On the basis of the autonomous differential equations model,the Regression analysis,and the optimization method,a food system model is propod to rebalance the human-influenced ecosystem.
At first,bad on the analysis of the interacting between the six species,an autonomous differential model is prented to simulate the original Bolinao coral reef ecosystem,through which the balanced number of each species is obtained.Then,the relationship between water quality and number of each species is determined on the basis of Regression analysis with historical date from the Bolinao.Accordi
ng to the original model,the water quality level is calculated with the proof that our model is fit for the coral reef.
Due to the human influence (feeding &catching),the differential model is modified by introducing new variables to reflect the factors concerned.Additionally,the water quality of three situations and the number of species are obtained by tting different parameters when the system is stable.Further analysis on the two Aquaculture methods reveals Poly-culture is able to improve the water quality.
Finally,the nonlinear programming model is prented to obtain the optimal harvest for various situations under the constraint of the water quality.By the Genetic Algorithm the problem is solved with the most valuable harvest ($38697per pen),better than that of monoculture milkfish($31311per pen),at a best feeding intensity (0.6)and fishing intensity(0.6for Milkfish,0.3for shrimp,0.3for a urchin,0.6for oysters,0.8for aweed).
The population of the species and the water quality at the situation of the original ecosystem and the optimality harvest is listed as follows:
We suggest the Pacific Marine Fisheries Council should remediate Bolinao via poly-culture and scientific management,which are helpful to protect the environment as well as to yield better harvest.
Significantly,our model may be applied to predict the time for remediating water quality.DOC(uM)DTN(uM)Chl a(ug/L)POC(ug/L)PTN(ug/L)
Original ecosystem
707.50.2915020Optimality harvest 8312.10.3225331Algae
Echinoderms Crustaceans Herbivorous fish Predatory fish Molluscs Original
ecosystem
2×105314.28188522531140231287Optimality
harvest 1.8×105232
1392127501250038950爱国读后感
The Remediate Model for the
Commercial Polyculture Ecosystem
1Introduction
什么是真分数
Corals play an extraordinarily important role in biodiversity. Corals partition the space and allow species to conden and coexist; corals provide some amount of food for filter animals, which help clean the water. As the striking ratio contrast suggests: Less than 1% of the ocean is covered by coral. Yet, 25% of the ocean’s biodiversity is supported in the areas.
While corals have a critical requirement for water quality, it only lives in clean and poor nutrition water. Unluckily, with commercial fishing in an channel of Philippines recent years, the quantity of corals declined sharply. Thus, a lot of wild fish died, since their habitats—coral reefs are damaged.
叠的组词To our relief, poly-culture can rebalance the damaged marine ecosystem. Poly-culture can make full u of Trophic Levels. Our poly-culture system consists of long food chains which is the quence of who eats whom in a biological community.
y Primary energy source: sun.
y Primary producers: photosynthetic plants.
y Primary consumers or herbivores: they feed on plants.
y Secondary consumers: they eat primary consumers.
y Decompor: they eat mud and digest organic molecules of it.
So rearch on how they interact with each other, how their initial quantity impacts the finally equilibrium point is interesting and valuable.
2Restatement of the Problem
Now that viable poly-culture system is an strategy experts come up to solve the recycle and to improve water quality, it is necessary to device a system which is economically interesting and environmentally friendly both in the short and long run. Hence, we are appointed with veral scenarios under different assumptions, to analysis their property respectively in order to achieve optimal in economy and environment is urgent. For convenience of latter discussion, we list them orderly.
y Model the original Bolinao coral reef ecosystem before fish farm introduction.
y Model the current Bolinao monoculture milkfish. Under the cond scenarios, we are tasked to consider a situation when all the other animal species except milkfish are moved away from the system .Determine the term to keep our model in equilibrium. What water quality will get on?
y Model the remediation of Bolinao via poly-culture.
y Discuss the harvesting of each species for human consumption. And maximize
the net value.
