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Inclusive FitnessTeasers

51Ht9P0jm3L._SY344_BO1,204,203,200_ A few years ago there was a huge stir caused by the publication in Nature of a somewhat mathematically abstruse paper, The Evolution of Eusociality. It was huge enough that it got a treatment in The New Yorker, Kin in Kind. Many of the reactions were basically tribal. Most geneticists were rather upset with the publication of this paper for a variety of reasons, both substantive and stylistic. In contrast, I’ve engaged in conversations with ecologists who assume that the authors of this paper basically proved that old-fashioned inclusive fitness theory, as first outlined by W. D. Hamilton in the 1960s, had been shown to be superfluous and irrelevant.

A major point by one of the authors of the original paper, Corina Tarnita, is that their detractors didn’t really engage with the model that they laboriously outlined. Well, until now. A new paper in PLOS BIOLOGY takes the model from the 2010 paper, and argues that it isn’t really all that robust, and therefore does not really speak to whether inclusive fitness is useful at all in comparison. The paper is Relatedness, Conflict, and the Evolution of Eusociality. Nicely it provides a lot of code to go along with the assertions, so I invite readers to dig into it, and the original Nature paper from 2010. And while you’re at it, W. D. Hamilton’s first volume of collected papers which addresses his work on social evolution, Narrow Roads of Gene Land, is highly recommended (if you want some full-throated anti-Hamiltonian viewpoints, Unto Others: The Evolution and Psychology of Unselfish Behavior, might interest you, though only the first half is much focused on evolutionary genetic aspects). 51aEM-jiATL._SY344_BO1,204,203,200_

If I had to bet I would say that inclusive fitness is very important across many branches of the tree of life. But, I’d also suggest that among organisms with particular complex and elaborated social structures (e.g., humans) there is probably a lot more going on. Also there is more than can be explained by reciprocal altruism. So I’ll go on the record that for humans something similar to multi-level selection theory does have something useful to add, especially when it comes to cultural evolution, where standard objections to low between group variance do not hold. It’s just that this is evolutionary, not revolutionary, science. I wish the enemies of inclusive fitness would calm down with the bromides, and just get on with good science. The truth will tell.

• Category: Science • Tags: Inclusive Fitness 

The fruits of human cooperation

ResearchBlogging.orgThe Pith: Human societies can solve the free rider problem, and generate social structure and complexity at a higher level than that of the band. That implies that much of human prehistory may have been characterized by supra-brand structures.

Why cooperation? Why social complexity? Why the ‘problem’ of altruism? These are issues which bubble up at the intersection of ethology and evolution. They also preoccupy thinkers in the social sciences who address fundamental questions. There are perhaps two major dimensions of the parameter space which are useful to consider here: the nature of the relationship between the cooperators, and the scale of the cooperation. An inclusive fitness framework tracks the relation between altruism and genetic relatedness. Reciprocal altruism and tit-for-tat don’t necessarily focus on the genetic relationship between the agents who exchange in mutually beneficial actions. But, in classical models they do tend to focus on dyadic relationships at a small scale.* That is, they’re methodologically individualistic at heart. So all complexity can be reduced to lower orders of organization. In economics a rational choice model of behavior is individualistic, as are the critiques out of behavioral economics.

There are other models which break out of this individualistic box, insofar as they make analogies between organisms at the individual scale to social entities which are aggregations of individuals (e.g., a colony or ethnic group). The society as an organism has an old intellectual pedigree, and was elaborated in great detail by Émile Durkheim. More recently David Sloan Wilson has attempted to resurrect this framework in an explicitly evolutionary sense. Wilson has also been the most vocal proponent of multi-level selection, which posits that the unit of selection can be above the level of the gene or individual. For example, selection operating upon distinctive ‘demes.’ Roughly, a breeding social unit.

