Competition Model Between the Invasive Sahara Mustard and Native Plants in the Sonoran Desert

Sahara Mustard (Brassica tournefortii) is an invasive weed that has become widespread throughout the southwestern United States. Its early germination, high fecundity, and dispersal effectiveness augment its ability to outcompete and possibly displace local flora. In this work, we model the dynamics of Sahara Mustard as it competes with winter annuals native to the Sonoran Desert, such as the widespread forb Lepidium lasiocarpum. A discrete‐time competition model of plant-plant interactions is constructed to study factors that may affect competition between invasive and native species in favor of the native species. Through a system of non‐linear difference equations we quantify each species' seed banks and flowering adult populations over several generations. We take into consideration the dependence of fecundity, survivability, and germination on total annual rainfall. We also examine the effect of seasonal variability on existence of native species in competition with Sahara Mustard. We found that rainfall variability was advantageous to the native population, though the native forbs that compete with Sahara Mustard will likely be reduced in population or driven to extinction in absence of any control strategy.