. 2015 May 14;11(5):e1004232. doi: 10.1371/journal.pcbi.1004232

Table 3. Equations and solutions of z* in Eq (6) for each type.

Type	Equation of z* in MIG	Solution of z* in S-MIG
P	−P ₁ z* = 0	0
R	R ₁ z* = R ₁	1
P+R	(R ₁−P ₁)z* = R ₁	no solution
PP	$z^{*} (- P_{1} - P_{P} + \frac{P_{P} + F_{P}}{F_{1}}) = 0$	not unique when μδ = 1
PR	$z^{*} (- P_{1} + \frac{- R_{P} + A_{P}}{F_{1}}) = 0$	0
PB	$z^{*} (- P_{1} - P_{P} + \frac{- R_{P} + P_{P} + A_{P} + F_{P}}{F_{1}}) = 0$	not unique when δ = 1
RP	$z^{*} (R_{1} + P_{R} + \frac{- P_{R} - F_{R}}{A_{1}}) = R_{1} + P_{R} + \frac{- P_{R} - F_{R}}{A_{1}}$	not unique when μδ = 1
RR	$z^{*} (R_{1} + \frac{R_{R} - A_{R}}{A_{1}}) = R_{1} + \frac{R_{R} - A_{R}}{A_{1}}$	1
RB	$z^{*} (R_{1} + P_{R} + \frac{R_{R} - P_{R} - A_{R} - F_{R}}{A_{1}}) = R_{1} + P_{R} + \frac{R_{R} - P_{R} - A_{R} - F_{R}}{A_{1}}$	not unique when δ = 1
P+RP	$z^{*} (R_{1} + P_{R} - P_{1} + \frac{- P_{R} - F_{R}}{A_{1} + F_{1}}) = R_{1} + P_{R} + \frac{- P_{R} - F_{R}}{A_{1} + F_{1}}$	no solution
P+RR	$z^{*} (R_{1} - P_{1} + \frac{R_{R} - A_{R}}{A_{1} + F_{1}}) = R_{1} + \frac{R_{R} - A_{R}}{A_{1} + F_{1}}$	no solution
P+RB	$z^{*} (R_{1} + P_{R} - P_{1} + \frac{R_{R} - P_{R} - A_{R} - F_{R}}{A_{1} + F_{1}}) = R_{1} + P_{R} + \frac{R_{R} - P_{R} - A_{R} - F_{R}}{A_{1} + F_{1}}$	no solution
PP+R	$z^{*} (R_{1} - P_{1} - P_{P} + \frac{P_{P} + F_{P}}{A_{1} + F_{1}}) = R_{1}$	$\frac{2 μ}{1 + μ - 2 μ δ} (> 1 or < 0)$
PR+R	$z^{*} (R_{1} - P_{1} + \frac{- R_{P} + A_{P}}{A_{1} + F_{1}}) = R_{1}$	$\frac{2 μ}{μ - 1} (> 1)$
PB+R	$z^{*} (R_{1} - P_{1} - P_{P} + \frac{- R_{P} + P_{P} + A_{P} + F_{P}}{A_{1} + F_{1}}) = R_{1}$	$\frac{1}{1 - δ} (> 1)$
PP+RP	$z^{*} (R_{1} + P_{R} - P_{1} - P_{P} + \frac{- P_{R} + P_{P} + F_{P} - F_{R}}{A_{1} + F_{1}}) = R_{1} + P_{R} + \frac{- P_{R} - F_{R}}{A_{1} + F_{1}}$	no solution
PP+RR	$z^{*} (R_{1} - P_{1} - P_{P} + \frac{R_{R} + P_{P} + F_{P} - A_{R}}{A_{1} + F_{1}}) = R_{1} + \frac{R_{R} - A_{R}}{A_{1} + F_{1}}$	$\frac{1 + μ}{2 (1 - μ δ)} (> 1)$
PP+RB	$z^{*} (R_{1} + P_{R} - P_{1} - P_{P} + \frac{R_{R} - P_{R} + P_{P} + F_{P} - A_{R} - F_{R}}{A_{1} + F_{1}}) = R_{1} + P_{R} + \frac{R_{R} - P_{R} - A_{R} - F_{R}}{A_{1} + F_{1}}$	$\frac{2 μ δ}{1 - μ} (> 1)$
PR+RP	$z^{*} (R_{1} + P_{R} - P_{1} + \frac{- P_{R} - R_{P} + A_{P} - F_{R}}{A_{1} + F_{1}}) = R_{1} + P_{R} + \frac{- P_{R} - F_{R}}{A_{1} + F_{1}}$	$\frac{2 μ δ + μ - 1}{2 (μ δ - 1)} (> 1)$
PR+RR	$z^{*} (R_{1} - P_{1} + \frac{R_{R} - R_{P} + A_{P} - A_{R}}{A_{1} + F_{1}}) = R_{1} + \frac{R_{R} - A_{R}}{A_{1} + F_{1}}$	no solution
PR+RB	$z^{*} (R_{1} + P_{R} - P_{1} + \frac{R_{R} - P_{R} - R_{P} + A_{P} - A_{R} - F_{R}}{A_{1} + F_{1}}) = R_{1} + P_{R} + \frac{R_{R} - P_{R} - A_{R} - F_{R}}{A_{1} + F_{1}}$	$\frac{2 μ δ + μ - 1}{2 μ δ - μ - 1} (> 1)$
PB+RP	$z^{*} (R_{1} + P_{R} - P_{1} - P_{P} + \frac{- P_{R} - R_{P} + P_{P} + A_{P} + F_{P} - F_{R}}{A_{1} + F_{1}}) = R_{1} + P_{R} + \frac{- P_{R} - F_{R}}{A_{1} + F_{1}}$	$\frac{2 μ δ + μ - 1}{μ - 1} (> 1)$
PB+RR	$z^{*} (R_{1} - P_{1} - P_{P} + \frac{R_{R} - R_{P} + P_{P} + A_{P} + F_{P} - A_{R}}{A_{1} + F_{1}}) = R_{1} + \frac{R_{R} - A_{R}}{A_{1} + F_{1}}$	$\frac{μ + 1}{1 + μ - 2 μ δ} (> 1 or < 0)$
PB+RB	$z^{*} (R_{1} + P_{R} - P_{1} - P_{P} + \frac{R_{R} - P_{R} - R_{P} + P_{P} + A_{P} + F_{P} - A_{R} - F_{R}}{A_{1} + F_{1}}) = R_{1} + P_{R} + \frac{R_{R} - P_{R} - A_{R} - F_{R}}{A_{1} + F_{1}}$	no solution