Icm: Coral Reef Ecosystem Model

Summary Coral reefs are fascinating ocean habitats which harbor an incredible diversity of marine life. The Lucero reef in the northwestern Philippines recently experienced a severe drop in its biodiversity and health, roughly coinciding with the increase in milkfish farming in Bolinao, Pangasinan. We establish a mathematical model to represent the Lucero reef ecosystem and to aid in predicting an economically viable solution that provides for the recovery of the reef. We reduce the ecosystem to a manageable complexity by modeling generalized trophic levels instead of individual species. In doing so, we limit the precision of our model, but are still able to predict trends based on pertubations to steady state conditions. Our model is based on the LotkaVolterra equations, diverging as necessary to accommodate the unique features of the reef ecosystem. The model indicates that reducing milkfish farming and increasing the harvest of algae and other primary producers such as seaweed will benefit the reef ecosystem by limiting algae overgrowth. Moreover, previous research has shown that seaweed mariculture is a satisfying economic solution. Thus we recommend a reduction in milkfish harvesting to be compensated by an increase in algae harvesting. This produces a compromise between the economic and environmental demands on the system.

Legalize (Sea)weed ICM Contest Question C Team # 5201 February 9, 2009

Contents 1

Introduction

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Background 2.1 Selected Components of the Reef Ecosystem 2.1.1 Coral . . . . . . . . . . . . . . . . . . . 2.1.2 Plankton . . . . . . . . . . . . . . . . . 2.1.3 Nutrients in the Environment . . . . . 2.1.4 Milkfish . . . . . . . . . . . . . . . . . 2.1.5 Herbivorous fish . . . . . . . . . . . . 2.1.6 Crustaceans . . . . . . . . . . . . . . . 2.1.7 Echinoderms . . . . . . . . . . . . . . 2.1.8 Molluscs . . . . . . . . . . . . . . . . . 2.1.9 Algae . . . . . . . . . . . . . . . . . . . 2.2 Assessing Water Quality . . . . . . . . . . . .

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Model 3.1 Goals . . . . . . . . . . . . . . . . . . . . 3.2 Existing Models . . . . . . . . . . . . . . 3.3 Assumptions . . . . . . . . . . . . . . . . 3.4 Our Models . . . . . . . . . . . . . . . . 3.4.1 Natural Ecosystem . . . . . . . . 3.4.2 Milkfish Monoculture Ecosystem 3.5 Model Limitations . . . . . . . . . . . . .

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Integrated Multi-trophic Aquaculture Design

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Results 5.1 Natural Ecosystem . . . . . . . . . . . . . 5.2 Milkfish Monoculture . . . . . . . . . . . . 5.3 Milkfish Mariculture . . . . . . . . . . . . 5.4 Fisheries Management Design . . . . . . . 5.4.1 Reduction of Milkfish Farming . . 5.4.2 Integrating Seaweed Aquaculture

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Future Work

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Conclusion

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Appendix 8.1 Call to Action: Recommendations for Conservation Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 8.1.2 Results of the Lucero Reef Model . . . . . . . . . . . . 8.1.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

Although coral reefs only cover about 0.1% of the ocean surface, they are home to nearly one-third of all ocean fish species. They represent a microcosm 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 human activity and show no promise of recovery.[7] This is a sobering fact for the state of our natural world, but it has immediate economic consequences as well. It is estimated that healthy reefs proivde as much as $350 billion per year in goods and services.[7] The combination of economic and environmental implications incentives a strong mathematical model which can be used to model the health of coral reefs and hopefully guide conservation policy. One reef which has been studied extensively in the literature is the Lucero Reef off the coast of Santiago Island in the Philippines. The Lucero Reef encapsulates many aspects of reef conservation. Historically it has been a good model of tropical biodiversity, with a mean biodiversity index of H 0 = 2.60.[1] However, in 1995 milkfish harvesting became a new, productive source of food and money and by 1998 there were an estimated 11,900 tons of milkfish farmed annually.[13] The milkfish farms have lead

