Inclusive fitness is simply the sum of an individual's fitness plus the additional benefits accrued through increasing the fitness of related individuals. In English: You're more fit not only if you reproduce, but also if relatives who share your genes reproduce, too.
Here's a simple example of inclusive fitness in action: Helping your identical twin sister have a baby that she would not have been able to have without your help is just as good a way to pass on your genes to the next generation as having a baby of your own. Most humans aren't one half of an identical pair, of course. To understand how inclusive fitness works in more common situations, you need to understand a concept called degree of relatedness, which simply means how many of your genes you share with others.
For sexually reproducing organisms (such as humans, antelope, or titmice), the degree of relatedness is as follows:
i Between parents and offspring: One half of an individual's genes come from its mother and half come from its father. The degree of relatedness between parent (mother or father) and offspring is one half (or 0.5).
i To full siblings (individuals that have the same mother and father):
Full siblings, on average, have half their genes in common. The degree of relatedness is 0.5.
i To half siblings (individuals that have either the same mother or the same father): Half siblings, on average, have one quarter of their genes in common. The degree of relatedness is 0.25.
i To your siblings' children: The degree of relatedness between you and any of your nieces and nephews is on average one quarter (0.25), because you share one half of your genes with your sibling, and that sibling shares half of his or her genes with his or her offspring.
So how many offspring do you have to help your siblings make to equal one of your own offspring? If you're an identical twin (that is, you and your twin have a degree of relatedness of 1.0 because you have exactly the same genes), helping her (or him) make an additional baby is just as good as making one of your own as far as your fitness is concerned. But if you're helping a non-identical full sibling reproduce at the expense of your own reproduction, to come out even you'd have to help produce at least two nieces or nephews for every one son or daughter you could have created yourself.
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