One of the main factors that determines habitat suitability for sessile and territorial organisms is the presence or absence of another competing individual in that habitat. This type of competition arises in populations occupying patches in a metacommunity. Previous studies have looked at this process using a continuous-time modeling framework, where colonizations and extinctions occur simultaneously. However, different colonization processes may be performed by different species, which may affect the metacommunity dynamics. We address this issue by developing a discrete-time framework that describes these kinds of metacommunity interactions, and we consider different colonization dynamics. To understand potential dynamics, we consider specific functional forms that characterize the colonization and extinction processes of metapopulations competing for space as their limiting factor. We then provide a mathematical analysis of the models generated by this framework, and we compare these results to what is seen in nature and in previous models.