Striving for Balance 141 Striving for Balance: Wh y Reintroducing More Species to Fish Farm Ecosystem Yields Bigger Profits Sean clement Timothy Newlin Joseph Lucas Dept of Mathematical Sciences U.S. Military Academy West Point ny Advisor: Kristin Aney S1 ruinary Demand for animal protein is the root problem that the people of Boli nao, Philippines have experienced over the last 15 years. Past solutions focused on harvesting large quantities of one type of fish using large cages nfortunately this approach failed to meet the demand for protein, ruined local water quality, and destroyed the coral reef Future technological innovations such as self-powered fish cages, alg based biodiesel fuel, and radio-frequency identification tracking offer great potential for waste reduction and improved open-water fish harvesting However, the people of Bolinao cannot wait; change must begin now. We must assist the transition, butultimately the people of Bolinao are the great est stakeholders in the future quality of life there Mathematics-based models show the various stages of this deterioration by demonstrating how the ecosystem in Bolinao once functioned before demand for fish grew dramatically in the early 1990s. We demonstrate the dangers to water quality of the current practice of farming only milkfish Finally, we show how introducing other species into commercial fish pens will allow equilibrium to recur, reducing levels of waste in the water and allowing the coral reef (a catalyst for growth) to return. The UMAP Journal30(2)(2009)141-157. @ Copyright 2009 by COMAP, Inc. Allrights reserved Permission to make digi ies of part or all of this work for personal or classroom use anted without fee e not made or distributed for profit or commercial notice. Abstracting with credit is permitted, but copyright for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP
Striving for Balance 141 Striving for Balance: Why Reintroducing More Species to Fish Farm Ecosystem Yields Bigger Profits Sean Clement Timothy Newlin Joseph Lucas Dept. of Mathematical Sciences U.S. Military Academy West Point, NY Advisor: Kristin Amey Summary Demand for animal protein is the root problem that the people of Bollnao, Philippines have experienced over the last 15 years. Past solutions focused on harvesting large quantities of one type of fish using large cages. Unfortunately this approach failed to meet the demand for protein, ruined local water quality, and destroyed the coral reef. Future technological innovations such as self-powered fish cages, algaebased biodiesel fuel, and radio-frequency identification tracking offer great potential for waste reduction and improved open-water fish harvesting. However, the people of Bolinao cannot wait; change must begin now. We must assist the transition, but ultimately the people of Bolinao are the greatest stakeholders in the future quality of life there. Mathematics-based models show the various stages of this deterioration by demonstrating how the ecosystem in Bolinao once functioned before demand for fish grew dramatically in the early 1990s. We demonstrate the dangers to water quality of the current practice of farming only milkfish. Finally, we show how introducing other species into commercial fish pens will allow equilibrium to recur, reducing levels of waste in the water and allowing the coral reef (a catalyst for growth) to return. The UMAP Journal 30(2) (2009)141-157. @Copyright2009by COMAP Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAR
142 The umaP Journal 30.2(2009) Combiningthe balancedecosystem withmarketpricing formulas demon strates how alternative fish-harvesting practices will lead to higherincome for the local population and provide the protein that they need. Fish is the most efficient source of animal protein for humans because it requires less feed to obtain the same amount of protein as chicken, beef, or pork. Akey limit of our models is scant data on prices and onratios of species necessary to recreate a balanced ecosystem. Still, our results demonstrate to the Bolinao people both the environmental and the economic value of °n8 om producing only mil由切 more diverse aquaculture wesuggestpolicy changes designed so thatthe people of Bolinao t have to choose between getting enough food to eat now and having a healthy environment in the future Table 1. Symbol key. bol Meaning Formula LmrstPPBSGDEP ant tiger praw current population of species x Pr-1 population of species X the previous month birth rate of species death rate of speciesx rate at which species X is eaten by a predator current population of algae SaPa-1+EaPr-1 P current population of mussels SiP-I+EiP, P current population of milkfish Pmyt Pmo Pmy current population of juvenile(young)milkfish BmPmo-1+0.066Pmy-1 Pmo cument population of breeding(old)milkfish SmPmo-1+0.066Pmy-1 current population of rabbitfisH P current population of starfish current population of giant tiger prawns StPt-1-EtPm-1 Cd evel of carbon dissolved YmPm+YPt -YPt Nd level of nitrogen dissolved YmPm+YPr -YP-YaPa level of chlorophyll Ya Cp level of particulate carbon YmPm+YP+YP-YPC Np level of particulate nitrogen YmPm+YtPt-YaPo level of bacteria created by individual species X
