Populations and biodiversity
Growth models and diversity indices.
Population dynamics. Change in population size :
Exponential growth. With unlimited resources, populations grow at a constant per-capita rate :
Logistic growth. Most realistic β growth slows as carrying capacity is approached:
The curve is S-shaped: rapid growth at first, then plateau at .
Carrying capacity (K) = maximum sustainable population size. Set by limiting factors: food, water, space, predation, disease.
Biodiversity measures.
Species richness = number of species in a community.
Species evenness = how evenly individuals are distributed among species. A community of 100 cows + 1 chicken has lower evenness than 50 cows + 51 chickens.
Simpson's diversity index:
where = number of each species, = total individuals. Ranges 0 (no diversity) to 1 (very diverse).
Worked example. A meadow has 20 dandelions and 30 buttercups. . .
- Exponential growth: unlimited resources.
- Logistic growth: slows as .
- Simpson's index: 1 β .