Goal functions and ecosystem contraints : thermodynamic goal functions, local stability, maximal resilience, and permanence

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