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Population Ecology & Demography Lab

Investigate how populations grow, compete, and respond to harvesting pressure. Compare exponential and logistic growth models, explore predator-prey oscillations with the Lotka-Volterra equations, and discover the maximum sustainable yield.

Guided Experiment: Exponential vs Logistic Growth

What happens to a population when resources are unlimited compared to when they are limited? At what population size does logistic growth slow down the most?

Write your hypothesis in the Lab Report panel, then click Next.

Controls

Initial Population (N₀)20
Time Span (tMax)50
Growth Rate (r)0.50
Carrying Capacity (K)500
Harvest Rate (h)0.00

Results

Run the simulation to see results.

N(t) Time Series

Growth Rate dN/dt vs N

Data Table

(0 rows)
#TrialTime(t)Population NdN/dtN/K Ratio
0 / 500
0 / 500
0 / 500

Reference Guide

Exponential Growth

With unlimited resources, populations grow exponentially. Each individual reproduces at a constant rate r.

N(t)=N0ertN(t) = N_0 e^{rt}

The population doubles every td=ln⁡2rt_d = \frac{\ln 2}{r} time units. Growth accelerates without bound.

Logistic Growth

Real populations face resource limits. Growth slows as population N approaches carrying capacity K.

N(t)=K1+(K−N0N0)e−rtN(t) = \frac{K}{1 + \left(\frac{K - N_0}{N_0}\right) e^{-rt}}

The growth rate peaks at N = K/2 (the inflection point). The S-shaped curve levels off at K.

Lotka-Volterra Predator-Prey

Predators and prey populations are coupled. Prey grow, predators eat prey and reproduce, then decline when prey is scarce.

dNdt=αN−βNPdPdt=δNP−γP\frac{dN}{dt} = \alpha N - \beta NP \quad \frac{dP}{dt} = \delta NP - \gamma P

Both populations oscillate with the predator peak lagging behind the prey peak.

Sustainable Harvest

Harvesting a fixed proportion h from a logistic population changes the equilibrium. The population can sustain harvest only if h < r.

MSY=rK4at N=K2\text{MSY} = \frac{rK}{4} \quad \text{at } N = \frac{K}{2}

Maximum Sustainable Yield (MSY) is the largest harvest a population can sustain indefinitely, occurring when the population is at half the carrying capacity.