y Maximize the value of the total harvests
3 Model design
In the ction, a food system model bad on the Logistic model, predator-prey model and competitive hunter model is propod to rebalance the human-influenced ecosystem. The detailed discussion consists of the following five subctions. Three basic models are introduced in ction 3.1. In ction 3.2, bad on the analysis of the interacting between the six species, an autonomous differential equation is prented to model the original Bolinao Coral Reef ecosystem without fishermen’s interference. We also discuss the steady state level of water quality. In ction 3.3, involving the human interference by means of giving fish food and fishing, we modify the differential equation to model the current bolinao monoculture milkfish and the remediation of bolinao via polyculture. The nonlinear programming model is prented to obtain the optimal harvest under the constraint of the water quality.
3.1 Basic Models
3.1.1 The Logistic Model
Logistic model which is also called limited growth model describes the population growth in a limited environment. Let be the population of a species living in an environment without native enemies or competitors of other species and a finite resource and space at time , it gives
()y t t ()()(1()dy t y t r dt N
=−y t (1.1) Where reprents the intrinsic growth rate of the species, which is the difference between normal reproduction rate and the mortality rate, stands for the maximum population of this species.
r N 3.1.2 A Predator-prey Model
Considering a space with two species, the relationship of the two species is predator-prey relationship. Assuming that the species C is a autotrophy and species D is a primary consumers. Let ()y t do d nate the population of C at time t , an ()x t tes the population of D at time t . In abnce of D, the growth rate of D is
dona
香料有哪些(())y p y t . If C doesn’t exist, D is decreasing, since there is no food. When introducing the other species in the system, the situation is changed. Let’s assume the increa of
乒乓球国家队名单
C during is t +(())y p y t minus a constant , which is related to the eating amount of D. The net growth population at time of
D increas. By assumption and analysis, the differential equations yield,
u ()()dy t p (())()()()()()y ()y t y t ax y t rx t bx t y t =−=−+t dt dx t dt
(1.2) 3.1.3 A competitive Hunter Model
船舶轮机
Let ()y t donate the population of A at time , and t ()x t donate the population of B at time . Suppo that when no competitor exits, the growth rate of species A and B is t (())x p x t ,(())y p y t respectively. The introduction of either species can decrea the other. We assume that the decrea rate is proportional to the total population of the other. Symbolically, we have
()(())()()()()(())()()()y x dy t p y t y t ax t y t dt dx t p x t x t t y t dt
=−=−bx (1.3) Where , donate the completive coefficient of B and A respectively. a b (())x p x t
reprents the practical growth rate of A and it’s the function of the population at time . It can be determined by growth pattern. t (())y p y t can be interpreted as the
same fashion of B.
3.2 The Original Model in abnce of human interference
3.2.1 Analysis of Task 1
In the first scenario, our ecosystem is constituted with six kinds of organisms: one predatory fish species, on into organics, mostly sugars .Herbivorous fish, crustaceans and echinoderms all prey on algae, so the relationship between two of them is
如懿传经典台词
competitive, and the relationship between them and algae is predator-prey. Predatory fish raven herbivorous fish. Outside the food chain, mollusks eat particles coming from the food leftover or dead body of organisms；Bacterium decompos all the carcass in the a.
Through the analysis above, we draw the tropic levels in a form of pyramid in Figure 1.
e particular herbivorous fish, one mollusk species, one crustacean species, one echinoderm species and one algae species. It’s esntial for us to analyze their relationship to establish function between them.
Algae are primary producers in our ecosystem; they make their food from sunlight using a process called photosynthesis. They turn the optical energy into chemical energy, and turn inorganic like water and carbon dioxide, nitrogen and phosphorus
Secondary
Consumer:
出国Milkfish
Primary Consumer:
Crustaceans,Ec
hinoderm,Herbi
vorous Fish
Primary Producer:
Algare
Figure 1 Food chain trophic levels
Relationship between the adjacent tophic levels is a predator-prey relationship.
The relationships between same levels are competitive if they compete for common food. Energies decrea with levels.
When sun and bacterium are included, we can draw a ecological recycle for this system as a supplement of Figure 1.
