Since he took office as District Eight supervisor in July, the single biggest concern driving constituents to call Rafael Mandelman’s office is homelessness.

The runner-up? San Francisco’s nascent tree-trimming program.

For just over a year, the Public Works Department has been dispatching arborists and tree-trimming crews across San Francisco to care for the roughly 125,000 trees that make up the city’s urban forest.

It’s the first wave of work stemming from 2016’s Proposition E, a ballot measure that shifted the responsibility of caring for all street trees in the public right of way to the city. The measure, which passed with 79 percent of the vote, swept aside the widely unpopular and often confusing practice of having property owners care for most of the city’s trees.

But the rollout of the new maintenance program has raised questions and concerns from residents in Mandelman’s district, which includes the Castro, Noe Valley and Glen Park.

“I think there is a lot of confusion and some anxiety from folks,” Mandelman said. “We hear both sides of the spectrum.”

Some people want answers about why a particular tree was removed, or when the city will tend to the trees outside their buildings. Others want to know whether they can opt out of the program and continue caring for their own trees, as in the past.

That’s why he plans to hold a hearing on the program — to give Public Works and its arborists the chance to explain the city’s long-term tree-trimming plan and answer questions, like how property owners can request to continue caring for trees themselves.

“The Bureau of Urban Forestry has just rolled it out this year, so there are going to be a lot of growing pains,” Mandelman said. “This is a massive new project for the city to be taking on, and it seemed like a good moment to just provide the (Public Works) department and the bureau an opportunity to talk about what they’ve been doing.”

Mandelman said he hopes to have the hearing “in the next month or two.”

Rachel Gordon, a spokeswoman for Public Works, said the agency welcomed the hearing on its street-tree initiative.

“Our goal is to make sure that property owners and residents are aware of the Street Tree SF program, its benefits and its rollout,” she said.

Prop. E set aside $19 million a year for Public Works’ Bureau of Urban Forestry to expand its tree-maintenance programs and hire more contractors and in-house personnel. As they prune gangly limbs and remove dead trees, Public Works crews are also smoothing out sidewalks buckled by belligerent roots.

Much of Street Tree SF is informed by a recently completed census of the city’s urban forest. The census, which took stock of every street tree and its condition, revealed 500 tree species and nearly 40,000 vacant locations where new trees could be planted. The final tally of just under 125,000 trees was 20,000 more than previously estimated.

The tree census also helped the city create several publicly available tools, including an online map showing the location, size and species of every street tree, and details like how much storm water it’s filtered, the volume of carbon dioxide it’s filtered from the air and whether it’s caused any sidewalk damage.

A second map organizes San Francisco into city blocks and assigns dates for when Public Works plans to service the trees on those blocks. Residents can enter their home address to get a sense of when crews will be headed their way. The map is updated regularly, but most of the city is on track to have its trees trimmed between 2020 and 2022.

Carla Short, superintendent of the Bureau of Urban Forestry, asked for the public’s patience as crews work through the initial rounds of pruning to get the city’s trees to a “baseline condition.” After that, subsequent rounds of maintenance should happen faster, especially as Public Works hires more in-house crews and contractors.

After having property owners care for street trees for so many years, “there’s been a lot of deferred maintenance both by the city and by property owners for lots of different reasons,” Short said. “We expect that this first round of pruning will be more time consuming than subsequent rounds.”

After examining the condition of each tree for the census, arborists prioritized the “worst first” — city blocks with clusters of trees in need of immediate attention. Dead trees, sick ones in a fatal decline and trees with serious structural flaws were given top priority, followed by trees with limbs that might be covering a streetlight or dangling over a roadway.

For efficiency and cost-savings, Short said that crews gravitate to the worst trees first and then prune the rest of the block.

“When you’re spreading out that $19 million over thousands of trees and sidewalk repairs ... we need to gain the efficiency of pruning the whole block when we’re in a certain area,” Short said.

Beyond learning more about how the city is pruning its trees, Mandelman wants to learn “how to get more trees into the city,” he said.

“How do we grow the canopy, rather than just maintain the canopy we have? Trees are so important to many neighborhoods,” he said. “They can really transform a block, and their absence can really transform a block.”

Dominic Fracassa is a San Francisco Chronicle staff writer. Email: dfracassa@sfchronicle.com Twitter: @dominicfracassa