Population dynamic models for the Aymara Population (1820–1960) using the exponential form of logistic growth with effects of tree-rings as a proxy of rainfall and economic growth (Royama 1992); parameter values are given in the equations.

The best model was chosen by using the Bayesian Information Critera (BIC). R t+1 = Realized per capita growth rates, X t+1 = ln population size, Rain t = Mean tree-rings data during the 10-year interval, GDP t = per capita Gross Domestic Product, ΔBIC = model BIC–lowest BIC, wi = BIC weigths, r2 = proportion of the variance explained by the model, r predictions = Pearson’s correlation coefficient between the observed and predicted dynamics.