Quantitative methods for ecological network analysis

The analysis of networks of ecological trophic transfers is a useful complement to simulation modeling in the quest for understanding whole-ecosystem dynamics. Trophic networks can be studied in quantitative and systematic fashion at several levels. Indirect relationships between any two individual taxa in an ecosystem, which often differ in either nature or magnitude from their direct influences, can be assayed using techniques from linear algebra. The same mathematics can also be employed to ascertain where along the trophic continuum any individual taxon is operating, or to map the web of connections into a virtual linear chain that summarizes trophodynamic performance by the system. Backtracking algorithms with pruning have been written which identify pathways for the recycle of materials and energy within the system. The pattern of such cycling often reveals modes of control or types of functions exhibited by various groups of taxa. The performance of the system as a whole at processing material and energy can be quantified using information theory. In particular, the complexity of process interactions can be parsed into separate terms that distinguish organized, efficient performance from the capacity for further development and recovery from disturbance. Finally, the sensitivities of the information-theoretic system indices appear to identify the dynamical bottlenecks in ecosystem functioning.

Sampling effects and the robustness of quantitative and qualitative food-web descriptors

Food-web descriptors serve as a means for among-web comparisons that are necessary for the discovery of regularities in respect to food-web structure. Qualitative descriptors were however found to be highly sensitive to varying levels of sampling effort. To circumvent these shortcomings, quantitative counterparts were proposed which take the magnitude of trophic interaction between species into consideration. For 14 properties we examined the performance with increasing sampling effort of a qualitative, an unweighted quantitative (giving the same weight to each taxon), and a weighted quantitative version (weighing each taxon by the amount of incoming and outgoing flows). The evaluation of 10 extensively documented quantitative webs formed the basis for this analysis. The quantitative versions were found to be much more robust against variable sampling effort. This increase in accuracy is accomplished at the cost of a slight decrease in precision as compared to the qualitative properties. Conversely, the quantitative descriptors also proved less sensitive to differences in evenness in the distribution of link magnitude. By more adequately incorporating the information inherent to quantitative food-web compilations, quantitative descriptors are able to better represent the web, and are thus more suitable for the elucidation of general trends in food-web structure.