Actually population declined after USSR.
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That's technically true. However, the pop. growth rate declined throughout the history of the USSR.
http://en.wikipedia.org/wiki/Demographics_of_the_Soviet_UnionYou could say that the current dismal outlook just continued the trend. On the upside for any lovers of communism, it can at least be argued that, while communism may correlate well with poverty, backwardness, a lack of property rights, oppression (at least for those who dare say no to collectivism), and a complete lack of profit motive incentives, it does NOT appear to foment the severe demographic problems faced by (wait a minute...) all the socialist nations of the Eu.
Either way, I don't think it's causal since, by the mass, greater Islam doesn't exactly have a booming free enterprise system either (though it's less collectivized, in many cases, than the socialistic nations of the West) - and they're pumping 'em out at a rate sufficient to engulf Russia and Europe besides.
There are confounding factors at play, imj - the bulk of which are religious/cultural.