Giving to the nation’s biggest and most popular charities grew by nearly 11 percent last year, fueled largely by affluent donors, who are reordering the top ranks of America’s nonprofits, according to The Chronicle of Philanthropy’s annual rankings of the 400 charities that collect the most from private sources.

The rankings demonstrate a shake-up in the nonprofit world as groups that raise money primarily from the affluent see their donations soar.

Four of the 10 charities that appear at the top of The Chronicle’s Philanthropy 400 are organizations that raise money mostly from the wealthy by offering donor-advised funds, including Fidelity Charitable (No. 2), which is less than $200-million shy of ousting United Way Worldwide from the top of the list. That’s an unusual accomplishment for a nonprofit only 23 years old.

At No. 8 is the Silicon Valley Community Foundation, which has raised $1.5-billion from Mark Zuckerberg and his wife, Priscilla Chan, in the past two years.

Rounding out the top 10 are: the Salvation Army (No.3), Schwab Charitable (No.4) Feeding America (No. 5), Task Force for Global Health (No. 6), Catholic Charities USA (No. 7), American Red Cross (No. 9), and Vanguard Charitable Endowment Program (No. 10).

Those groups are displacing nonprofits that were once mainstays at the top of the list, like the American Cancer Society, which was No. 7 in 2010 and is now No. 16. Also losing ground are organizations that focus primarily on serving the needy abroad, like the AmeriCares Foundation, which was No. 3 in 2010 and now is No. 25, and World Vision, which was No. 8 five years ago and is now No. 26.

Stock-Market Influence

The 30-percent gain in the stock market was a key reason donors gave so generously last year. The increase for the 330 groups on the 400 for whom comparable data are available amounts to a 9.3 percent gain after inflation. That came on top of a 4-percent increase in giving in 2012.

The results were far stronger than those of smaller groups. The total gain in giving to all causes last year was 4.4 percent, or 3 percent after inflation, according to “Giving USA.”

And looking ahead to the crucial year-end giving season, confidence in the fundraising climate appears to be rising: Thirty-five organizations in the survey that provided or estimated fundraising returns through the end of 2014 expect giving to rise 6.9 percent.

An unusual circumstance catapulted one group that is not normally in the top fundraising ranks high on the 400.

The National Academy of Sciences received $500-million as part of a settlement over the BP oil spill and placed No. 27, with a nearly 1,000-percent increase in gifts.

The National Fish and Wildlife Foundation, which is getting $2.5-billion from BP over five years, is likely to make a similar leap in coming years. It now ranks No. 248.

The most stunning changes were those achieved by the groups that offer donor-advised funds, which outstripped the percentage gains of nonprofits like United Way and the Salvation Army that depend largely on middle-class donors.

Schwab Charitable Fund increased donations by 165 percent, to nearly $1.9-billion. It, too, is a new organization, created in 1999. And Vanguard Charitable Endowment Program grew by nearly 19 percent. It was founded in 1997.

The Chronicle’s rankings count only those donations that come from individuals, companies, and foundations; it does not count money raised abroad or from governments.

The Philanthropy 400 was compiled by Mary Bowerman, Sandhya Kambhampati, Lance Lambert, and Anu Narayanswamy.