Demographic matrix models are increasingly used in practice to guide management and conservation decisions. Traditional analyses of these models rely on long-term, asymptotic behavior of the models; however, recently theoretical results have emphasized the potential importance of transient dynamics. Most methods for analyzing transient responses, such as reactivity, maximum amplification, maximum attenuation, and first step attenuation, are based on comparing asymptotic estimates of population size and growth rate to those produced by populations with extreme deviations from the stable stage distribution (SSD) of the model. The response that a population actually experiences will depend on how different the population stage structure is from the SSD. While several studies have begun to compare these measures of transient response across species, we lack basic information on how often populations experience transient responses that are similar to those produced by these maximum deviations. To this end, I used models from three long-term plant demographic studies to simulate variation in stage distributions under stable environmental variation and determine a range of distances from the population average SSD. These distances then serve as a basis for comparing simulated transient responses with measures of transient potential based on extreme deviations.
Results/Conclusions
The average distance between the stage structures in the simulated populations and the corresponding SSD are far smaller than the distances required for producing maximum transient responses. Within the observed range of variation, amplification and reactivity in the simulated populations were dampened, but still strongly correlated with the maximum amplification and reactivity based on maximum deviations. A similar pattern was found for patterns of attenuation; however, the difference between simulated estimates of attenuation and measures based on extreme deviations was reduced compared to patterns in amplification. These results suggest that while measures of transient response based on maximum deviations may be informative of the relative transient potential for a population, they may overestimate the role of transient dynamics in practical applications. Where estimates of population stage structure are available, this information can be used to help determine whether to prioritize transient dynamics in practice.
