You should always provide for an alternate beneficiary in case the first one dies before you and there is no chance for you to make out a new will.
Survivors or Descendants
Suppose your will leaves your property to your sister and brother, but your brother predeceases you. Should his share go to your sister or to your brother's children or grandchildren?
If you are giving property to two or more persons and you want it all to go to the other if one of them dies, then you would specify "or the survivor of them."
If, on the other hand, you want the property to go to the children of the deceased person, you should state in your will, "or their lineal descendants." This would include his or her children and grandchildren.
Family or Person
If you decide you want your estate to go to your brother's children and grandchildren, you must next decide if an equal share should go to each family or to each person.
Example: If your brother leaves three grandchildren, and one is an only child of his daughter and the others are the children of his son, should all the grandchildren get equal shares, or should they take their parent's share?
When you want each family to get an equal share, it is called per stirpes. When you want each person to get an equal share, it is called per capita. The most common way property is left is per stirpes.
Example: Alice leaves her property to her two daughters, Mary and Pat, or to their lineal descendants, in equal shares, per stirpes. Both daughters die before Alice. Mary leaves one child; Pat leaves two children. In this case, Mary's child would get half of the estate and Pat's children would split the other half of the estate. If Alice had specified per capita instead of per stirpes, each child would have gotten one-third of the estate.