Estimating minimum sample size for detecting phenotypic dimorphism using computational simulations

Abstract Polymorphism, the occurrence of different morphs of a trait within the population of a single species, plays a crucial role in species diversification, genetic variation, and adaptation. Detecting polymorphism in a single character helps us to understand population dynamics, particularly in species that inhabit diverse environments. However, detecting polymorphisms in fossil taxa is challenging due to the fragmentary and incomplete records. Dimorphism, defined as the occurrence of different morphs of a trait within the population of a single species, represents the simplest and most common form of polymorphism. This study focuses on dimorphism instead of polymorphism, which allows for a more streamlined analysis. We use computational simulation experiments to estimate the minimum sample size required to detect bimodal distribution in univariate morphological variables. We describe the morphological diversity of a measured variable (e.g., body mass or skeletal length) as a probability density distribution with specific parameter sets. Subsequently, we simulate the diversity of the measured variable with varying sample sizes and conduct resampling procedures to ensure the robustness. Four key parameters that characterize the probability distribution are identified as having significant influence on the minimum sample size for dimorphism recognition. According to the simulation experiments, a model is built to estimate the minimum sample size for dimorphism recognition based on these parameters. A dataset from extant avian and reptilian species is used to test the model. Furthermore, we calculate a reference for the minimal sample size required for assessing phenotypic dimorphism in fossil avian taxa by applying parameters derived from extant avian species.