Toward canonical trophic aggregations

The attractiveness of the trophic concept is that it was the first attempt at a holistic perspective on an ecosystem which met with any degree of success. Just as temperature, pressure, and volume allow one to characterize the incomprehensible multitude of particulate motions in a simple gas, the hope is that a small set of figures, such as trophic storages or trophic efficiencies, permit one to compare two ecosystems with overwhelmingly disparate complexities. Thus, if it were possible to demonstrate that an arbitrary network of ecosystem flows could be reduced to a trophic configuration, the aggregation process thus defined would become a key component of the evolving discipline of "macroscopic ecology" (see also Odum 1977 and Ulanowicz 1979).

Recruitment as an evolving random process of aggregation and mortality

The dynamics of the survival of recruiting fish are analyzed as evolving random processes of aggregation and mortality. The analyses draw on recent advances in the physics of complex networks and, in particular, the scale-free degree distribution arising from growing random networks with preferential attachment of links to nodes. In this study simulations were conducted in which recruiting fish 1) were subjected to mortality by using alternative mortality encounter models and 2) aggregated according to random encounters (two schools randomly encountering one another join into a single school) or preferential attachment (the probability of a successful aggregation of two schools is proportional to the school sizes). The simulations started from either a “disaggregated” (all schools comprised a single fish) or an aggregated initial condition. Results showed the transition of the school-size distribution with preferential attachment evolving toward a scale-free school size distribution, whereas random attachment evolved toward an exponential distribution. Preferential attachment strategies performed better than random attachment strategies in terms of recruitment survival at time when mortality encounters were weighted toward schools rather than to individual fish. Mathematical models were developed whose solutions (either analytic or numerical) mimicked the simulation results. The resulting models included both Beverton-Holt and Ricker-like recruitment, which predict recruitment as a function of initial mean school size as well as initial stock size. Results suggest that school-size distributions during recruitment may provide information on recruitment processes. The models also provide a template for expanding both theoretical and empirical recruitment research.