# Table 4 Balance equations and time-scale constraints for each species and for each collective species chosen

Balance equations Time-scale constraints
S 1 ρ13=ρ14 $γ≤ α 1 −max( ρ 13 , ρ 14 )$
S 2 $max( ρ 3 , ρ 4 , ρ 5 , ρ 6 , ρ 7 , ρ 8 )=max( ρ 2 , ρ 9 )$ $γ≤ α 2 −max( ρ 2 , ρ 3 , ρ 4 , ρ 5 , ρ 6 , ρ 7 , ρ 8 , ρ 9 )$
S 3 $ρ 2 =max( ρ 3 , ρ 5 , ρ 6 , ρ 7 )$ $γ≤ α 3 −max( ρ 2 , ρ 3 , ρ 5 , ρ 6 , ρ 7 )$
S 4 ρ6=ρ18 $γ≤ α 4 −max( ρ 6 , ρ 18 )$
S 5 ρ5=ρ16 $γ≤ α 5 −max( ρ 5 , ρ 16 )$
S 6 $max( ρ 7 , ρ 8 , ρ 12 , ρ 15 )=max( ρ 9 , ρ 10 , ρ 17 )$ $γ≤ α 6 −max( ρ 7 , ρ 8 , ρ 9 , ρ 10 , ρ 12 , ρ 15 , ρ 17 )$
S 7 $ρ 9 =max( ρ 8 , ρ 15 )$ $γ≤ α 7 −max( ρ 8 , ρ 9 , ρ 15 )$
S 8 $max( ρ 1 , ρ 12 )=max( ρ 10 , ρ 11 )$ $γ≤ α 8 −max( ρ 1 , ρ 10 , ρ 11 , ρ 12 )$
S 9 ρ10=ρ12 $γ≤ α 9 −max( ρ 10 , ρ 12 )$
S2 + S3 + S7 ρ4=ρ15 $γ≤max( α 2 , α 3 , α 7 )−max( ρ 4 , ρ 15 )$
S2 + S3 $max( ρ 4 , ρ 8 )= ρ 9$ $γ≤max( α 2 , α 3 )−max( ρ 4 , ρ 8 , ρ 9 )$
S2 + S7 $max( ρ 3 , ρ 4 , ρ 5 , ρ 6 , ρ 7 )=max( ρ 2 , ρ 15 )$ $γ≤max( α 2 , α 7 )−max( ρ 2 , ρ 3 , ρ 4 , ρ 5 , ρ 6 , ρ 7 , ρ 15 )$
S6 + S7 + S9 ρ7=ρ17 $γ≤max( α 6 , α 7 , α 9 )−max( ρ 7 , ρ 17 )$
S6 + S7 $max( ρ 7 , ρ 12 )=max( ρ 10 , ρ 17 )$ $γ≤max( α 6 , α 7 )−max( ρ 7 , ρ 10 , ρ 12 , ρ 17 )$
S6 + S9 $max( ρ 7 , ρ 8 , ρ 15 )=max( ρ 9 , ρ 17 )$ $γ≤max( α 6 , α 9 )−max( ρ 7 , ρ 8 , ρ 9 , ρ 15 , ρ 17 )$
S8 + S9 ρ1=ρ11 $γ≤max( α 8 , α 9 )−max( ρ 1 , ρ 11 )$
1. In each case, either the balance equation or the time-scale constraint must hold.