Table 2.

Metrics of trophic interaction modification strength, discussed in more detail in the main text. Indices: i = prey, j = predator, k = modifier species

Metric	Composition	Explanation
Modification parameter	$c_{ijk}$	Parameter in function that links modifier species density to consumption rate in the functional response model (van Veen et al. 2005)
Modification term	$f(c_{ijk},k)$	The term by which a functional response parameter, such as attack rate, is modified. It incorporates modifier density and TIM model structure (Golubski & Abrams 2011)
Flux change	${\mathrm{\Delta }}_{rel}=\frac{f(i,j,k_{=0})}{f(i,j,k)}$	The difference in the interaction strength (as measured by biomass or energy flux) due to the modifier, as either a raw difference or a ratio (Peacor & Werner 2004)
	${\mathrm{\Delta }}_{abs}=f\left(i,j,k_{=0}\right)-f(i,j,k)$
Change in $B_{CR}$	$\frac{I^{\ast }}{I_{c_{ijk}=0}^{\ast }}$	The relative change in biomass potential of the resource ($B_{CR}$, computed from the relative change in equilibrium density of the resource in the presence of the consumer, Gilbert et al. 2014) due to a TIM as the ratio of the equilibrium value of the prey with and without the TIM
Coefficient of variation in modification	$\frac{{\mathit{\sigma }}_{f\left(k\right)}}{{\mathit{\mu }}_{f\left(k\right)}}$	For non‐stationary systems, the ratio of the standard deviation of the interaction strength modification divided by the mean modification over a period of time
Elements of Jacobian matrix	${\displaystyle \frac{\mathrm{\partial }\dot{I}}{\mathrm{\partial }K},\frac{\mathrm{\partial }\dot{J}}{\mathrm{\partial }K}}$	TMII framework metric representing the direct effects of the modifier species on each interactor (Abrams 2008; Okuyama & Bolker 2012)
Partial derivatives of Jacobian matrix	$\frac{\mathit{\partial }}{\mathit{\partial }K}{A}_{ij},\frac{\mathit{\partial }}{\mathit{\partial }K}{A}_{ji}$	The change in direct interaction strengths between the interactors with respect to modifier density
Partial derivatives of inverse negative Jacobian matrix	${\displaystyle \frac{\mathrm{\partial }}{\mathrm{\partial }K}{(-A^{-1})}_{ij},\frac{\mathrm{\partial }}{\mathrm{\partial }K}{(-A^{-1})}_{ji}}$	The change in total (indirect and direct) interaction strength between the interactors with respect to modifier density