It wasn’t much of a trail that led me there, just a U-shaped detour at the corner of East Rock and Livingston that pierced the perimeter of the park. It was only about a hundred yards from end to end, but I couldn’t have known that when I decided to explore it. The bright sign forbidding all traffic but foot traffic piqued my interest.

There wasn’t anyone around and I was determined to find in the New Haven area some proof of migratory birds, the kind I have hunted with my father and brother since I was young. This spot has as much a chance as any, I thought.

I discovered that the short path briefly meets the west bank of the Mill River, which isn’t much of a river downstream from Lake Whitney and its dam. It wanders weakly under East Rock on its way out to the Sound. As I wound my way around, too, on my bike, I noticed through the foliage a large white form moving skillfully in the shallows.

Stopping my bike slowly and leaving it on the trail, I made my way carefully down the steep dirt embankment toward the water. The form became a swan, and I saw another adult and three muddled cygnets not far upstream. They were no more than 40 feet away and casually making their way in my direction, stopping here and there to feed indiscriminately on the grassy bottom.

From the deep orange and black bills of the adult pair — swan mate for life — I determined them to be Mute Swan. Their weak banter confirmed this, a stark contrast to the guttural human moans of their Whistling cousins. I remember winter nights on duck-hunting trips when Whistlers made sleep almost impossible. I always knew the alarming cries of hundreds out over the river to be a raft of them, restless. But their call is so cheerless and so human that, when heard in numbers it’s impossible to separate from a sense of unfolding tragedy.

Whistling swan are cagey migrating birds. At times, they’re downright mean. They travel great distances south to winter in the mid-Atlantic, and when they get here they are in not much in the mood for encounters with humans.

The mutes I stumbled on, however, most likely had never left New Haven. Mutes are rather lazy and tame, and the stagnant water of the dam outlet left his brood a feast of the underwater vegetation they like.

Even when they noticed my presence — they all looked at once for no particular reason I could perceive — they did not shy. I believe if I had offered corn or breadcrumbs, the whole family would have eaten from my hand.

I sat on the bank and watched for 15 minutes as they groomed themselves and bobbed nearby for food among the lily pads. Occasionally, they watched me back. I had rarely encountered swan at such close range, and had never seen them so amiable.

A mild morning last October, on a kayaking excursion on Squibnocket Pond on Martha’s Vineyard, my aunt, uncle and I encountered a large raft of Whistlers on a layover from the north. At about 50 yards, we spooked them and they took off together, running across the surface collectively like a seaplane going airborne. My uncle, a news photographer, snapped a few pictures through a telephoto and I have one on my wall. His lens allowed me to pretend we’d been closer than we actually were.

Another time — the only other time — I watched a Whistler struggle hopelessly just feet above the racing traffic of Route 50 on the Eastern Shore of Maryland. It hadn’t allowed enough water to take off from a cove just feet from the shoulder, and the cars stole precious air it needed for lift. I was long-gone west before it came down, but I knew its fate.

That September Saturday, though, it wasn’t migratory birds I met. Those Mutes had been residents of New Haven far longer than me, and they knew I knew it. I suspect that’s why they gave me one last collective glance before turning to slip away back upstream.