Field of Science

What's the deal with inclusive fitness theory?

You may not be aware of it, but there is a battle afoot in the theory of evolution.  The fight is over inclusive fitness theory—an approach to studying the evolution of cooperation.  I, together with mathematical biologist Martin Nowak and naturalist E. O. Wilson, just published an article pointing out weaknesses in the theory, and suggesting that it might not tell us much about why cooperation actually evolves.  This is my attempt to explain the controversy—and our new paper—to those who may not know anything about it. The essential question is, "Why do organisms sometimes help others at a cost to themselves?"  Such helping behaviors have been observed from microbes to insects to humans.  At first glance, these behaviors may appear to contradict natural selection, since the cost of helping reduces the chances that the behavior is passed on to offspring. 

Theorists have identified a number of different ways that costly helping can actually be favored by natural selection.  One way is if the help is primarily directed toward close relatives. These relatives have a good chance of sharing the "helping" gene, so that help increases the overall prevalence of this gene.  This mechanism is called kin selection.

Inclusive fitness theory is one way of representing the idea of kin selection.  Let's say you have some gene that makes you sacrifice your time and energy to help others.  This help affects fitness—the number of healthy offspring you produce.  ("Healthy" offspring are the ones that will eventually grow up and have offspring of their own.)  The first idea is to split fitness into the offspring that you produce on your own, and those which can be attributed to help from others:

The idea of inclusive fitness is to disregard the offspring that others help you produce, but instead count the ones that you help others produce:

To determine the overall effect on the helping gene, offspring that you help others produce must be weighted by the probability that they share the helping gene, which can be interpreted as your "relatedness" to them.  (For example, help you give to your siblings is weighted by one-half, equal to the probability that you inherited the same parental copy of the helping gene.)  Adding up these amounts of help times relatedness gives your inclusive fitness.  In some simplified models, it can be shown that natural selection favors organisms that have the highest inclusive fitness. 

At this point you may be asking "Wait, does it really make sense to divide offspring into those  produced on one's own versus those produced by help from others?"  This is exactly the problem!  Aside from the obvious point that no one reproduces without help in sexual species, nature is full of synergistic and nonlinear interactions, so that making clean divisions like this is impossible in most situations.  Thus the idea of inclusive fitness theory only works in simplified toy models of reality. 

Nowak and Wilson, together with mathematician Corina Tarnita, made this point forcefully in a 2010 Nature article.  In response, more than 100 authors signed a letter saying that inclusive fitness theory has no limitations, and is as general as natural selection itself.  (There were also heated blog posts and a talking bear video!)

What are we to make of this claim that inclusive fitness theory has no limitations at all?  This claim turns out to be based on the idea that, however complex the interactions are in nature, one can always use linear regression to split one's offspring into those attributable to oneself versus others.

Our new paper shows that this approach is not exactly wrong, but nonsensical.   To see why, let's consider a hypothetical helping trait (call it Trait X), and see if this approach can tell us whether and how this trait is selected for. 

Can the this method predict whether Trait X will succeed in evolution?  No, because in order to even set up the regression, one must know in advance whether it succeeds not.  The whole method is based on retrospectively analyzing known results of natural selection, and so it logically cannot predict anything new.

Ok, so if we must know in advance whether or not Trait X is favored, can this method at least help us understand why it succeeds or fails?  The answer is no again, at least not in general.  The reason is that the regression method looks for correlations between having type X as a partner and having high fitness.  If there is a positive correlation, this method says that trait X is "altruistic".  But as any statistics student knows, correlation does not imply causation.  In fact, it is easy to come up with examples where the regression method misidentifies the nature of a trait.

For example, suppose Trait X is actually a jealous trait—if you have it, it makes you want to find high-fitness individuals and attack them, reducing their fitness as well as your own.  A hypothetical example with numbers is illustrated here:

The greenish numbers are the fitnesses before the attack; while the red numbers indicate the results of the attack.  The individual with Trait X (indicated in red) found the highest-fitness individual (5, in this case) and attacked him, reducing each of their fitnesses by one.  But since the attacked individual still has fitness 4, there is a positive correlation between having Trait X as your partner and having high fitness.  So the regression method calls this "altruism" when it clearly is not.

In short, the regression method generates a "just-so-story", which is often wrong, for an outcome that is already known.  The fact that this method is trumpeted as "the very foundation of social-evolution theory" indicates a weird state of affairs in this corner of biology.  My reading is that many researchers fell in love with inclusive fitness theory (which admittedly can be elegant and intuitive when it works), and tried to stretch it to include all of natural selection.  Similar problems exist in economics, in that some researchers fall in love with the elegant mathematics of their theories and forget that they may not always apply to the real world.

