I think there won't be any effect if Bitcoin has less than 50% of the total cryptocurrency "market cap".
The more interesting scenario is if an altcoin like ETH or LTC manages to get 50% of Bitcoin's market cap. That would transform it into a serious contender. In this case, all depends on the user base it is able to "steal" from Bitcoin's ecosystem.
If, for example, ETH manages to establish an efficient payment system (apart from its smart contract platform) that's really used, e.g. for eCommerce, then the argument that "altcoins aren't used for anything" or "altcoins are only a bubble" wouldn't hold anymore, and Bitcoin really will begin to face competition. Same for a LTC with Lightning or even sidechains (the barrier for sidechains is actually less relevant in altcoins).
BTC's marketdominance will go to 30%
And still it will moon bigtime, it will scale and AFTER ALL THAT, it will go mainstream.
Alts will get 70% marketshare, but they will be a lot more scatered than now, ETH and LTC's marketdominance will also decrease BIGTIME.
Crypto is just in the second marketphase, maturing.
Early adoptors : 2013-2016
Early majority : 2017-......
Late majority :...............
Lagards : +/- 2030 ?