Grazing-induced production of DMS can stabilize food-web dynamics and promote the formation of phytoplankton blooms in a multitrophic plankton model

Abstract

Volatile infochemicals including climatically relevant dimethylsulphide (DMS) have been suggested to play important roles in the structuring and functioning of marine food webs. Experimenting with complex natural plankton communities or several trophic levels in laboratory microcosms is challenging and, as a result, empirical data confirming the role of DMS in trophic interactions is lacking. Models are a suitable tool to provide insight into such complex interactions. Here we consider a model of the interactions between three trophic levels of plankton: phytoplankton, grazing microzooplankton and predatory mesozooplankton. We show that the inclusion of a grazing-induced DMS production term has a stabilizing effect on the system dynamics under the assumption that DMS acts as an info-chemical and increases the rate of mesozooplankton predation on grazing microzooplankton. We further demonstrate how this feedback between trophic levels can potentially lead to the formation of a phytoplankton bloom. The model provides a suitable framework for further study into the possible role of DMS in the ecology of marine food webs beyond its recognised role as a climate-cooling gas.

Appendix

Here we show the derivation of Eqs. 1–2 and parameters m and λ. We start with a full model with phytoplankton (P), microzooplankton (M), copepods (Z, which we assume is constant due to the fact that we only consider a short time-scale of a few days) and DMS (C) are:

$$ \frac{dP}{dt} = r(P)P - f(P)M $$

(3)

$$ \frac{dM}{dt} = \gamma f(P)M - \mu M - \beta ZM(1 + \xi C) $$

(4)

$$ \frac{dC}{dt} = \eta f(P)M - \nu C $$

(5)

where

$$ r(P) = r\left( {1 - \frac{P}{K}} \right) $$

$$ f(P) = \frac{aP}{1 + bP} $$

and

• μ is the background mortality of microzooplankton as described in the Methods section of the main text.

• β and ξ correspond to copepod predation; copepods consume microzooplankton at a linear rate β in the absence of DMS (a linear rate is chosen for simplicity because a type II response leads to similar model results). In the presence of DMS, the overall predation rate is increased by a multiplicative factor of 1 + ξC, where the parameter ξ represents how much an increase in levels of DMS leads to an increase in predation by copepods.

• DMS is produced in the system at a rate η proportional to microzooplankton grazing and leaves the system at a rate ν (as a result of flux to the atmosphere, bacterial consumption etc.).

C is a fast variable under assumption (ii) from the methods; C will quickly return to the underlying background concentration after any perturbation and hence we assume that dC/dt ≈ 0. Rearranging Eq. 5 for C under this assumption and substituting back into Eq. 4 gives the following system:

$$ \frac{dP}{dt} = r(P)P - f(P)M $$

(6)

$$ \frac{dM}{dt} = \gamma f(P)M - mM - \lambda f(P)M^{2} $$

(7)

where $m = (\mu + \beta Z)$ and $\lambda = \frac{\eta \beta Z\xi }{\nu }.$

Specifying that phytoplankton grow logistically, r(P), and that microzooplankton follow a type II functional response, f(P), gives Eqs. 1–2 in the main text.