Background 

 

Less than 1% of the ocean floor is covered by coral. Yet, 25% of the ocean's biodiversity is supported in these areas. Thus, conservationists are concerned when coral disappears, since the biodiversity of the region disappears shortly thereafter. 

 

Consider an area in the Philippines located in a narrow channel between Luzon Island and Santiago Island in Bolinao, Pangasinan, that used to be filled with coral reef and supported a wide range of species (Figure 1). The once plentiful biodiversity of the area has been dramatically reduced with the introduction of commercial milkfish (Chanos chanos) farming in the mid 1990's. It's now mostly muddy bottom, the once living corals are long since buried, and there are few wild fish remaining due to over fishing and loss of habitat. While it is important to provide enough food for the human inhabitants of the area, it is equally important to find innovative ways of doing so that allow the natural ecosystem to continue thriving; that is, establishing a desirable polyculture system that could replace the current milkfish monoculture. The ultimate goal is to develop a set of aquaculture practices that would not only support the human inhabitants financially and nutritionally, but simultaneously improve the local water quality to a point where reefbuilding corals could recolonize the ocean floor and co-exist with the farms. 

 

A desirable polyculture is a scenario where multiple economically valuable species are farmed together and the waste of one species is the food for another. For example, the waste of a fin-fish can be eaten by filter feeders and excess nutrients from both fish and filter feeders can be absorbed by algae which can also be sold, either as food or commercially useful by-products. Not only does this reduce the amount of nutrient input from the fish farming into the surrounding waters, it also increases the amount of profit a farmer can make by using the fish waste to generate a greater quantity of usable products (mussels, seaweed, etc.) 

 

For modeling purposes, the primary animal organisms involved in these biodiverse environments can be partitioned into predatory fish (phylum Chordata, subphylum Vertebrata); herbivorous fish (phylum Chordata, subphylum Vertebrata); molluscs (such as mussels, oysters, clams, snails, etc., phylum Mollusca); crustaceans (such as crabs, lobsters, barnacles, shrimp, etc., phylum Arthropoda, subphylum Crustacea); echinoderms (such as star fish, sea cucumbers, sea urchins, etc.; phylum Echinodermata); and algae. By feeding types, there are primary producers (photosynthesizers--these can be single cell phytoplankton, cyanobacteria, or multicellular algae); filter feeders (strain plankton, organic particles, and sometimes bacteria out of the water); deposit feeders (that eat mud and digest the organic molecules and nutrients out of it); herbivores (eat primary producers); and predators (carnivores). Just as on land, most of the carnivores eat herbivores or smaller carnivores, but in the ocean they can also eat many of the filter feeders and deposit feeders. Most animals have growth efficiencies of 10-20%, so 80-90% of what they ingest ends up as waste in one form or another (some dissipated heat, some physical waste, etc.). The role of coral in this biodiverse environment is largely to partition the space and allow species to condense and coexist by giving a large number of species each its own chance at a livable environment in a relatively small space--the aquatic analogue of high-rise urbanization. Coral also provides some amount of filter feeding, which helps clean the water. The ability of an area to support coral depends on many factors, the most important of which is water quality. For example, corals in Bolinao are able to live and reproduce in waters that contain half a million to a million bacteria per milliliter and 0.25ug chlorophyll per liter (a proxy for phytoplankton biomass). The fish pen channel currently sees levels upwards of ten million bacteria per milliliter and 15ug chlorophyll per liter. Excess nutrients from the milkfish farms encourage fast-growing algae to choke out coral growth, and particulate influx from the milkfish farms reduces corals ability to photosynthesize. Therefore, before coral larvae can begin to grow, acceptable water quality must be established. Other threats to coral include degradation from increasing ocean acidity due to increased atmospheric CO2, and degradation from increasing ocean temperature due to global warming. These can be considered second order threats which we will not specifically address in this problem. 

 

Problem Statement

The challenge for this problem is to come up with viable polyculture systems to replace the current monoculture farming of milkfish that would improve water quality sufficiently that coral larvae could begin settling and recolonizing the area. Your polyculture scenario should be economically interesting and environmentally friendly both in the short and long term. 

