Competition Model of Brassica Tournefortii and Native Plants in the Sonoran Desert

Brassica tournefortii (Sahara Mustard) is an invasive weed that has become widespread throughout the southwestern United States. Following a series of especially wet seasons from 2004-2005, the range of Sahara Mustard increased significantly in the Sonoran Desert. Its early germination and high fecundity make it an especially succesful invasive species. This, coupled with its efficient seed dispersal methods, has caused it to become a direct competitive threat to local flora, and thus an indirect threat to the fauna of these desert ecosystems. This paper seeks to mathematically analyze the dynamics of B. tournefortii as it competes with native flora. This is accomplished through a competition model of plant-plant interactions using a system of finite difference equations. These equations track quantities in each species’ seed banks and flowering adult populations over several years. We take into account the dependence of fecundity, survivability, and seed viability on variations in annual rainfall. A stochastic simulation is used to model this behavior. We find the level of intervention necessary for the containment of Sahara Mustard. We also observe the relationship between the spread of Sahara Mustard and differing weather conditions. Through these methods, a better understanding of the behavior of the invasive B. tournefortii is gained.