(imagen de Francisco Javier Jimenez colores de Soni Sánchez Orgaz) Mathematical models are a helpful tool that can help palaeoecology research advance in similar ways as the ones already used in theoretical ecology. In this article, we use a mathematical model based on differential equations to estimate the past Mammuthus columbi population in the Valsequillo Basin, Puebla, Mexico. We calibrated the model based on the biological and etiologic parameters of the African elephant Loxodonta africana. In addition to the mean population, the analysis allows inferring the population dynamics of the M. columbi on the Valsequillo Basin. The model is based on the ecological interactions between M. columbi and its food resource. It was found that the population must have been oscillating before an equilibrium was reached. Several potential scenarios based on on-site food production (grass) are here analysed. It was found that a good efficiency of the M. columbi to find food can lead to recurrent cycles of abundance and famine. In this situation, the M. columbi populations must have emigrate and then immigrate in periodic circles to avoid starvation.