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

On math and magic

I've been on a kick lately of re-reading my old favorite fantasy novels. I started with some of Lloyd Alexander's Prydain Chronicles, and am now going back through Ursula K. LeGuin's Earthsea Trilogy. I haven't touched this books—or anything in the fantasy genre—since my early teens, and its been interesting to see how differently I relate to them now.

...from another former obsession

One moment in particular struck me. In LeGuin's A Wizard of Earthsea, there's a scene in which a young apprentice-mage sneaks a look at his master's dusty old spellbooks and becomes transfixed by the ancient runes inside. I realized that the visceral feeling evoked by this passage (and others like it throughout the fantasy genre) is exactly what I felt as a college freshman exploring the math section of my undergraduate science library. I would spend hours at a time browsing dusty old math books, the more arcane the better, trying to decipher their internal logic. Yes, I wanted to learn new math, but I was also hooked on the feeling of being lost in these mysterious tomes. Like the mage's spellbooks, these math books contained strange symbols describing deep and powerful truths, which could only be understood through long, deep study.

A sample from a recent article of mine. Doesn't math look cool?

Reflecting back on these moments highlights how my relationship to mathematics has changed.  I was initially drawn to math because of its beauty, elegance, mystery, and because it contained a kind of absolute truth.  But after teaching for three years and studying differential geometry for one, I found that abstract beauty and truth were no longer enough to sustain my excitement.  I wanted to discover and describe important patterns in the world, not just relationships between abstract constructs.  Metaphorically speaking, I wanted to work my magic in the world, not just study it for its own sake.  This lead me to study study of complex systems and eventually evolutionary dynamics.  Mathematics has lost none of its beauty or mystery for me, but my focus now is on its connection to the world rather than its absolute, self-contained truths.

This parallels, in some ways, the differences I've noticed in the way I approach these fantasy novels now.  As a hyper-imaginative pre-teen, I wanted to lose myself in these fantasy worlds, to blur the lines in my mind between these worlds and my own.  Re-reading them now, I have no desire to escape into these worlds.  Rather I look for metaphors and themes connecting these worlds to mine. These books (and the genre as a whole) seem obsessed with the idea of power: discovering one's own power, learning about different sources of power, coming to grips with the dangers and limitations of power, avoiding the temptation to use power for evil.  As a researcher, a future professor, and simply an adult actor in this world, I have a certain measure of real-world power now that I lacked as a bookish pre-teen. In these books, I'm finding an opportunity to reflect on how to wield that power, and the responsibility that comes with it.

Perhaps the larger theme is this: I used to think I needed to escape from the world in order to be myself.  Now my goal is to connect to the world, as much as possible, while still being deeply, authentically, myself.

Can we find meaning in evolution?

I'm a mathematician who studies evolution. I'm also a person who thinks about how people can find meaning and purpose in their lives. And so, combining these, I've spent a fair bit of time thinking about what, if anything, evolution can tell us about the meaning and purpose of human life.

My friend Connor Wood recently wrote on this topic. Specifically, he probed the question of why, precisely, many conservative religious traditions find the idea of evolution so objectionable. His argument is encapsulated in this quote:

I strongly suspect that evolutionary theory makes people so uncomfortable, not because it disagrees with Genesis (lots of things contradict Genesis), but because it presents a vision of a natural world whose “values” are fundamentally opposed to those of our religious cultures.

By "values" (in quotes because evolution is an amoral process), Connor is referring to the often violent struggle to survive and reproduce one's genes, which includes such behavior as infanticide in some mammals and birds. While I agree with Connor's basic argument, I think it's not primarily the violence and struggle that offends some religious sensibilities (the Old Testament and many other religious texts are full of violence) but rather the inherent randomness and lack of ultimate purpose in the process.

