Asked about the qualities he’s seeking in the 49ers’ next head coach, CEO Jed York said he wanted a teacher who “understands how to get more out of less.”

And that helps explain why defensive line coach Jim Tomsula is a well-respected figure in the organization and a candidate to be the next head coach: Tomsula has specialized in extracting unexpected results from the unheralded during his eight seasons with the 49ers.

Consider these defensive linemen: Tony Jerod-Eddie (49ers), Ian Williams (49ers), Mike Purcell (49ers), Will Tukuafu (Seahawks) and Demarcus Dobbs (Seahawks).

The common thread? They are undrafted free agents who have NFL careers, which have mostly been spent being tutored by Tomsula. In addition, there is Colts defensive end Ricky Jean-Francois, a 2009 seventh-round pick who signed a four-year, $22 million contract with Indianapolis last year after he spent his first four seasons with Tomsula.

Jerod-Eddie, who arrived in 2012 and has four career starts, has credited Tomsula’s details-oriented teaching for his transformation.

“Jimmy is just on you about every little thing,” Jerod-Eddie said. “Now I appreciate him for it because I’ve come a long ways.”

All-Pro defensive lineman Justin Smith has termed Tomsula perhaps the best coach he’s had in his 14-year career. And Jim Harbaugh made it clear last year why Tomsula is the longest-tenured member of the 49ers’ staff. He’s the only coach to work for Mike Nolan, Mike Singletary and Harbaugh, who didn’t hesitate to retain him.

“It was a very easy decision after speaking with him,” Harbaugh said. “He’s had a special gift of presence, personality, of teaching ability and that came shining through. I remember that first meeting. And that’s one position I’ve just never had to worry about since I’ve been here as the head coach.”

It’s not known if Tomsula has already interviewed for the 49ers’ opening. Last year, he interviewed for the Vikings’ position that went to Bengals defensive coordinator Mike Zimmer, but his current candidacy comes with question marks.

Tomsula had a one-game stint as the 49ers’ interim coach during the 2010 season but has never been an NFL coordinator. Beyond a host of outside candidates, he also faces in-house competition from defensive coordinator Vic Fangio, who interviewed Tuesday and is expected to leave if he’s passed over for Tomsula. The obvious question: Why would the 49ers prefer Tomsula over Fangio, who is above him on the totem pole and has 15 seasons of experience as an NFL coordinator?

Unlike Fangio, Tomsula, 46, does have head-coaching experience: In addition to his interim gig, he became NFL Europe’s youngest head coach when he led the Rhein Fire in 2006.

He drew rave reviews for his one-week interim job with the 49ers, partly because of his self-deprecating humor. He termed himself a “little fat guy,” “Jim Nobody from Nowhere” and said he was grateful the players put up with him: “Nobody put me in a garbage can.”

He came across as a blue-collar everyman, a man of the people who probably wasn’t the man to lead an NFL team on full-time basis. His players, however, blew his cover, noting he was doing plenty of teaching to a 5-10 team that beat Arizona, 38-7, with him in charge.

“(The season) was defined by mental mistakes,” Jean Francois said after the 2010 finale. “Not being prepared for certain situations. When situations happened, I felt like we weren’t prepared for that moment and it slipped out of our hands.

“This week of practice, with Tomsula, it was like we were preparing for every situation: four minutes, two minutes. What happens when it’s 3rd-and-1? What happens when we’re backed up in the end zone? He worked on every different situation so that when we got in the game it didn’t feel brand new.”

In the moments after that game, Tomsula was asked if he was still, technically, the 49ers’ coach.

“I just finished,” he said, laughing. “There’s a search.”

Three years later, there’s another search. This time, Tomsula is in the midst of it.

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Niners offensive coordinator Greg Roman interviewed for the same position with the Buccaneers today in Los Angeles, FOX Sports reported.

Tampa Bay, which has the No. 1 pick in the draft, was in Los Angeles for Thursday night’s Rose Bowl, presumably to scout Oregon quarterback Marcus Mariota and Florida State’s Jameis Winston.

Roman, of course, isn’t expected to remain with the 49ers after he came under fire this season. The 49ers ranked 20th in the NFL in total yards, 25th in points and scored just two offensive touchdowns in the fourth quarter.

Before joining the 49ers in 2011, Roman spent two seasons with Jim Harbaugh at Stanford, which was his only college job since 1993. His NFL-heavy background could explain why it doesn’t appear he’ll follow Harbaugh to Michigan.

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Niners co-offensive line coach Reggie Davis has been hired as Nebraska’s running backs coach, Rivals.com reported. Davis, who played with Jim Harbaugh with the Chargers, shared offensive line duties with Mike Solari after spending the previous three seasons as tight ends coach.