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