For example, Refardt, Bergmiller & Kummerli (Proceedings Royal Society-B, 2013; http://rspb.royalsocietypublishing.org/content/royprsb/280/1759/20123035.full.pdf) model bacteria that have been infected and that commit suicide in order to prevent the spreading infection to the rest of the population. They do so even though relatedness is low, approaching zero.
In section 3c, they write
(A)ltruistic host suicide cannot evolve with $r=0$ because populations go extinct before invasion of the Abi trait is possible. Thus, we predict marginal relatedness ($r < 0$) to be required for successful invasion.
I am assuming this is a typo and they mean $r>0$?
In a situation in which altruism is not directed toward any particular individual(s) but is rather allocated to the whole population, doesn't $r$ depend upon the frequency of the allele that is engaging in the altruism? If it is a new mutation and there is no other allele in the population to receive the benefit, then r=0. If the allele has gained fixation, $r=1$ and selection is much more likely to favor the altruism.
What is a way of modeling whether selection will favor fixation of a new mutation that allocates benefits to the population but not any particular individual (e.g., by committing suicide), given that the new mutation is not shared by (m)any other individuals and consequently, $r$ is initially very low? I would think there is a way of determining the odds that genetic drift would lead the new mutation to develop a substantial enough frequency to increase the odds that the resources would benefit holders of the allele. But I am unfamiliar.