 

1. MODEL THE ORIGINAL BOLINAO CORAL REEF ECOSYSTEM BEFORE FISHFARM INTRODUCTION: Develop a model of an intact coral reef foodweb containing the milkfish as the only predatory fish species, one particular herbivorous fish (of your choice), one mollusc species, one crustacean species, one echinoderm species, and one algae species. Specify the numbers of each species present in a way you find reasonable; cite the sources you use or show the estimates you make in arriving at these population numbers. In articulating your model, specify how each species interacts with the others Show how your model predicts a steady state level of water quality sufficient for the continued healthy growth of your coral species. If your model does not yield a high enough level of water quality, then adjust your number of each species in a way you find most reasonable until you do achieve a satisfactory quality level, and describe clearly which species numbers you adjusted and why your changes were reasonable. 

 

2. MODEL THE CURRENT BOLINAO MONOCULTURE MILKFISH: 

a. First examine the impact if milkfish farming were to suppress other animal species. Do this by removing (setting the population to zero of) all herbivorous fish, all molluscs, all crustaceans, and all echinoderms. Set all other populations to be the same as in your full model above. Since you have removed the milkfish's natural food supply, you will need to introduce a constant term that models farmer feeding of the penned milkfish; choose this term to keep your model in equilibrium. What steady state level of water quality does your model now predict? Is water quality sufficient for the continued healthy growth of your coral species? Compare and describe how your result compares to observations. 

b. Milkfish farming does not totally suppress all other animal species and water quality is probably not as bad as your results from part 2a suggest, so use your model to simulate the current Bolinao situation by reintroducing all deleted species and adjust only those populations until water quality matches that currently observed in Bolinao. Compare your populations with those currently observed in Bolinao and discuss what changes to your model could bring your population predictions into closer agreement with observations. 

 

3. MODEL THE REMEDIATION OF BOLINAO VIA POLYCULTURE: You now strive to replace the current monoculture with a polyculture industry, seeking to make the water clear enough that the original reef ecosystem that you modeled in part 1 can re-establish itself without any help from humans. The idea is to introduce an interdependent set of species such that, whatever feed the milkfish farmer puts in, the combination of all of his/her "livestock" will use it entirely so that there are no (or only minimal) leftover nutrients and particles (feed and feces) falling onto the newly growing reef habitat below. Additionally, you seek to commercially harvest edible biomass from this polyculture in order to feed humans and increase value. 

a. Develop a commercial polyculture to remediate Bolinao. Do this by starting with your "current" penned model from part 2b, and introduce into it additional species that both help clean the water and yield valuable, harvestable biomass. For example, you could line the pens with mussels, oysters, clams or other economically valuable filter feeder to remove some of the waste from the milkfish. Economically valuable algae could be grown on the sides of the pens near the surface (where they get enough light), and some of these could feed the small herbivorous fish that feed the milkfish. Clearly present your model and its steady state populations. 

b. Report on the outputs of your model. What did you optimize, what constraints did you enforce, and why? What water quality does your model yield? How much harvest does your model yield, and what is its economic value? How much does it cost you to further improve water quality? In other words, from your optimal scenario, how many dollars of harvest does it cost you to improve water quality by one unit? 

 

4. SCIENCE: Discuss the harvesting of each species for human consumption. How do we use your model for predicting or understanding harvesting for human consumption? Does a harvested pound of carnivorous fish count the same as a harvested pound of seaweed so that we seek to maximize total weight harvested, or do we differentiate by value (as measured by price of each harvested species) so that we seek to maximize the value of the harvest? Or do we seek to maximize the total value of harvest minus cost of milkfish feed? Should we define the value of edible biomass as the sum of the values of each species harvested, minus the cost of milkfish feed? 

 

5. MAXIMIZE THE VALUE OF THE TOTAL HARVEST: We now wish to maintain an acceptable (maximal) level of water quality while harvesting a high (maximal) value of marketable (because edible and sell-able for byproducts are equally legitimate ways to maximize value) biomass from all living species in the model for human consumption. Change your model to harvest a constant amount from each species. What is the total value of biomass (as defined above) you can harvest and the corresponding water quality? Try different harvesting strategies and different levels of milkfish feeding (always choosing values that will keep your model in equilibrium), and graph water quality as a function harvest value. What strategy is optimal and what is the optimal harvest? 

