“…During the development of multicellular systems, the expression of patterning genes dynamically evolves and stochastically fluctuates ( Dubuis et al, 2013 ; Gregor et al, 2007a ; Gregor et al, 2007b ; Jaeger et al, 2004 ; Kanodia et al, 2009 ; Liu et al, 2013 ; Yang et al, 2018 ).The high degree of accuracy ( Dubuis et al, 2013 ; Gregor et al, 2007a ) and robustness ( Houchmandzadeh et al, 2002 ; Inomata et al, 2013 ; Liu et al, 2013 ; Lucchetta et al, 2005 ) that developmental patterning achieves is intriguing. Two hypotheses have been proposed to explain these traits: one is the threshold-dependent positional information model, that is the French flag model, which assumes that the positional information is faithfully transferred from precise upstream patterning ( He et al, 2008 ; Wolpert, 2011 ; Gregor et al, 2007a ); the other is the self-organized filtering model, which assumes that noisy upstream patterning needs to be refined to form downstream patterning with sufficient positional information ( Dubuis et al, 2013 ; Houchmandzadeh et al, 2002 ; Jaeger et al, 2004 ; Kanodia et al, 2009 ; Manu et al, 2009 ).…”