142 The UMAP Journal 30.2 (2009) Combiningthe balanced ecosystemwithmarketpricingformulas demonstrates how alternative fish-harvesting practices will lead to higher income for the local population and provide the protein that they need. Fish is the most efficient source of animal protein for humans because it requires less feed to obtain the same amount of protein as chicken, beef, or pork. A key limit of our models is scant data on prices and on ratios of species necessary to recreate a balanced ecosystem. Still, our results demonstrate to the Bolinao people both the environmental and the economic value of transitioning from producing only milkfish to a more diverse aquaculture. Finally, we suggestpolicy changes designedso thatthe people of Bolinao don't have to choose between getting enough food to eat now and having a healthy environment in the future. Table 1. Symbol key. Symbol Meaning Formula algae blue mussels milkfish rabbitfish starfish giant tiger prawn current population of species X population of species X the previous month birth rate of species X survivability rate of species X growth rate of species X death rate of species X rate at which species X is eatenby a predator current population of algae current population of mussels current population of milkfish current population of juvenile (young) milkfish current population of breeding (old) milkfish current population of rabbitfish current population of starfish current population of giant tiger prawns level of carbon dissolved level of nitrogen dissolved level of chlorophyll level of particulate carbon level of particulate nitrogen level of bacteria created by individual species X market price for species X G.z -- Dx SaP,,-, + EaPt,.I SIPjI- + BIP.-i P,lt + Pi. BmP . - "-i O.+066P,,y-1 SmrPino-1 ""+ 0.066Pt,,,-l SIP,-I ErPn-i StPt-i -FtP,_l YnP6 + YtPt- YIP YnPm + YrPr YIPL YaPa YaPa YMP7 + YrPr + YSPS -YIPL Y7nPm + YtPt - YaPa a 1~?r S t PX Pm Pt P. P. Pt PM PV Wa Chd Mx
iving for balance Problem Approach Task 1 To model water quality before milkfish dominated the local ecosystem, we create formulas that model the interactions among the species in the ecosystem. This model focuses on a steady-state equilibrium of water qt We firstestablishhow to measure the changein water quality, as thesum of the waste products of each species. Some species, such as the blue mus- sel, which consumes the waste of other species, contribute negative waste and thus help improve water quality. We develop functions to describe the population of each species at any given time; the population determines the waste produced by that species and thus the water quality. The formula for each species calculates the change in the population by adding the number of new individuals( based on the determined growth rate)and subtracting the number eaten by other species as well as the number that die naturally We determine a steady state by running the whole model for several iterations until the level of the water quality stabilizes. Adjusting the num- ber of each species in the system while keeping the ratios among species constant should allow prediction of population levels before the disruption of overfishing that led to the commercial milkfish monoculture Task 2 We set to zero the populations of all species except milkfish and algae and run the model to determine water quality. Based on the known current water quality, we attempt to determine the current populations of a variety of Task 3 latn etting the water quality to an acceptable desired constant,werunsimu- would reestablish an equilibrium polyculture. This polyculture would con- sume the waste products of the milkfish and keep the growth of algae under control. We expect to determine different combinations for how many of various species would need to be introduced to the sites in the bolinao region to reestablish acceptable water quality and create coral growth Task 4 Ne determine from data the dollar values for each species
Striving for Balance 143 Problem Approach Task 1 To model water quality before milkfish dominated the local ecosystem, we create formulas that model the interactions among the species in the ecosystem. This model focuses on a steady-state equilibrium of water quality. We first establish how to measure the change in water quality, as the sum of the waste products of each species. Some species, such as the blue mussel, which consumes the waste of other species, contribute negative waste and thus help improve water quality. We develop functions to describe the population of each species at any given time; the population determines the waste produced by that species and thus the water quality. The formula for each species calculates the change in the population by adding the number of new individuals (based on the determined growth rate) and subtracting