But heavy rains in Texas — the No. 2 pecan producing state behind Georgia — are taking their toll. Nationally, as many as 350 million in-shell pounds of pecans are consumed each year.

Big Valley Pecan Farm in San Saba County, with an asking price of $25 million, belongs to the third-generation heirs of one O.P. Leonard, who was born in northeast Texas at the tail end of the ...