The authors of this paper repeatedly use the term "algebraic tail" when describing some of the distributions they observed:
...the probability of remaining in a small, spatially confined region for a time T is dominated by algebraically long tails that attenuate the superdiffusive spread...
Despite systematic deviations for short distances, all distributions show an algebraic tail with the same exponent $\beta \approx 0.6$, which confirms that the observed power-law is an intrinsic and universal property of dispersal.
Therefore, we conclude that the slow decay in $P_0(t)$ reflects the effect of an algebraic tail in the distribution of rests $\phi(t)$ between displacements.
I haven't been able to find a definition of this term anywhere else. Are they just using it as a synonym for "tail of a power law distribution", or are they referring to a particular subtype of power-law distribution, or something else entirely?
D. Brockmann et al., The scaling laws of human travel, Nature 439, 462 (2005).