Even though scientists generally don't intend it as such, evolution fills the role of a creation story. Like other creation stories, it explains where we came from and how we got here. But unlike other creation stories, it gives us few clues as to where we're going or what we're supposed to do. In fact, it tells us that we're the product of random events. If this randomness had gone differently, we might not be here at all. I think the randomness and lack of purpose implied by this story is why many people—including some who believe it as a scientific hypothesis—find the idea of evolution disturbing.

Where did all this come from??  What does it mean??

Interestingly, several thinkers have tried to turn this equation around, claiming that evolution can, in fact, satisfy our deepest psychological/spiritual needs. One of these is Stuart Kauffman, one of the biggest names in complex systems. Kauffman's latest book, Reinventing the Sacred, argues that evolution is such a creative and fundamentally unpredictable process that it can provide us with all the divine-like inspiration we need.

Unfortunately, Kauffman's idea doesn't quite get there for me. It's true that the variety of life is awe-inspiring, with more and more surprises the closer one looks. However, I think that just being awestruck by the beauty and creativity of nature is insufficient: it doesn't satisfy the questions of why we're here or what we should try to do with our lives.

Another approach is to focus on the potential of evolution to produce cooperation, creativity, and complexity. These aspects of evolution are highlighted in Supercooperators, the new book by my boss and mentor Martin Nowak. I think one of the reasons for the past few decades' surge of research into this side of evolution (the "snuggle for existence") is that it changes the story evolution tells about us, allowing us to understand how love, empathy, and compassion are also products of our evolutionary history.

But I don't find this to be of great philosophical comfort either. First, for every example of the evolution of cooperation, there's a complementary example of evolved selfishness and violence. Second, knowing that my feelings of love and empathy exist because they were successful traits in my ancestors doesn't make me feel better about them. In fact, it makes me feel worse. I want to think of these as fundamental to who I am, not some ploy to reproduce my genes. Every time I try to think about all my love and altruism as being a product of evolution, I become sad and want to stop thinking about it. Perhaps I'm just not thinking about it right, but I imagine others may have this difficulty too.

I made a handy (oversimplified) chart to summarize what I think evolution can and can't do for us in terms of filling philosophical/spiritual voids:

In short, my answer is that no, I don't think evolution can provide us with satisfying answers to many of our deepest questions.

Some atheists/materialists argue that the conversation should end here: There is no larger meaning or purpose to life, and any quest for such is a waste of time. But these questions are a real part of who I am, as real as love or anything else I feel. Doubtless, such searchings are products of evolution themselves. Yet to rationalize them away would be to deny a fundamental part of myself. Besides, if life truly has no purpose, then what would my time be better spent doing? Reproducing my genes? Why should I care about that either, if that's also just another artifact of evolution?

My approach is to grapple with these questions head on, knowing that there are no easy answers. Evolution—the most credible scientific theory as to how we got here—doesn't tell us where we're going or what to strive for. And yet it has implanted us with a deep need to plumb these questions. One could, I suppose, see this as a cruel joke that our evolutionary history has played on us. But I think these questions are as real and important as anything else we experience in life, and there is fulfillment and self-knowledge to be found in exploring them, even if we strongly suspect that satisfying answers will never be found.

The Origins of Inequality

Inequality is a national conversation topic now, thanks largely to the efforts of Occupy Wall Street and the broader Occupy movement. Fundamental questions are being asked, such as "Must inequality necessarily be a part of human society?", "Are we genetically disposed toward hierarchy or egalitarianism?", and "What would a global egalitarian human society look like?"

We can gain a bit of perspective on these questions by looking at the evolutionary history of humans and our primate relatives:

