories, that fashions result from individuals signaling their social status, or from individuals randomly copying each other, do not satisfactorily reproduce these empirical observations.     

Random mating with a finite number of matings

Random mating is the null model central to population genetics. One assumption behind random mating is that individuals mate an infinite number of times. This is obviously unrealistic. Here we show that when each female mates a finite number of times, the effective size of the population is substantially decreased.     

Species richness, endemism, and abundance patterns: tests of two fractal models in a serpentine grassland

Although scaling relationships that characterize fractal species distributions offer an exciting potential for unification in biogeography, empirical support for fractal theory remains the subject of debate. We synthesize and test multiple predictions of two interrelated fractal models and a null model of random placement using Californian serpentine grassland data describing the spatial location of over 37 000 individually identified plants. The endemics–area relationship and species‐abundance distribution recently derived from a community‐level fractal property performed poorly because of an inaccurate assumption of homogeneity among species. In contrast, a species‐level fractal model that incorporates species‐level differences predicted abundances well, but systematically overestimated endemism and predicted a species–area relationship that violated the observed power law. These findings indicate that in order to make predictions based on the existence of a power‐law species–area relationship, ecologists need a unifying theory of how the community‐level fractal property arises in the presence of species‐level distributional differences.     

Selecting factors predictive of heterogeneity in multivariate event time data

In multivariate survival analysis, investigators are often interested in testing for heterogeneity among clusters, both overall and within specific classes. We represent different hypotheses about the heterogeneity structure using a sequence of gamma frailty models, ranging from a null model with no random effects to a full model having random effects for each class. Following a Bayesian approach, we define prior distributions for the frailty variances consisting of mixtures of point masses at zero and inverse-gamma densities. Since frailties with zero variance effectively drop out of the model, this prior allocates probability to each model in the sequence, including the overall null hypothesis of homogeneity. Using a counting process formulation, the conditional posterior distributions of the frailties and proportional hazards regression coefficients have simple forms. Posterior computation proceeds via a data augmentation Gibbs sampling algorithm, a single run of which can be used to obtain model-averaged estimates of the population parameters and posterior model probabilities for testing hypotheses about the heterogeneity structure. The methods are illustrated using data from a lung cancer trial.     

Detecting temporal trends in species assemblages with bootstrapping procedures and hierarchical models

Quantifying patterns of temporal trends in species assemblages is an important analytical challenge in community ecology. We describe methods of analysis that can be applied to a matrix of counts of individuals that is organized by species (rows) and time-ordered sampling periods (columns). We first developed a bootstrapping procedure to test the null hypothesis of random sampling from a stationary species abundance distribution with temporally varying sampling probabilities. This procedure can be modified to account for undetected species. We next developed a hierarchical model to estimate species-specific trends in abundance while accounting for species-specific probabilities of detection. We analysed two long-term datasets on stream fishes and grassland insects to demonstrate these methods. For both assemblages, the bootstrap test indicated that temporal trends in abundance were more heterogeneous than expected under the null model. We used the hierarchical model to estimate trends in abundance and identified sets of species in each assemblage that were steadily increasing, decreasing or remaining constant in abundance over more than a decade of standardized annual surveys. Our methods of analysis are broadly applicable to other ecological datasets, and they represent an advance over most existing procedures, which do not incorporate effects of incomplete sampling and imperfect detection.     

THE COMPARISON OF QUANTITATIVE GENETIC PARAMETERS BETWEEN POPULATIONS

A statistical method for comparing matrices of genetic variation and covariation between groups (e.g., species, populations, a single population grown in distinct environments) is proposed. This maximum-likelihood method provides a test of the overall null hypothesis that two covariance component matrices are identical. Moreover, when the overall null hypothesis is rejected, the method provides a framework for isolating the particular components that differ significantly between the groups. Simulation studies reveal that discouragingly large experiments are necessary to obtain acceptable power for comparing genetic covariance component matrices. For example, even in cases of a single trait measured on 900 individuals in a nested design of 100 sires and three dams per sire in each population, the power was only about 0.5 when additive genetic variance differed by a factor of 2.5. Nevertheless, this flexible method makes valid comparison of covariance component matrices possible.     

On the number of independent cultural traits carried by individuals and populations

In species subject to individual and social learning, each individual is likely to express a certain number of different cultural traits acquired during its lifetime. If the process of trait innovation and transmission reaches a steady state in the population, the number of different cultural traits carried by an individual converges to some stationary distribution. We call this the trait-number distribution. In this paper, we derive the trait-number distributions for both individuals and populations when cultural traits are independent of each other. Our results suggest that as the number of cultural traits becomes large, the trait-number distributions approach Poisson distributions so that their means characterize cultural diversity in the population. We then analyse how the mean trait number varies at both the individual and population levels as a function of various demographic features, such as population size and subdivision, and social learning rules, such as conformism and anti-conformism. Diversity at the individual and population levels, as well as at the level of cultural homogeneity within groups, depends critically on the details of population demography and the individual and social learning rules.     

