Managing population spread: Prediction and analysis using a structured invasion model

Matrix models are of great use in directing the management of populations. Techniques such as perturbation analysis can allow testing of the main drivers of population change and the impact of different management techniques. Recent developments have combined matrix models describing population growth with integrodifference equations describing dispersal (the Neubert-Caswell model) which allow the modelling of population spread through analysis of wavespeeds. We used these methods to analyse spread of a re-introduced meadow annual plant Rhinanthus minor. We measured actual spread of populations under four management regimes in a replicated experiment. We also carried out independent measures of demographic and dispersal variables under these managements and used these data to construct wavespeed models. Actual and modelled wavespeeds were very similar and showed the same pattern of response to managements, varying over an order of magnitude. Various aspects of demography and dispersal differed among the managements and we used new developments in Life Table Response Experiments to determine the main drivers of wavespeed differences. Dispersal differences accounted for about 70% of changes in wavespeed and the 2% furthest dispersing seeds accounted for about 98% of the dispersal contribution. This study suggests that, despite its simplifying assumptions, the wavespeed modelling approach can accurately model population spread and provides a tool which allows managers to identify the variables which contribute most to spread. This can be used to aid either the control of invasions or the facilitation of re-introductions.