There has always been talk of the alpha male, but what of its female equivalent? Who is she, asks Clare Longrigg

Alastair Campbell's political obituaries contained many references to the alpha male, a description which, applied to humans, apparently denotes physical prowess, high achievement, bullying and sexual attraction. It is not an entirely flattering term, calling to mind the aggressive chest-beating of a silverback gorilla, but perfectly describes someone who bends others to his will.

But what of alpha female? Alexandra Shulman, editor of Vogue, wrote in a recent column that alpha female would never get lost on the North Circular, and would look good in a miniskirt. Is she, like Shirley Conran's Superwoman, all things to all people? Is alpha female someone we like, or admire? Does she even exist?

If we base alpha female on the male model, we will find her in the boardroom, impersonating his bullying and overriding ambition. Sexuality plays a big part in alpha male's success, and alpha female Margaret Thatcher was a tremendous flirt, who spent a lot of effort on her appearance. Anna Wintour, editor of US Vogue, is a classic example of alpha female, driven by insecurity and ruling by fear. She is aloof, inscrutable behind those dark glasses.

There are very few alpha females of this order, since most women have had the alpha-male qualities conditioned out of them and have been steered towards nurturing roles rather than world domination.

"Alpha female is pretty exceptional," says columnist Polly Toynbee. "There are not a whole lot of people trying to be like her, whereas there are a lot of men behaving in the same way, clambering over each other to reach the top of the tree. Those women who do get to the top are mavericks, hybrids and deny that they are like other women. Women do not like alpha female very much, nor do they want to be like her. Women want to be liked, which holds them back.

"Mrs Thatcher refused to have anything to do with the sisters. She always said, 'Don't ask me about being a woman.' Hers was the only cabinet with no other women in it."

There is no one in British politics today who could be described as alpha female: to most commentators they are not bruisers, but nannies. They are not frightening or domineering, and as a result, they will never make it to the top job.

In Hollywood films, any female character with alpha-male attributes is a monster. In The Last Seduction, Linda Fiorentino was clever, sexually voracious and heartless, a villainess for our time. In Fatal Attraction, Glenn Close refused to take abandonment in a submissive way. These were alpha anti-heroines, while in Alien, Sigourney Weaver combined courage with nurturing. As film producer Lizzie Francke points out, we have not seen alpha female in Hollywood for some years: today's action heroines, Lara Croft and the Terminatrix, are comic-book figures: "These action women are very sexualised, fetishised in leathers and tight body suits: it's boys' wet-dream material. We're not seeing career women in clicking heels any more. The difficult, truculent alpha female has been sexualised."

Beyond Hollywood, Sarah Dunant, writer and author of The Birth of Venus, sees alpha female as inhuman rather than superhuman. Her life is ordered by employees while she focuses on achievements and looking good. "Alpha female, like alpha male, depends on such a sense of innate superiority that she's probably not aware of her status. While she would be effortlessly talented and capable, she would need a reduced capacity for empathy, because otherwise it would derail her. If she has children, they only come out between 7-8pm, washed, dressed and brought up by someone else. I envisage the mind of Mary Warnock, the body of Kate Moss and the humanity of Leni Riefenstahl."

Achievement is the focus of alpha female's life; anything else is secondary. She does not obsess about relationships. She is dominant: if she married alpha male, there would be a bloodbath. Novelist Fay Weldon sees alpha female running corporations, paying little or no attention to the domestic sphere - which is where she differs from Superwoman: "Superwoman was everything man and woman wanted her to be: she did everything and was a good wife, earned a good salary and kept the carpets shampooed. Alpha woman wouldn't concern herself with housework: she would find someone else to whom she would delegate.

"We don't really like alpha woman very much, she's not a nurturer. She is not married - she's too focused to get married. She despises alpha males and they are terrified of her. She does have friends in the way the rich have friends, and flies them over to her parties. There are so few like her that it is a lonely life, but it may be worth it.

"Nicole Kidman might be more like alpha woman than anyone else: physically perfect, shrewd, intelligent, good at making money."

It may be that we are mistaken in looking for the qualities of alpha male in alpha female. Perhaps the model is entirely different, embodying the best female qualities rather than aping the male.

If we turn to nature for clues, we could look not at gorillas but elephants. Elephant society is a matriarchy, led by the biggest, strongest female, perceived as wise and kind - keeping the group together. This model of alpha female has different qualities from the male; she shares his leadership and strength, but also promotes community. She is a woman of substance, who combines physical potency with seriousness of purpose.

According to the elephantine model, motherhood is essential to alpha female's humanity: she is mature and connected. Even so, she is not hampered or compromised by motherhood in any way. Nobody would accuse her of juggling, or coping: she has staff.

Most people's images of alpha female conjure an impossible hybrid, a denatured thing. But are there alpha women who have not, as historian Professor Joanna Bourke puts it, become "men in drag"?

"I think there is a difference between alpha female and alpha male," says Bourke. "The women I would nominate have changed the world by their philosophy and writings, and they have made an impact by the way they live, or lived, their lives: Simone de Beauvoir, Virginia Woolf and Germaine Greer. In their sexual identity, in the way they constructed their domestic lives, they strove to be true to themselves. If they were confrontational, it was not for its own sake, but to say: 'This is what I am.' They acknowledge their own complexities. Alpha males do not go down that route."

"Alpha male is such a male concept," says Julia Peyton-Jones, director of the Serpentine Gallery. "It's not a term you would apply to women. Women can be as powerful as men, but to call them alpha females would be limiting. On the whole, women have to be more inventive and they have the skills to get what they want without being so crude about it."

Professor Susan Greenfield seems a candidate for alpha status: she is top of her field and still makes time to look good. She says alpha female would be in a minority, possibly the only woman in a group of men - something that, as a scientist, she knows a bit about. "She would be a leader, but not masculine in her virtues. Elizabeth I, my great heroine, was a leader, but not as a man might have been: she was feminine, stylish and very able."

Another nominee is the epitome of glorious womanhood: Dolly Parton. "She is a flawless image of womanhood who doesn't alienate other women," says writer and broadcaster Muriel Gray. "She is talented and financially powerful, she doesn't have children so she can't be a bad mother. And she is self-created. Couldn't be better."

Alpha male is driven by insecurity and fear: aware that there are many similar males climbing the ladder behind him, he clings to old-fashioned hierarchies. According to students of modern workplace culture, he may soon become redundant. This thesis was borne out by the sight of last year's Wall Street CEOs and over-promoted, hyperambitious dealers dragged before the courts. The charismatic chief executive has, it seems, become a thing of the past. We may be looking at a new generation of leaders who are consensus-builders, who don't lead from the front but push their teams forward, using traditional female skills such as listening. Whatever else he does, alpha male does not listen.

Did you hear that, Mr Campbell? Mr Campbell?