“…The system of phytoplankton and the limiting nutrient on the vertical axis has often been utilized to study the depth, intensity and persistence of the SCML. Major theoretical results include photoacclimation (increase in chlorophyll per cell) (Steele, 1964;Fennel and Boss, 2003), bistability (Yoshiyama and Nakajima, 2002;Ryabov et al, 2010), oscillating SCM (Huisman et al, 2006), hysteresis conditions (Kiefer and Kremer, 1981;Navarro and Ruiz, 2013) and the ESS (evolutionary stable strategy) depth obtained by gametheory approach (Klausmeier and Litchman, 2001;Mellard et al, 2011). Recent mathematical studies solved the persistence and uniqueness of the steady-state solution (Du and Hsu, 2010;Hsu and Yuan, 2010;Du and Mei, 2011) and gave rigorous proofs for the abovementioned ESS depth and the game-theory approach (Du and Hsu, 2008a, b).…”