  We study the one-dimensional Bak-Sneppen model for the evolution of species
in an ecosystem. Of particular interest are the temporal fluctuations in the
fitness variables. We numerically compute the power spectral density and apply
the finite-size scaling method to get data collapse. A clear signature of
$1/f^{\alpha}$ noise with $\alpha\approx 1.2$ (long-time correlations) emerges
for both local and global (or average) fitness noises. The limiting value 0 or
2 for the spectral exponent corresponds to the no interaction or random
neighbors version model, respectively. The local power spectra are spatially
uncorrelated and also show an additional scaling $\sim 1/L$ in the frequency
regime $L^{-\lambda}\ll f\ll 1/2$, where $L$ is the linear extent of the
system.