the number eaten by other species as well as the number that die naturally. We determine a steady state by running the whole model for several iterations until the level of the water quality stabilizes. Adjusting the number of each species in the system while keeping the ratios among species constant should allow prediction of population levels before the disruption of overfishing that led to the commercial milkfish monoculture. Task 2 We set to zero the populations of all species except milkfish and algae Sand run the model to determine water quality. Based on the known current water quality, we attempt to determine the current populations of a variety of species. Task 3 Setting the water quality to an acceptable desired constant, we run simulations of adjusting the populations of species in different combinations that would reestablish an equilibrium polyculture. This polyculture would consume the waste products of the milkfish and keep the growth of algae under control. We expect to determine different combinations for how many of various species would need to be introduced to the sites in the Bolinao region to reestablish acceptable water quality and create coral growth. Task 4 We determine from data the dollar values for each species
144 The UMAP Journal 30.2 (2009) Task 5 Based on the values from Task 4, we assess which combinations from Task 3 are likely to create the most economic value for owners. Task 6 o We address policy changes that the Pacific Marine Fisheries Council can lopt to assist the Philippines in implementing long-term viability of a self-sustaining ecosystem. These policies center on harvesting all species at rates that keep the milkfish population under control and thus m polycultu Assumptions The growth rates of species are constant. Variability of amount of eggs laid by species is normally distributed. Humans are the only predator of milkfish The channel is not a closed system; excess population can emigrate to other reef locations The algae are a mix of cyan bacteria and red varieties(this assumption provides more-realistic results) Milkfish stop being omnivores when they mature, after which they eat only other animals It takes five years for milkfish to become sexually mature [Luna 2009] An adult milkfish is capable of eating an adult rabbitfish The fish pens currently hold approximately 58. 5 million fish. Milkfish weigh 500-600 g [Hambrey 19991 None of the other five species in the ecosystem model eats starfish Rabbitfish waste has the same composition as milkfish waste The prices found in Task 4 are estimates assumed from solitary sources Giant tiger prawns spawnnightly at a rate of 7.6% to 9% but only half of spawn hatch [Bray and Lawrence 1998 Giant tiger prawns have a mortality rate of 10% to 40% and an average weight of 106 g [Bray and Lawrence 1998]. Rabbitfish double in population every 1.4 to 4.4 years
144 The UMAP Journal 30.2 (2009) Task 5 Based on the values from Task 4, we assess which combinations from Task 3 are likely to create the most economic value for owners. Task 6 We address policy changes that the Pacific Marine Fisheries Council can adopt to assist the Philippines in implementing long-term viability of a self-sustaining ecosystem. These policies center on harvesting all species at rates that keep the milkfish population under control and thus maintain the polyculture. Assumptions "* The growth rates of species are constant. "* Variability of amount of eggs laid by species is normally distributed. "* Humans are the only predator of milkfish. "* The channel is not a dosed system; excess population can emigrate to other reef locations. "* The algae are a mix of cyan bacteria and red varieties (this assumption provides more-realistic results). "* Milkfish stop being omnivores when they mature, after which they eat only other animals. "* It takes five years for milkfish to become sexually mature [Luna 2009]. "* An adult milkfish is capable of eating an adult rabbitfish. "* The fish pens currently hold approximately 58.5 million fish. "* Milkfish weigh 500-600 g [Hambrey 19991. "* None of the other five species in the ecosystem model eats starfish. "* Rabbitfish waste has the same composition as milkfish waste. "* The prices found in Task 4 are estimates assumed from solitary sources. "* Giant tiger prawns spawn nightly at a rate of 7.6% to 9% but only half of spawn hatch [Bray and Lawrence 1998]. "* Giant tiger prawns have a mortality rate of 10% to 40% and an average weight of 106 g [Bray and Lawrence 1998]. "* Rabbitfish double in population every 1.4 to 4.4 years
