Transient sensitivities of non-indigenous shrub species indicate complicated invasion dynamics

As biological invasions increasingly affect natural systems, the need for methods that can quantify the processes responsible for invasion success has increased. Further, methods should be geared to the formulation of management strategies. Demographic analyses are designed to explore the causes and properties of population change. Matrix population models, a commonly used technique for demographic analysis, have been applied to the analysis of stage-structured populations. However, most commonly, analyses have focused on long-term outcomes dynamics (ergodic dynamics). The methods available for analysis of matrix population models have recently been extended to facilitate analysis of the transient dynamics most important to invasion analysis. In this paper we analyze the transient population dynamics of three invasive shrubs and compare them to ergodic dynamics. Cytisus scoparius, Clidemia hirta, and Ardisia elliptica come from different parts of the world and are all now found in the United States of America. They also have published transition matrices that measure the probabilities that any one life-history stage will transition to another over an annual time step. These matrices have been estimated from multi-year data collected from plots in various environments. Our comparative study of transient and ergodic dynamics of invasive shrubs shows that, for all the considered shrub species, there was a clear difference between the sensitivities drawn from these two approaches. The transient sensitivities of earlier life-history transitions showed magnified importance relative to ergodic sensitivities. This was especially true of A. elliptica for which the stable population structure was most different from the starting structure analyzed in detail here. For other species, as stable population structures were heavily weighted towards early stages, the differences in the importance of early transitions transiently and ergodically were less dramatic. Late life transitions showed magnified importance in areas towards the center of the invasion or in older invasion areas. Finally, populations with shorter estimated generation times show greater transient sensitivity to early life-history stages; but the pattern was complex and varied according to species, and was also observed across other life-history transitions. Overall, the ambiguity and complexity of the results highlight the power of considering transient population dynamics for invading species, as well as the importance of specific biological and ecological knowledge of the invading species. Although there may be commonalities across invasions, important decisions on control or inference on population dynamics should treat invasions as individual, unique events.