Table 1.

Model parameters. The subscript i indicates the species or trophic level: basal resource (1), primary producer (2), primary consumer (3), secondary consumer (4) and tertiary consumer (5). For numerical simulations, initial conditions were taken as the equilibrium values in the absence of stochasticity. Parameter values were chosen to guarantee the presence of a stable, interior equilibrium and were held constant across food chains (e.g. a₂ = 0.2 for bi- to penta-trophic food chains). Variances of white noise were equal for all species and were chosen such that stochastic effects neither perturbed the system out of the coexistence basin of attraction nor caused the stochastic additive terms to exceed mortality.^a

parameter	interpretation	value
I	baseline rate of resource influx	variable [5, 150]
I	resource loss rate	0.1
ai	predator predation rate	a2 = a3 = a4 = 0.2 a5 = 0.5
bi	biomass conversion efficiency	b2 = b3 = 0.3 b4 = b5 = 0.4
mi	mortality rate	0.1
ɛI	white noise (rate of resource influx)	$\sim N(0,{\zeta }_I)$
ɛi	white noise (per species)	$\sim N(0,{\xi }_i)$
ζI	variance of white noise (rate of resource influx)	0.0100
ξi	variance of white noise (per species)	0.0025
T	simulation time horizon	1500
Δt	simulation step size	0.1

^aAs pointed out by a reviewer, in order to be a truly self-contained food chain the effect of stochasticity on population biomass should come in the form of mortality only. Indeed, if a positive stochastic effect were to exceed mortality then it would result in a net input or subsidy to biomass.