• Our two closest animal relatives are chimpanzees and bonobos. Chimpanzee society is characterized by a strict hierarchy of males, with frequent aggressive conflicts between them to maintain or challenge dominance order. In bonobo society, on the other hand, hierarchies are weak, and conflict resolution is peaceful, often involving sex play.
• Baboon societies in the wild are also characterized by a strict dominance hierarchy, in which higher-ranking males regularly harass lower-ranking ones and commandeer their food or resting spots. There is one notable exception, however. In 1982, all of the dominant males in a baboon tribe observed by Robert Saplosky were suddenly wiped out by a tuberculosis outbreak, leaving only the lower-ranking males. There followed a marked shift in the culture of the troop: hierarchy remained, but those at the top were much less likely to harass lower-ranking males or steal their food. Moreover, this more relaxed culture was observed in the same tribe two decades later, even after all the males present during the original shift had died or migrated to other tribes (Saplosky and Share 2004).
• Modern hunter-gatherer societies, the closest analogue we know of to our distant ancestors, are uniformly characterized by a strong egalitarian ethos, in which resources are shared and those who attempt to hoard them are ostracized (Boehm 2001). On the other hand, the transition to agriculture lead to the advent of unequal social classes, with the lower classes often suffering from malnutrition (Diamond 1987).

From left to right: Chimpanzee, Bonobo, Olive Baboon.  Source: Primate Info Net

Taken together, these examples suggest that humans aren't inevitably predisposed to either hierarchy or egalitarianism. Rather, we are capable of either mode of society. These examples also suggest that, like the baboons, we might be able to shift from one mode to the other in the wake of a destabilizing catastrophe.

A mathematician, economist, or theoretical biologist would call this an example of multiple equilibria. The situation might be depicted like this:

That is, there are two stable configurations of society (really, much more than two, but we're simplifying here): hierarchical and egalitarian. Each equilibrium is stabilized by different mechanisms. In hierarchical societies, those at the top have enough power to squelch any attempt at overthrowing the hierarchy. In egalitarian societies, those who attempt to selfishly amass resources or power are ostracized by the rest of the group. Christopher Boehm discovered these mechanisms for egalitarianim in his survey of modern hunter-gatherer societies

I discovered that their egalitarian political arrangements were quite deliberate. They believed devoutly in maintaining political parity among adults. This belief was so strong that males who turned into selfish bullies, or even tried to boss others around for reasons useful to the group, were treated brutally, as moral deviants. (Boehm 2007)

Because of these mechanisms, the two extreme ends of this spectrum are quite stable. Escaping them is very difficult without a demographic catastrophe like the tuberculosis outbreak in baboons, a major technological shift like the development of agriculture, or a "starting over" opportunity like the colonization of a new continent.

The middle regions of this spectrum, however, are less stable. In these regions, some individuals wield a disproportionate share of power, but not enough to completely suppress the interests of the less-powered classes (the 99%). This leads to persistent power struggles between these classes, in which the balance could ultimately be tipped in either direction.

The United States has always been an unequal society, but the checks and balances of democracy have thus far kept it from sliding into despotic hierarchy. The balance of power has fluctuated throughout our history, with periods of robber baron-style capitalism alternating with progressivist movements. I'm worried, however, that we're currently sliding toward self-reinforcing inequality, as the moneyed elite increase their influence over politics, which leads to policies that make them richer, which gives them even greater influence over politics, and so on.

This multiple equilibria model tells us that we may have only a limited window of opportunity to correct this slide. If an equilibrium of extreme inequality is reached, only an enormous catastrophe would be able to undo it.
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Sapolsky, R. and Share, L. (2004). A Pacific Culture among Wild Baboons: Its Emergence and Transmission PLoS Biology, 2 (4) DOI: 10.1371/journal.pbio.0020106

Demographic Transitions and the Future of Humanity

This week, the field of science bloggers are addressing the question "Are we doomed?"  It's a good question.  There is no shortage of evidence that we are, in fact, doomed.  But as an incorrigible optimist, my response is a cautious "maybe not?"

