Ecosystem Simulator

Predator-Prey Population Dynamics

In any ecosystem, populations of species are linked through feeding relationships. Predators eat prey; prey eat plants. These links create time-delayed feedback loops that produce characteristic oscillating cycles � observed in real data from Canadian lynx and snowshoe hare populations (Hudson's Bay Company records, 1845�1935).

The classic Lotka-Volterra model captures these oscillations mathematically:

Where N = prey population, P = predator population, and a, �, d, ? are positive constants. Solutions are closed orbits in the (N, P) phase plane � populations oscillate indefinitely and out of phase: prey peak precedes predator peak.

Key Predictions of Lotka-Volterra

• Predator and prey populations oscillate with the same period, predators lagging prey by ~� cycle
• The average prey population equals ?/d regardless of initial conditions
• The average predator population equals a/� regardless of initial conditions
• Increasing prey growth rate (more food) paradoxically raises predator abundance, not prey

Carrying Capacity and Logistic Growth

Real populations cannot grow exponentially forever � environmental limits set a maximum sustainable population, the carrying capacity K. The logistic growth equation modifies the simple exponential model:

When N � K, growth is approximately exponential at rate r. As N approaches K, growth slows and stops. If N exceeds K (e.g. after an unusually productive breeding season), the population declines back toward K.

Biotic and Abiotic Factors

Biodiversity Indices

Biodiversity is more than just a count of species. It includes the evenness � how equally distributed individuals are among species. Two well-known metrics:

Shannon Diversity Index H

Where p? is the proportion of individuals belonging to species i. H ranges from 0 (one species only) to ln(S) (all S species equally abundant). Most natural communities score H = 1.5�3.5.

Simpson Diversity Index D

D ranges from 0 (no diversity) to 1 - 1/S (maximum). It is less sensitive to rare species than Shannon H.

Species richness S and evenness E

A community where all species have equal proportions has E = 1. When one species dominates (e.g. after an invasive introduction), E drops sharply � even if total richness S is unchanged.

Trophic Levels and Food Webs

Only ~10% of energy transfers between trophic levels (the 10% rule), explaining why apex predator populations are always orders of magnitude smaller than primary producers. The simulator reflects this: plant populations vastly outnumber predators.

Trophic Cascades

Removing or adding a top predator can cause cascading effects through the food web. Famous examples:

• Yellowstone wolves � wolf reintroduction (1995) controlled deer, allowing riverbank vegetation to recover, changing hydrology
• Sea otters � their removal allows sea urchin populations to explode, destroying kelp forests
• Dingo removal � in Australia, fence exclusion of dingoes caused kangaroo and rodent eruptions

Try setting Human Impact high in the Grassland preset � the fox/hawk collapse releases rabbit populations, which then overgraze the grass.

Invasive Species

Invasive species cause ~40% of all animal extinctions since 1500. They succeed because:

• No evolved predators in the new environment
• High reproductive rates (r-strategy)
• Generalist diet and tolerance of disturbed habitats
• Pre-adaptation to conditions in the new range

In the simulator's Invasive preset, the introduced rat (🐀) has a reproduction threshold of just 45 energy units versus 90 for deer. This allows it to multiply twice as fast, outcompeting deer for plant resources. Shannon diversity H will typically drop from ~1.5 to <0.8 within 1000 ticks.

Management Strategies

Curriculum Connections

Related Simulations & Articles