ICM: Coral Reef Ecosystem Model

Summary

Coral reefs are fascinating ocean habitats which harbor an incredible diver-sity of marine life. The Lucero reef in the northwestern Philippines recentlyexperienced a severe drop in its biodiversity and health, roughly coincidingwith the increase in milkfish farming in Bolinao, Pangasinan. We establisha mathematical model to represent the Lucero reef ecosystem and to aid inpredicting an economically viable solution that provides for the recoveryof the reef.

We reduce the ecosystem to a manageable complexity by modeling gen-eralized trophic levels instead of individual species. In doing so, we limitthe precision of our model, but are still able to predict trends based onpertubations to steady state conditions. Our model is based on the Lotka-Volterra equations, diverging as necessary to accommodate the unique fea-tures of the reef ecosystem. The model indicates that reducing milkfishfarming and increasing the harvest of algae and other primary producerssuch as seaweed will benefit the reef ecosystem by limiting algae over-growth. Moreover, previous research has shown that seaweed maricul-ture is a satisfying economic solution. Thus we recommend a reduction inmilkfish harvesting to be compensated by an increase in algae harvesting.This produces a compromise between the economic and environmental de-mands on the system.

Legalize (Sea)weed

ICM Contest Question C

Team # 5201

February 9, 2009

Contents

1 Introduction 2

2 Background 42.1 Selected Components of the Reef Ecosystem . . . . . . . . . 4

2.1.1 Coral . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1.2 Plankton . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1.3 Nutrients in the Environment . . . . . . . . . . . . . . 52.1.4 Milkfish . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.5 Herbivorous fish . . . . . . . . . . . . . . . . . . . . . 52.1.6 Crustaceans . . . . . . . . . . . . . . . . . . . . . . . . 62.1.7 Echinoderms . . . . . . . . . . . . . . . . . . . . . . . 62.1.8 Molluscs . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.9 Algae . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Assessing Water Quality . . . . . . . . . . . . . . . . . . . . . 7

3 Model 73.1 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 Existing Models . . . . . . . . . . . . . . . . . . . . . . . . . . 73.3 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.4 Our Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.4.1 Natural Ecosystem . . . . . . . . . . . . . . . . . . . . 93.4.2 Milkfish Monoculture Ecosystem . . . . . . . . . . . . 11

3.5 Model Limitations . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Integrated Multi-trophic Aquaculture Design 13

Page 1 of 24

Team # 5201 Page 2 of 24

5 Results 135.1 Natural Ecosystem . . . . . . . . . . . . . . . . . . . . . . . . 135.2 Milkfish Monoculture . . . . . . . . . . . . . . . . . . . . . . . 135.3 Milkfish Mariculture . . . . . . . . . . . . . . . . . . . . . . . 145.4 Fisheries Management Design . . . . . . . . . . . . . . . . . . 17

5.4.1 Reduction of Milkfish Farming . . . . . . . . . . . . . 175.4.2 Integrating Seaweed Aquaculture . . . . . . . . . . . 17

6 Future Work 19

7 Conclusion 19

8 Appendix 208.1 Call to Action: Recommendations for Conservation Manage-

ment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 208.1.2 Results of the Lucero Reef Model . . . . . . . . . . . . 218.1.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 21

1 Introduction

Although coral reefs only cover about 0.1% of the ocean surface, they arehome to nearly one-third of all ocean fish species. They represent a micro-cosm of biodiversity with profound implications for the health of the ocean,yet over 20% of the world’s coral reefs have been destroyed due to humanactivity and show no promise of recovery.[7] This is a sobering fact for thestate of our natural world, but it has immediate economic consequences aswell. It is estimated that healthy reefs proivde as much as $350 billion peryear in goods and services.[7] The combination of economic and environ-mental implications incentives a strong mathematical model which can beused to model the health of coral reefs and hopefully guide conservationpolicy.

