Do you think the recent spate of big deals is a harbinger of an M&A wave?

We had a nuclear winter for about five years after the financial crisis, and it was like nothing I’ve ever seen. But we’re now seeing the return of LBOs and strategic acquisitions.

One of the things that investors like is that Trian can act as a balance to the LBO activity. A successful private equity deal transfers a great amount of wealth from the long-standing shareholders to a private equity firm and its investors. Many of the things that private equity does could be accomplished in the public market in order to unlock value. We like collaborating with management and boards of companies to make this happen for the benefit of all shareholders.

You’ve had success investing in retail. What should investors look for?

One of the most important things is to determine early whether the Internet will turn a particular business into a dinosaur. If a company sells burgers, the Internet probably won’t have an impact. But if it’s selling books or certain other consumer goods, there could be a problem. I’m not sure what the plan is for Amazon. It sells things at virtually no margin, and yet the market pays a handsome multiple for the stock, but it’s certainly hurting a lot of traditional retailers in the process.

Are there any retail stocks you like?

We like Family Dollar. One of my partners, Ed Garden, is on the board. It is a defensive story with a lot of room for growth yet trades at a low multiple of cash flow and earnings. The stores cater to a certain consumer who is clearly at the lower end of the economic spectrum but is very loyal and whose shopping patterns probably won’t be disrupted by online retail. The company is also a play on convenience, which is where we believe the world is moving. When consumers run short of a staple, like milk or paper towels, they don’t want to have to walk through a massive parking lot and a store the size of a football field to find the one or two items they need. They want to go down the block to the neighborhood Family Dollar.

Do you have particular red flags?

We typically avoid family-controlled companies because those shareholders might have a certain uneconomic affection for the business as opposed to being willing to maximize value for all shareholders. We also won’t invest in companies with super voting stock.

Should investors pay attention to high-profile activist battles with boards or with other activists?

Some of those battles are interesting and fun to watch. But you don’t necessarily want to make investment decisions based on them. When you listen to what an activist is saying, ask if it’s logical. Does the solution offered make good common sense? If you owned 100% of that company — if your entire net worth was tied up in it — would you do what the activist is suggesting? If you agree, then buy the stock. If you don’t, move on.

You’re also an investor in the mutual fund company Legg Mason, and you’ve driven lots of changes there.

We’re very proud of the recent changes at Legg Mason. I am thrilled — and I don’t use that word lightly — to have Joe Sullivan as the new CEO. He was the No. 1 choice of the board, the search committee, and the company’s affiliates. I think shareholders are starting to realize that Legg Mason is changing, and for the better. You can already see it in the stock price.

What trends do you see in asset management?

We believe there’ll be further consolidation in the asset-management industry. It’s sort of like the food industry. When the distributors or retailers, like Kroger or Wal-Mart, get bigger, the manufacturers also must get bigger. The Merrill Lynches and Morgan Stanleys of the world have consolidated and grown, so therefore their suppliers must get bigger as well. There are lots of duplicate costs to be taken out of the money-management industry, and the firms that consolidate will get stronger and much more profitable.

This story is from the April 29, 2013 issue of Fortune.