According to Native American culture, white buffaloes are considered to be sacred signs of spiritual importance. That association most likely had to do with their rarity; the National Bison Association estimates that only one out of every 10 million buffalo are born white.

But very little is known about their polar opposites on the color spectrum: the black buffalo.

Pat Jamieson, the outdoor recreation planner for the National Bison Range Wildlife Refuge in Moiese, Montana, said that is most likely due to the fact that black buffaloes are even rarer than their albino-looking counterparts.

And Eva Fearn of the Wildlife Conservation Society Institute at the Bronx Zoo explained that black buffalo are so unusual that there are no tangible statistics that document their birth rate. Referencing the “Guide to North American Mammals,” which includes detailed descriptions of more than 400 native species, Ms. Fearn said, “there is no mention at all of buffalo born black.”

So, it is easy to imagine Edwin Tuccio’s surprise when, a few weeks ago, he discovered that two black bison were born on his 250-acre North Quarter Farm in Riverhead.

“With my experience in the bison industry, I know how rare black buffalo are,” Mr. Tuccio said. “Being the only bison farmer on Long Island, I knew that to have not only one, but two black buffalo makes us unique,” Mr. Tuccio said.

Mr. Tuccio, who owns five buffalo farms on the North Fork, sits on the board of the National Bison Foundation, an organization that is dedicated to ensuring the future of these majestic mammals. Mr. Tuccio also owns Tweed’s Restaurant and Buffalo Bar on Main Street in Riverhead and he is now holding a contest in which he is seeking the public’s input to help name these unusual offspring. As of right now, neither mammal has a name.

The two people who come up with the most unique names will each receive a $50 gift certificate to Mr. Tuccio’s restaurant, where they will be able to taste buffalo meat, which is billed as a healthy alternative to red meat. Those interested in participating in the contest should call the restaurant at 208-3151 prior to Monday, July 6.

Mr. Tuccio has been raising bison for more than 25 years and, according to him, there has been only one other time that a black bison was born on one of his farms. He said that birth occurred several years ago.

Though there is no concrete way to be certain, Mr. Tuccio thinks that the same bull is responsible for the two latest additions to his bison family. “I only have a few bulls on my farm to prevent them from fighting over the females during mating season,” he said, “so it is highly possible that one of them has the genetic make up to create a baby black buffalo.”

Many experts believe that black bison are most likely a genealogical phenomenon.

“These [black] calves have something called melanism, which is the opposite of albinism.” Ms. Jamieson said. “In albinism, there is no pigment formed, which creates the white color. In melanism, there is a high concentration of melanin, which produces the dark coloration of the fur.”

Another possible explanation can be traced back to the early 1900s, when private ranchers began cross-breeding bison with cattle, the latter of which are typically black in color.

“Bison were on the brink of extinction at this time,” Ms. Fearn said. “Around the same time, farmers would cross-breed them with domesticated livestock to create a heartier animal that could withstand winters.”

In spite of their unusual coloring, the two black calves will be raised in the same conditions as their lighter herd mates. Mr. Tuccio explained that his buffalo typically spend between 18 and 30 months on his farm, at which time they are sold to wholesalers and restaurants across Long Island.

He explained that buffalo meat is in high demand because it contains a fraction of the fat contained in red meat, and about half the cholesterol that comes with comparable portions of fish and meat. Due to its leanness, bison meat can be enjoyed even by those with meat allergies, he said.

“People are allergic to beef because they can’t digest fat,” Mr. Tuccio said. “But bison meat has very little fat.”

He added that his two black calves might not end up between a sesame seed bun, or accompanied by a side order of spinach or roasted potatoes. After naming them, Mr. Tuccio said will consider selling his two black buffalo to researchers interested in trying to solve the mystery of their origin.