The bicyclists come in rolling waves: speedy exercisers, slow meanderers or 13-deep packs of foreign-tongued tourists, heads craned in search of the Dakota or the towering San Remo.

Beside them in precarious proximity are the runners, streams of pounding feet that seem, on an unseasonably warm fall Sunday, to never let up. Nearby are the pedicabs and the scooters. The father learning to skateboard. Central Park, the beloved backyard for millions of New Yorkers, is a weekly recreational battlefield. “There’s no such thing as personal space here,” a horse-drawn carriage driver sagely warns his out-of-town fare as they trot alongside the bicycles and the bodies.

It is a story as old as the city: the cherished and overloved public space; the small routines transformed into pitched disputes among New Yorkers who take seriously every syllable of the old movie line: “Hey, I’m walking here!”

But the death of a 75-year-old Upper East Side jogger, Irving Schachter, in August, followed recently by that of a Connecticut woman, Jill Tarlov, 58, shocked even some longtime park users. Both were struck along what is, arguably, among the most crowded and contested roadways in the country.