146 The UMAP Journal 30.2(2009) Humans 1r3 Fish Rabbit Fish Algae Sea sta Figure l Food web. To produce this model, we researched the relationships among the var- Lous species and determined appropriate rates of population growth pat- terns. We use a general formula to calculate the current population Pz of speciesX, given the population Pa-1 of Xin the previous month, the growth rate G- the death rate De and the amount e, P, of X eaten by each other eciesy in the system: P2=P21+P-1C2-P1D2-∑P We obtain the overall bacterial level in the water as the sum over all species of its population P times its rate W= of bacteria waste production. The same calculation applies to calculating levels of all waste products(Cd Na, Chl, Cpr Np) Our model executed for enough iterations, should have converged to an equilibrium for water quality; but it did not. The main reason was that our model set the growth rates and death rates to remain constant, wl does not occur in nature due to the conservation of mass. An example of the more natural trend of this relationship is depicted in Figure 2. As the fish population increases, the rate at which they are eaten increases, so the rate at which they survive decreases In any closed system, the overall mass of the system must stay the sat hus, the addition of any new member to the system precludes the growth of something else either immediately or in the future. An example is that when the fish populationis larger, the death rate should be greater at some oint because fish are more easily caught by their predators.146 The UMAP Journal 30.2 (2009) Figure 1. Food web. To produce this model, we researched the relationships among the var￾ious species and determined appropriate rates of population growth pat￾terns. We use a general formula to calculate the current population P, of species X, given the population P -i of Xinthe previous month, the growth rate G=, the death rate D=, and the amount E.Py of X eaten by each other species y in the system: P. := P.-i + P.-iG.-P.-iD. -ZEEYPV We obtain the overall bacterial level in the water as the sum over all species of its population P. times its rate W, of bacteria waste production. The same calculation applies to calculating levels of all waste products (Cd, Nd, Chl, Cp, Np). Our model, executed for enough iterations, should have converged to an equilibrium for water quality; but it did not. The main reason was that our model set the growth rates and death rates to remain constant, which does not occur in nature due to the conservation of mass. An example of the more natural trend of this relationship is depicted in Figure 2. As the fish population increases, the rate at which they are eaten increases, so the rate at which they survive decreases. In any dosed system, the overall mass of the system must stay the same. Thus, the addition of any new member to the system precludes the growth of something else either immediately or in the future. An example is that when the fish population is larger, the death rate should be greater at some point because fish are more easily caught by their predators