2019年美赛优秀论文--Dragon and Ecology

杨利霞

2019年美赛优秀论文--Dragon and Ecology

This paper analyzed dragon’s biological attributes, energy requirements and its interraction
with environment by stepwise modeling.
To study the relationship between dragon’s weight w and its age a, we apply Logistics model
after biological analysis. Then we use provided body mass data of dragon at different age, to fit
the weight-age curve. It was found that the dragon grew rapidly from age 3 to age 5, then almost
reached the maximum at age 8, and then grew slowly. The maximum body weight was about
14.8 × 105 kg.
Then we set a model to find the relationship between daily energy consumption q, daily caroles
intake u and age a of the dragon, according to Kleiber’s law (the relationship between the energy
consumption and body weight w is q ∝ w3/4) and the law of biological growth(consumption and
expenditure determines the weight increase). An adult dragon would eat around 4.8×106 kcal per
day.
Under different climate conditions, area required to support a dragon varies. To simplify,
we refer to the novel and we found dragons mostly eat sheep. So the food chain is herbage,
sheep, dragon. First we calculated how many sheep will 3 dragons eat per day, then we use
Malsus model to estimate the required sheep population. To analyze how mush area is required
to support sheep group, we set a Integral regression model to calculate herbage yield, and use
realworld temperature, rainfall, sunshine data to quantize it. In arid, temperate, arctic area,
about 3738hm2, 2383hm2, 4843hm2 of pasture is required respectively.
Providing different levels of assistance to dragons corresponds to various community size, we
defined 7 levels corresponding to 7 types of ecosystem. Using unit area biomass of them, we get
the community size. When it’s on level 5, dragon lives in temperate grassland, 3.81 × 107kg of
biomass is required.
An active dragon will affect surrounding ecosystem, we use species extinction speed, NPP(net
primary production) and biomass decrease to measure degradation of ecosystem. E.g. a grown
up dragon will wipe out a 20, 000 group of cattle in 103 days, also let a temperate evergreen
forest degrade to grassland, so the NPP will decrease 1.75 × 107 per year, biomass will decrease
8.35 × 108per year.
In practical, the model can be applied to analyze agribusiness problems, or invasive species.
This paper also analyzed the model’s sensitivity to dragon’s origin weight data , if it’s increased
by 3%, the calculated adult weight will change by 5.36%, its daily energy expenditure will change
by 8.98%, so the origin data has affect on model’s stability, but the result is still acceptable.
Keywords: Logicstics, Intake and Expenditure, Ecosystem Balance, Integral Regression