What am I referring to here?  In talking to friends concerned about the future of the world, many express a fear that the human population and its economies will continue to grow until they can no longer be sustained by the resources available on the planet.  At this point there will be a great "crunch", as billions die and the rest endure a life of scarcity and strife.  This fear is not new; it dates back to Thomas Robert Malthus, who wrote in his 1798 "Essay on the Principle of Population" that

The power of population is so superior to the power of the earth to produce subsistence for man, that premature death must in some shape or other visit the human race. The vices of mankind are active and able ministers of depopulation. They are the precursors in the great army of destruction, and often finish the dreadful work themselves. But should they fail in this war of extermination, sickly seasons, epidemics, pestilence, and plague advance in terrific array, and sweep off their thousands and tens of thousands. Should success be still incomplete, gigantic inevitable famine stalks in the rear, and with one mighty blow levels the population with the food of the world.

So the Maltusian prediction is yes, we are doomed. But according to contemporary demographic forecasters, Malthus was, surprisingly, wrong. The human population is not growing without bound. Rather, the growth rate is slowing, so that the total population level is headed for a peak—and relatively soon! A 2001 study entitled "The End of World Population Growth" put the chances at 85% that the human population will peak before 2100.  Here's a graph of their projections, with the most likely outcomes shaded darkest:

The numbers on the right-hand side are probabilities of being less than some number.  For example, there is an estimated 14.4% chance that the population will be less than 6 billion in 2100, and an 89.4% chance it will be less than 12 billion.  The thick white line is a UN prediction, not part of this study, provided for the sake of comparison.

This turnaround is remarkable, since the human population has been growing exponentially, with few declines, since the beginnings of recorded history.  So what's behind this unprecedented reversal?

It turns out that Malthus didn't know everything about human nature.  Population scientists have noticed a surprising, yet robust, pattern in human societies, which they call the "demographic transition".  This transition occurs in stages, which are linked to economic and social development.

1. In pre-industrial societies, parents have many children, since the survival of each individual child is uncertain.
2. As improvements are made to food supply, hygiene, health care, and infrastructure, more children survive. This leads to a period of rapid population growth.
3. As the society becomes increasingly urbanized, children become less of an asset (for helping with farmwork) and more of an expense (they must be educated in order to participate in the economy). Increasing education also gives women options other than motherhood. Access to and acceptance of contraception increases. As a net result, birth rates fall.
4. Eventually, birth rates decrease to levels comparable to or even less than the death rate. The population level then stabilizes or even contracts.

This transition can be seen clearly in the birth and death rates of Sweden:

Lines indicate number of births (blue) and deaths (red) per 1000 people per year.

Note that the death rate in Sweden now exceeds the birth rate.  This is also true of most European nations, as well as Canada, Russia, Iran, Japan, China, and many other countries.  The United States is an exception for now—but the New England states are an exception to the exception!   Many more developing countries have declining birth rates, so that their populations are predicted to stabilize within decades. 

The idea of the demographic transition, and its robustness across human societies, gives me hope.  Not only because it predicts the end of population growth, but also because it suggests a new paradigm of human existence.  A paradigm where quality of life is valued over quantity of life.  A paradigm where each individual is cared for, educated, and allowed to dictate the course of his or her own life.  A paradigm where the population is stabilized not by coercion, disease, wars or famine (as Malthus predicted) but by the free choices of happy and healthy people.

Of course, there are still major obstacles to overcome before we can live sustainably on this planet.  Even as our population stabilizes, irreparable damage to our environment continues.  Global consensus remains elusive on challenges such as climate change, deforestation, and biodiversity loss.  And conflict, inequality, and oppression squander much of our global human potential.

But the existence of the demographic transition suggests a goal for humanity: 

We must facilitate and manage the demographic transition across human societies, in an environmentally sustainable way.

If we achieve this goal, we will be on our way toward a healthy and happy, indefinitely sustainable human population.  So maybe, just maybe, we are not, in fact, doomed.

#SciDoom

Freedom and the Public Goods

Last post, I used the example of a protest against peanut allergy-related procedures to explore how the American conception of "rights" may be changing. In particular, I suggested that ideas of common or collective good were being displaced by an increasingly narrow and selfish definition of individual liberty.