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directly to increased nutrient levels in the reef area.[19] High levels of nutrients such as carbon, nitrogen, and phosphorous compounds have been linked to algal blooms, which negatively impact coral life.[25], [19] As such, these milkfish farms have a negative impact on the reef ecosystem, disrupting the delicate balance of biodiversity and threatening its long-term survival. In creating conservation policy surrounding this reef ecosystem, it is important to balance environmental and economic aspects of the issue. One cannot ignore the commercial advantages of milkfish farming, both as a source of food and income to island inhabitants, but taken to an extreme milkfish farming can disrupt other local fishing industries if the coral reef ecosystem collapses. Hence it is imperative both for environmental and economic reasons to arrive at a sustainable solution for the island’s needs. Aquaculture is the practice of designing controlled populations for fish farming. Integrated multi-trophic aquaculture (IMTA) is a more recent approach in Western aquaculture that attempts to create a sustainable ecosystem. The right balance of species provide resource recycling that preserves a greater fish diversity, where the wastes of one become the resources of another. This contrasts monocultures, high-densities of a single fish species that propagate in regions where one species has become financially successful, which are prone to deterioration through environmental degradation and disease outbreaks.[17] Many IMTA projects have begun throughout the world in recent years, though we found no particular projects for an ecosystem containing coral reefs. Our challenge is to incorporate the IMTA framework 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 commercialization of milkfish farming. The model is based off of the Lotka-Volterra equation, using trophic levels to represent the various species in a reef ecosystem. We then extended this model to apply to the milkfish farming 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 predict changes that could be made to the mariculture ecosystem to reduce these levels.

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Background

2.1

Selected Components of the Reef Ecosystem

The reef ecosystem is intractably complex; modeling every component of the ecosystem with good precision would provide ground-breaking insight into the functional relationships within the ecosystem, but it would be exceedingly difficult. Realistically, to come to a conclusion in a reasonable amount of time, we must reduce the ecosystem to relatively few generalized components and relationships. To reveal some of the intricacy of the reef ecosystem and to illustrate its basic structure and dynamics, we describe its more prevalent components. 2.1.1

Coral

Most corals are colonial organisms consisting of hundreds of thousands of individual polyps.[34] The reefs formed by some corals contribute significantly to biodiversity by partitioning the environment and providing for herbivores.[32] Reef-building corals often contain photosynthetic algae called zooxanthellae, which offer a crucial mutualistic relationship to the corals. While the coral protects the zooxanthellae and provides it with the nutrients it requires for photosynthesis, the zooxanthellae removes wastes from the coral and provides it with vital nutrients - oxygen, glucose, glycerol, and amino acids. Because of this relationship between the coral and zooxanthellae, coral tend to respond to the environment like plants, thriving in clear water that is easily permeable by sunlight.[36] Furthermore, coral primarily exist in nutrient-poor water, as nutrient-rich water promotes overgrowth of algae which can easily choke the coral. The removal of the zooxanthellae, due to inadequate environmental conditions or otherwise, is known as coral bleaching, and prolonged bleaching can cause the coral 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 concentration and other environmental conditions. Plankton are divided into three functional categories: Phytoplankton, zooplankton, and bacterioplankton. [30] Phytoplankton, a subset of algae, are microscopic organisms that rely on photosynthesis for sustenance; as such they are primary producers, converting simple molecules and energy from sunlight into complex

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organic molecules that are used by other organisms in the ecosystem.[29] Zooplankton are small animals, including some crustaceans and larval stages of larger animals like fish, that feed primarily on phytoplankton. Bacterioplankton are microorganisms including bacteria and archaea. [30] 2.1.3

Nutrients in the Environment

Reef nutrients take several forms, including sunlight and chemical compounds such as ammonium, nitrite, nitrate, phosphate, and silicate.[31] Such nutrients are the primary sources of growth for algae and other primary producers, so nutrient-rich waters promote overgrowth of algae and make a poor environment for coral reefs. Another significant form of nutrient found in the water is detritus, organic material that includes fragments of dead organisms and feces.[10] Detritus is an important source of food for much of the life in a marine ecosystem, including crustaceans and herbivorous fish. 2.1.4

