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 various species and determined appropriate rates of population growth patterns. 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
for Balance Figure 2. Change in rates due to population change Our model did not include any upper limit on the population of any ne species within the ecosystem. So over time, the population of all organ- isms continued to grow at similar rates, and water never reached an equilibrium value. In reality, there has to be a natural limit, if for no other reason than that if the fish waste grows uncontrollably, it will eventually occupy all of the space, choking off nutrient access. One possibility would be to introduce an assumed limit to the ecosystem by confining the space to the Bolinao region. The water area of Bolinao covers 1170 ha. Based on the limit in the problem statement that the farmers currently use 50,000 milkfish to a pen and operate 10 pens per hectare, a natural limit is 585 million milkfish(500,000 milkfish/ ha x 1170 ha) Assuming this upper bound, we can base the growth rate from a factor of the difference between the current population of milkfish and the upper limit of 585,000,000, via the formula G(585000000-Pm) Despite the difficulty in achieving steady-state equilibrium of water quality, we still produce a model that demonstrates the general trend that should have been presentin the ecosystem before mass-farming of milkfish Task 2: Current Water Quality Poor water quality and the destruction of coral don' t really seem like problems to people who are trying to meet basic needs and keep their children healthy. It is difficult to show people how their actions now are ultimately leading to greater problems for them and their children in the future. The current thought process is that growing just one type of fish
Striving for Balance - Poly. (S.M1l. _PO,y. (Eaten) PuM ropulanan Jun-I Figure 2. Change in rates due to population change. Our model did not include any upper limit on the population of any of the species within the ecosystem. So over time, the population of all organisms continued to grow at similar rates, and water quality never reached an equilibrium value. In reality, there has to be a natural limit, if for no other reason than that if the fish waste grows uncontrollably, it will eventually occupy all of the space, choking off nutrient access. One possibility would be to introduce an assumed limit to the ecosystem by confining the space to the Bolinao region. The water area of Bolinao covers 1170 ha. Based on the limit in the problem statement that the farmers currently use 50,000 milkfish to a pen and operate 10 pens per hectare, a natural limit is 585 million milkfish (500,000 milkfish/ha x 1170 ha). Assuming this upper bound, we can base the growth rate from a factor of the difference between the current population of milkfish and the upper limit of 585,000,000, via the formula G.(585000000 - Pmo). Despite the difficulty in achieving steady-state equilibrium of water quality, we still produce a model that demonstrates the general trend that should have been present in the ecosystem before mass-farming of milkfish. Task 2: Current Water Quality Poor water quality and the destruction of coral don't really seem like problems to people who are trying to meet basic needs and keep their children healthy. It is difficult to show people how their actions now are ultimately leading to greater problems for them and their children in the future. The current thought process is that growing just one type of fish z Zýs \