A DIFFUSION-MODEL FOR DISPERSAL OF OPUNTIA-IMBRICATA (CHOLLA) ON RANGELAND

(1) The dispersal of Opuntia imbricata (cholla) on rangeland may be directly or indirectly affected by the presence of livestock and wildlife. Overgrazing creates gaps or open spaces for seeds or stems that fall to the ground to become established (passive dispersal). In addition., livestock or wildlife may cause stems and fruits to fall to the ground (active dispersal). (2) A theoretical model is formulated for the dispersal of plants based on the diffusion equation which assumes one or more mechanisms of dispersal (e.g. passive and active dispersal). The CHI-2 goodness-of-fit test is used to determine whether the data may be explained by one or by two mechanisms of dispersal. Methods for estimating the model parameters are presented based on the CHI-2 method and the method of moments. (3) The model and analytical techniques are applied to field data on the spatial distribution of Opuntia imbricata in four different pastures. (4) The results indicate that dispersal of cholla can be attributed to two dispersal mechanisms. Passive dispersal alone cannot account for the current spread of cholla on some of the pastures.