  Background: Zipf's law and Heaps' law are two representatives of the scaling
concepts, which play a significant role in the study of complexity science. The
coexistence of the Zipf's law and the Heaps' law motivates different
understandings on the dependence between these two scalings, which is still
hardly been clarified.
  Methodology/Principal Findings: In this article, we observe an evolution
process of the scalings: the Zipf's law and the Heaps' law are naturally shaped
to coexist at the initial time, while the crossover comes with the emergence of
their inconsistency at the larger time before reaching a stable state, where
the Heaps' law still exists with the disappearance of strict Zipf's law. Such
findings are illustrated with a scenario of large-scale spatial epidemic
spreading, and the empirical results of pandemic disease support a universal
analysis of the relation between the two laws regardless of the biological
details of disease. Employing the United States(U.S.) domestic air
transportation and demographic data to construct a metapopulation model for
simulating the pandemic spread at the U.S. country level, we uncover that the
broad heterogeneity of the infrastructure plays a key role in the evolution of
scaling emergence.
  Conclusions/Significance: The analyses of large-scale spatial epidemic
spreading help understand the temporal evolution of scalings, indicating the
coexistence of the Zipf's law and the Heaps' law depends on the collective
dynamics of epidemic processes, and the heterogeneity of epidemic spread
indicates the significance of performing targeted containment strategies at the
early time of a pandemic disease.