One reef which has been studied extensively in the literature is theLucero Reef off the coast of Santiago Island in the Philippines. The LuceroReef encapsulates many aspects of reef conservation. Historically it hasbeen a good model of tropical biodiversity, with a mean biodiversity in-dex of H′ = 2.60.[1] However, in 1995 milkfish harvesting became a new,productive source of food and money and by 1998 there were an estimated11,900 tons of milkfish farmed annually.[13] The milkfish farms have lead


directly to increased nutrient levels in the reef area.[19] High levels of nu-trients such as carbon, nitrogen, and phosphorous compounds have beenlinked to algal blooms, which negatively impact coral life.[25], [19] As such,these milkfish farms have a negative impact on the reef ecosystem, disrupt-ing the delicate balance of biodiversity and threatening its long-term sur-vival.

In creating conservation policy surrounding this reef ecosystem, it isimportant to balance environmental and economic aspects of the issue. Onecannot ignore the commercial advantages of milkfish farming, both as asource of food and income to island inhabitants, but taken to an extrememilkfish farming can disrupt other local fishing industries if the coral reefecosystem collapses. Hence it is imperative both for environmental andeconomic reasons to arrive at a sustainable solution for the island’s needs.

Aquaculture is the practice of designing controlled populations for fishfarming. Integrated multi-trophic aquaculture (IMTA) is a more recent ap-proach in Western aquaculture that attempts to create a sustainable ecosys-tem. The right balance of species provide resource recycling that preservesa greater fish diversity, where the wastes of one become the resources of an-other. This contrasts monocultures, high-densities of a single fish speciesthat propagate in regions where one species has become financially suc-cessful, which are prone to deterioration through environmental degrada-tion and disease outbreaks.[17] Many IMTA projects have begun through-out the world in recent years, though we found no particular projects for anecosystem containing coral reefs. Our challenge is to incorporate the IMTAframework specifically into the Bolinao region of Pangasinan, Philippines,keeping the overarching goal of preserving the coral reef.

We began by creating a model of the Lucero Reef before the commercial-ization of milkfish farming. The model is based off of the Lotka-Volterraequation, using trophic levels to represent the various species in a reefecosystem. We then extended this model to apply to the milkfish farm-ing pens, and obtained a high steady state value of nutrients and algae.These values are detrimental to the coral, so we used our model to predictchanges that could be made to the mariculture ecosystem to reduce theselevels.


2 Background

2.1 Selected Components of the Reef Ecosystem

The reef ecosystem is intractably complex; modeling every component ofthe ecosystem with good precision would provide ground-breaking insightinto the functional relationships within the ecosystem, but it would be ex-ceedingly difficult. Realistically, to come to a conclusion in a reasonableamount of time, we must reduce the ecosystem to relatively few general-ized components and relationships. To reveal some of the intricacy of thereef ecosystem and to illustrate its basic structure and dynamics, we de-scribe its more prevalent components.

2.1.1 Coral

Most corals are colonial organisms consisting of hundreds of thousandsof individual polyps.[34] The reefs formed by some corals contribute sig-nificantly to biodiversity by partitioning the environment and providingfor herbivores.[32] Reef-building corals often contain photosynthetic algaecalled zooxanthellae, which offer a crucial mutualistic relationship to thecorals. While the coral protects the zooxanthellae and provides it with thenutrients it requires for photosynthesis, the zooxanthellae removes wastesfrom the coral and provides it with vital nutrients - oxygen, glucose, glyc-erol, and amino acids. Because of this relationship between the coral andzooxanthellae, coral tend to respond to the environment like plants, thriv-ing in clear water that is easily permeable by sunlight.[36] Furthermore,coral primarily exist in nutrient-poor water, as nutrient-rich water pro-motes overgrowth of algae which can easily choke the coral. The removalof the zooxanthellae, due to inadequate environmental conditions or other-wise, is known as coral bleaching, and prolonged bleaching can cause thecoral to die from malnutrition.[35]

