One of those imaginary animals carries a twist in her tale. "Rita the Rat was a character originally written as a kind of hippy. I made her into a Jewish hippy, complete with Klezmer music."
Really? A Jewish rat?
"I was trying to turn the stereotype upside-down and stick it back at the anti semites!" Picker declares.
"Because of a deal Rita the Rat makes with Fantastic Mr Fox, the foxes are saved, so she's a heroine. But the Nazis used to caricature Jews as rats in cartoons, so her words very much fit with what she is speaking for me as a Jew. She talks about being hated and not understanding why; then she says: 'You're afraid of our intellect, you're afraid of our souls and your only goal is to revile us… "
Picker was born into an artistically-oriented New York Jewish family in 1954. His father wanted to be a writer, but earned his living preparing radio news scripts; his mother was a successful fashion designer, and a painter in her spare time. "My grandfather on my father's side came from Belarus and he was a cantor - he was said to have a very beautiful voice," Picker says.
"Growing up in that home gave me a view on life and culture that was very special. I was taught about great music and great art from the time I was a small child, and I used to love the smell of oil paint because it meant my mother was painting. I was taught about art and I listened to Beethoven and Brahms. And I think my father's interest in literature had a big impact on me. When I was commissioned by the Metropolitan Opera, the subject I chose was my father's favourite book, An American Tragedy by Theodor Dreiser."
There was one problem: Picker developed Tourette's Syndrome while he was still a child. This condition has often been misunderstood: "It is not about uncontrollable swearing" (a relatively rare manifestation of it that Picker does not have). Instead, he suffers literally thousands of uncontrollable physical tics every day.
There is no known medical cure. But extraordinarily, what does help is music. Picker featured in Oliver Sacks's book, Musicophilia, in a section exploring how Tourette's appears to leave its sufferers when they are concentrating on playing the piano, or composing.
"The piano was a solution for me when I was studying, playing and performing," Picker says. "I wanted to perform as much as possible because the Tourette's always left me when I was on the stage - I felt I had conquered it. But now it's composing that is the cure: when I'm writing music, I don't think I have any Tourette's. That's common to people with the syndrome: focusing on something can harness this energy into the activity. Actually composing is the cure for everything for me. I cannot be happy if I'm not writing music."
But does Tourette's affect the music that he writes? "It may be true that there's a 'Tourettic energy' that fuels my work to some degree," Picker suggests. "Sometimes my music strikes me as having Tourettic characteristics in its sometimes irrational changeability and sudden outbursts. But I don't believe that it's the most important thing."
Instead, he says he feels his music-making is powered by "ancestral energies - music being such an important part of life for the Jews".
He set his heart upon being a composer when he was only 15 and went on to study at the Manhattan School of Music, the Juilliard School and Princeton University.
Since then has written prolifically. The Wall Street Journal has called him 'our finest composer for the lyric stage'; his operas to date include the highly successful Emmeline (1996), Therese Raquin, based on Zola's novel, and An American Tragedy (2005).
But it would be a mistake to pigeon-hole him: 'I'm about to write my fifth opera, but at least 70 to 80 of my works are not operas," he stresses. "I'm just finishing a commission for a piano quintet. After the next opera I'm doing a concerto for orchestra for the National Symphony Orchestra and the conductor Christoph Eschenbach. ."
Picker describes his own music as "highly emotionally charged. I think there's an influence of Jewish music in everything I write. I don't feel I have a choice just as I don't have a choice about being Jewish."
This summer's British performances of Fantastic Mr Fox are part of a busy year for Picker. In August the Tanglewood Festival in Massachusetts features two of his works; in September another production of Fantastic Mr Fox is scheduled for Pittsburgh; and the premiere of his new piano quintet is due in October in Houston.
But though Picker has conquered considerable adversity to become one of the most sought-after of contemporary composers, he takes everything quietly in his stride. "I just continue doing what I do," he smiles.
