I don't suppose you mean by rising in "price" only - because that has already proven itself to be true - all the coin markets fluctuate and at certain times, some markets will outperform bitcoin.
However in the long run, I still do not see any existing altcoin "taking over" Bitcoin in a sense of being the #1 cryptocurrency in the world in terms of security, usage, and network value (not just market capitalization). Sure we'll run into problems like today's scaling debate and BU vs CORE drama going on; but the Bitcoin network has been time- and battle-tested, and will survive many more attacks to come.
My opinion is that Bitcoin is here to stay. Altcoins with great tech, leaders, and community will rise up, not to compete with BTC, but to exist alongside BTC in a bid to pursue their own unique vision by their own principles.