The Mediterranean Basin is threatened by climate change, and there is an urgent need for studies to determine the risk of plant range shift and potential extinction. In this study, we simulate potential range shifts of 176 plant species to perform a detailed prognosis of critical range decline and extinction in a transformed mediterranean landscape. Particularly, we seek to answer two pivotal questions: (1) what are the general plant‐extinction patterns we should expect in mediterranean landscapes during the 21st century? and (2) does dispersal ability prevent extinction under climate change?. We gathered information on the dispersal traits of 176 plant species (dispersal vector, average and maximum dispersal distances, shape of the dispersal kernel). We used these data to feed a stochastic dynamic species distribution model (a combination of a cellular automaton with an ensemble of species distribution models) to simulate plant range shift under climate change with realistic dispersal under two different warming scenarios. We compared dispersal and non‐dispersal simulations to assess the influence that climate change and species‐distribution characteristics exert on plant‐extinction patterns. The dispersal simulation showed a lower percentage of extinct (−1%) and quasi‐extinct species (−19%) than did the non‐dispersal simulation. Summer temperatures of 37 °C and 33 °C, respectively, accelerated the critical range decline and extinction rates. The average elevation of the plant populations was the variable with the highest influence on extinction probability. Stochastic dynamic species distribution models proved to be useful when there was lack of data on dispersal distances and population dynamics. Dispersal ability showed minor effectiveness in preventing extinction, but greatly reduced the likelihood of critical range decline for a significant percentage of species.