16 An introduction to Ecosim

Ecosim provides a dynamic simulation capability at the ecosystem level, with key initial parameters inherited from the base Ecopath model.

The key computational aspects are in summary form,

• Use of mass-balance results (from Ecopath) for parameter estimation;
• Variable speed splitting enables efficient modelling of the dynamics of both “fast” (e.g., phytoplankton) and “slow” groups (e.g., whales);
• Effects of micro-scale behaviours on macro-scale rates: top-down vs. bottom-up control incorporated explicitly.
• Includes biomass and size structure dynamics for key ecosystem groups, using a mix of differential and difference equations. As part of this EwE incorporates:
• Multi-stanza life stage structure by monthly cohorts, density- and risk-dependent growth – described in the Age-structured dynamics chapter;
• Stock-recruitment relationship as “emergent” property of competition/predation interactions of juveniles.

Ecosim uses a system of differential equations that expresses biomass flux rates among pools as a function of time varying biomass and harvest rates, (for equations see Walters et al., 1997^[1]; Walters et al., 2000^[2]; Christensen and Walters, 2004^[3]). Predator prey interactions are moderated by prey behaviour to limit exposure to predation, such that biomass flux patterns can show either bottom-up or top down (trophic cascade) control. By doing repeated simulations, Ecosim allows for the fitting of predicted biomasses to time series data.

The simplest, default version of Ecosim represents biomass dynamics using a series of coupled differential equations. The equations are of the basic form:

[latex]\frac{dB_i}{dt}=g_i\sum\limits_{i=1}^{n}Q_{ij}-\sum\limits_{j=1}^{n}Q_{ji}+I_i-(F_i+e_i+M0_i) B_i\tag{1}[/latex]

where dB_i/dt represents the growth rate during the time interval dt of group i in terms of its biomass, B_i, g_i is the net growth efficiency (production/consumption ratio), M0_i the non-predation (“other”) natural mortality rate, F_i is fishing mortality rate, e_i is emigration rate, I_i is immigration rate, (and e_i·B_i-I_i is the net migration rate). The two summations estimate consumption rates, the first expressing the total consumption by group i, and the second the predation by all predators j on the prey group.

Ecopath is used to provide the initial (t=0) biomasses, and some of the rate parameters (like MO).  Ecosim parameters for the flow or consumption rates Q_ij are set partly from Ecopath base estimates of those flows, with addition information needed to represent how the flow rates vary with biomasses and other circumstances.

The consumption rates, Q_ji and Q_ij, represent consumption by group j on i and by i on j, respectively, and are calculated based on foraging arena theory, where B_i’s are divided into vulnerable and invulnerable components^[4], and it is the transfer rate (v_ij) between these two components that determines if control is top-down (i.e., Lotka-Volterra), bottom-up (i.e., donor-driven), or of an intermediate type. See the vulnerability multiplier chapter.

The set of differential equations is solved in Ecosim using a 4^th order Runge-Kutta routine (see the A primer on dynamic modelling chapter).  For groups like phytoplankton and small zooplankton that turn over (have P/B) greater than 10 and are likely to exhibit boom-bust dynamics on time scales shorter than one month, the numerical integration prediction is replaced with a prediction based on the equilibrium of the Ecosim rate equation of the likely average over the month.