The general form of Hamilton’s rule makes no predictions and cannot be tested empirically

Abstract

Hamilton's rule asserts that a trait is favored by natural selection if the benefit to others, B, multiplied by relatedness, R, exceeds the cost to self, C. Specifically, Hamilton's rule states that the change in average trait value in a population is proportional to BR − C. This rule is commonly believed to be a natural law making important predictions in biology, and its influence has spread from evolutionary biology to other fields including the social sciences. Whereas many feel that Hamilton's rule provides valuable intuition, there is disagreement even among experts as to how the quantities B, R, and C should be defined for a given system. Here, we investigate a widely endorsed formulation of Hamilton's rule, which is said to be as general as natural selection itself. We show that, in this formulation, Hamilton's rule does not make predictions and cannot be tested empirically. It turns out that the parameters B and C depend on the change in average trait value and therefore cannot predict that change. In this formulation, which has been called "exact and general" by its proponents, Hamilton's rule can "predict" only the data that have already been given.amilton's rule is a widely known concept in evolutionary biology. It has become standard textbook knowledge and is encountered in undergraduate education. For many, Hamilton's rule expresses the intuition that cooperation evolves more easily when there are frequent interactions among relatives, because relatives are likely to share the cooperative trait. However, Hamilton's rule goes beyond this intuition by positing a quantitative condition, BR − C > 0, which is said to predict whether or not a trait will be selected. Specifically, it is claimed that the change in average trait value from one time point to the next is proportional to BR − C .We immediately encounter the question of how the "benefit," B , the "relatedness," R, and the "cost," C , are calculated for a given system. Surprisingly, there is no consensus about the correct method. A variety of derivations have been proposed over the years (1-10), which define B , R, and C in distinct (nonequivalent) ways. In the empirical literature, peer reviewers often disagree over which method should be used in a particular manuscript (11).A number of recent papers (7, 9, 10) have endorsed a particular formulation (4, 5) as the exact, general, and even "canonical" version of Hamilton's rule. This formulation, called "Hamilton's rule-general" (HRG) (12, 13), is claimed to be as general as natural selection itself (7,14). The derivation, which we recapitulate below, is simple and contains only a few steps.The mathematical investigation of HRG reveals three astonishing facts. First, HRG is logically incapable of making any prediction about any situation because the benefit, B , and the cost, C , cannot be known in advance. They depend on the data that are to be predicted. At the outset of an experiment, B and C are unknown, and so there is no way to say what Hamilton's rule would predict. Once the experiment is ...

Hamilton's inclusive fitness maintains heritable altruism polymorphism through rb = c

“…A major implication of our work is to offer a fundamental support for Hamilton's theory of inclusive fitness (1), a critical concept in the textbooks of evolutionary biology and sociobiology but the focus of controversy, especially during recent years (25,26). The evidence of altruism heritability is consistent with the core premise of Hamilton's theory: altruistic behavior can evolve through kin selection depending on a genetic component (1)(2)(3)8).…”

Inclusive fitness is an indispensable approximation for understanding organismal design

“…Recently some authors (Nowak et al. ) have confused this general, regression form of Hamilton's rule with the simple one discussed here. While it's true that this general form of Hamilton's rule (sometimes referred to as ‘HRG’, Birch ) gains generality at the cost of empirical utility, the simple Hamilton's rule we have discussed (or versions of it), defined in terms of effects on offspring number, is the one that has been used to enormous empirical success, as outlined above and reviewed by, for example, Foster (), Abbot et al.…”

“…They can no longer be understood as simple effects on offspring number, we no longer have a simple interpretation of social behavior, and, without knowing genetics, the parameters are no longer easily measurable in the field and in the laboratory. Recently some authors (Nowak et al 2017) have confused this general, regression form of Hamilton's rule with the simple one discussed here. While it's true that this general form of Hamilton's rule (sometimes referred to as 'HRG', Birch 2014) gains generality at the cost of empirical utility, the simple Hamilton's rule we have discussed (or versions of it), defined in terms of effects on offspring number, is the one that has been used to enormous empirical success, as outlined above and reviewed by, for example, Foster (2009), Abbot et al (2011) (Tables 1 and 2), Bourke (2011), andDavies et al (2012).…”

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“…The value of such general and somewhat abstract models is one of many highly divisive issues related to social evolution theory. In brief, perhaps the main criticism is that they cannot make testable predictions [32]. The main line of defence is that prediction is not the aim of this type of model, and instead the most general, regression-based formulation forms a robust conceptual and theoretical foundation [29], and provides an organising framework for social evolution theory [18].…”