I'm not proposing that we replace inclusive fitness theory with some other all-encompassing theory or framework.  Rather, I'm suggesting that the method of analysis be tailored to the problem at hand.  A variety of mechanisms can support the evolution of cooperation, and a variety of approaches are needed to understand them.  The only truly general theory in evolutionary biology is the theory of evolution itself. 

Allen B, Nowak MA, & Wilson EO (2013). Limitations of inclusive fitness. Proceedings of the National Academy of Sciences of the United States of America PMID: 24277847

Gardner A, West SA, & Wild G (2011). The genetical theory of kin selection. Journal of evolutionary biology, 24 (5), 1020-43 PMID: 21371156

Nowak MA, Tarnita CE, & Wilson EO (2010). The evolution of eusociality. Nature, 466 (7310), 1057-62 PMID: 20740005


  1. Great to see you back to blogging. We read (and enjoyed) your paper in our last journal club. I believe the issues underlying your main point are also somehow close to our take on the Price equation. Hopefully we'll (slowly?) move to a state where most models approach evolution with true dynamics.

    The analogy with economic theory is a good one and has surfaced here many times in discussions over coffee.

  2. Thanks Julian! I agree, pretty much any approach that uses the Price equation as a starting point is subject to the same flaws. Your group's takedown of the Price equation definitely informed my thinking on this.

  3. Nice post, and nice paper! (I'm probably burning bridges to some very serious people in the mathematical biology world by saying so, but hey, New England gets chilly.) One thought, following up on this part of it:

    Although modern formulations of inclusive fitness theory use different relatedness coefficients [Frank 1998; Gardner, West and Wild 2011; Rousset 2004], all other aspects of Hamilton’s definition remain intact.

    This reminds me of an issue I've had with the work I've seen which tries to understand spatially explicit evolutionary models using inclusive fitness. Someone defines a stochastic model in terms of lattice sites changing states following certain reactions; then they wrench the equations around, say by writing a pair approximation, linearizing the dynamics and then checking the sign of an eigenvalue to test the stability of a fixed point. The result is "Hamilton's rule": something that we can write as BR > C, if we're willing to draw a big circle around a bezoar of algebra and call it the "relatedness." There then follow the claims that inclusive fitness works for this system, that (if the author is feeling ecumenical) kin selection and group selection are herein proved equivalent, etc., etc. However, first, whatever "Hamilton's rule" that comes out of such an analysis is no better than the assumptions which went into it: that pair approximation is viable for that scenario, that the stability of the chosen fixed point tells us everything we need to know about the trajectory of natural selection and so forth. Second, the definition of "relatedness" we obtain is model-specific. In order to "apply Hamilton's rule," we have to solve the problem using dynamical methods. Saying at the end that the sign of BR - C predicts the outcome isn't exactly a "just-so story," here; it's not a case of descriptive statistics masquerading as predictive dynamics. It's more like an epilogue tacked onto the story at studio insistence, which only makes it harder to judge the story on its own merits.

  4. Second, the definition of "relatedness" we obtain is model-specific.

    THIS! A "general theory" should at least have consistent definitions. If not, then how is one to know which of the myriad different definitions is actually relevant for cooperation in nature? Or, as my friend Matthijs likes to say, a rule is not a rule if it changes from case to case.

  5. I'm not qualified to do the math, but am concerned that others are extracting natural selection from mutation-initiated natural selection. What happens to the theory of evolution is that it then becomes simply mutation-driven evolution with no mention of what is selected, how it is selected, or how it increases fitness. There is also no mention of the biophysical constraints on adaptation that ensure mutations are not adaptations, because they perturb the thermodynamics of intercellular signaling that result in de novo creation of genes that is required for organism-level thrermoregulation in ever-changing ecological and social niches.

    In "Evolution of transcriptional enhancers and animal diversity," the authors conclude: The articles, reviews and perspectives that follow this introduction shed more light in the still murky and mysterious world of gene expression evolution in the animal kingdom. Each of these papers, in one way or another, consolidates the idea that there will probably be no fixed law, like gravity, to explain at the molecular level how endless forms most beautiful and most wonderful have been, and are being evolved. It rather seems that a wide variety of peculiar molecular mechanisms perform, together, the complex task of putting the genome in action, in each cell type of each animal species, at every moment in life and under every possible physiological and environmental circumstance."


      I'm not sure I understand. I don't think anyone would argue that evolution is driven only by mutations and that fitness is unimportant. Both sides of this debate are talking about fitness--in particular how the behavior of one organism affects the fitness of others.

      Thank you for that quote. I agree completely. I think some people regard inclusive fitness as the "E=mc^2 of biology", when in fact biology just does not admit simple equations the way physics does.

  6. Nowak and Wilson, together with mathematician Corina Tarnita, made this point forcefully in a 2010 Nature article.

    The link to the PDF appears to be broken. I found this alternative, which works at the moment.


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