2.1.2 Plankton

Plankton are drifting organisms in oceans and other water environments.Abundance and distribution of plankton depend heavily on nutrient con-centration and other environmental conditions. Plankton are divided intothree functional categories: Phytoplankton, zooplankton, and bacterioplank-ton. [30] Phytoplankton, a subset of algae, are microscopic organisms thatrely on photosynthesis for sustenance; as such they are primary produc-ers, converting simple molecules and energy from sunlight into complex


organic molecules that are used by other organisms in the ecosystem.[29]Zooplankton are small animals, including some crustaceans and larval stagesof larger animals like fish, that feed primarily on phytoplankton. Bacterio-plankton are microorganisms including bacteria and archaea. [30]

2.1.3 Nutrients in the Environment

Reef nutrients take several forms, including sunlight and chemical com-pounds such as ammonium, nitrite, nitrate, phosphate, and silicate.[31]Such nutrients are the primary sources of growth for algae and other pri-mary producers, so nutrient-rich waters promote overgrowth of algae andmake a poor environment for coral reefs. Another significant form of nutri-ent found in the water is detritus, organic material that includes fragmentsof dead organisms and feces.[10] Detritus is an important source of foodfor much of the life in a marine ecosystem, including crustaceans and her-bivorous fish.

2.1.4 Milkfish

Milkfish, or Chanos chanos, are a species of predatory fish found primarily inthe Indo-Pacific region along continental shelves and islands.[6] Their dietconsists primarily of small invertebrates, cyanobacteria, and soft algae.[6]The average milkfish weighs roughly 1.5 kg[5], and in captivity is reportedto excrete 83 grams of waste per fish per day, which is composed of 11%Carbon, 0.4% Nitrogen, and 0.6% Phosphorus. Based on this data, thefish must consume about 30 kg per year. However, numbers reported byHomer et al. (2002) on feeding rates indicated that milkfish consume only1.2 kg per year. One report indicates that other omnivorous fish consumeroughly 30 kg per year per kg of biomass, which translates into roughly45 kg per fish per year.[16] This number is on par with the estimate we ar-rived at based on the weight of excrement, so we will use that estimate inour model. Discrepancies in the paper by Homer, et al. are likely causedby the fact that the reported consumption rate was based on supplimentalfeed provided by milkfish farmers and certainly did not take into accountother sources of food.

2.1.5 Herbivorous fish

Herbivorous fish in reef habitats feed primarily on algae, corals, and phyto-plankton. Besides this direct interaction with the coral habitat, they also af-


fect the environment indirectly by recycling nutrients through feeding anddefection.[32] We chose to study the representative species Scarus ghobban,a member of the family Scaridae, more commonly known as Parrotfish.[27]Parrotfish play an important role in the health of reef ecosystems, eatingthe turf algae which would otherwise choke out the coral. They consumeapproximately 109.1 grams of food per day, which translates into roughly103 grams of turf algae per day.[27] Parrotfish have also been reported toexcrete 12 grams of waste per day.[27]

2.1.6 Crustaceans

The subphylum Crustacea is a large, diverse group of invertebrates. Themost well-known, and also the largest, crustaceans include crabs, lobsters,and shrimp, However, there are many other, smaller varieties unknown inpopular culture.[8] Crabs, for example, are generally omnivorous, feedingon algae, plankton, detritus, and small invertebrates. Smaller crustaceans,like barnacles, feed primarily on plankton and detritus.[2]

2.1.7 Echinoderms

Echinoderms are a group of marine animals that live on the sea floor. Theirfeeding habits vary significantly by species; echinoderms can be suspen-sion feeders, herbivores, detritivores, and predators. The most commongroups in the Lucero reef, sea urchins and sea cucumbers, feed primarilyby grazing on algae. [28] Sea urchins therefore serve an important role tocoral health by keeping algae growth in check.

2.1.8 Molluscs

Molluscs, particularly bivalves, such as clams, fill an important niche inreef ecosystems. Most bivalves feed by using large gills to capture nutrientparticles directly from the ocean water.[3] Bivalves thus reduce the nutri-ent concentration in the water, thereby limiting the growth of algae andbacteria. While this in turn limits the growth of herbivores who feed onthe algae, it positively affects the health of the reef by keeping algae fromovergrowing the coral.

