Matrix population models (MPMs) applied to ecology: a gentle guide from theory to practice

Abstract

The use of matrix population models (MPMs) to portray the life cycles of organisms is a powerful tool for ecological and evolutionary approaches. However, MPMs have been underutilized, despite their importance in demographic studies. One explanation is that students and young researchers are not encouraged to explore the MPMs’ potential. MPMs are often absent in elementary textbooks, and specialized literature can be mathematically challenging, especially if it lacks basic concepts of matrix algebra. Consequently, MPMs’ bibliography is limited to a few books, their application is concentrated in the United States and Europe, and errors are not rare in the literature. Here, we advocate broadening the use of structured populations, where individuals contribute to the population growth rate according to their age, sex, or other variables. We present the theoretical development of the MPMs, relevant examples of ecological studies, and their mathematical proprieties. Finally, we offer mathematical formulation and practical exercises in R in the appendices. We conceived this manuscript to be the first stop for those students and researchers interested in entering the literature about MPMs.