Crude periodicity finding

Discover the periods in evolution of animal populations (../../../../data/populations.txt)

Load the data

import numpy as np
data = np.loadtxt('../../../../data/populations.txt')
years = data[:, 0]
populations = data[:, 1:]

Plot the data

import matplotlib.pyplot as plt
plt.figure()
plt.plot(years, populations * 1e-3)
plt.xlabel('Year')
plt.ylabel(r'Population number ($\cdot10^3$)')
plt.legend(['hare', 'lynx', 'carrot'], loc=1)

<matplotlib.legend.Legend object at 0x7fe7b09f2af0>

Plot its periods

import scipy as sp

ft_populations = sp.fftpack.fft(populations, axis=0)
frequencies = sp.fftpack.fftfreq(populations.shape[0], years[1] - years[0])
periods = 1 / frequencies

plt.figure()
plt.plot(periods, abs(ft_populations) * 1e-3, 'o')
plt.xlim(0, 22)
plt.xlabel('Period')
plt.ylabel(r'Power ($\cdot10^3$)')

plt.show()

/opt/build/repo/intro/scipy/examples/solutions/plot_periodicity_finder.py:37: RuntimeWarning: divide by zero encountered in divide
  periods = 1 / frequencies

There’s probably a period of around 10 years (obvious from the plot), but for this crude a method, there’s not enough data to say much more.