By 2020, Bitcoin will have the largest capitalization in the market, but will continue to lose dominance.
Even if by 2020 there won't be new global financial crisis, capital from countries with unstable currencies will continue to run into cryptocurrencies, and we have already seen how this happens (Argentina, Venezuela and Cyprus) China is also concerned about the risks associated with capital flight, and therefore “tightens the screws” with respect to cryptocurrencies.
Globally, nothing will change. Alts will not replace bitcoin