New York has gone to the dogs, but the rabbits and rhinos aren’t far behind in their assault.

With little fanfare, Gillie and Marc Schattner, married Australian artists, have marshaled their brash bronze menagerie up and down Avenue of the Americas from Greenwich Village to Rockefeller Center, along Astor Place and over to Downtown Brooklyn. Their anthropomorphic statues — genteel Weimaraners, ladylike hares and gymnastic wildlife — are leaving behind indelible pawprints in the duo’s covert conquest of New York sidewalks. And in the process, the Schattners have become the most prolific creators of public art in the city’s history, to the dismay of leading art historians.

“Nothing we’ve done has ever really been planned,” Mr. Schattner, 57, said during a December Skype call from their studio in Sydney. Improvisation is a running theme for the couple, who first met on a shoot in Hong Kong (Gillie was the model and Marc the creative director) before eloping to the foothills of Mount Everest for a Hindu marriage just seven days later, jilting their respective fiancés.

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Still, it’s a modest explanation for a pair who have received eight art commissions on the streets since 2016, half of them on public land. It’s an unprecedented pace for a city whose cultural programs come wrapped in streams of bureaucratic red tape. (It took Christo and Jeanne-Claude, by comparison, 30 years of efforts to win approval for “The Gates” in Central Park.) And in August, Gillie and Marc, as they are known, plan to unveil their most ambitious project yet, at Rockefeller Plaza: 10 “Statues for Equality” will depict powerful women, including Beyoncé and Angelina Jolie. The Schattners said that their project intends to highlight the gender gap in the city’s public statues, of which only 3 percent are of women.