 

6. CALL TO ACTION: Write an information paper to the director of the Pacific Marine Fisheries Council summarizing your findings on the relationship between biodiversity and water quality for coral growth. Include a strategy for remediating an area like Bolinao and how long it will take to remediate. Present your optimal harvesting/feeding strategy from part 5 above along with persuasive justification, and present suggested fishing/harvest quotas that will implement your plan. Show the leverage of your strategy by presenting the ratio of the harvest value under your plan to the harvest value under the current Bolinao scenario. Discuss the pros and cons from an ecological perspective of implementing your polyculture system. 

 

Getting Started References 

 

http://en.wikipedia.org/wiki/Integrated_Multi-trophic_Aquaculture 

http://en.wikipedia.org/wiki/Coral_reef 

http://www.seaworld.org/infobooks/Coral/home.html 

建立新的食物链系统(美国竞赛2009年C题) 

 

背景 

 

只有不到1%的海底是由珊瑚覆盖的。然而, 这些海域却支持了25%的海洋生物多样性。环保工作者非常关心珊瑚的消失, 因为从此该地区的生物多样性也将很快消失。 

 

考虑在菲律宾的位于Pangasinan(邦阿西楠)的Bolinao(波里纳奥)的Luzon(吕宋)岛和Santiago(圣地亚哥)岛之间的狭窄的通道区域, 那里过去曾经布满了珊瑚礁并支持着大量物种的生存(图1)。由于1990年代中期引进的商业性的虱目鱼(Chanos Chanos)养殖, 该海域曾经有过的丰富的生物多样性大大降低了。现在那里大部分都变成了浑浊多泥的海底, 曾经活着的珊瑚早就被埋葬了, 由于过度的捕捞和鱼类栖息地的丧失只剩下很少的野生鱼种了。尽管对于哪个地区的居民来说提供足够的食物是重要的, 但是同样重要的是要寻找一种能使自然的生态系统能够继续欣欣向荣的革新的方法; 即建立一种能够代替目前的虱目鱼单一养殖的令人满意的混养体制。最终目标是研发一套水产养殖的做法使得不仅能够支持人类居民经济上和营养上的需求, 而且能够同时改善当地的水质到一定的水平使得在暗礁上建立起来的珊瑚能重新拓展到海底并和养殖场共存。 

 

令人满意的混养体制应该展现这样一种情景: 多个有经济价值的物种养殖在一起, 而一个物种的排泄物正好是另一个物种的食物。例如, 有鳍鱼的排泄物可供滤食性动物食用而且有鳍鱼和滤食性动物的过量的营养物质可以被海藻吸收, 海藻既可以作为食物也可以作为商业上有用的副产品。这不仅减少了从鱼类养殖输入到周围水体的营养物质, 也由于利用鱼的排泄物生成大量的有用的产品(贻贝、海藻等)而使渔民增加了收益。 

 

