Toy models for macroevolutionary patterns and trends

Many models have been used to simplify and operationalize the subtle but complex mechanisms of biological evolution. Toy models are gross simplifications that nevertheless attempt to retain major essential features of evolution, bridging the gap between empirical reality and formal theoretical understanding. In this paper, we examine thirteen models which describe evolution that also qualify as such toy models, including the tree of life, branching processes, adaptive ratchets, fitness landscapes, and the role of nonlinear avalanches in evolutionary dynamics. Such toy models are intended to capture features such as evolutionary trends, coupled evolutionary dynamics of phenotype and genotype, adaptive change, branching, and evolutionary transience. The models discussed herein are applied to specific evolutionary contexts in various ways that simplify the complexity inherent in evolving populations. While toy models are overly simplistic, they also provide sufficient dynamics for capturing the fundamental mechanism(s) of evolution. Toy models might also be used to aid in high-throughput data analysis and the understanding of cultural evolutionary trends. This paper should serve as an introductory guide to the toy modeling of evolutionary complexity.