Accurate age estimation in small-scale societies

Precise estimation of age is essential in evolutionary anthropology, especially to infer population age structures and understand the evolution of human life history diversity. However, in small-scale societies, such as hunter-gatherer populations, time is often not referred to in calendar years and accurate age estimation remains a challenge. We address this by proposing a Bayesian approach that accounts for age uncertainty inherent to fieldwork data. We developed a Gibbs sampling Markov chain Monte Carlo algorithm that produces posterior distributions of ages for each individual, based on a ranking order of individuals from youngest to oldest and age ranges for each individual. We first validate our method on 65 Agta foragers from the Philippines with known ages, and show that our method generates age estimates which are superior to previously published regression-based approaches. We then use data on 587 Agta collected during recent fieldwork to demonstrate how multiple partial age ranks coming for multiple camps of hunter-gatherers can be integrated. Lastly, we exemplify how the distributions generated by our method can be used to estimate important demographic parameters in small-scale societies, here agespecific fertility patterns. Our flexible Bayesian approach will be especially useful to improve cross-cultural life history datasets for small-scale societies for which reliable age records are difficult to acquire. SIGNIFICANCE STATEMENT Understanding demographic and evolutionary processes shaping human life history diversity depends on precise age estimations. This is a challenge in smallscale societies, and especially those who do not follow a calendar year. Our method opens new possibilities in demographic and life history studies allowing for crosssectional data to be incorporated in cross-cultural comparisons and for a better understanding of the adaptive importance of human life history variation. \body INTRODUCTION Accurate estimation of the age of individuals is essential in evolutionary anthropology. Major questions in the field require an accurate inference of the timing of life history events, such as age at menarche, age at first reproduction, age at cessation of reproduction, inter-birth intervals and death. Age is also essential when assessing infant growth, developmental trajectories and estimating age structure properties of a population (e.g. the potential for population growth or decline, recovering signatures of epidemics and assessing vulnerability to ecological perturbations). Humans have important derived life history features, such as shorter inter-birth intervals, longer lifespan, extended post-reproductive longevity and childhood dependence (1). These life history traits vary across species in the slowfast continuum (2), and they likely vary within humans in response to differences in ecology such as differential mortality rates (3) and energetics (4). However, due to unreliable age estimates, very few studies have highlighted variability in life history traits in traditional societies (3, 5-6). The challenge of estimating ages is particularly problematic for populations where individuals do not relate their age to calendar years, as is the case among many hunter-gatherer and other small-scale societies (7-8). Although longitudinal studies are an ideal approach to address questions about variation in life history traits in small-scale populations, these are rare (although see 7, 9). There is consequently a need for methods to estimate ages based on cross-sectional data from these populations. A few approaches have been proposed to estimate ages in small-scale societies (reviewed in 7). The simplest one is visual inspection and approximate clustering into age cohorts (e.g., infant, child, teen, adult, old age). A clear disadvantage of this method is its lack of precision, as establishing life history strategies requires a refined age structure. Furthermore, differences in physical appearance trajectories in forager populations in comparison to western counterparts are likely to cause misattribution of ages. For instance, forager infants are often small and underdeveloped, appearing younger than their western peers, while older individuals may appear older when compared to western individuals of the same age. An alternative class of approaches are indirect demographic models developed in the field of human demography (21), which are characterized by model parameters that are estimated based on actual population data. For example, Howell (8) applied a ‘steady-state model’ approach to the Dobe ! Kung foragers. This method assumes a stable population structure, ascertains a relative age list of all individuals and estimates the death and fertility rates of the population. This approach permits an approximation of the population age structure by mapping these rates onto different life-tables (in which, for example, 80% live to age 1, 75% live to age 2, etc.) and selecting the life-table with the best correspondence. Given that these life tables are created from very different populations, caveats of this approach include the difficulty to find matching life tables, particularly for growing or declining populations for which these rates are unknown (7). Crucially, stable population models fix the proportion of individuals that live up to a certain age, which may obscure differences in life history adaptations and demography. To overcome these problems, Hill and Hurtado (7, but also see 10 for the Hadza) designed an alternative method to estimate the ages of Ache huntergatherers that did not assume a stable population. It is based on a relative age list including all individuals, with absolute ages for a subset of individuals. The relative age list was constructed by first dividing the population into age cohorts containing individuals of approximately the same age. Each individual ranked all others within their cohort, as well as those in the cohorts above and below them (i.e. either older or younger than themselves). These relative lists were combined into cohorts and then a master population list by selecting the rankings with the smaller number of contradictions. The absolute ages of some of the individuals were obtained from birth certificates, estimated from known events, or by an “age-difference chain” (individuals were questioned about their age at the time a younger individual was born by picking an individual of a known age and matching their age at the time of birth of the younger individual, 7). Given these absolute ages and the relative age list, a fifth-order polynomial curve was fitted with relative age rank as independent and age as dependent variables. Finally, the ages of the remaining individuals were estimated as the value of the polynomial curve at the corresponding rank. Despite improving upon previous methods, this approach still presents several drawbacks. First, the choice of fifth-order polynomial is arbitrary. Previous authors (10) have, for example, used third-order polynomials. Some ages may be fitted poorly by a polynomial, while overfitting may also be an issue, especially for data sets with few known ages. In addition, the uncertainty associated with any age estimate is not taken into account. This is particularly problematic in age-difference chains as the error is cumulative, leading to high uncertainty, especially for older individuals. For example, for the Ache with known ages Hill and Hurtado (7) have shown that the error in age estimates using this age-difference chain is approximately +0.5 years (SD=1.2) for each 12.5 year interval. Although relatively small, with the oldest individuals potentially overestimated in age by an average of ~2 years, this method does not control for the concomitant increase in error with age. Based on standard deviations this would be between +8.6 and -3.4 years for the oldest individuals based on their predicted age from the regression model. This has particular relevance to the estimation of age at some important life history events in later life, such as age at last reproduction and menopause. Here, we present a new Bayesian method for age estimation improving upon previous approaches. Bayesian approaches have previously been designed and successfully applied in, for example, Paleodemography (19-20) and Radiocarbon dating in Archaeology (22), however, they are not readily applied to data typically collected in anthropological fieldwork on small-scale societies. Our method requires two inputs. First, a single ranking or multiple partial rankings of individuals by age obtained from interviewing members of the population. And second, an arbitrary a priori age distribution per individual chosen by the researchers familiar with the population, that can be either based on accurate measures or ‘eyeballing’. These two pieces of information are combined using a statistical inference technique called Gibbs sampling, generating a posterior age distribution for each individual. This posterior distributions represent all that can be known about the ages of that individual given the age ranks and prior age distributions. We show that our method generates more accurate age estimates than regression-based approaches on 65 individuals from a hunter-gatherer society with known ages. As further empirical validation, and to show the flexibility of our method for actual fieldwork, we present a case study on Agta foragers from Palanan, the Philippines. Finally, we analyse agespecific fertility patterns in the Agta, fully integrating the uncertainties in the estimated ages of mother and offspring. This demonstrates how the posterior distributions produced by our method can be reliably used for estimating important demographic parameters in small-scale societies for which precise dates of birth do not exist. Our method opens new possibilities in demographic and life history studies, allowing for cross-sectional data to be incorporated in cr