为了建模的目的, 在这种生物多样性的环境里主要的动物生物体可以分为捕食鱼类(脊索动物门、脊椎动物亚门); 食草鱼类(脊索动物门、脊椎动物亚门); 软体动物(诸如贻贝、牡蛎、蛤蜊、蜗牛等, 软体动物门); 甲壳类动物(诸如蟹、龙虾、藤壶、河虾等, 节肢动物门, 甲壳动物亚门); 棘皮动物(诸如星鱼、海参、海胆等, 棘皮动物门); 还有藻类。就喂养的类型而言, 有初级生产者(光合作用制造者 -- 它们可以是单细胞浮游植物、蓝藻或多细胞藻类); 滤食动物(菌株浮游生物、有机颗粒, 有时候是水里的细菌); 食碎屑动物(吃泥土并消化其中的有机分子和养分); 食草动物(吃初级生产者); 以及捕食动物(食肉动物)。和在陆地上一样, 大多数食肉动物吃食草动物或更小的食肉动物, 但是在海洋里它们也吃很多滤食动物和食碎屑动物。大多数动物具有10-20%的生长效率, 所以它们所摄入物的80-90% 转化这种或那种形式的排泄物(一些转化为耗散的热量、另一些转化为身体的排泄物, 等)。在生物多样性环境中珊瑚的作用主要是划分空间, 并通过给予大多数物种在其相对比较小的空间里有其自己发展的生存环境使得各物种可以凝聚和共存 -- 都市化高层建筑在水里的类似做法。珊瑚还可以提供有助于清洁海水的一定数量的滤食动物。海域能支持珊瑚生长的能力有赖于许多因素, 最重要的因素是水质。例如, Bolinao的珊瑚可以在含有50-100万个细菌/每毫升和0。25 ug 叶绿素/每升(一种光合作用的生物量的替代物)的海水中能够生存和繁殖。而在用围栏圈养鱼的水域里当前看到的情况却是高于1000万个细菌/每毫升和15 ug 叶绿素/每升。由于虱目鱼渔场过量的营养物促进了窒息珊瑚生长的海藻的快速生长, 以及来自虱目鱼渔场的颗粒流降低了珊瑚进行光合作用的能力。所以, 在珊瑚幼体能够开始生长前, 必须确立可以接受的海水的质量。对珊瑚的其他威胁包括由于大气中二氧化碳的增加导致的海水酸度的增加造成的珊瑚礁的退化, 以及由于全球变暖导致的海水温度升高造成的珊瑚礁的退化。可以把这些看作是二级威胁, 在本问题中我们不予专门的处理。 

 

问题的陈述 

 

本问题的挑战在于要提出切实可行的混养系统来替代当前虱目鱼的单一养殖使之能够大大改善水质, 从而使珊瑚幼体能够在该区域生根扩展。无论从短期和长期的角度看, 你们的混养系统都应该经济上是吸引人的而且对环境是无害的。 

 

1. 对引进渔场前Bolinao原先的珊瑚礁生态系统进行建模: 研制一个完整的珊瑚礁食物网的模型,该食物网包括唯一的捕食鱼种虱目鱼, (由你们选择的)一种特殊的食草鱼, 一种软体动物, 一种甲壳动物, 一种棘皮动物以及一种海藻。以一种你们认为是合理的方式详细说明每个物种的数量; 列出你们所用的原始资料或者说明你们是怎么估计出这些种群的数量。就清楚表述你们的模型而言,详细说明每个物种怎样和其他物种相互作用。说明你们的模型是怎样预测足以保证珊瑚物种能够持续健康生长的稳定的水质水平的。如果你们的模型没有给出足够高的水质水平, 那么就按你们认为最合理的方式来调整每个物种的数量直到确实达到了满意的水质水平为止, 并清楚描述你们调整了那些物种的数量以及为什么你们所做的改变是合理的。 

 

2. 对Bolinao当前的虱目鱼单一养殖建模 

a. 首先假设虱目鱼的养殖会抑制其他动物物种的生长, 研究它将产生的影响。通过移去(即,令种群数目为零)所有的食草鱼, 所有的软体动物, 所有的甲壳动物以及所有的棘皮动物。令所有的其他物种数量和你们在上面的完整模型中的数量相同。因为你们已经移去了虱目鱼的自然食物供应; 你们需要引进一个常数项, 该常数项是渔民对圈养虱目鱼的喂养; 选择这项使得你们的模型保持平衡。你们的模型现在预测的是什么样的稳定水质水平? 该水质水平足以保证你们珊瑚物种能够持续健康生长? 与观察结果比较, 并描述怎样把你们的结果与观察结果进行比较。 

b. 虱目鱼的养殖并非完全抑制所有其他的动物物种的生长, 而且水质也可能并不像你们在2a中建议的那么坏, 所以通过重新引进所有被移去的物种并且只调整它们的数量直到水质和当前在Bolinao观察到的水质一致来模拟当前Bolinao的生态情况。把你们得到的这些物种的数量与它们当前在Bolinao观察到的这些物种的数量进行比较, 并讨论对你们的模型做什么样的改变会使得你们对各种群数量预测与观察结果更加接近。 

