Table 2. Comparison of the stiffest eigenparameters ${\widehat{\mathbf{\theta }}}_{\mathbf{1}}$, ${\widehat{\mathbf{\theta }}}_{\mathbf{2}}$, and ${\widehat{\mathbf{\theta }}}_{\mathbf{3}}$ (associated with the largest eigenvalues λ₁, λ₂, and λ₃) considering a multivariate log-normal prior distribution for the parameters to fit the ecosystem model (table S1) to data (Fig. 3B).

Each ${\widehat{\mathrm{\theta }}}_1$, ${\widehat{\mathrm{\theta }}}_2$, and ${\widehat{\mathrm{\theta }}}_3$ is identified via Eq. 8 after obtaining eigenvalues (fig. S6) and eigenvectors from matrices H (or L), P, and G. Stiff eigenparameters from matrix H (or L) are obtained at two sets of best-fit parameter values ${\mathbf{\theta }}_1^{\star }$ and ${\mathbf{\theta }}_2^{\star }$ (fig. S5). Matrix H (or L) returns different stiff eigenparameters when evaluated at two distinct sets of best-fit parameter values, while matrices P and G return different stiff eigenparameters because the prior influences the model-data fit.

Eigenparameter ${\widehat{\mathbf{\theta }}}_{\mathit{i}}$	Sensitivity matrices
	H or L evaluated at		P	G
	${\mathbf{\theta }}_1^{\star }$	${\mathbf{\theta }}_2^{\star }$
1	(cN/aN)(aM/cM)0.4	(cM/aM)(aN/cN)0.9	$a_P^{0.9}/c_P$	(cM/aM)(aN/cN)0.9
2	(cM/aM)(cN/aN)0.4	(cN/aN)(cM/aM)0.9	cN/aN	(cN/aN)(cM/aM)0.9
3	$c_P/(a_P^{0.9}{d}_N^{0.4})$	$c_P/a_P^{0.9}$	cM/aM	$c_P/a_P^{0.9}$