2019年美赛优秀论文 Dragons and Ecosystem: 1 + n Meta-population Model

杨利霞

2019年美赛优秀论文 Dragons and Ecosystem: 1 + n Meta-population Model

Dragons are the virtual creatures in the fifictional television series Game of Thrones. It is
interesting and meaningful to consider what would happen if the three dragons were living
today. The purpose of this problem is to simulate the competition game when new species
are introduced into the ecosystem. And the result of the simulation can be used for reference
in the realistic situations.
Our paper propose the 1 + n Meta-population Model, where 1 refers to the Growth
Model Based on Energy Flow focus on the dragon’s growth and n refers to the Improved
n-population Meta-populaiton Model focus on the ecosystem.
We fifirst form the Growth Model Based on Energy Flow to represent the growth process
of dragons in the food chain. We calculate the energy expenditure using the Kleiber’s Law
and fifind the relationship between the energy intake and dragon’s mass based on the energy
flflow in the food chain. Referencing the animals similar to dragons, we set the upper bound
of dragon’s mass as 1.17 × 103kg and time-varying growth rates.
Then Improved n-population Meta-populaiton Model is generated to quantatively es
timate the dragons’ inflfluence on the populations in the ecosystem. Based on the Tilman
n-population Meta-population Model, we form the initial ecosystem including n kinds of
populations and then introduce dragons into it. We regard dragons as the interference in the
ecosystem. According to the amount and the abundance of living beings in the ecosystem,
we can analyze the inflfluence of dragons. Besides, we further take human beings’ recon
struction of environment into consideration, offering guidance for human beings.
After that, we apply our models to the different kinds of environments including temper
ate deciduous forest, desert and ice sheet. By calculating, we know that an adult dragon per
should take in 2.4 × 1011J energy per month and the region must be larger than 1.8 × 107m2
to support three dragons.
We then analyze the ecological response when dragons are introduced in the ecosystem,
which conforms to strong population extinction mechanism and Odd-even Symmetry Law.
In addition, we conduct sensitivity analysis about the area of the habitat and the time-lag.
Finally, we discuss strengths and weaknesses of our models.
Keywords: Energy Flow; n-population Meta-population Model; Growth Model; Habitat
occupancy Proportion; Ecosystem inflfluence