  This paper uses new and recently established methodologies to study the
evolutionary dynamics of the cryptocurrency market, and compares the findings
with that of the equity market. We begin by applying random matrix theory and
principal components analysis (PCA) to correlation matrices of both
collections, highlighting clear differences in the eigenspectra exhibited. We
then explore the heterogeneity of both asset classes, studying the time-varying
dynamics of underlying sector behaviours, and determine the collective
similarity within each collection. We then turn to a study of structural break
dynamics and evolutionary power spectra, where we quantify the collective
affinity in structural breaks and evolutionary behaviours of underlying sector
time series. Finally, we implement two algorithms simulating `portfolio choice'
dynamics to compare the effectiveness of stock selection and sector allocation
in cryptocurrency portfolios. There, we highlight the importance of both
endeavours and comment on noteworthy implications for cryptocurrency portfolio
management.
