MANY WRITERS of fiction feel that if you are really to know somebody, know the characters in your book, you must track them back the Biblical four generations. Whether you tell the whole story or not you know who are those antecedent people. In Dinner at the Homesick Restaurant Anne Tyler tells the generational story.

Dinner at the Homesick Restaurant begins with the dying of old Pearl Cody Tull and reflects backwards through the 80 years that span the American century. There is a glimpse of her beginnings in some girlish diaries whose entries are almost entirely on the order of "Worked my yellow gown, made salt-rising bread, played Basket Ball," nothing of her family. One deduces Pearl's mother and father, flat and formal small-town people. There is, however, a recorded instant in the diaries which the dying Pearl is anxious to recover: "Early this morning . . . I went out behind the house to weed. Was kneeling in the dirt by the stable with my pinafore a mess and the perspiration rolling down my back, wiped my face on my sleeve, reached for the trowel, and all at once thought, Why I believe that at just this moment I am absolutely happy."

Otherwise the young Pearl seems to have been unremarkable, without very much charm, and destined to remain single, when at 30 she is inexplicably the heart's choice of the dashing Beck Tull, a 24-year-old salesman whose company will shift him all his life from town to town. When they are in Baltimore with three children, ages 9 to 14, Beck tells Pearl that he doesn't want to stay married any longer. She asks him why, but he never answers. She is uncomprehending and bitter. Without roots, without friends, peckish to the outside world, she narrows grimly to the task of rearing her children, leaving them with very few memories of a light and gay order--Cody, the eldest, remembers there were no pictures on the wall, no perfume bottles on a bureau, no friends welcomed to supper, and even at Christmas, no turkey.

Cody, handsome, sharp, with a sadistic streak, is scarred by the loss of his father, and singularly ruled by a perverse love-hate and jealousy of his younger brother, Ezra, a dull sweet fellow, a sort of Lenny-like figure, not harmful but thought by some to be retarded. Cody will go on to college, to financial success; he will steal Ezra's back-country near-illiterate girl because she is Ezra's girl, marry her, put Baltimore behind him, but not his obsession. Eventually he will even think Ezra is stealing his teenage son. Cody's trouble might stem from his defaulting father or it might be, as his mother once told him, "You've been mean since the day you were born." This seems true on the evidence.

Jenny, a scattered girl, is the youngest of the three and one is surprised to learn that she aspires to be a doctor, let alone that she manages her education and training. She will break down, and she will recover. At the end we see her coming towards middle age, a sort of frowsy, laid-back pediatrician who is married to her third husband and has taken on the rearing of countless stepchildren--"I mean you got those children the way other people get weekend guests," says her mother. Jenny is the neurotically thin, endlessly dieting daughter of that spare Pearl, and will be in turn, the mother of her own teenage anorexic Becky.

As Cody is as mean as Iago, Ezra is as sweet as treacle. And just as Cody and Jenny never really develop, so Ezra remains steadfastly naive, forgiving, unperceptive. At 18 he falls in love with a neighborhood restaurant, and with the sophisticated older woman, Mrs. Scarlatti, its owner, a love never quite acknowledged. When she dies Ezra inherits the restaurant, drops the black-tied waiters and French cuisine, changes its name to the Homesick Restaurant, and begins cooking emotionally warm and therapeutic meals for troubled customers. From time to time he summons the family for a celebration, dinner at the Homesick Restaurant, but it is always a disaster with Pearl marching out.

In her earlier days Pearl was given to rages and slamming her children around, but once they're grown and off, she becomes reflective: "Pearl believes now that her family has failed. Neither of her sons is happy and her daughter can't seem to stay married. There is no one to accept the blame for this but Pearl herself, who raised these children single-handed and did make mistakes, oh, a bushel of mistakes. Still, she sometimes has the feeling that everything has been assigned, has been preordained, everyone must play his role. Certainly she never intended to foster one of those good son/bad son arrangements, but what can you do when one son is consistently good and the other consistently bad?" While handily forgetting her record of child-abuse, she does seem to have become philosophic, to have grown, which her curiously static children never do. It is difficult to believe that they will acquit themselves in medicine, industry and the restaurant business.

Anne Tyler has dealt wonderfully in her many previous books with a lot of fringey loners in whom the reader is happily persuaded to believe. With a certain grand authority she has brought to life quite a number of real nuts, having us fascinated to follow them as they bound off in improbable directions. In Earthly Possessions, as an example, Charlotte Emory's life takes a bizarre turn, which she tells us about in her entirely persuasive voice, wry, ironic, funny by turns. Indeed there are several beguiling voices in that book, the muse is in her place, and Anne Tyler triumphs.

What may he the trouble with Dinner at the Homesick Restaurant is that the Tull family is not marginal enough, its members are too grave a proposition for a mind so full of mischief as Anne Tyler's. They've depressed her. It does happen to a writer that your characters can wrap themselves around your neck and choke the life out of all of you. And, also, there are times when you aren't ruthless, when you can't detach yourself. You're sentimental. To go back four generations, those crucial parents of Pearl Cody left their child wooden, flat, unimaginative, which is, of course a pity. And Anne Tyler has labored soberly to make the lives of Pearl and her descendants worthy to be recorded, but her gift as a writer lies elsewhere. John Updike has called her "wickedly good" Her lot, her gift is to be wicked.