In mutualism under spatial structure, asynchrony between the dispersions of the interacting species can be a key determinant of their dynamics. We focused on the plant-mycorrhizal fungi system to theoretically analyze the colonization process by calculating the probability of colony establishment under environmental fluctuation. This can be considered a joint process of two sub-processes before and after the association between the host plant and the mycorrhizal fungi in a novel habitat. When colony growth undergoes environmental fluctuation, the dynamics of colony size can be considered a combination of the two stochastic sub-processes that mediated the association event between the plant and the fungi. Therefore, properties of whole system are influenced by five parameters, means and variances of colony growth rates of two sub-systems, and a rate of association of plant and fungi. For the successful establishment of a colony, the second sub-process must start before the first sub-process finishes (i.e., extinction), which we refer to as "stochastic tunneling." Our analysis of the establishment probability of a plant colony based on this concept revealed that (1) the mean colony growth rates of the host alone and the symbiotic association affect establishment probability in different ways, (2) the variance of colony growth rate of the symbiotic association reduces the establishment probability, although the variance of growth rate of the host alone facilitates the establishment probability when the mean growth rate of the host alone is negative, and (3) a trade-off between the mean colony growth rates of the host alone and the symbiotic association could result in the evolution of either a symbiotic or parasitic relationship, based on a host decision. The model we present is widely applicable to the colonization processes of both positive and negative species relationships, where the interacting species disperse independently.