Cropp & Gabric (2002) used a three-compartment food web model to demonstrate a similarity between the parameter set that maximised resilience and the parameter set that maximised the thermodynamic goal functions: 'maximise autotroph biomass', 'maximise heterotroph biomass', ‘maximise the flux of nutrients', and 'maximise the flux to biomass ratio'. Laws, Falkowski, Smith, Ducklow & McCarthy (2000) used a 10 compartment food web model to demonstrate that the ratio of nutrient loading rate to total primary production could be predicted accurately when free parameters in the model were selected such that the model ecosystem had maximal resilience.
Cropp & Gabric (2002) suggested that ecosystems maximise resilience as a consequence of maximising other goal functions. I use Cropp & Gabric's (2002) model to demonstrate that, while maximising resilience offers a compromise between the thermodynamic goal functions, maximising the thermodynamic goal functions does not necessarily optimise resilience. I explore the possibility that maximal resilience could be used as a heuristic - a way to compromise between the thermodynamic goal functions. It is found that maximal resilience does offer a compromise between the thermodynamic goal functions, however that is not a sufficient reason to recommend the use of resilience as a goal function.
The Laws et al. (2000) model is used to demonstrate that the predictive ability of maximal resilience in their model is independent of the relationship between maximal resilience and the thermodynamic goal functions. A system-level feedback mechanism is explored as a potential explanation for this observation. It is found that the feedback mechanism does not maximise resilience. However, given certain assumptions, the system will have high resilience. The assumptions are: the system is small, the system is simple, and the perturbation strength and frequency is moderate. 'Maximise resilience' can be used to predict the attributes of the system when the mapping from attribute space to resilience is peaked.
The predictions of the feedback mechanism are tested on the Laws et al. (2000) model and field data. Evidence for high resilience is found, however the model and field data do not show evidence of the existence of the feedback mechanism.
The maximal resilience goal function is applied to the Fasham, Ducklow & McKelvie (1990) model to find the reason behind the success of 'maximise resilience'. It is found that the feasible-stable region shows predictive ability in the Fasham et al. (1990) model. Therefore, because the Laws et al. (2000) model preserves the feasible-stable region in the peaks of the resilience surface, it also preserves the predictive ability of the Fasham et al. (1990) model. Thus, the resilience hypothesis is reformulated: maximal resilience is an effective goal function when peaks in the resilience surface correspond to the feasible-stable region in the real system.
To explore the hypothesis that stability and feasibility constrain ecosystems, a food web building algorithm is created using permanence as a constraint, and the attributes of the model webs resulting from the algorithm are compared with the attributes reported in the literature for real systems. Evidence is found for the restriction of food web attributes by a permanence constraint for: maximal chain length, link density, and basal fraction. Attributes such as basal-top link-type fraction require more than permanence to explain their patterns.