Striving for Balance 145 Prawns excrete 0.028 mg of ammonia per gram of body weight per hour Burford and Williams 2001] Molluscs urinate up to 45% of their body weight per day. Each year, 55% of blue mussels die Femalemussels release 1 millioneggs semi-annually, of which 30% hatch Japanese starfish release 10 million to 25 million eggs per year a starfish has an average lifespan of 3 years. e a starfish eats 36 g of mussels each month. Task 1: Water Quality before Disruption For a long time, the amount of fish in the area was more than adequate to meet the needs of the population. However, as people sought better nutrition by eating more fish protein, they fished more intensively using dynamite and sodium cyanide, until the local population of wild fish was lo longer large enough to sustain itself. These techniques killed off not only milkfish but other species that kept the ecosystem in balance. The re sulting uncontrollable growth of algae, in combination with the destruction caused by explosives, destroyed parts of the coral reef by depriving it of the nutrients and sunlight needed for it to grow. The people built the milkfish population back up by introducing them in large numbers and keeping them in large cages where they could be fed until they were large enoug to harvest. Using better-quality fish feed allowed the milkfish population to grow more quickly but also increased pollution in the local waters as a result of the fish waste. Previously, other species, such as the blue mus- el mollusc(which feeds on the waste of milkfish), kept water pollution in check. Other herbivorous fish, such as the rabbitfish and echinoderms such as the starfish, helped contain algae growth. The starfish also ate the blue mussels. As seen in Figure 1, the food web of this ecosystem allowed for different species to coexist in certain ratios to one another, which kept the water clean and allowed the coral reef to By allowing special feed to replace the natural diet of the milkfish, the imultaneousiy dst eple ted the quality of the local wa乎Pyhe catalyst for the growth of the overall system by providing shelter for certain species from their predators By modeling the earlier stability, it is possible to sho different populations were previously required to maintain a balanced
Striving for Balance 145 "* Prawns excrete 0.028 mg of ammonia per gram of body weight per hour [Burford and Williams 2001]. "* Molluscs urinate up to 45% of their body weight per day. "* Each year, 55% of blue mussels die. "* Female mussels release I millioneggs semi-annually, of which30% hatch. "* Japanese starfish release 10 million to 25 million eggs per year. "* A starfish has an average lifespan of 3 years. "* A starfish eats 36 g of mussels each month. Task 1: Water Quality before Disruption For a long time, the amount of fish in the area was more than adequate to meet the needs of the population. However, as people sought better nutrition by eating more fish protein, they fished more intensively, using dynamite and sodium cyanide, until the local population of wild fish was no longer large enough to sustain itself. These techniques killed off not only milkfish but other species that kept the ecosystem in balance. The resulting uncontrollable growth of algae, in combination with the destruction caused by explosives, destroyed parts of the coral reef by depriving it of the nutrients and sunlight needed for it to grow. The people built the milkfish population back up by introducing them in large numbers and keeping them in large cages where they could be fed until they were large enough to harvest. Using better-quality fish feed allowed the milkfish population to grow more quickly but also increased pollution in the local waters as a result of the fish waste. Previously, other species, such as the blue mussel mollusc (which feeds on the waste of milkfish), kept water pollution in check. Other herbivorous fish, such as the rabbitfish, and echinoderms, such as the starfish, helped contain algae growth. The starfish also ate the blue mussels. As seen in Figure 1, the food web of this ecosystem allowed for different species to coexist in certain ratios to one another, which kept the water dean and allowed the coral reef to grow. By allowing special feed to replace the natural diet of the milkfish, the people unknowingly depleted the quality of the local water supply while simultaneously destroying the coral reef. This coral reef had served as a catalyst for the growth of the overall system by providing shelter for certain species from their predators. By modeling the earlier stability, it is possible to show what levels of different populations were previously required to maintain a balanced ecosystem. These ratios can then serve as a helpful starting point for reestablishing a new balance within commercial milkfish farms
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 \
