how such slow dynamics can prevent estimation of the distance to the threshold from fluctuations in the susceptible population .
that they still provide useful insight into systems with a range of population sizes , environmental noise and observation schemes .
Here , we show analytically how such slow dynamics can prevent estimation of the distance to the threshold from fluctuations in the susceptible population .
Although these results are exact only in the limit of long - term observation of a large system , simulations show that they still provide useful insight into systems with a range of population sizes , environmental noise and observation schemes .