An unusual goose resides at Elisha Smith’s farm in Oak Bluffs: a goose who thinks she is a cow.

In the normal world of farm animals, species stick together. The cows hang with the cows, the chickens move together in a wave across the field, and the geese fly into the barn and out together, as a flock.

In this case, one goose will have nothing to do with the other geese. This seven or eight-year-old Toulouse goose has identified herself in a manner quite unlike her kind. She hangs with the cows and shows particular affection for one of them.

“I have been farming since I was five years old,” said 85-year-old Mr. Smith. “I’ve never seen this before.”

The farmer has 15 geese, but this one is never with the flock. “I don’t name my animals,” Mr. Smith said, “my wife [Denise] names them.” She calls this bird Cow Goose.

The cow in question is named Momma’s Girl. Momma’s Girl is a black cross Angus and Hereford cow with a distinct white face.

Cow Goose and Momma’s Girl are a pair. The two are always together; they eat together, walk together. Cow Goose becomes agitated when a stranger approaches Momma’s Girl.

For those inclined to associate intelligence with an animal, it is pretty clear Cow Goose behaves as though she is the smarter of the two.

There is nothing subtle about their bond. On a recent afternoon, looking across an empty yard, the two animals could be seen close together, oblivious to the world around them. The goose is the talker.

Their presence is acceptable to all the other animals on the farm. And it is acceptable to Mr. and Mrs. Smith, though certainly a curious sight. “They are always together,” Mrs. Smith said.

Every day Cow Goose makes herself clear, she isn’t one of the fowl. When the geese show up at the barn for a meal, Cow Goose isn’t among them. When Mr. Smith feeds the cows, Cow Goose is there.

“My grandfather, George Smith, he used to let the pigs run with the cows, but I’ve never seen this,” Mr. Smith said.

Mr. Smith’s farming heritage goes back generations, and the soil under his feet is history, though there has been plenty of change in just the past 20 years. His small farm is located behind what was once known as Wind Farm and for a time was a golf practice range. Today, the property next door is a growing subdivision. The Smith farm is a fraction of what it once was.

Mr. Smith recalls when his grandfather tilled the soil and raised farm animals — pigs, cows, chickens, the list goes on. The soil is the Island’s sweetest, set at the head of Lagoon Pond, with stunning vistas. Cow Goose and Mama’s Girl couldn’t enjoy their friendship at a better place. The farm abuts the 42-acres of the Martha’s Vineyard Land Bank’s Weahtaqua Spring Preserve, the core of which is a tract of overgrown woodlands, once farmland.

The Smith family once worked this land on the edge of a rolling landscape, too, but that was long ago. “I remember seeing my grandfather go down the hill. He mowed hay,” Mr. Smith said. “He plowed it. I recall him planting potatoes.” Mr. Smith said his grandfather farmed land reaching all the way to the Tisbury town line, including parts of Norton farm.

Though the farm has shrunk, Mr. Smith still works the family land. “No, I am not retired,” Mr. Smith said. On eight acres, he has 100 chickens, 15 geese and 10 cows. He also oversees three farming sites Up-Island. “People who retire, they don’t hang around long,” he said, repeating, “I am not retired.”

Meal time for the cows at Mr. Smith’s farm is a big event, and Cow Goose wouldn’t miss it. Mr. Smith serves vegetables discarded from Cronig’s Market and bread from Black Dog Bakery. The meals are served in farmyard fashion, in empty ancient enamel bathtubs. When a stranger walks near the cows at mealtime, Cow Goose starts honking, expressing her singular opinion.

Mr. Smith said he raises the cows for beef. The geese are the barnyard doorbell. Few visitors arrive unannounced. “They are good watchdogs,” Mr. Smith said.

Geese generally aren’t social and friendly. Some time ago, Mr. Smith recalled when one of his geese acted out and was in need of an attitude adjustment. “I had one gander, it grabbed my great grandson Alex Flynn by the leg. I shooed him off.”

Later when a visitor came seeking a goose for dinner, Mr. Smith had no trouble figuring out which one to offer: “‘You see that one over there?’ I told him. ‘If you can catch him, you can have him.’”

Cow Goose’s position on the farm, however, is more secure. She walks across the yard as though she owns the place. She has established herself as the cow’s barnyard matron.