Milkfish

Milkfish, or Chanos chanos, are a species of predatory fish found primarily in the Indo-Pacific region along continental shelves and islands.[6] Their diet consists primarily of small invertebrates, cyanobacteria, and soft algae.[6] The average milkfish weighs roughly 1.5 kg[5], and in captivity is reported to 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, the fish must consume about 30 kg per year. However, numbers reported by Homer et al. (2002) on feeding rates indicated that milkfish consume only 1.2 kg per year. One report indicates that other omnivorous fish consume roughly 30 kg per year per kg of biomass, which translates into roughly 45 kg per fish per year.[16] This number is on par with the estimate we arrived at based on the weight of excrement, so we will use that estimate in our model. Discrepancies in the paper by Homer, et al. are likely caused by the fact that the reported consumption rate was based on supplimental feed provided by milkfish farmers and certainly did not take into account other sources of food. 2.1.5

Herbivorous fish

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

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fect the environment indirectly by recycling nutrients through feeding and defection.[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, eating the turf algae which would otherwise choke out the coral. They consume approximately 109.1 grams of food per day, which translates into roughly 103 grams of turf algae per day.[27] Parrotfish have also been reported to excrete 12 grams of waste per day.[27] 2.1.6

Crustaceans

The subphylum Crustacea is a large, diverse group of invertebrates. The most well-known, and also the largest, crustaceans include crabs, lobsters, and shrimp, However, there are many other, smaller varieties unknown in popular culture.[8] Crabs, for example, are generally omnivorous, feeding on 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. Their feeding habits vary significantly by species; echinoderms can be suspension feeders, herbivores, detritivores, and predators. The most common groups in the Lucero reef, sea urchins and sea cucumbers, feed primarily by grazing on algae. [28] Sea urchins therefore serve an important role to coral health by keeping algae growth in check. 2.1.8

Molluscs

Molluscs, particularly bivalves, such as clams, fill an important niche in reef ecosystems. Most bivalves feed by using large gills to capture nutrient particles directly from the ocean water.[3] Bivalves thus reduce the nutrient concentration in the water, thereby limiting the growth of algae and bacteria. While this in turn limits the growth of herbivores who feed on the algae, it positively affects the health of the reef by keeping algae from overgrowing the coral. 2.1.9

Algae

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

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essential part of the food chain that converts light and chemicals from their environment into biomass. A representative species for our model is Gelidium pusillum, a red algae[21] common in the province of Pangasinan.[33] Gelidium pusillum forms algal turfs,[22] which are apt to overgrow and choke coral. 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 studies dating from the mid-1970’s.[25] As such, algal biomass in a reef ecosystem is strongly correlated to the health of the coral and hence the health of the entire system. Although there is debate in the literature,[24] algal blooms have been linked by several studies to a combination of increased nutrients (such as nitrates and phosphates) in the water and a decrease in grazing from herbivorous species.[25],[26] Because nutrients impact algae growth and thus indirectly impact the health of coral, it is important to model this relationship. In our model, nutrient levels will be measured by a water quality score, which takes into account the nitrates and phosphates linked to algal blooms.

3 3.1

Model Goals

We want to create a model that incorporates the entire foodweb of the Bolinao coral reef ecosystem. Data we wish to retain from the model includes water quality levels, amount of fish harvesting, and steady state levels of fish population. This values are ultimately used to evaluate suggestions for an 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 that model the interaction of phytoplankton, zooplankton, and nutrients. Other models, particularly those used in fishery management decisions, rely on survey data to model fish populations at a higher trophic level while ignoring the bottom. Furthermore, ecology modeling comprises of two distinct approaches, state variable and individual-based modeling. State variables encapsu-

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late the many facets of a species population into a single state, typically the biomass of the species. This disregards important distinctions among the individuals. In some cases, aggregation among the individuals was found to correlate to similar patterns in a state variable model. However, individual-based modeling is more often used on more narrow scales than which we are concerned for this problem,[23] so we will focus on a state variable model. The integration of multiple trophic levels is a difficult modeling problem still today that requires a great deal of research. [18] A 2003 survey of ecosystem models found that ECOPATH was that only model that used a multispecies approach: Despite broad discussion of the need to consider multispecies issues in marine conservation and fisheries management we know of only one model that focuses explicitly on multispecies aspects 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 eaten by another organism or natural death. To conserve mass, some of the loss of one state’s mass becomes a sink for another’s. The remaining mass excreted as nutrients or other particles. Either growth or loss can occur from migration. The Population Law of Mass Action describes these rates of changing mass. It states that the rate of change of the mass of two interacting species is proportional to the product of their masses. This principle is used in modeling predator-prey relations in the Lotka-Volterra model, x 0 = (− a + by) x = − ax + bxyy0 = (c − kx )y = cy − kxy where x is the predator mass and y is the prey mass. The bxy and −kxy terms represent the predation, a source of growth for the predators but a sink for the prey. To close the model, − ax represents the natural death of the predator (i.e. in isolation of the prey), and cy represents the natural growth of the prey. [4]