2.1.9 Algae

Algae are a very broad group of photosynthetic, multicellular and unicel-lular organisms. Most algae are primary producers, meaning they are an


essential part of the food chain that converts light and chemicals from theirenvironment into biomass. A representative species for our model is Ge-lidium pusillum, a red algae[21] common in the province of Pangasinan.[33]Gelidium pusillum forms algal turfs,[22] which are apt to overgrow and chokecoral. Algal turfs also trap detritus and form sites for bacterial growth,thereby providing food for detritivores and some herbivores.[32]

2.2 Assessing Water Quality

Algal blooms have been directly linked to coral death in several studiesdating from the mid-1970’s.[25] As such, algal biomass in a reef ecosystemis strongly correlated to the health of the coral and hence the health of theentire system. Although there is debate in the literature,[24] algal bloomshave been linked by several studies to a combination of increased nutrients(such as nitrates and phosphates) in the water and a decrease in grazingfrom herbivorous species.[25],[26] Because nutrients impact algae growthand thus indirectly impact the health of coral, it is important to model thisrelationship. In our model, nutrient levels will be measured by a waterquality score, which takes into account the nitrates and phosphates linkedto algal blooms.

3 Model

3.1 Goals

We want to create a model that incorporates the entire foodweb of the Boli-nao coral reef ecosystem. Data we wish to retain from the model includeswater quality levels, amount of fish harvesting, and steady state levels offish population. This values are ultimately used to evaluate suggestions foran integrated multi-trophic aquaculture for the Bolinao region.

3.2 Existing Models

There is a long history of models on the lower part of the food chain thatmodel the interaction of phytoplankton, zooplankton, and nutrients. Othermodels, particularly those used in fishery management decisions, rely onsurvey data to model fish populations at a higher trophic level while ignor-ing the bottom.

Furthermore, ecology modeling comprises of two distinct approaches,state variable and individual-based modeling. State variables encapsu-


late the many facets of a species population into a single state, typicallythe biomass of the species. This disregards important distinctions amongthe individuals. In some cases, aggregation among the individuals wasfound to correlate to similar patterns in a state variable model. However,individual-based modeling is more often used on more narrow scales thanwhich we are concerned for this problem,[23] so we will focus on a statevariable model.

The integration of multiple trophic levels is a difficult modeling prob-lem still today that requires a great deal of research. [18] A 2003 survey ofecosystem models found that ECOPATH was that only model that used amultispecies approach:

Despite broad discussion of the need to consider multispeciesissues in marine conservation and fisheries management we knowof only one model that focuses explicitly on multispecies as-pects of marine reserves. [12]

Population dynamics are based on a conservation of mass principle,[9]where the change in biomass of a species over time is based on growth(sources of mass) or loss (sinks of mass). Loss can come from being eatenby another organism or natural death. To conserve mass, some of the lossof one state’s mass becomes a sink for another’s. The remaining mass ex-creted as nutrients or other particles. Either growth or loss can occur frommigration. The Population Law of Mass Action describes these rates ofchanging mass. It states that the rate of change of the mass of two interact-ing species is proportional to the product of their masses. This principle isused in modeling predator-prey relations in the Lotka-Volterra model,

x′ = (−a + by)x = −ax + bxyy′ = (c− kx)y = cy− kxy

where x is the predator mass and y is the prey mass. The bxy and −kxyterms represent the predation, a source of growth for the predators but asink for the prey. To close the model, −ax represents the natural death ofthe predator (i.e. in isolation of the prey), and cy represents the naturalgrowth of the prey. [4]

3.3 Assumptions

The life-cycle of a marine organism involves distinct phases. However, weassume that all biomass of a species has the same consumption pattern.


This pattern is determined as a rough average of consumption patternsover all stages of life, weighted by biomass.

Nutrient uptake by phytoplankton is a function of both light and tem-perature since it is dependent on the amount of photosynthesis that theorganism can perform.[9] We assume that nutrient uptake can be approxi-mated as a temperature-invariant and light-invariant function.

