On the level of genes there is no inclusive fitness
I think this is a fairly straightforwardly mistaken idea. The basic logic of Hamilton's 1964 paper applies to genes too. Hamilton claimed that organisms are not just be driven by self interest, and concern for their offspring, but can be expected be interested in the welfare of their other relatives too (brothers, cousins, parents, etc). Similarly, genes aren't just out for themselves. They also act as though they are concerned about their relatives.
With genes the situation is simpler to analyze. To a first approximation,
most other genes are related to them by either being identical clones -
or by being completely unrelated. These situations correspond to
r=0 - in the standard inclusive fitness
mathematical formalism. If you plug these numbers into Hamilton's
rule, you get sensible results. Genes often act as though they
do care about the welfare of identical copies of themselves.
The inclusive fitness of a gene can be calculated in the same way as the inclusive fitness of an organism - by adding and subtracting fitness components due to self and relatives - as described by Hamilton.
West, Gardner and I are all in agreement on this issue. In 2013, they said:
Even at the level of the gene, we would still want to know what the maximand is, and the answer is ‘the inclusive fitness of the gene’So: what was Martin Nowak thinking about? Perhaps he meant to write that inclusive fitness was not a necessary concept at the level of the gene. For example, if you think of genes as being informational, then it is conventional to refer to all the copies of a particular physical nucleotide sequence as representing the same "gene" (or "allele", as some people prefer to say). In which case, talk of "inclusive fitness" is unnecessary.
However, the concept of inclusive fitness is applicable on the level of the genes. I think to claim otherwise is just to invite confusion and misunderstanding.