3.3

Assumptions

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

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This pattern is determined as a rough average of consumption patterns over all stages of life, weighted by biomass. Nutrient uptake by phytoplankton is a function of both light and temperature since it is dependent on the amount of photosynthesis that the organism can perform.[9] We assume that nutrient uptake can be approximated as a temperature-invariant and light-invariant function. Our models do not incorporate variations due to seasonal cycles. For instance, the vertical mixing of ocean layers occurs in greater proportion in winter 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 a very complex ecosystem, we have chosen to represent generalized trophic groups instead of individualized species. Any attempts to use the specific grazing patterns of any one species as representative for the entire trophic group lead to nonsensical results because it assumes a closed system when in reality there are many other species and factors at play. For example, if we chose precise initial conditions for our primary producers off of the absolute biomass of algae, our ecosystem would be underfed because it neglects other primary producers such as seagrass and seaweed. Instead, we chose to look at rough production and consumption ratios for each trophic group and then force the grazing coefficients to achieve a steady state. Although this does not precisely reflect reality, it gives sensical results and we claim that the grazing coefficients represent a complicated mass balancing that occurs behind the scenes in the way we calculated them.

3.4 3.4.1

Our Models Natural Ecosystem

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

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ergy in biological systems for basic life processes), we introduced a constant term α which represents energy flowing into the system and augments the nutrient term consumed by the algae. This term can be conceptualized as a measure of the sunlight adding energy to the ecosystem. Below is a mathematical representation of our model: N 0 = dH + dA + dM + 0.9 ∗ gm MZ − ga N A A0 = ga ( N + α) A − gh AH − dA H 0 = egh AH − egm HM − dH M0 = egm HM − dM

Table 1: Initial Conditions Symbol N A H M

Name Nutrients Algae Herbivores Predators

Initial Value 0.032 0.3 50 0.92

We chose initial conditions based on estimations of biomass consumption and production per year for each class of animal.[16] The algae is represented by phytoplankton, the herbivores are represented in general by Parrotfish, and the predators are represented by milkfish.1 Nutrient levels were chosen to be a low steady state value based on data in the literature.[15] We assumed that these numbers represent a stable equilibrium, and hence solved the set of steady-state equations: 0 = N 0 = dH + dA + dM + 0.9 ∗ gm MZ − ga N A 0 = A0 = ga ( N + α) A − gh AH − dA 0 = H 0 = egh AH − gm HM − dH

(1)

0

0 = M = egm HM − dM 1 In reality, milkfish are not solely predators. However for the purposes of this model we are assuming that they only eat herbivores

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The death rate and efficiency coefficients were set to d = .125 e = .1 as a way to calibrate the model. The efficiency parameter mirrors the fact that only 10% of energy is passed up each trophic level, and the death rate was set heuristically assuming that the biomass of each population is recycled every eight years. The result of these calculations is the set of parameters shown in table 2 which solve the steady state equations (1). Table 2: Simplified Model Steady State Parameters Symbol α e d ga gz gh

Name Resource Input Energy Efficiency Death Rate Algae Grazing Rate Herbivore Grazing Rate Predator Grazing Rate

Value 0.2865 0.1 0.125 774.7 4.93 0.025

When perturbed from the steady state, this model behaves as expected. An increase in predator biomass causes a decrease in herbivore biomass and hence an increase in algae biomass. Similarly, an decrease in predator has the reverse effect, and an increase in herbivore biomass results in a decrease of algae biomass and increase in predator biomass. However, over several generations these transient responses even out and return to close to the original steady state. This corresponds to what we see in the natural world. Within reason, perturbations from natural steady state values does not cause the entire world ecosystem to collapse; instead, there is a 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 the way in which the reef ecosystem operates. We chose to model the ecosystem 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 steady state values of algae (which is our indicator of coral survival). Using the