Our models do not incorporate variations due to seasonal cycles. Forinstance, the vertical mixing of ocean layers occurs in greater proportion inwinter than summer, which effects the flux of organisms and particles.[18]They also do not take into account the acidity or temperature of the water,bacteria, or virus levels.

Additionally, because it is not feasible to model every single species in avery complex ecosystem, we have chosen to represent generalized trophicgroups instead of individualized species. Any attempts to use the specificgrazing patterns of any one species as representative for the entire trophicgroup lead to nonsensical results because it assumes a closed system whenin reality there are many other species and factors at play. For example,if we chose precise initial conditions for our primary producers off of theabsolute biomass of algae, our ecosystem would be underfed because it ne-glects other primary producers such as seagrass and seaweed. Instead, wechose to look at rough production and consumption ratios for each trophicgroup and then force the grazing coefficients to achieve a steady state. Al-though this does not precisely reflect reality, it gives sensical results and weclaim that the grazing coefficients represent a complicated mass balancingthat occurs behind the scenes in the way we calculated them.

3.4 Our Models

3.4.1 Natural Ecosystem

We began by creating a simplified model of the reef ecosystem based offof the Lotka-Volterra equation. Algae compete for nutrients, and are eatenby herbivores which represent trophic level III (which would include crus-taceans and echinoderms). It is widely accepted and several sources con-firm that only about 10% of the energy at any trophic level moves up to thenext trophic level, which we represent in our model by an efficiency coeffi-cient e.[16] The herbivores are eaten by predatory fish, and finally there isan extinction term that represents the rate at which the algae, herbivores,and predators die and are returned to the nutrient sink. Because our systemlooses energy at each trophic level (mirroring the 90% consumption of en-


ergy in biological systems for basic life processes), we introduced a constantterm α which represents energy flowing into the system and augments thenutrient term consumed by the algae. This term can be conceptualized as ameasure of the sunlight adding energy to the ecosystem. Below is a math-ematical representation of our model:

N′ = dH + dA + dM + 0.9 ∗ gm MZ− gaNAA′ = ga(N + α)A− gh AH − dAH′ = egh AH − egmHM− dHM′ = egmHM− dM

Table 1: Initial Conditions

Symbol Name Initial ValueN Nutrients 0.032A Algae 0.3H Herbivores 50M Predators 0.92

We chose initial conditions based on estimations of biomass consump-tion and production per year for each class of animal.[16] The algae isrepresented by phytoplankton, the herbivores are represented in generalby Parrotfish, and the predators are represented by milkfish.1 Nutrientlevels were chosen to be a low steady state value based on data in theliterature.[15] We assumed that these numbers represent a stable equilib-rium, and hence solved the set of steady-state equations:

0 = N′ = dH + dA + dM + 0.9 ∗ gm MZ− gaNA0 = A′ = ga(N + α)A− gh AH − dA0 = H′ = egh AH − gmHM− dH (1)0 = M′ = egmHM− dM

1In reality, milkfish are not solely predators. However for the purposes of this model weare assuming that they only eat herbivores


The death rate and efficiency coefficients were set to

d = .125e = .1

as a way to calibrate the model. The efficiency parameter mirrors the factthat only 10% of energy is passed up each trophic level, and the death ratewas set heuristically assuming that the biomass of each population is recy-cled every eight years. The result of these calculations is the set of parame-ters shown in table 2 which solve the steady state equations (1).

Table 2: Simplified Model Steady State Parameters

Symbol Name Valueα Resource Input 0.2865e Energy Efficiency 0.1d Death Rate 0.125ga Algae Grazing Rate 774.7gz Herbivore Grazing Rate 4.93gh Predator Grazing Rate 0.025

When perturbed from the steady state, this model behaves as expected.An increase in predator biomass causes a decrease in herbivore biomassand hence an increase in algae biomass. Similarly, an decrease in preda-tor has the reverse effect, and an increase in herbivore biomass results ina decrease of algae biomass and increase in predator biomass. However,over several generations these transient responses even out and return toclose to the original steady state. This corresponds to what we see in thenatural world. Within reason, perturbations from natural steady state val-ues does not cause the entire world ecosystem to collapse; instead, there isa transient flux until the system can find a new equilibrium. Our model,although simplified, also has this characteristic.

