  Periodic travelling waves (PTW) are a common solution type of partial
differential equations. Such models exhibit multistability of PTWs, typically
visualised through the Busse balloon, and parameter changes typically lead to a
cascade of wavelength changes through the Busse balloon. In the past, the
stability boundaries of the Busse balloon have been used to predict such
wavelength changes. Here, motivated by anecdotal evidence from previous work,
we provide compelling evidence that the Busse balloon provides insufficient
information to predict wavelength changes due to a delayed loss of stability
phenomenon. Using two different reaction-advection-diffusion systems, we relate
the delay that occurs between the crossing of a stability boundary in the Busse
balloon and the occurrence of a wavelength change to features of the essential
spectrum of the destabilised PTW. This leads to a predictive framework that can
estimate the order of magnitude of such a time delay, which provides a novel
``early warning sign'' for pattern destabilization. We illustrate the
implementation of the predictive framework to predict under what conditions a
wavelength change of a PTW occurs.
