Filamentous fungi are ubiquitous in nature and have high societal significance, being both major (food-borne) pathogens and important industrial organisms in the production of antibiotics and enzymes. In addition, fungi are important model organisms for fundamental research, such as studies in genetics and evolutionary biology. However, mechanistic models for population growth that would help understand fungal biology and fundamental processes are almost entirely missing. Here we present such a mechanistic model for the species Aspergillus nidulans as an exemplar of models for other filamentous fungi. The model is based on physiological parameters that influence colony growth, namely mycelial growth rate and sporulation rate, to predict the number of individual nuclei present in a colony through time. Using population size data for colonies of differing ages, we find that our mechanistic model accurately predicts the number of nuclei for two growth environments, and show that fungal population size is most dependent on changes in mycelial growth rate.