Growth and Populations by Computer

Name: Growth and Populations by Computer
Author: StemPy Lab

Model a population step by step: exponential growth and doubling time, logistic growth with a carrying capacity, and fitting a growth curve to real counts.

3 lessons, about 1 h 30 min3 simulations10 problems3 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 30 min
Exponential growth step by step
A bacterium splits in two by fission, so a culture doubles again and again. A loop doubles the count step by step, the formula $N = N_0 \times 2^{t/T}$ jumps to any time, and a numpy array gives every count at once. On a log axis the growth is a straight line, and the doubling time follows from the growth rate.
1 simulation1 practice question3 Python programs4 problems
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Lesson 2about 30 min
Logistic growth and the carrying capacity
No population doubles for ever: food and space run short. Logistic growth slows the rate by the factor $1 - \dfrac{N}{K}$ , so the count follows an S-curve and levels off at the carrying capacity K. A loop steps the growth in small time steps; the step must be small, or the answer drifts from the exact curve.
1 simulation1 practice question2 Python programs3 problems1 Python lab
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Lesson 3about 30 min
Fitting growth curves to data
Real counts are scattered, so a model is fitted to them. For exponential growth, a straight line through $\ln N$ against $t$ gives the growth rate as its slope, and np.polyfit finds it. For logistic growth, scipy's curve_fit searches for the r and K that make the curve pass closest to the counts.
1 simulation1 practice question3 Python programs3 problems1 Python lab1 question set1 note
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Growth and Populations by Computer: Coding Test

10 questions · 20 min

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Growth and Populations by Computer

Course outline (3 lessons)

Exponential growth step by step

Logistic growth and the carrying capacity

Fitting growth curves to data

Test Your Learning

Your teacher

Discussion (0)