Species interactions – competition, predation, parasitism and mutualism (Lotka–Volterra)
BiologyEcology & EnvironmentAges 17–18
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Sign in to playTwo species with six switchable interactions: Lotka–Volterra competition dN₁/dt = r₁N₁(K₁ − N₁ − α₁₂N₂)/K₁, predator–prey, host–parasite, mutualism, commensalism and amensalism (allelopathy). Population graphs, a phase plane with zero-growth isoclines and equilibrium points, and a niche plot on a resource axis show competitive exclusion, coexistence through niche separation, and fundamental versus realised niches, with Gause's Paramecium experiment as the classic example.
Lesson: Community ecology: interactions between species (competition, predation, parasitism, mutualism, commensalism, amensalism); ecological niche
What it shows
Species in a community affect each other's population growth. In the Lotka–Volterra competition model each species grows logistically towards its carrying capacity K, and every individual of the other species counts as α individuals of its own. Where the zero-growth isoclines lie decides the outcome: one species excludes the other, both coexist, or the winner depends on the starting numbers. Overlapping niches on a resource axis give large α, so Gause's two Paramecium species could not coexist. Predation, parasitism, mutualism, commensalism and amensalism change the signs of the effects (+, − or 0).
How to use
Choose an Interaction and press Play. Compare solid curves (together) with dashed curves (each species alone). For competition, change K₁, K₂, α₁₂ and α₂₁ and watch where the isoclines cross in the phase plane; drag in the plane to choose a new starting point. Tick α from niche overlap and change Niche separation d. Gause's experiment loads the classic example.
Parameters you can change
- Interaction Competition (−/−), Predation (+/−), Parasitism (+/−), Mutualism (+/+), Commensalism (+/0), Amensalism – allelopathy (0/−)
- Growth rate r₁ of species 1 0.05–2 per day
- Carrying capacity K₁ of species 1 10–500
- Growth rate r₂ of species 2 0.05–2 per day
- Carrying capacity K₂ of species 2 10–500
- Coefficient α₁₂: effect of species 2 on species 1 0–2.5
- Coefficient α₂₁: effect of species 1 on species 2 0–2.5
- Calculate α from niche overlap
- Niche separation d (in niche widths) 0–4
- Attack rate a (predation, parasitism) 0.001–0.05 per individual per day
- Conversion efficiency e (prey → offspring) 0.05–1
- Death rate m of species 2 0.05–1 per day
- Starting population N₁ 1–500
- Starting population N₂ 1–500
- Time span 10–200 days
- Show Gause's data (approximate)
Questions to explore
- Which conditions on K₁, K₂, α₁₂ and α₂₁ let both competing species coexist?
- How far apart must the two niches be before the species can coexist?
- Why does the predator peak always come after the prey peak?