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simplified ecosystem model above, we modified some of the conditions to reflect the nature of the milkfish monoculture ecosystem. If we were to use the exact same model, the extremely high density of milkfish in the pens would overwhelm the herbivore population and hence lead to a near exponential growth of algae. Additionally, because the milkfish consume the herbivore population so quickly, it would lead to a rapid decline in milkfish population after an initial peak. However, these effects result from some simple assumptions that change in a mariculture ecosystem. First of all, the milkfish are being fed and harvested so that the total population remains almost constant. Hence, we can assume that M0 = 0. Another difference between the mariculture and natural ecosystem is that in the mariculture environment, milkfish derive most of their diet from the food given to them by the farmers. We estimated that farmed milkfish only eat one tenth as much from the herbivore group as they do in a natural environment. Finally, because the milkfish are being farmed, their dead biomass does not return to the nutrient compartment. These changed assumptions resulted in the following set of differential equations: N 0 = dH + dA + 0.9 ∗ gm MZ − ga N A A0 = ga ( N + α) A − gh AH − dA H 0 = egh AH − 0.1 ∗ gm HM − dH M0 = 0 These equations will be solved numerically given an elevated milkfish population 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 general trophic level is a significant limitation to the model. It does not take into account the varied grazing patterns of different organisms, and does not have very high resolution to look at the ecosystem on a per species level. Additionally, it neglects the complexity of the detritus cycle by assuming that nutrients get converted into algae biomass with perfect efficiency. This leaves out whole classes of organisms such as molluscs which can feed off of dendrite. It also ignores the fact that very few species are truly either carnivores or herbivores. In reality, milkfish (which were the focus of our model) feed off of algae and detritus as well as off of small fish, floating fish eggs, and small invertebrates. However, our model tries

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to capture the general flow of energy between trophic levels, and even after 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 will occur given a certain set of input. Instead, it is meant to give a general trend for different perturbations to the reef ecosystem which may not be readily obvious upon inspection. Further development is needed for more precise quantitative measures.

4

Integrated Multi-trophic Aquaculture Design

Developing a sustainable ecosystem for the Bolinao coral reef involves a delicate balance. Excess nutrients allow the growth of algae, which compete with coral for sunlight used in photosynthesis by covering surface area of the ocean. We agreed with the several sources proclaiming the importance of building a resilient coral reef ecosystem. By this, we mean the ability of the reef to 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 combination of factors that make the system vulnerable to events that trigger the actual shift.[14] As an example of resilience, the large number of sea urchins allowed the Caribbean reef to recover from a 1981 hurricane that destroyed much of it. it soon after suddenly was severely hindered by brown algae.

5 5.1

Results Natural Ecosystem

We calibrated our model to a steady state representing the species populations 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 was introduced to Bolinao. To simplify the model, milkfish were set to the pop-

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Figure 1: With no herbivorous species, our model predicts algae growing without bound. ulation described by [13]2 and the herbivore species were reduced to zero. The nutrient levels greatly exceed the threshold determined by [25]. Combined with a zero population of herbivores, this fact leads to the uncontrolled growth of algae seen in the above figure. Clearly this result is not physical. Algae would eventually reach a the carrying capacity of the environment, and it is also unlikely that the herbivore population would ever be zero. However, these limitations of our model do not detract from the fact that a low herbivore population and high milkfish population would lead 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 population to 500 g/m2 such that we were able to get a nutrient level corresponding to the current levels as reported by [20]. This population level compares to 247 g/m2 , the actual populations in Bolinao.[16] The herbivore population would need to increase to compensate for the algae blooms caused by waste nutrients from the milkfish. 2 We

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

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

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

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

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

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5.4 5.4.1

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Fisheries Management Design Reduction of Milkfish Farming

Since large levels of algae threaten the health of reefs, we first investigated a simple way to reduce the amount of algae. Limiting the mass of milkfish by 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 milkfish farming

5.4.2

Integrating Seaweed Aquaculture

An alternate idea to simply attempting to decrease milkfish levels is to incorporate the idea of a integrated multi-trophic aquaculture by introducing seaweed to the fish pens. This keeps the algae from the possibility of damaging the coral and also allows the profitable harvest of milkfish. Our model predicts that we can harvest 2 kg/m2 of algae per year without destroying 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 decrease in the herbivore life in the fish pens. However, a healthy coral reef due to lower nutriet levels may still allow the herbivores to thrive there.