A few friends pointed out that I may have unfairly maligned libertarians, anarchists, and others wary of government power.  These people aren't necessarily opposed to volunteerism or helping others; they just don't want to be coerced into doing so (or have their money taken for these purposes).  

This is a fair point.  However, it doesn't make me feel much better about the "leave me alone" political philosophy.  I don't think this philosophy will ever be up to solving our common challenges.  To illustrate why, I'd like to bring in a concept from game theory.

The Public Goods Game represents situations in which there is a common resource ("public good") that benefits all members of a group.  The public good might be a clean kitchen, a functioning electrical grid, or a healthy environment.  This good cannot be maintained without contributions from some group members.  Contributions can be in the form of doing something (washing dishes, working in the community garden, donating to NPR) or not doing something (not littering in a public park, not overfishing a lake).

The dilemma is this: everyone benefits from the public good, but contributions are voluntary.  The public goods game has no built-in incentive to contribute, beyond the desire to make things better for everyone.  So "free-riders" can benefit from others' contributions without contributing anything themselves. 

Both theory and experiment predict that cooperation cannot be sustained in such a game.  A typical experimental result looks like this:

Horizontal axis is time (number of game rounds)  SOURCE: Fehr and Gaechter (2000)

Contributions decline over time to virtually nothing. This is not because the participants are inherently selfish.  Indeed, at the start of the game, many people are inclined to contribute.  However, they realize at some point that others are exploiting their generosity.  Not wanting the benefits of their hard work to reward those who don't contribute, people eventually stop contributing altogether.  This unfortunate outcome has a name: the Tragedy of the Commons. 

Economists and social scientists have identified a few mechanisms that can reverse this tragedy.  If the participants know each other, and also interact in settings aside from the game, then concern for one's reputation can motivate people to contribute (Milinski et al. 2002, Rand et al. 2009).  This helps explain why co-ops can be successful: everyone knows each other.  They can reward or punish others based on their contributions to cooking, cleaning, and other tasks. 

But what about global challenges like climate change, environmental conservation, and sustainable use of resources?  These involve billions of players across the globe, and there are strong financial incentives to exploit the public good for individual gain.  Furthermore, it can be difficult to trace problems like pollution or overfishing to the individuals or companies responsible.  How these large-scale challenges be solved?

Research has identified only one answer. If the game is too large and complex for individual interactions to maintain cooperation, the solution is for the participants to invest in institutions (Gureck et al., 2006; Sigmund et al., 2010).  These institutions must have the power to investigate the actions of individuals, and reward or punish them based on their contributions. In other words, a social contract is needed, together with institutions to enforce it.

Of course, powerful institutions have inherent potential for corruption and abuse.  This is what worries libertarians and anarchists.  I share that concern.  But the solution, in my view, is to build in democratic checks, so that these institutions are as responsive as possible to the people they serve.

It's hardly a perfect solution.  Institutions can become entangled with those they should regulate.  Democratic checks can be co-opted. 

But to solve the largest problems that face humanity, we can't count on good will and personal responsibility alone.

References:

Ernst Fehr, & Simon Gaechter (2000). Cooperation and Punishment in Public Goods Experiments American Economic Review, 90 (4)

Özgür Gürerk, Bernd Irlenbusch, & Bettina Rockenbach (2006). The Competitive Advantage of Sanctioning Institutions Science, 312 (5770), 108-111 DOI: 10.1126/science.1123633

Milinski, M., Semmann, D., & Krambeck, H. (2002). Reputation helps solve the ‘tragedy of the commons’ Nature, 415 (6870), 424-426 DOI: 10.1038/415424a

Rand, D., Dreber, A., Ellingsen, T., Fudenberg, D., & Nowak, M. (2009). Positive Interactions Promote Public Cooperation Science, 325 (5945), 1272-1275 DOI: 10.1126/science.1177418

Sigmund, K., De Silva, H., Traulsen, A., & Hauert, C. (2010). Social learning promotes institutions for governing the commons Nature, 466 (7308), 861-863 DOI: 10.1038/nature09203