A Polarity-Energy Food Chain Trophic Cascade Model: Implications to Fishery Management

Abstract

The paper develops a model that extends the classical Oksanen Polarity Theorem for simple food chains to accommodate the analyses of energy transfers from one trophic level to another. The Polarity-Energy Food Chain Trophic Cascade model developed is then used in the analysis of data obtained by researchers for sardines (Sardinella lemuru) and lake herring ( Coregonous artedii). Results revealed that for the sardine population in the east coast of Siberut Island, a stable logistic population growth is observed. These information means that population of this pelagic fish species increases (as a function of time n) until it reaches a stable population if left on its own based on the logistic growth hypothesis. However, over-predation by the top level consumer (over-fishing) can disrupt this approach to stability ( i.e. fishing intensity of δ > 14.5%) or if fish larvae are caught by very fine gill nets (i.e. causing a reduction in the value of r). Fishery closure during spawning period (September to October) up to March or April each year ensures sustainable catch for this fish species. On the other hand, for the population of lake herring in the Great Lakes displayed large fluctuations in both yield and effort. Data tend to support a growth rate r > 3.5 if a logistic growth model were used because of the observed chaotic fluctuations. This means that fishing has caused a decreased in fecundity (as reported) leading to a greater value of the growth rate r (ratio of average eggs per female to fecundity). Overall, the Polarity-Energy Food Chain Model developed supports temporary fishing ban or permanent identification of marine protected areas (MPA) to preserve the natural logistic growth patterns of economically-important fish species. In the former case, fishing is timed with the observed population periodicities while in the latter case, fishing can be allowed outside of the protected area which benefits from spill-over effects of the MPA.