 

3. 对经由混养来抢救Bolinao的生态环境进行建模: 你们要寻求无须人类活动的帮助的前提下力争用混养渔业来替代当前的单一养殖使得海水足够清洁从而能够重建你们在问题1 中建模的原来的珊瑚生态系统。想法就是引进一组互相依赖的物种使得无论养殖虱目鱼的渔民投放的是什么样的饲料, 他/她的“牲畜”都会把它们全部吃掉, 而不会有(或只有极少的)剩余营养物和颗粒物(饲料和粪便)掉进下面的新长出来的珊瑚生长地。此外, 为了向人类提供食物并增加其价值你们还要设法从这种混养系统中获得具有商业价值的可以食用的生物物质。 

a. 研发一种商业性的混养系统来抢救Bolinao的生态环境。从你们在2b部分的“当前”的圈养模型开始, 并且引入既能清洁海水又能生产有价值、可收获的生物物质的额外的物种来做这件事。例如, 你们可以用贻贝，牡蛎，蛤蜊或者其他的有经济价值的滤食动物排成围拦来去掉虱目鱼的某些排泄物。有经济价值的藻类植物可以在靠近水面的围拦边上生长(在那里他们可以获得足够的光线), 而且某些藻类还可以作为喂养虱目鱼食物的小食草鱼的饲料。清楚地表述你们的模型以及达到稳定状态的各物种的数量。 

b. 报告你们的模型的输出信息。你们优化的是什么, 所加的约束是什么, 为什么? 你们的模型给出的是什么样的水质? 你们的模型给出的收获有多少, 其经济价值怎样? 为进一步改善水质你们要付出多少费用? 换言之, 从你们的最优的结果而言, 为提高水质一个单位你们要付出的费用相当于多少与收获物等价的美元? 

 

4. 科学: 讨论人类消耗所需的各物种的捕捞量。我们怎样利用你们的模型来预测或者理解人类消耗所需的捕捞量? 捕捞一磅食肉动物的鱼类和捕捞一磅海藻同样重要, 所以我们应该寻求极大化总的捕捞重量, 或者我们应该区分(按照每种鱼种的价格来度量的)价值所以我们应该寻求极大化所捕捞的物种的价值? 或者我们应该极大化所捕捞的物种的总价值减去饲养虱目鱼的费用? 我们是否应该把可以食用的生物量的价值定义为各捕捞物种的价值之和再减去饲养虱目鱼的费用? 

 

5. 极大化总捕捞量的价值: 现在我们希望在人类消耗模型中在保持一种可接受(最好的)水质水平的同时使来自所有活的物种的捕捞量达到高(最大)的市场价值(因为可食用和可销售的副产品都是极大化价值的合法的方式)。改变你们的模型使得捕捞的各个物种等于常量。什么是你们可以捕捞的(如同上面定义的)生物量的总价值以及相应的水质? 试一下不同的捕捞策略和不同的虱目鱼喂养水平(永远选择能够使你们的模型保持平衡的价值), 并且画出水质作为捕捞价值的函数的图像。什么样的策论是最优的以及什么是最优的捕捞量? 

 

6. 号召采取行动: 给Pacific Marine Fisheries Council (太平洋水产委员会)的主任写一份你们发现的有关珊瑚生长中生物多样性和水质的关系的结论的信息报告。报告要包括修复像Bolinao那样的生态环境的策略以及要多长时间才能修复。用有说服力的理由来提出第5 部分中你们的最优捕捞/喂养策略, 并提出能执行你们的计划的捕捞/喂养配额策略。通过提出你们计划下的捕捞价值和当前Bolinao情况下的捕捞价值之比来说明你们的策略的优势。从生态学的角度来讨论你们的混养系统的利弊得失。 

 

开始你们的研究时可以利用的参考资源 

 

http://en.wikipedia.org/wiki/Integrated_Multi-trophic_Aquaculture 

http://en.wikipedia.org/wiki/Coral_reef 

http://www.seaworld.org/infobooks/Coral/home.html