Alu and LINE1 distributions in the human chromosomes: evidence of global genomic organization expressed in the form of power laws

Spatial distribution and clustering of repetitive elements are extensively studied during the last years, as well as their colocalization with other genomic components. Here we investigate the large-scale features of Alu and LINE1 spatial arrangement in the human genome by studying the size distribution of interrepeat distances. In most cases, we have found power-law size distributions extending in several orders of magnitude. We have also studied the correlations of the extent of the power law (linear region in double-logarithmic scale) and of the corresponding exponent (slope) with other genomic properties. A model has been formulated to explain the formation of the observed power laws. According to the model, 2 kinds of events occur repetitively in evolutionary time: random insertion of several types of intruding sequences and occasional loss of repeats belonging to the initial population due to "elimination" events. This simple mechanism is shown to reproduce the observed power-law size distributions and is compatible with our present knowledge on the dynamics of repeat proliferation in the genome.     

Population fluctuations,power laws and mixtures of lognormal distributions

A number of investigators have invoked a cascading local interaction model to account for power‐law‐distributed fluctuations in ecological variables. Invoking such a model requires that species be tightly coupled, and that local interactions among species influence ecosystem dynamics over a broad range of scales. Here we reanalyse bird population data used by Keitt & Stanley (1998, Dynamics of North American breeding bird populations. Nature, 393, 257–260) to support a cascading local interaction model. We find that the power law they report can be attributed to mixing of lognormal distributions. More tentatively, we propose that mixing of distributions accounts for other empirical power laws reported in the ecological literature.     

The Method of Local Restriction: in search of potential great ape culture-dependent forms

Humans possess a perhaps unique type of culture among primates called cumulative culture. In this type of culture, behavioural forms cumulate changes over time, which increases their complexity and/or efficiency, eventually making these forms culture-dependent. As changes cumulate, culture-dependent forms become causally opaque, preventing the overall behavioural form from being acquired by individuals on their own; in other words, culture-dependent forms must be copied between individuals and across generations. Despite the importance of cumulative culture for understanding the evolutionary history of our species, how and when cumulative culture evolved is still debated. One of the challenges faced when addressing these questions is how to identify culture-dependent forms that result from cumulative cultural evolution. Here we propose a novel method to identify the most likely cases of culture-dependent forms. The ‘Method of Local Restriction’ is based on the premise that as culture-dependent forms are repeatedly transmitted via copying, these forms will unavoidably cumulate population-specific changes (due to copying error) and therefore must be expected to become locally restricted over time. When we applied this method to our closest living relatives, the great apes, we found that most known ape behavioural forms are not locally restricted (across domains and species) and thus are unlikely to be acquired via copying. Nevertheless, we found 25 locally restricted forms across species and domains, three of which appear to be locally unique (having been observed in a single population of a single species). Locally unique forms represent the best current candidates for culture-dependent forms in non-human great apes. Besides these rare exceptions, our results show that overall, ape cultures do not rely heavily on copying, as most ape behaviours appear across sites and/or species, rendering them unlikely to be culture-dependent forms resulting from cumulative cultural evolution. Yet, the locally restricted forms (and especially the three locally unique forms) identified by our method should be tested further for their potential reliance on copying social learning mechanisms (and in turn, for their potential culture-dependence). Future studies could use the Method of Local Restriction to investigate the existence of culture-dependent forms in other animal species and in the hominin archaeological record to estimate how widespread copying is in the animal kingdom and to postulate a timeline for the emergence of copying in our lineage.     

Detecting wholesale copying in cultural evolution

A cultural practice can spread because it is transmitted with high fidelity, but also because biased transformation leads to its reinvention. The respective effect of these two mechanisms, however, may only be quantified if we can measure and detect high-fidelity transmission. This paper proposes wholesale copying, the reproduction of a set of elements as a set, as an operational definition. Using two corpus of heraldic designs (total n = 13,453), we apply information-theoretic tools to detect cases of wholesale copying and gauge their incidence. Heraldic designs are composed according to rigorous combinatorial rules. Wholesale copying causes the frequency of a design to increase out of proportion with the frequency of the motif and tinctures that make it up. Comparing the frequency of designs with that of their component motifs and tinctures, we show that the amount of information carried by a design tracks its inheritance along family lines. A model predicting the frequency of heraldic designs based solely on the frequency of their component parts systematically outperforms one that assumes a mix of wholesale copying and random mutation (with realistic mutation rates). These findings are consistent with low but non-null incidences of wholesale copying in the diffusion of heraldic designs.