3.4.2 Milkfish Monoculture Ecosystem

In many ways the milkfish mariculture system in the Philippines alters theway in which the reef ecosystem operates. We chose to model the ecosys-tem inside the fish farm pens where there is a high density of predator (ie.,milkfish) in order to discover what effects fish farming has on the steadystate values of algae (which is our indicator of coral survival). Using the


simplified ecosystem model above, we modified some of the conditions toreflect the nature of the milkfish monoculture ecosystem.

If we were to use the exact same model, the extremely high density ofmilkfish in the pens would overwhelm the herbivore population and hencelead to a near exponential growth of algae. Additionally, because the milk-fish consume the herbivore population so quickly, it would lead to a rapiddecline in milkfish population after an initial peak. However, these effectsresult from some simple assumptions that change in a mariculture ecosys-tem. First of all, the milkfish are being fed and harvested so that the totalpopulation remains almost constant. Hence, we can assume that M′ = 0.Another difference between the mariculture and natural ecosystem is thatin the mariculture environment, milkfish derive most of their diet from thefood given to them by the farmers. We estimated that farmed milkfish onlyeat one tenth as much from the herbivore group as they do in a naturalenvironment. Finally, because the milkfish are being farmed, their deadbiomass does not return to the nutrient compartment. These changed as-sumptions resulted in the following set of differential equations:

N′ = dH + dA + 0.9 ∗ gm MZ− gaNAA′ = ga(N + α)A− gh AH − dAH′ = egh AH − 0.1 ∗ gmHM− dHM′ = 0

These equations will be solved numerically given an elevated milkfishpopulation to study the effects of fish farming on the reef environment.

3.5 Model Limitations

The simplification we made by representing different species by their gen-eral trophic level is a significant limitation to the model. It does not takeinto account the varied grazing patterns of different organisms, and doesnot have very high resolution to look at the ecosystem on a per specieslevel. Additionally, it neglects the complexity of the detritus cycle by as-suming that nutrients get converted into algae biomass with perfect effi-ciency. This leaves out whole classes of organisms such as molluscs whichcan feed off of dendrite. It also ignores the fact that very few species aretruly either carnivores or herbivores. In reality, milkfish (which were thefocus of our model) feed off of algae and detritus as well as off of smallfish, floating fish eggs, and small invertebrates. However, our model tries


to capture the general flow of energy between trophic levels, and even af-ter the simplification can give some meaningful physical results. However,any interpretation from our data must be taken in the context of the model;our results are not meant to show conclusively that any one outcome willoccur given a certain set of input. Instead, it is meant to give a general trendfor different perturbations to the reef ecosystem which may not be readilyobvious upon inspection. Further development is needed for more precisequantitative measures.

4 Integrated Multi-trophic Aquaculture Design

Developing a sustainable ecosystem for the Bolinao coral reef involves adelicate balance. Excess nutrients allow the growth of algae, which com-pete with coral for sunlight used in photosynthesis by covering surface areaof the ocean.

We agreed with the several sources proclaiming the importance of build-ing a resilient coral reef ecosystem. By this, we mean the ability of the reefto withstand unforeseen major changes.

Reef ecosystems seem to shift between alternative stable states,rather than responding in a smooth way to changing conditions.The shift to algae in Caribbean reefs is the result of a combina-tion of factors that make the system vulnerable to events thattrigger the actual shift.[14]

As an example of resilience, the large number of sea urchins allowedthe Caribbean reef to recover from a 1981 hurricane that destroyed much ofit. it soon after suddenly was severely hindered by brown algae.

5 Results

5.1 Natural Ecosystem

We calibrated our model to a steady state representing the species popula-tions in the coral reef ecosystem prior to milkfish farming in Bolinao.

