The aim of the present study is to test the resource economic monopolization hypothesis and the hypothesis of monogamy using the shrimp Alpheus estuariensis as a model. The shrimps were collected in two areas in the Vaza-Barriz estuary, north-east Brazil, from August to November 2016. The average abundance of refuges was obtained through 30 random replicates. The shrimp presented a random distribution in both areas. Males and females found together showed a weak relation between their sizes, with males being larger than females. In addition, the cheliped of males grows proportionally more than that of females. The great abundance of refuges present in the environment, added to the aforementioned results, do not support the idea of refuge-guarding behaviour or monogamy. These results, which are in disagreement with those already found for some shrimps of the same family, genus, and even species, reinforce the idea that Alpheidae can be used as a model in the study of how environmental conditions are capable of shaping the social behaviour of a species.