148 The UMAP Journal 30.2(2009) (milkfish)and feeding them specially formulated fishmeal creates the larger amounts of fish necessary to meet growing demand. Doing so also doesn't require the sustenance of a variety of different creatures. Why is it not possible simply to apply modernagriculture methods to aquaculture? Why shouldnt Filipinos continue to increase the yield of milkfish with specially- designed fishmeal, just as a farmer in America s Midwest increases the yield of a soybean or corn harvest by using specially-formulated seed and fertilizer? Initial observations may lead to the conclusion that such an approach is both viable and desirable. After all, why not simply remove the excess fish waste and sell it as fertilizer for local farmers? That might be possible. However, just as land farmers eventually realized that growing certain crops year afteryear leads to decreased yields because of nutrient depletion in the soil, fish farmers encounter the threat of decreased over because growing only milkfish depletes water quality by causing algae and waste to grow uncontrollably. The excess algae reduce coral growth in the same way that lack of crop rotation depletes the soil of nitrogen. Both conditions appear to offer better results in the short term but destroy the longer-term viability of the system. Still, for people to change behavioral practices, it is important to demonstrate the limiting effects of the current system. For our model, this requires showing that farming only milkfish causes water quality and the amount of harvestable fish to decline. To model the current system, we took our model from Task 1 and set th e values for the populations of everything but milkfish and algae to zero. population chokes off the viability of the milkfish because of the increased oxygen demanded by the algae and consequently the decreased quantity available to the fish However, it is unrealistic to assume the current system consists only of milkfish and algae. We know that the current system has a water quality of 100bacteria/ml and 15 ug/lof chlorophyll, both of which are much greater than the suggested 0.5-1.0 x10 bacteria/mI and 0. 25 pg/l of chlorophyll suggested to be acceptable for adequate coral growth Coral growth acts like a skyscraperin that it allows more fish to grow in a given space through vertical partitioning. Therefore, we gradually adjust ne populations of the various species in our model to achieve the level of a steady-state equilibrium of water quality when the ecosystem consists of only milkfish and algae, because the algae do not entirely dispose of the waste from the milkfish; without another species such as blue mussels to reduce the waste of the milkfish, the milkfish grow uncontrollably, even if the 20% that mature each year are removed by humans after reproducing If humans harvest also immature milkfish the level of milkfish will drop below sustainability. This human harvesting can reduce the level of waste in the water somewhat, although it is insufficient to achieve a steady state
148 The UMAP Journal 30.2 (2009) (milkfish) and feeding them speciallyformulatedfishmeal creates the larger amounts of fish necessary to meet growing demand. Doing so also doesn't require the sustenance of a variety of different creatures. Why is it not possible simply to applymodern agriculture methods to aquaculture? Why shouldn't Filipinos continue to increase the yield of milkfish with speciallydesigned fishmeal, just as a farmer in America's Midwest increases the yield of a soybean or corn harvest by using specially-formulated seed and fertilizer? Initial observations may lead to the conclusion that such an approach is both viable and desirable. After all, why not simply remove the excess fish waste and sell it as fertilizer for local farmers? That might be possible. However, just as land farmers eventually realized that growing certain crops year after year leads to decreased yields because of nutrient depletion in the soil, fish farmers encounter the threat of decreased overall yield because growing only milkfish depletes water quality by causing algae and waste to grow uncontrollably. The excess algae reduce coral growth in the same way that lack of crop rotation depletes the soil of nitrogen. Both conditions appear to offer better results in the short term but destroy the longer-term viability of the system. Still, for people to change behavioral practices, it is important to demonstrate the limiting effects of the current system. For our model, this requires showing that farming only milkfish causes water quality and the amount of harvestable fish to decline. To model the current system, we took our model from Task 1 and set the values for the populations of everything but milkfish and algae to zero. Figure 3 shows the decline in water quality over time. The rise in algae population chokes off the viability of the milkfish because of the increased oxygen demanded by the algae and consequently the decreased quantity available to the fish. However, it is unrealistic to assume the current system consists only of milkfish and algae. We know that the current system has a water quality of 1010 bacteria/ml and 15 Mg/l of chlorophyll, both of which are much greater than the suggested 0.5-1.0 x106 bacteria/ml and 0.25 Mg/1 of chlorophyll suggested to be acceptable for adequate coral growth. Coral growth acts like a skyscraper in that it allows more fish to grow in a given space through vertical partitioning. Therefore, we gradually adjust the populations of the various species in our model to achieve the level of current water pollution in Bolinao. Again, our model is unable to produce a steady-state equilibrium of water quality when the ecosystem consists of only milkfish and algae, because the algae do not entirely dispose of the waste from the milkfish; without another species such as blue mussels to reduce the waste of the milkf•sh, the milkfish grow uncontrollably, even if the 20% that mature each year are removed by humans after reproducing. If humans harvest also immature milkfish, the level of milkfish will drop below sustainability. This human harvesting can reduce the level of waste in the water somewhat, although it is insufficient to achieve a steady state
