SimuVeda

Biology · Simulator 039

Food Web

A small grassland ecosystem: grass, rabbits, grasshoppers, mice, birds, snakes and hawks. Remove a species, add more of one, or change how fast the grass grows, and watch the effects spread up and down the food web, including some surprising indirect ones.

How the model works

Each species' population changes according to a generalised Lotka–Volterra model:

dNᵢ/dt = Nᵢ ( −d − cᵢNᵢ + e Σⱼ aᵢⱼ Nⱼ − Σₖ aₖᵢ Nₖ )

  • Grass grows logistically instead (rate r, capacity K). Animals die at base rate d when they have no food.
  • aᵢⱼ is how often eater i finds food j; a fraction e = 10% of what is eaten becomes new eater biomass (the classic trophic-transfer rule of thumb).
  • cᵢ is crowding within a species (competition for space and territory), which keeps the web stable.

Arrows point from food to eater (the direction energy flows). Effects travel both ways. Removing a predator lets its prey boom, which can then overgraze their own food (a trophic cascade). Two prey that share a predator can harm each other indirectly (apparent competition).

An illustrative seven-species model with made-up but plausible rates, starting at its balanced state and integrated with small Euler steps. Real ecosystems contain many more links, seasons and spatial structure.

Guided experiments

  1. Remove the hawks. Prediction: snakes and small birds increase; mice and grasshoppers, their prey, decline. The effect alternates down the chain.
  2. Drought. Halve grass growth. Prediction: grass and herbivores fall by about 40%, and the predators follow with a delay, ending even lower in proportion.
  3. Rabbit boom. Triple the rabbits. Prediction: crowding pulls rabbits back within a few time units. Meanwhile grass dips and hawks get a boost, so mice fall about 10%, though mice and rabbits never meet (apparent competition).

Challenge

Why do food chains rarely have more than four or five levels?

Reveal the explanation

Only about 10% of the energy at one level becomes biomass at the next. After four transfers, just 0.01% of the grass's energy reaches the top. There isn't enough to support another viable predator population. In the model, compare total biomass at each level in the readout.

References

  • OpenStax, Biology 2e, §46.1 “Ecology of Ecosystems” and §46.2 “Energy Flow through Ecosystems”.
  • Estes et al. (2011), “Trophic downgrading of planet Earth”, Science 333: 301–306.