Viruses like influenza have long coevolved with host immune systems, gradually shaping the evolutionary trajectory of these pathogens. Host immune systems develop immunity against circulating strains, which in turn avoid extinction by exploiting antigenic escape mutations that render new strains immune to existing antibodies in the host population. Infected hosts are also mobile, which can spread the virus to regions without developed host immunity, offering additional reservoirs for viral growth. While the effects of migration on viral persistence have been investigated, we know little about how antigenic escape coupled with migration changes the survival and spread of emerging viruses. By considering the two processes on equal footing, we show that on short timescales an intermediate host mobility rate increases the survival probability of the virus through antigenic escape. We show that more strongly connected migratory networks decrease the survival probability of the virus. Using data from high traffic airports, we argue that current human migration rates are beneficial for viral survival.

The critical brain hypothesis proposes that neural systems operate near a phase transition to optimize information processing. A key method for investigating this hypothesis is the phenomenological renormalization group (pRG), which looks for scale-invariant features across levels of coarse-graining. One such feature is the power-law scaling of eigenvalues of covariance matrices of coarse-grained variables. However, the estimation of this scaling exponent, $\mu$, often relies on linear regression over arbitrarily selected ranges of the plot of eigenvalues versus rank. This heuristic “eyeballing” introduces uncontrolled bias and complicates the interpretation of observed scaling relationships. In order to obtain a more robust estimation of $\mu$, we do not fit the standard eigenvalue-vs-rank relationship, but rather the density of eigenvalues, for which standard protocols exist for fitting power laws to empirical data distributions. We demonstrate this approach using a synthetic model that replicates the scaling signatures of neural data while providing control over the system’s exponents as well as neural data obtained from publicly available Neuropixels recordings. We also establish standards for the minimal data required to quantify power-law behavior in a pRG eigenvalue analysis. Our approach contributes a tool for understanding the fundamental limitations imposed by spatial and temporal constraints of experimental datasets, which is required to rigorously assess the neural criticality hypothesis.