“…Additionally, a critical limitation to highlight is that our theoretical framework, under the assumption of global stability, does not accommodate the complex invasion phenomenon known as “residents strike back” (Mylius and Diekmann, 2001). Nevertheless, our proposed probabilistic frameworks has already been successfully applied to understand the behavior of communities that involve a wide range of interactions, dynamics, and populations (Allen-Perkins et al, 2023, Angulo et al, 2021, Bartomeus et al, 2021, Cenci et al, 2018, Deng et al, 2021, 2022, García-Callejas et al, 2023, Luo et al, 2022, Medeiros et al, 2021, Saavedra et al, 2017a, Song et al, 2018, 2017, Song and Saavedra, 2018, Song et al, 2023, 2021b, Tabi et al, 2020).…”