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

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

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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 represented in Bolinao. A more accurate model, incorporating the variety of omissions characterized previously, would give a better representation of the changes that would occur when testing the possibilities for a new polyculture. Additional data to improve the accuracy of parameters of the model would provide similar improvements. The great diversity of sea life means that many solutions may potentially exist to a integrated multi-trophic aquaculture in Bolinao. This is an area of active research, and keeping an eye on the developments in similar fisheries, particularly in coral reefs, may provide some additional insight into designing a management that provides continued harvesting value through a sustainable ecosystem.

7

Conclusion

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

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troducing other forms of harvestable herbivores leads to a lower steady state value of algae. Combined with the harvesting of algae this can lead to a viable economic and environmental solution. Our models showed that perturbations to the steady state (through constant harvesting terms) does little to affect the overall stability, leading to the conclusion that high levels of harvesting can be sustained. We believe a conservation policy built around this model has a decent chance at reversing the trends seen today in the Bolinao reef system.

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Appendix

8.1 8.1.1

Call to Action: Recommendations for Conservation Management Introduction

Conservation management is an important issue facing many nations as they try to balance the economic and food needs of their country with the needs of natural ecosystems. Nowhere is this balance more pronounced than in coastal reef ecosystems, which house over one third of all ocean fish species and a vast amount of the biodiversity found in ocean environemnts. The incredible complexity of these ecosystems also makes them incredibly fragile; as such, conservation management becomes especially important. We realize fully the difficult challenges posed by creating stable, viable ecosystems which also produce harvestable product. Our team of researchers has created a mathematical model to assist with these challenges, providing a way to visualize the impact of different changes to the system. In modeling the Lucero Reef system on the coast of Pangasinan, Philippines, we found that milkfish farming could be sustainable given a controlled number of fish and a polyculture of other organisms. We recommend cutting the number of farmed milkfish in half and making up for lost profits through harvesting algae. This would not only keep algae at acceptable levels for coral survival, but provide a viable economic model which includes food and income for island inhabitants. In our readings of the literature, we found a strong correlation between algae levels and coral health. If algae becomes too pervasive, they compete with the coral for vital resources and effectively ”choke out” the coral. Because coral is such a vital piece of the reef ecosystem, coral death would ultimately lead to the ecosystem’s collapse. This is an outcome any conservation management program should be designed to avoid. Below we present

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specific results from our model of the Lucero Reef to justify our claims. We then provide an economic assessment, demonstrating a strengthening of the 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 of milkfish farming. Our model demonstrated stable steady state values centered on estimates of relative biomasses of three main trophic levels, namely, the primary producers, herbivores, and predators. Perturbations to this system behaved in the way we expected, quickly returning to the steady state values. This demonstrates the robustness of the reef ecosystem, modeling in a simple way a complex polyculture of organisms which keep each other in balance. The model was then extended to apply to a mariculture ecosystem. Currently, milkfish farming is common along the outer edges of the reef. In the milkfish pens, the steady state of the ecosystem is disrupted. High levels of nutrients from the fish food and excrement lead to high levels of algae. We found that reducing the milkfish from 10,000 g/m2 to 5,000 g/m2 in combination with introducing new herbivores would cut the algae to 10 g/m2 . Although this is still much higher than an acceptable value, harvesting the algae could bring the number down to an environmentally friendly range. Algae is reported to have brought in $6.2 billion in 2008, so harvesting this aglae for economic profit is a viable commercial solution to an environmental problem. Our model predicts that we can harvest 2 kg/m2 of algae per year without destroying the ecosystem. At a calculated rate of $1.40 per kilogram 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 the detrimental trends present in the Bolinao reef system. With a conscious effort, conservation management can produce a vibrant economic and environmental solution to this problem.