5.2 Milkfish Monoculture

We next modeled the ecosystem of the fish pens after milkfish farming wasintroduced to Bolinao. To simplify the model, milkfish were set to the pop-


Figure 1: With no herbivorous species, our model predicts algae growingwithout bound.

ulation described by [13]2 and the herbivore species were reduced to zero.The nutrient levels greatly exceed the threshold determined by [25]. Com-bined with a zero population of herbivores, this fact leads to the uncon-trolled growth of algae seen in the above figure. Clearly this result is notphysical. Algae would eventually reach a the carrying capacity of the envi-ronment, and it is also unlikely that the herbivore population would everbe zero. However, these limitations of our model do not detract from thefact that a low herbivore population and high milkfish population wouldlead to dangerously high levels of algae which would threaten the coral.

5.3 Milkfish Mariculture

We adjusted the fish pen ecosystem model by setting the herbivore popula-tion to 500 g/m2 such that we were able to get a nutrient level correspond-ing to the current levels as reported by [20]. This population level comparesto 247 g/m2, the actual populations in Bolinao.[16] The herbivore popula-tion would need to increase to compensate for the algae blooms caused bywaste nutrients from the milkfish.

2We calculated a milkfish biomass of 10 kg/m2 inside the pens.


Figure 2: Species biomass in present Bolinao fish pen conditions over 10year span.

Figure 3: Algae biomass in Bolinao over 31 weeks. The biomass spikes toabout 150 g/m2 about a week after the milkfish are added.


Figure 4: Nutrient levels in present Bolinao fish pen conditions over 10 yearspan. (Steady state value is approximately 2.5 g/m2)

Figure 5: Herbivore biomass (g/m2) present in Bolinao fish pen conditionsover 10 year span.


5.4 Fisheries Management Design

5.4.1 Reduction of Milkfish Farming

Since large levels of algae threaten the health of reefs, we first investigateda simple way to reduce the amount of algae. Limiting the mass of milkfishby half and then to 10% decreased the levels of algae from about 20 g / m2

to near 10 g / m2 and 2 g / m2, respectively.

Figure 6: Algae levels decreased proportional to the reduction in milkfishfarming

5.4.2 Integrating Seaweed Aquaculture

An alternate idea to simply attempting to decrease milkfish levels is to in-corporate the idea of a integrated multi-trophic aquaculture by introduc-ing seaweed to the fish pens. This keeps the algae from the possibility ofdamaging the coral and also allows the profitable harvest of milkfish. Ourmodel predicts that we can harvest 2 kg/m2 of algae per year without de-stroying the ecosystem. At a calculated rate of $1.40 per kilogram of algae,this comes out to roughly $3,000 per pen per year.[11]

As indicated in the final figure, this model unfortunately predicts a de-crease in the herbivore life in the fish pens. However, a healthy coral reefdue to lower nutriet levels may still allow the herbivores to thrive there.


Figure 7: After introducing seaweed harvesting, nutrient levels decreasedto an acceptable level.

Figure 8: An equilibrium state of algae is still maintained after harvestingseaweed from the fish pens.


Figure 9: Herbivore life in the fish pens is reduced to a low level.

6 Future Work

Our model provides only a glimpse in the complex ecosystem representedin Bolinao. A more accurate model, incorporating the variety of omissionscharacterized previously, would give a better representation of the changesthat would occur when testing the possibilities for a new polyculture. Ad-ditional data to improve the accuracy of parameters of the model wouldprovide similar improvements.

The great diversity of sea life means that many solutions may poten-tially exist to a integrated multi-trophic aquaculture in Bolinao. This is anarea of active research, and keeping an eye on the developments in similarfisheries, particularly in coral reefs, may provide some additional insightinto designing a management that provides continued harvesting valuethrough a sustainable ecosystem.

