Inferring processes of cultural transmission: the critical role of rare variants in distinguishing neutrality from novelty biases

Neutral evolution assumes that there are no selective forces distinguishing different variants in a population. Despite this striking assumption, many recent studies have sought to assess whether neutrality can provide a good description of different episodes of cultural change. One approach has been to test whether neutral predictions are consistent with observed progeny distributions, recording the number of variants that have produced a given number of new instances within a specified time interval: a classic example is the distribution of baby names. Using an overlapping generations model we show that these distributions consist of two phases: a power law phase with a constant exponent of -3/2, followed by an exponential cut-off for variants with very large numbers of progeny. Maximum likelihood estimations of the model parameters provide a direct way to establish whether observed empirical patterns are consistent with neutral evolution. We apply our approach to a complete data set of baby names from Australia. Crucially we show that analyses based on only the most popular variants, as is often the case in studies of cultural evolution, can provide misleading evidence for underlying transmission hypotheses. While neutrality provides a plausible description of progeny distributions of abundant variants, rare variants deviate from neutrality. Further, we develop a simulation framework that allows for the detection of alternative cultural transmission processes. We show that anti-novelty bias is able to replicate the complete progeny distribution of the Australian data set

Demography and Language Competition

Attempts to describe language competition and extinction in a mathematical way have enjoyed increased popularity recently. In this paper I review recent modeling approaches and, based on these findings, propose a model of reaction-diffusion type. I analyze the dynamics of interactions of a population with two monolingual groups and a group that is bilingual in these two languages. The results show that demographic factors, such as population growth or population dispersal, play an important role in the competition dynamic. Furthermore, I consider the impact of two strategies for language maintenance: adjusting the status of the endangered language and adjusting the availability of monolingual and bilingual educational resources

Inference of Cultural Transmission Modes Based on Incomplete Information

In this paper we explore the theoretical limits of the inference of cultural transmission modes based on sparse population-level data. We approach this problem by investigating whether different transmission modes produce different temporal dynamics of cultural change. In particular we explore whether the distributions of the average time a variant stays the most common variant in the population, denoted by tmax, conditioned on the considered transmission modes are sufficiently different to allow for inference of underlying transmission modes. We assume time series data detailing the frequencies of different variants of a cultural trait in a population at different points in time and investigate the temporal resolution (i.e. the length of the time series and the distance between consecutive time points) that is needed to ensure distinguishability between transmission modes. We find that under complete information most transmission modes can be distinguished on the base of the statistic tmax, however we should not expect the same results if only infrequent information about the most common cultural variant in the population are available

Parabolische Randanfangswertprobleme mit zufälliger Anfangsbedingung

In dieser Arbeit werden parabolische Randanfangswertprobleme mit zufälliger Anfangs- und Neumann-Randbedingung betrachtet. Die zufälligen Einflußgrößen werden dabei als epsilon-korrelierte, zufällige Felder modelliert. Das Hauptinteresse liegt auf der Berechnung stochastischer Kenngrößen der auf Basis der Finite-Elemente Methode erhaltenen Lösung des Randanfangswertproblems. Für die Korrelationsfunktion der Lösung wird eine Entwicklung nach der Korrelationslänge sowie eine explizite Berechnung für spezielle Typen der Vernetzung vorgestellt. Anhand von numerischen Beispielen werden abschließend die auf den verschiedenen Wegen erhaltenen Varianzen mit der einer simulierten Lösung verglichen

Identifying innovation in laboratory studies of cultural evolution: rates of retention and measures of adaptation

In recent years, laboratory studies of cultural evolution have become increasingly prevalent as a means of identifying and understanding the effects of cultural transmission on the form and functionality of transmitted material. The data sets generated by these studies may provide insights into the conditions encouraging, or inhibiting, high rates of innovation, as well as the effect that this has on measures of adaptive cultural change. Here we review recent experimental studies of cultural evolution with a view to elucidating the role of innovation in generating observed trends. We first consider how tasks are presented to participants, and how the corresponding conceptualisation of task success is likely to influence the degree of intent underlying any deviations from perfect reproduction. We then consider the measures of interest used by the researchers to track the changes that occur as a result of transmission, and how these are likely to be affected by differing rates of retention. We conclude that considering studies of cultural evolution from the perspective of innovation provides valuable insights which help to clarify important differences in research designs, which have implications for the likely effects of variation in retention rates on measures of cultural adaptatio

