We　formulate　a　single-species　population　model　with　fluctuations　and　migrations　between　two　different　patches　(the　nature　reserve　and　the　natural　environment)　to　describe　the　situation　that　endangered　species　often　meets　with.　Firstly,　we　prove　that　there　exists　a　unique　global　positive　solution　to　a　stochastic　single-species　model　with　any　positive　initial　value.　Then,　sufficient　conditions　that　guarantee　extinction　and　persistence　in　the　mean　of　solutions　are　derived　as　the　main　results.　It　turns　out　that,　under　moderate　fluctuation　conditions,　migration　rates　play　significant　roles　for　the　persistence　of　endangered　species　in　nature　reserve　and　the　natural　environment.　We　further　provide　the　sustainable　strategies　for　local　managers　to　avoid　the　extinction　of　endangered　species,　and　separately　carry　out　illustrative　examples　and　numerical　simulations　at　the　end　of　this　contribution.　(C)　2019　Elsevier　Inc.　All　rights　reserved.