American Society of Naturalists

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“Spite and the geometry of negative relatedness”

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Philip G. Madgwick (Nov 2020)

New analysis of negative relatedness shows that harming alleles are greenbeards

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Making sense of the theory of negative relatedness: mechanisms, properties, and challenges

The evolutionary explanation of altruism through inclusive fitness theory is a celebrated and enormously successful area of research that has illuminated the puzzling helping behaviors of diverse species by recognizing that help is given when individuals share genes by common ancestry. In comparison, the evolutionary explanation of spite has floundered, as much less attention is given to harming behaviors, which almost gives the impression that these traits are rare or unimportant. But there are numerous potential examples of spite from across the realms of natural history, even if these systems have not received experimental study. So why is spite thought to be so rare in nature? The study of altruism was guided by suggested examples (especially sterile social insect castes), but the study of spite is mostly shaped by a theoretical argument about the peculiar conditions that it requires. In short, as altruism requires positive relatedness from common ancestry, spite requires negative relatedness – but how this can generally arise has remained elusive. Additionally, it does not help that negative relatedness is not an intuitive concept. Here, the paper briefly describes how negative relatedness arises, simply demonstrates how negative relatedness fundamentally differs from positive relatedness through being frequency-dependent, and uncovers how the calculation of negative relatedness can often mismatch the biological mechanism of how it arises.

The key finding is that, through frequency dependence, genes for spite are like greenbeards, which are a special kind of gene for social behavior that generate assortment among individuals based on the presence (or absence) of the greenbeard gene – rather than a kin-selected gene that relies on assortment based on the probability of sharing genes by common ancestry. Greenbeard and kin-selected genes differ in the profile that relatedness has across the genome, and so genes for spite are like greenbeards in having non-uniform relatedness across the genome. Linking genes for spite to greenbeards provides some suggested theory for how these genes evolve and some suggested examples from the burgeoning experimental study of greenbeards. Although it is amongst the first steps, the hope is that theory laid out in this paper will contribute toward making the study of spite more accessible for experimental research into the future.


Spite is the most surprising prediction of inclusive fitness theory because it suggests that a gene can be favored by natural selection despite causing harm to both the individuals that carry it and those around them. A gene for spite can only be favored because of negative relatedness, which means that the actor that carries the gene is less likely to share the gene for spite with the surrounding recipients than the random expectation. Whilst positive relatedness can be simply reduced the intuitive concept of kinship, negative relatedness is deeply counterintuitive. Here I clarify that negative relatedness is frequency dependent, and I identify a hidden assumption in its widely used formula. Accordingly, whilst the well-studied ‘lighter’ side of inclusive fitness (with helping behaviors and positive relatedness) is dominated by traits that are favored under kin selection, I predict that the understudied ‘darker’ side of inclusive fitness (with harming behaviors and negative relatedness) is dominated by traits that are favored under greenbeard/kind selection – and I discuss the existing evidence that tentatively supports this hypothesis.