Environmental heterogeneity conditions the structure of population dynamics. In this paper, by means of a mathematical model we study the effects of a singular (different kind of) patch on the persistence of a population distributed over patches in a one-dimensional environment. It is assumed that there is migration between any two adjacent patches, and that there is a constant rate of leakage in the migration process. The population in the singular patch is assumed to have growth and emigration rates different from the corresponding rates in the other patches. By means of the eigenvalue estimation, it is quantitatively studied how population persistence is influenced by: (a) the location of the singular patch, (b) the difference in the growth and emigration rates from the corresponding rates in the other patches, and (c) the total number of patches in the system.