Herbivores shape plant invasions through impacts on demography and dispersal, yet only demographic mechanisms are well understood. Although herbivores negatively impact demography by definition, they can affect dispersal either negatively (e.g. seed consumption), or positively (e.g. caching). Exploring the nuances of how herbivores influence spatial spread will improve forecasting of plant movement on the landscape. Here, we aim to understand how herbivores impact how fast plant populations spread through varying impacts on plant demography and dispersal. We strive to determine if, and under what conditions, we see net positive effects of herbivores, in order to find scenarios where herbivores can help promote spread. We draw on classic invasion theory to develop a stage-structured integrodifference equation model that incorporates herbivore impacts on plant demography and dispersal. We simulate seven herbivore `syndromes' (combinations of demographic and/or dispersal effects) drawn from the literature to understand how increasing herbivore pressure alters plant spreading speed. We find that herbivores with solely negative effects on plant demography or dispersal always slow plant spreading speed, and that the speed slows monotonically as herbivore pressure increases. However, we also find that plant spreading speed can be hump-shaped with respect to herbivore pressure: plants spread faster in the presence of herbivores (for low herbivore pressure) and then slower (for high herbivore pressure). This result is robust, occurring across all syndromes where herbivores have a positive effect on plant dispersal, and is a sign that the positive effects of herbivores on dispersal can outweigh their negative effects on demography. For all syndromes we find that sufficiently high herbivore pressure results in population collapse. Thus, our findings show that herbivores can speed up or slow down plant spread. These insights allow for greater understanding of how to slow invasions, facilitate native species recolonization, and shape range shifts with global change. 

This is a theoretical datset created in MATLAB based on equations. We have processed that data in MATLAB as well.