References [1] A. Acosta and R. Turingan. Coral reef fisheries at cape bolinao, philippines: Species composition, abundance and diversity. Asian Fisheries Science, 4:295–306, 1991.

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[2] Barnacles. Available online, 2009. URL http://www.chesapeakebay.net/bfg%5Fbarnacles.aspx?menuitem=14468. Accessed February 8th, 2009. [3] Bivalvia. Available online, 2001. URL http://www.ucmp.berkeley.edu/taxa/inverts/mollusca/bivalvia.php. Accessed February 8th, 2009. [4] R.L. Borrelli and C.S. Coleman. Differential Equations: A Modeling Perspective. John Wiley and Sons, New York, 2004. [5] Chanos chanos. Available online, 2009. URL http://www.fao.org/fishery/culturedspecies/Chanos%5Fchanos. Accessed February 7th, 2009. [6] Chanos chanos, Milkfish. Available online, 2009. URL http://www.fishbase.org/Summary/SpeciesSummary.php?id=80. Accessed February 5th, 2009. [7] I. Cote and J. Reynolds, editors. Coral Reef Conservation. Cambridge University Press, Vancouver, BC, 2006. [8] crustacean. Available online, 2009. URL http://www.britannica.com/EBchecked/topic/144848/crustacean. Accessed February 8th, 2009. [9] D.M. DiToro, D.I. O’Connor, and R.V. Thomann. A dynamic model of the phytoplankton population in the sacromento-san joaquin delta. Advances in Chemistry Series, 106:131–180. [10] Earth Observatory Glossary. Available online, 2009. http://earthobservatory.nasa.gov/Glossary/?mode=all. cessed February 9th, 2009.

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[14] M. Scheffer et al. Catastrophic shifts in ecosystems. Nature, 413:591– 596, . [15] M.L. San Diego-McGlone et al. Eutrophic waters, algal bloom and fish kill in fish farming areas in bolinao, pangasinan, philippines. 57: 295–301, . [16] P.M. Alino et al. Initial parameter estimations of a coral reef flat ecosystem in bolinao, pangasinan, northwestern philippines. ICLARM, Manila, pages 252–258, 1993. [17] T. Chopin et al. Integrating seaweeds into marine aquaculture systems: A key toward sustainability. Journal of Phycology, 37(6):975–986, . [18] W. Fennel and T. Neumann. Introduction to the Modelling of Marine Ecosystems. Elsevier, Amsterdam, 2004. [19] M. Garren and et. al. Gradients of costal fish farm effluents and their effect on coral reef microbes. Environmental Microbiology, 10(9):2299– 2312, 2008. [20] M. Garren, S. Smirga, and F. Azam. Gradients of coastal fish farm effluents and their effect on coral reef microbes. Environmental Microbiology, 10(9):2299–2312. [21] Gelidium. Available online, 1999. URL http://www.mbari.org/staff/conn/botany/reds/sharon/index.htm. Accessed February 7th, 2009. [22] Gelidium pusillum (Stackhouse) Le Jolis. Available online, 2008. URL http://www.algaebase.org/search/species/detail/?species%5Fid=17. Accessed February 7th, 2009. [23] V. Grimm. Ten years of individual-based modelling in ecology: what have we learned and what could we learn in the future? Ecological Modelling, 115:129–148. [24] T. Hughes, A. Szmant, R. Steneck, R. Carpenter, and S. Miller. Algal blooms on coral reefs: What are the causes? Limnology and Oceanography, 44(6):1583–1586. [25] B. Lapointe. Nutrient thresholds for bottom-up control of macroalgal blooms on coral reefs in jamaica and southeast florida. Limnology and Oceanography, 42(5):1119–1131.

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[26] L. J. McCook. Macroalgae, nutrients and phase shifts on coral reefs: scientific issues and management consequences for the great barrier reef. Coral Reefs, 18:357–356, 1999. [27] D. Ochavillo, P. Dixon, and P. Alino. The daily food ration of parrotfishes in the fringing reefs of bolinao, pangasinan, northwestern philippines. Proceedings of the Seventh International Coral Reef Symposium, Guam, 2:927–933, 1992.

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