A generative inference framework for analysing patterns of cultural change in sparse population data with evidence for fashion trends in LBK culture

Cultural change can be quantified by temporal changes in frequency of different cultural artefacts and it is a central question to identify what underlying cultural transmission processes could have caused the observed frequency changes. Observed changes, however, often describe the dynamics in samples of the population of artefacts, whereas transmission processes act on the whole population. Here we develop a modelling framework aimed at addressing this inference problem. To do so, we firstly generate population structures from which the observed sample could have been drawn randomly and then determine theoretical samples at a later time t2 produced under the assumption that changes in frequencies are caused by a specific transmission process. Thereby we also account for the potential effect of time-averaging processes in the generation of the observed sample. Subsequent statistical comparisons (e.g. using Bayesian inference) of the theoretical and observed samples at t2 can establish which processes could have produced the observed frequency data. In this way, we infer underlying transmission processes directly from available data without any equilibrium assumption. We apply this framework to a dataset describing pottery from settlements of some of the first farmers in Europe (the LBK culture) and conclude that the observed frequency dynamic of different types of decorated pottery is consistent with age-dependent selection, a preference for 'young' pottery types which is potentially indicative of fashion trends

Tradeoffs between the strength of conformity and number of conformists in variable environments

Organisms often respond to environmental change phenotypically, through learning strategies that enhance fitness in variable and changing conditions. But which strategies should we expect in population exposed to those conditions? We address this question by developing a mathematical model that specifies the consequences of different mixtures of individual and social learning strategies on the frequencies of different cultural variants in temporally and spatially changing environments. Assuming that alternative cultural variants are differently well-adapted to diverse environmental conditions, we are able to evaluate which mixture of learning strategies maximises the mean fitness of the population. We find that, even in rapidly changing environments, a high proportion of the population will always engage in social learning. In those environments, the highest adaptation levels are achieved through relatively high fractions of individual learning and a strong conformist bias. We establish a negative relationship between the proportion of the population learning socially and the strength of conformity operating in a population: strong conformity requires fewer conformists (i.e. larger proportion of individual learning), while many conformists can only be found when conformist transmission is weak. Investigations of cultural diversity show that in frequently changing environments high levels of adaptation require high level of cultural diversity. Finally, we demonstrate how the developed mathematical framework can be applied to time series of usage or occurrence data of cultural traits. Using Approximate Bayesian Computation we are able to infer information about the underlying learning processes that could have produced observed patterns of variation in the dataset

A non-equilibrium neutral model for analysing cultural change

Neutral evolution is a frequently used model to analyse changes in frequencies of cultural variants over time. Variants are chosen to be copied according to their relative frequency and new variants are introduced by a process of random mutation. Here we present a non-equilibrium neutral model which accounts for temporally varying population sizes and mutation rates and makes it possible to analyse the cultural system under consideration at any point in time. This framework gives an indication whether observed changes in the frequency distributions of a set of cultural variants between two time points are consistent with the random copying hypothesis. We find that the likelihood of the existence of the observed assemblage at the end of the considered time period (expressed by the probability of the observed number of cultural variants present in the population during the whole period under neutral evolution) is a powerful indicator of departures from neutrality. Further, we study the effects of frequency-dependent selection on the evolutionary trajectories and present a case study of change in the decoration of pottery in early Neolithic Central Europe. Based on the framework developed we show that neutral evolution is not an adequate description of the observed changes in frequency

The zoo of models of deliberate ignorance

This chapter looks at deliberate ignorance from a modeling perspective. Standard economic models cannot produce deliberate ignorance in a meaningful way; if there were no cost for acquisition and processing, data could be looked at privately and processed perfectly. Here the focus is on cases where the standard assumptions are violated in some way. Cases are considered from an individual’s perspective, without game-theoretic (strategic) aspects. Different classes of “not wanting to know” something are identified: aside from the boring case of the cost of information acquisition being too high, an individual may prefer to not know some information (e.g., when knowledge would reduce the enjoyment of other experiences) or may want to not use some information (e.g., relating to a lack of self-control). In addition, strategic cases of deliberate ignorance are reviewed, where obtaining information would also signal to others that information acquisition has occurred, and thus it may be better to remain ignorant. Finally, the possibility of deliberate ignorance emerging in population-level models is discussed, where there seems to be a relative dearth of models of the phenomenon at present. Throughout, the authors make use of examples to summarize different classes of models, ideas for how deliberate ignorance can make sense, and gaps in the literature for future modeling