Striving for -water Quanity Figure 3. Water quality when only milkfish are present. because there is still nothing to reduce the waste except the algae-which will grow uncontrollably to consume the milkfish waste, thus raising the level of chlorophyll to the point where it chokes off the sunlight and nutri- ents needed for the coral reef to grow [Environmental Protection Agency 2004. While it is possible to reduce the levels of waste through harvesting, doing so will only reduce the rate at which the waste level of bacteria grows (a more gradual slope), not cause it to decline Task 3: Water Quality of a Polyculture Before the farming of massive quantities of milkfish in pens, there was a balanced ecosystem of a variety of species that coexisted in ratios that allowed the waste of certain animals to serve as food for others. However the demand for milkfish led to a disruption of this balance The ecosystem is not as ideal as it once was, as we modeled in Task 1; but it is not as blea a situation as the milkfish monoculture that we modeled in Task 2. The second model in that task shows that the quantities of other species in the current system are insufficient to reach target levels of water quality-ones that would maximize the value ofbiomass available for harvest by restoring the natural catalyst of coral growth. The coral serves as protective shelter for all of these species. Coral grows very slowly, on average only 80 mm/yr [Roth 1979]
Striving for Balance 149 3WO 300- 250 200 - Water Quality - Liunear (Water Quality) 150 100 so 0 5 10 25 20 25 30 35 Figure 3. Water quality when only milkfish are present. because there is still nothing to reduce the waste except the algae-which will grow uncontrollably to consume the milkfish waste, thus raising the level of chlorophyll to the point where it chokes off the sunlight and nutrients needed for the coral reef to grow [Environmental Protection Agency 2004]. While it is possible to reduce the levels of waste through harvesting, doing so will only reduce the rate at which the waste level of bacteria grows (a more gradual slope), not cause it to decline. Task 3: Water Quality of a Polyculture Before the farming of massive quantities of milkfish in pens, there was a balanced ecosystem of a variety of species that coexisted in ratios that allowed the waste of certain animals to serve as food for others. However, the demand for milkfish led to a disruption of this balance. The ecosystem is not as ideal as it once was, as we modeled in Task 1; but it is not as bleak a situation as the milkfish monoculture that we modeled in Task 2. The second model in that task shows that the quantities of other species in the current system are insufficient to reach target levels of water quality-ones that would maximize the value of biomass available for harvest by restoring the natural catalyst of coral growth. The coral serves as protective shelter for all of these species. Coral grows very slowly, on average only 80 mm/yr [Roth 1979]
150 The UMAP Journal 30.2(2009) By determining the quantities of species required to reach the desired water quality of0.5-1.0×10° bacteria/ ml and0251/ 1 of chlorophyl让 is possible to increase the overall yield of fish available for harvest while recreating a polyculture thatis sustainable. Through modeling this process, we determine how to recreate the stable ecosystem present before commer- cial milkfish farming. This process will also reduce the cost of overall feed we determine what combinations of populations of the species could be self-sustaining. Still, this practice requires guidelines for harvesting only a portion of any species, so as to prevent recreating the overfishing problem that was the cause for the rise of commercial fish-farming, which created the issues with water quality and coral reef destruction in the firs e condi- Re-establishing the balance that occurred in the region under the tions present in the model from Task 1 is difficult. It requires introducing other species into the commercial fish pens that help to keep the other pop ulations under control. However, our model demonstrates the pattern of what would occur to waste levels over time if such a combination is at- tempted. This process was possible by taking data from Internet sources to determine sustainability rates for each of the species