7 Conclusion

Milkfish farming destroyed the once diverse aquatic life and beautiful coralof Bolinao. But the technology of integrated multi-trophic aquaculture canchange that, allowing the coral to rebuild. Many fisheries are now beingmanaged with a sustainable recycling of wastes while still supporting anacceptable level of harvesting. Our model demonstrates that this result isa possibility in Bolinao. Reducing the penned milkfish by a half and in-


troducing other forms of harvestable herbivores leads to a lower steadystate value of algae. Combined with the harvesting of algae this can leadto a viable economic and environmental solution. Our models showed thatperturbations to the steady state (through constant harvesting terms) doeslittle to affect the overall stability, leading to the conclusion that high lev-els of harvesting can be sustained. We believe a conservation policy builtaround this model has a decent chance at reversing the trends seen todayin the Bolinao reef system.

8 Appendix

8.1 Call to Action: Recommendations for Conservation Manage-ment

8.1.1 Introduction

Conservation management is an important issue facing many nations asthey try to balance the economic and food needs of their country with theneeds of natural ecosystems. Nowhere is this balance more pronouncedthan in coastal reef ecosystems, which house over one third of all oceanfish species and a vast amount of the biodiversity found in ocean envi-ronemnts. The incredible complexity of these ecosystems also makes themincredibly fragile; as such, conservation management becomes especiallyimportant. We realize fully the difficult challenges posed by creating sta-ble, viable ecosystems which also produce harvestable product. Our teamof researchers has created a mathematical model to assist with these chal-lenges, providing a way to visualize the impact of different changes to thesystem. In modeling the Lucero Reef system on the coast of Pangasinan,Philippines, we found that milkfish farming could be sustainable given acontrolled number of fish and a polyculture of other organisms. We rec-ommend cutting the number of farmed milkfish in half and making up forlost profits through harvesting algae. This would not only keep algae atacceptable levels for coral survival, but provide a viable economic modelwhich includes food and income for island inhabitants.

In our readings of the literature, we found a strong correlation betweenalgae levels and coral health. If algae becomes too pervasive, they competewith the coral for vital resources and effectively ”choke out” the coral. Be-cause coral is such a vital piece of the reef ecosystem, coral death would ul-timately lead to the ecosystem’s collapse. This is an outcome any conserva-tion management program should be designed to avoid. Below we present


specific results from our model of the Lucero Reef to justify our claims. Wethen provide an economic assessment, demonstrating a strengthening ofthe Bolinao mariculture industry under our proposed plan.

8.1.2 Results of the Lucero Reef Model

We first modeled the Lucero Reef ecosystem before the introduction ofmilkfish farming. Our model demonstrated stable steady state values cen-tered on estimates of relative biomasses of three main trophic levels, namely,the primary producers, herbivores, and predators. Perturbations to thissystem behaved in the way we expected, quickly returning to the steadystate values. This demonstrates the robustness of the reef ecosystem, mod-eling in a simple way a complex polyculture of organisms which keep eachother in balance.

The model was then extended to apply to a mariculture ecosystem. Cur-rently, milkfish farming is common along the outer edges of the reef. In themilkfish pens, the steady state of the ecosystem is disrupted. High levels ofnutrients from the fish food and excrement lead to high levels of algae. Wefound that reducing the milkfish from 10,000 g/m2 to 5,000 g/m2 in com-bination with introducing new herbivores would cut the algae to 10 g/m2.Although this is still much higher than an acceptable value, harvesting thealgae could bring the number down to an environmentally friendly range.Algae is reported to have brought in $6.2 billion in 2008, so harvesting thisaglae for economic profit is a viable commercial solution to an environmen-tal problem. Our model predicts that we can harvest 2 kg/m2 of algae peryear without destroying the ecosystem. At a calculated rate of $1.40 perkilogram of algae, this comes out to roughly $3,000 per pen per year.

8.1.3 Conclusion

We suggest implementing these recommendations quickly to reverse thedetrimental trends present in the Bolinao reef system. With a consciouseffort, conservation management can produce a vibrant economic and en-vironmental solution to this problem.

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ICM: Coral Reef Ecosystem Model

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