Editing Long tail (section)

===Turnover within the long tail===
The long-tail distribution applies at a given point in time, but over time the relative popularity of the sales of the individual products will change.<ref>{{cite journal | doi = 10.1016/j.evolhumbehav.2006.10.002 | volume=28 | issue=3 | title=Regular rates of popular culture change reflect random copying | year=2007 | journal=Evolution and Human Behavior | pages=151–158 | last1 = Bentley | first1 = R. Alexander | last2 = Lipo | first2 = Carl P. | last3 = Herzog | first3 = Harold A. | last4 = Hahn | first4 = Matthew W.| citeseerx=10.1.1.411.7668 }}</ref>  Although the distribution of sales may appear to be similar over time, the positions of the individual items within it will vary. For example, new items constantly enter most fashion markets. A recent fashion-based model <ref>{{cite news|url=https://www.telegraph.co.uk/connected/main.jhtml?xml=/connected/2004/06/16/ecfpop16.xml&sSheet=/connected/2004/06/14/ixconn.html |archive-url=https://web.archive.org/web/20060223153629/http://www.telegraph.co.uk/connected/main.jhtml?xml=/connected/2004/06/16/ecfpop16.xml&sSheet=/connected/2004/06/14/ixconn.html |url-status=dead |archive-date=23 February 2006 |title=Why are they so popular? |first=Roger |last=Highfield |newspaper=The Daily Telegraph |date=16 June 2004 |access-date=25 December 2011}}</ref> of [[consumer choice]], which is capable of generating power law distributions of sales similar to those observed in practice,<ref>{{cite journal | last1 = Bentley | first1 = R.A. | last2 = Hahn | first2 = M.W. | last3 = Shennan | first3 = S.J. | year = 2007 | title = Random drift and culture change | url= | journal = Proceedings of the Royal Society | volume = 271 | issue = 1547| pages = 1443–50 | doi = 10.1098/rspb.2004.2746 | pmid = 15306315 | pmc = 1691747 }}</ref> takes into account turnover in the relative sales of a given set of items, as well as innovation, in the sense that entirely new items become offered for sale.

There may be an optimal inventory size, given the balance between sales and the cost of keeping up with the turnover.  An analysis based on this pure fashion model<ref>{{cite journal | arxiv=0808.1655 | doi=10.1016/j.physa.2008.11.009 | title=Physical space and long-tail markets | year=2009 | last1=Bentley | first1=R. Alexander | last2=Madsen | first2=Mark E. | last3=Ormerod | first3=Paul | journal=Physica A: Statistical Mechanics and Its Applications | volume=388 | issue=5 | pages=691–696 | bibcode=2009PhyA..388..691B }}</ref> indicates that, even for digital retailers, the optimal inventory may in many cases be less than the millions of items that they can potentially offer. In other words, by proceeding further and further into the long tail, sales may become so small that the marginal cost of tracking them in rank order, even at a digital scale, might be optimised well before a million titles, and certainly before infinite titles.  This model can provide further predictions into markets with long-tail distribution, such as the basis for a model for optimizing the number of each individual item ordered, given its current sales rank and the total number of different titles stocked.