Life Sciences · Ecology · Evolution · Research / Principles and Exploration
Predator–prey dynamics — principles and investigation
As the number of prey increases, the number of predators may also increase, but the change does not occur at the same moment. Change the initial number of rabbits and foxes and the conditions for growth, predation, and death, and compare the time differences between the two curves. It is a predator-prey model that reads a time graph and a graph depicting the relationship between two populations.
How does it work?
As prey increases, predators follow suit, and as predation pressure increases, prey decreases. Outside of equilibrium, it moves in a closed orbit.
dx/dt=αx−βxy · dy/dt=δxy−γy
Try this investigation
- The rabbit and fox icons in the grassland increase and decrease depending on the population. The numbers below are continuous values and the icons are bundles.
- Run for 90 model hours and record the average time difference between the two-hour curve/phase plane and the rabbit maximum followed by the fox maximum.
- Change the predation rate and fox mortality rate one by one and compare the equilibrium point and time lag. The fox conversion coefficient δ=0.02 is fixed.
Interpreting your results
What is the equilibrium point at which the two populations remain unchanged?
dx/dt=x(α−βy), dy/dt=y(δx−γ). The positive equilibrium where both are 0 is x*=γ/δ, y*=α/β.
Assumptions and limitations
It is a Lotka-Volterra model with a closed population without immigration or exodus, unlimited food resources, uniform encounters, and constant coefficients. RK4 spacing is 1/60 model time. We omit the environmental carrying capacity, diseases, seasons, shelter, and contingencies of the actual ecosystem. One icon is approximately 2 items, and a maximum of 90 can be drawn. The time difference is averaged only for the completed maximum value pairs, and if there are no pairs in the interval, it is displayed as unmeasured.