Transient synchronization following invasion: revisiting Moran's model and a case study

Synchrony in forest insect outbreaks is important because the resulting regionalized outbreak dilutes the regulating effects of natural enemies, reduces the landscape's ability to buffer the disturbance, exacerbates the economic burden on individual stakeholders, and overwhelms the logistical abilities of managers to suppress populations and mitigate impacts. Understanding the process of synchronization of dynamics is therefore a crucial aspect of understanding outbreak dynamics. We studied the second-order log-linear (autoregressive) model to ask what patterns of synchronization across invasion fronts may be expected from Moran's model. Generally, we show that the time to synchronization in the log-linear model is a complex function of a number of parameters of which the overall strength of regulation, the strength of delayed statistical density dependence, and the relaxation time seem to be of particular importance. Interestingly, while environmental correlation is the crucial determinant of the magnitude of asymptotic synchrony, it does not appear to influence the transient process of synchronization. However, synchronization proceeds much more quickly among weakly periodic populations than among populations that are strongly periodic. As a case study, we investigate synchronization following colonization by gypsy moth (Lymantria dispar) populations located along the species's expanding invasion front in northeastern USA. Data consisted of more than 100 years of county quarantine records and 30 years of detailed defoliation maps. We found that the dynamics of new populations tended to be initially out of synch with the broadly synchronized outbreaks within the established range. However, the outbreak dynamics of these new populations lock on to the regional patterns very quickly-within 10-15 years of invasion. Focusing on parameters that produce periodicity comparable to that seen in real gypsy moth populations, we discuss how the observed synchronization compares to that predicted by the log-linear model. While our results are equivocal, the synchronization appears to be surprisingly rapid, so more mechanistic models may be needed to explain the synchronization observed in this case study.