Spread of organisms: can travelling and dispersive waves be distinguished?

Organisms may spread as travelling waves proceeding with a constant velocity, or as dispersive waves with a continuously increasing velocity. Whereas theory predicts existence of dispersive waves, experimental proof is virtually absent from literature. One major problem is to distinguish between the increasing velocity of a travelling wave during the build-up phase and the continuously increasing velocity of a dispersive wave. In general, experiments are limited in scale with respect to both, space and period of monitoring spread of an organism rendering a distinction between travelling and dispersive waves troublesome. We used a stepwise approach to determine whether epidemics of the rust fungus Puccinia lagenophorae on the annual plant Senecio vulgaris develop as travelling or dispersive waves. In the first step we determined the net reproductive number R-0 and the contact distribution D using a small-scale field experiment, in which one generation of the pathogen developed. The estimated parameters were used in the second step, in which the fate of travelling and dispersive waves was evaluated using modelling. The predictions derived from modelling were tested in relatively large-scale field experiments of the third step. Various density functions could be fitted to data of the contact distribution including both exponentially bound and non-bound functions. We concluded that distinguishing travelling and dispersive waves solely based on data of the contact distribution is not possible. Modelling indicated that travelling and dispersive waves can be distinguished based on the fate of velocity and the dynamics of the shape of the wave front. The modelling results suggested that hardly any build-up phase is present at the relatively high R-0 of our study system. Assuming the build-up phase was negligible, we concluded from the results of the relatively large-scale field experiments that epidemics of P. lagenophorae expand as dispersive waves.