and then adjusting the populations of each species to achieve the desired water quality levels The results of this model rely heavily on increasing the population of blue mussel to control the waste levels of bacteria from the growing milkfish population. The downward trend in the level of bacteria present in the water is depicted in Figure 4. In a few years, the population ofblue mussels almostentirely eliminates the bacteria waste. Similarly rabbitfish reduce the level of chlorophyl through consumption of gae, a process that provides more sunlight and nutrients for coral to grow again [Capuli and Kesner-Reyes 2008]. The milkfish keep the rabbitfish under control, and tiger prawns provide the milkfish an alternative food source so that the milkfish don't wipe out the rabbitfish population. Moreover, starfish consume the mussels to keep them from growing uncontrollably The reproductive rate of starfish can vary widely. If an overpopulation of starfish occurs before blue mussels can grow sufficiently, the waste lev- els of bacteria can grow upward exponentially because the blue mussel is not yet able to sustain its own survivability. Thus, the process requires a reduced presence of starfish early in the biodiversity effort and a greater number of blue mussels. After about six to eight months, the mussels have grownenough thatmore starfishcangraduallybeintroduced Ifthestarfish reproduce too quickly early, it may be necessary to add more blue mussels periodically, because there is no effective control on the starfish population Ir model requires introduction of certain quantities of starfish, rab bitfish, blue mussels, and giant tiger prawn to re-establish a sustainable polyculture that would support the milkfish while improving water qual
150 The UMAP journal 30.2 (2009) By determining the quantities of species required to reach the desired water quality of 0.5-1.0 X10 6 bacteria/mI and 0.25 ILg/1 of chlorophyll, it is possible to increase the overall yield of fish available for harvest while recreating a polyculture that is sustainable. Through modeling this process, we determine how to recreate the stable ecosystem present before commercial milkfish farming. This process will also reduce the cost of overall feed for the milkfish, since they can eat some of the other species. By fixing the goals of acceptable water quality as the output of this model, we determine what combinations of populations of the species could be self-sustaining. Still, this practice requires guidelines for harvesting only a portion of any species, so as to prevent recreating the overfishing problem that was the cause for the rise of commercial fish-farming, which created the issues with water quality and coral reef destruction in the first place. Re-establishing the balance that occurred in the region under the conditions present in the model from Task 1 is difficult. It requires introducing other species into the commercial fish pens that help to keep the other populations under control. However, our model demonstrates the pattern of what would occur to waste levels over time if such a combination is attempted. This process was possible by taking data from Internet sources to determine sustainability rates for each of the species and then adjusting the populations of each species to achieve the desired water quality levels. The results of this model rely heavily on increasing the population of blue mussel to control the waste levels of bacteria from the growing milkfish population. The downward trend in the level of bacteria present in the water is depicted in Figure 4. In a few years, the population of blue mussels almost entirely eliminates the bacteria waste. Similarly, rabbitfish reduce the level of chlorophyll through consumption of algae, a process that provides more sunlight and nutrients for coral to grow again [Capuli and Kesner-Reyes 20081. The milkfish keep the rabbitfish under control, and tiger prawns provide the milkfish an alternative food source so that the milkfish don't wipe out the rabbitfish population. Moreover, starfish consume the mussels to keep them from growing uncontrollably. The reproductive rate of starfish can vary widely. If an overpopulation of starfish occurs before blue mussels can grow sufficiently, the waste levels of bacteria can grow upward exponentially because the blue mussel is not yet able to sustain its own survivability. Thus, the process requires a reduced presence of starfish early in the biodiversity effort and a greater number of blue mussels. After about six to eight months, the mussels have grown enough thatmore starfish can graduallybe introduced. If the starfish reproduce too quicldy early, it maybe necessary to add more blue mussels periodically, because there is no effective control on the starfish population. Our model requires introduction of certain quantities of starfish, rabbitfish, blue mussels, and giant tiger prawn to re-establish a sustainable polyculture that would support the millfish while improving water qual-
