It seems to me, that Alexa rating or perhaps other behavior pattern (click through rate) might be influencing SERP. I noticed a big drop in SERP after Alexa rating went up from 50k+ to 114k+ in one day. And the reverse have been true even through my traffic is relatively stable (I have a combination of PPC + search engine traffic) While I'd like to believe it's the backlinks that determinates the SERP, I think Alexa rating could be one of the 200+ ranking algorithm for Google SERP. I believe click through rate, amount of time stayed on site could also influence SERP from what I hear from other SEO. High bounce rate and low stay time = bad SERP compare to the day before. I am wondering, if people are interested in doing a bit of experiment, click on my first link in sig using the Alexa toolbar, stay on it for 30 seconds, and I will do the same for your site. I'd like to do this for a month, and plot the Alexa rating versus search volume and see if there is any correlation.
Alexa rating depends on traffic....so if alexa rating decreases SERP will also get affected......but If SEO is done superbly then without googd alexa rating ...SERP can be improved..
Alexa has no bearing on SERP. You could TECHNICALLY be #1 in google for the most competitive keyword with an alexa of 9,999,999
Alexa does not have any effect on organic search results. The info in Alexa is not even that accurate.