- Inclusive fitness is an unnecessary construct
- Hamilton’s rule has no predictive power
- It is important to study kin selection, but inclusive fitness theory is inadequate for the task
Inclusive fitness theory is an approach that is based on assigning fitness effects of social interactions to individuals. It is assumed that personal fitness can be written as the sum of components caused by individual actions weighted by relatedness. An attractive (but ultimately incorrect) claim of the theory is that organisms evolve as if to maximize their inclusive fitness. Proponents of inclusive fitness think that this theory is an important tool of evolutionary analysis and has explanatory power for many phenomena.
Our own view is that inclusive fitness is a limited approach, which has hindered precise mathematical investigations in many areas of social evolution. A rigorous study of kin selection is possible once it is understood that inclusive fitness theory is only a particular accounting method that rests on specific and limiting assumptions. The quantity “inclusive fitness” does not exist for the vast majority of evolutionary processes. Hence, organisms cannot evolve as to maximize inclusive fitness, because they cannot maximize a quantity which does not exist.
Even in special situations where inclusive fitness exists, Hamilton’s rule in the simple form br>c is usually wrong. Attempts to generalize Hamilton’s rule and make it “always true” are vacuous. Consequently, Hamilton’s rule has no predictive power at all.
Many papers in the literature contain statements of the form “Inclusive fitness theory predicts …”. But these statements are usually empty, because they are not based on any calculation of evolutionary dynamics.
Contrary to many popular claims, inclusive fitness theory has never been tested empirically. Testing inclusive fitness theory is a logical impossibility: it does not apply in most cases, and when it applies, it gives the same predictions as any valid mathematical approach to evolution. There are no specific predictions of inclusive fitness theory that could be tested.
We do not claim that relatedness is unimportant in general. Relatedness is an aspect of population structure, which can affect evolution. However, relatedness cannot be correctly interpreted without a meaningful model of the evolutionary process in question. Once such a model has been constructed, there is no need for inclusive fitness theory: all consequences of relatedness can be understood on the level of genes.
Here is a list of our main publications on this topic:
1. Nowak MA, CE Tarnita, EO Wilson (2010). The evolution of eusociality. Nature 466 (7310): 1057-1062
The main points of the paper are as follows: (i) Inclusive fitness, as defined by Hamilton and as used in all meaningful papers on the subject ever since, is a limited concept, which does not exist for the majority of evolutionary processes. Consequently, whenever biologists use the term “inclusive fitness” to refer to an actual population, they are almost certainly in a situation in which that quantity does not exist. (ii) There is a powerful mathematical theory of evolution, which can explain social behavior without using inclusive fitness. (iii) Eusociality can arise by a simple mutation that causes some offspring to stay at their mother’s nest. The success of eusociality depends on demographic and ecological parameters, while relatedness is the same for all species under primary consideration.
Part A of the supplementary information contains the mathematical proof that inclusive fitness is a limited concept. None of our critics have ever pointed out a mathematical problem in our argument.
2. Nowak MA, CE Tarnita, EO Wilson (2011). Nowak et al. reply. Nature 471 (7339): E9-E10.
In response to NTW (2010), proponents of inclusive fitness submitted various letters to Nature. The original versions of the letters contradicted each other in that two letters stated that it has long been known that inclusive fitness was a limited concept, while the main letter (signed by more than 100 people) stated that inclusive fitness had no limitations. This confusion was resolved in favor of the view that inclusive fitness had no limitations, which is in contradiction to the mathematical results of NTW (2010), but no mistake in the mathematical analysis of NTW was pointed out.
Text of the reply [PDF file]
3. A brief statement about inclusive fitness and eusociality, June 2011
This is a short statement published on our website in June 2011. The aim is to maintain clarity and remove obfuscations introduced by our critics.
Text of the statement [PDF file]
4. Allen B, Nowak MA, Wilson EO (2013) Limitations of inclusive fitness. Proc Natl Acad Sci USA 110(50): 20135-20139
There exists a method based on linear regression, which is used by some inclusive fitness theorists to claim that inclusive fitness theory (i) predicts the direction of allele frequency changes, (ii) reveals the reasons for these changes, (iii) is as general as natural selection, and (iv) provides a universal design principle for evolution. In this paper we prove that the method is vacuous and that those claims are unfounded.
Text of the paper [PDF file]
5. Nowak MA & Allen B (2015) Inclusive fitness theorizing invokes phenomena that are not relevant for the evolution of eusociality. PLoS Biol 13(4): e1002134.
This is a formal comment on Liao, Rong & Queller (LRQ), PLoS Biology (2015). In an attempt to uphold inclusive fitness, LRQ introduce hypothetical phenomena that do not exist in nature and have no consequence for the evolution of eusociality. LRQ’s paper highlights the state of weakness and confusion of inclusive fitness theory. Although their aim is to defend inclusive fitness theory, they do not offer an inclusive fitness calculation for their models.
Text of the paper [PDF file]
6. Allen B & Nowak MA (2015). Games among relatives revisited, J Theor Biol 378: 103-116.
In this paper, we study evolutionary games among relatives using a straightforward analysis of change in gene frequency. We also analyze our model with inclusive fitness. We find that the quantity of inclusive fitness does not exist for general games. For special games, where inclusive fitness exists, it provides less information than the straightforward analysis.
Text of the paper [PDF file]