Food Chain

The above prey-predator model may be easily extended to a food chain with more than two trophic levels. Such a model may be written as follows:

dNi/dt — rNi (1 -Ni/K) - viNlN2¡{hl + N¡) dN2/dt — b1v1N1N2/(h1 + N1) - v2N2N2/(h2 + N2) - m2N2

dN„/dt — b„ -1 Vn -1 N„ -1 N„/(h1 + N„ -1) - m„N„

The food chain has n + 1 equilibrium solutions. One of these equilibrium solutions may signify persistence of all trophic levels. If this equilibrium is stable, it makes sense to investigate effects of management changes.

There are two most often generated anthropogenic impacts on a food chain: (1) increase in the inflow of food to the chain and hence an increase in K, and (2) harvesting all, some, or the top trophic level.

Nutrients continuously added to the first trophic level induce an increase in carrying capacity and this phenomenon is called eutrophication. There are several effects on the food chain as a whole. The first is that after enough time the average concentration of the top trophic level (the top predator) will increase. Also, the (n — 1)th trophic level will decrease. In general, if the food chain has an even (odd) number of trophic levels, the concentration of all the odd (even) trophic levels will decrease and all even (odd) trophic levels will increase. Hence, the biomass in the first trophic level will decrease (increase) in a food chain with an even (odd) number of trophic levels.

The second impact is if only the top predator is harvested. In the food chain having an even (odd) number of trophic levels, all odd (even) trophic levels will increase and even (odd) trophic levels will decrease.

The above are just two examples of systems properties of a food chain; more have been discovered and many more remain to be discovered, especially with regard to persistence of the chain as a whole subject to various external perturbations.

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