Table 2.

The eigenvalues describing the linear stability of the steady states

State	Description	${\lambda }_1$	${\lambda }_2$	${\lambda }_3$	${\lambda }_4$	${\lambda }_5$	Stability
SS0	Healthy tissue	0	− 1	$-{\rho }_L$	${\rho }_T(1-c_S)$	${\rho }_T(1-c_S)$	Yes
SS1	$T_{\mathrm{A}}$ Monoculture	0	$-{\rho }_T$	$-{\rho }_L$	$1-\delta$	${\mathit{\rho }}_{\mathbf{T}}({\mathbf{1}-\mathbf{c}}_{\mathbf{A},\mathbf{M}})$	If $c_{\mathrm{A},\mathrm{M}}>1$
SS2	$T_{\mathrm{M}}$ Monoculture	$\mathbf{1}$	$-{\rho }_T$	$-{\rho }_L$	$-\kappa$	${\mathit{\rho }}_{\mathbf{T}}({\mathbf{1}-\mathbf{c}}_{\mathbf{M},\mathbf{A}})$	No
SS3	$T_{\mathrm{A}}-T_{\mathrm{M}}$ Coexistence	$-{\rho }_T$	$-{\rho }_L$	$\frac{{\mathit{\rho }}_{\mathbf{T}}(\mathbf{1}+{\mathbf{c}}_{\mathbf{A},\mathbf{M}}{\mathbf{c}}_{\mathbf{M},\mathbf{A}}-{\mathbf{c}}_{\mathbf{A},\mathbf{M}}-{\mathbf{c}}_{\mathbf{M},\mathbf{A}})}{{\mathbf{c}}_{\mathbf{A},\mathbf{M}}{\mathbf{c}}_{\mathbf{M},\mathbf{A}}-\mathbf{1}}$	$\frac{\mathit{\kappa }({\mathbf{1}-\mathbf{c}}_{\mathbf{A},\mathbf{M}})}{{\mathbf{c}}_{\mathbf{A},\mathbf{M}}{\mathbf{c}}_{\mathbf{M},\mathbf{A}}-\mathbf{1}}$	$\frac{{\mathit{\rho }}_{\mathbf{T}}({\mathbf{1}+\mathbf{c}}_{\mathbf{M},\mathbf{A}}\mathit{\delta }-{\mathbf{c}}_{\mathbf{A},\mathbf{M}}{\mathbf{c}}_{\mathbf{M},\mathbf{A}}-\mathit{\delta })}{{\mathbf{1}-\mathbf{c}}_{\mathbf{A},\mathbf{M}}{\mathbf{c}}_{\mathbf{M},\mathbf{A}}}$	If $c_{\mathrm{A},\mathrm{M}},c_{\mathrm{M},\mathrm{A}}<1$
SS4	Stroma-$T_{\mathrm{A}}$ Coexistence			See Fig. 7			No
SS5	Stroma-$T_{\mathrm{M}}$ Coexistence	− 1	${\mathit{\rho }}_{\mathbf{L}}$	${\mathit{\rho }}_{\mathbf{T}}({\mathbf{c}}_{\mathbf{S}-\mathbf{1}})$	$\mathit{\kappa }({\mathbf{c}}_{\mathbf{S}-\mathbf{1}})$	${\mathit{\rho }}_{\mathbf{T}}({\mathbf{1}+\mathbf{c}}_{\mathbf{M},\mathbf{A}}{\mathbf{c}}_{\mathbf{S}}-{\mathbf{c}}_{\mathbf{S}}-{\mathbf{c}}_{\mathbf{M},\mathbf{A}})$	No
SS6	Stroma-$T_{\mathrm{A}}-T_{\mathrm{M}}$ Coexistence			See Fig. 7			No

Stability is assessed based on the parameter values in Table 1. Bold values indicate eigenvalues that are positive in at least parts of the parameters space. For SS4 and SS6, no simple analytic forms were attainable, and instead stability was assessed numerically (see Fig. 7)