There are major theoretical and practical issues with evaluating social units as ‘organisms.’ I will set those aside for now, and shift the focus to humans. I do so because some of those theoretical and practical issues abate when you put the spotlight on higher order cultural structure and variation. In a more technical sense it seems rather obvious that humans have the ability to throw up a large amount of between group ‘memetic’ variance, and maintain that variance, long enough that selection may be able to operate across the two different phenotypes which are homogeneous within group and utterly disjoint across group.

But even if such ‘cultural group selection’ is possible, that does not negate the power of kin, as well as other ‘lower level’ dynamics which may operate at cross-purposes with organismic social units. The biggest problem which comes to mind is the ‘free rider,’ the individual who takes from the benefits accrued to group harmony, but does not put anything into the system and so incur a cost. Over the long term evaluated on the individual scale the free rider is the fit, and therefore the group will become far less effective as its phenotype and genotype wax. This powerful logic is why individualist dynamics are so much more attractive. By simply optimizing fitness through invariant individual behavior you don’t have to confront the specter of the long term futility of the group strategy in the face of self-interested personal tactics.

Yet if you think about it the same problem confronts conventional biological organisms at the scale of the individual. We’re a coalition of disparate cells, some of which even retain their own distinctive genetic lineage (mitochondria). How is the problem of cooperation at this scale solved? If you want a book-length treatment, get Mark Ridely’s The Cooperative Gene: How Mendel’s Demon Explains the Evolution of Complex Beings. But we do have a variety of tactics to stall the ourselves from self-destructing via intra-organismic competition, though in many cases those tactics are futile by the end of your life. I’m referring here to the high probability that you’ll develop cancers, which are basically individual cells whose selfish replicative propensities destroy the useful equilibrium of tissues which help to maintain the integrity of the individual. Over the short to medium term cancerous lines of cells are highly fit, as they spread throughout your body. But over the long term they are self-defeating, insofar as the organism which they parasitize as free riders eventually comes crashing down due to the weight of the stresses which the selfish cells impose on the complex cooperative edifice that is the individual.

Many of these same dynamics have social applicability. In fact the metaphors at the level of cell and tissue derive from older social concepts. So let’s move back to humans. One extreme model of social complexity posits that all the baroque richness of human societies we see today are ad hoc extrapolations and reconfigurations of impulses and instincts which were shaped in an environment of evolutionary adaptedness (EEA) of the hunter-gatherer band. As an example, the idea of meta-ethnic spiritual brotherhood which is common to many ‘higher religions’ is simply an elaboration on our cognitive disposition to think in terms of kinship due to the evolutionary effect of inclusive fitness. Many individual selectionists, most radically George C. Williams, but also Richard Dawkins, seem to posit that human nature is at base positively evil in its selfish intent. Despite Dawkins’ atheism and anti-Christianity I have wondered on occasion if he didn’t have some similarities to a particular sort of reactionary Roman Catholic who took St. Augustine’s theories of original sin too much to heart. Be as that may be, these sorts of individual models generally either imply that social order and complexity are incidental, if valuable, byproducts of proximate instincts, or, social constructions emerge out of phenomena operating at cross-purposes with the stream of evolution (e.g., a complex ideological system constructed from our general intelligence).

This is of course one end of the spectrum. At the other end are a range of broad families of ideas which are group selectionist, or posit a more complex and nested array of dynamics and forces. Williams and his admirers were certainly right to point out the inchoate and woolly nature of much of the ‘survival of the species’ talk which was in the air in the mid-20th century. And, I think talking of taxon level biological selection is something we should do very cautiously if at all. In other words, I accept the general scale independence of evolution. But I do not believe that the 50,000 year experiment of human beings with social complexity is one long extended spandrel. Assuming infinite time for the human experiment to work itself out I can accept that social complexity is due to collapse because of its internal contradictions, but I am but a man alloted a mere few score years, and tend to assent to the proposition that phenomena which span millennia have some right to be accorded the due respect given to the ‘permanent things.’

A new paper in PNAS looks at a society of people who operate in the gray land between ‘small-scale hunter-gatherer bands’ and national entities with all the institutional accoutrements which that entails. The focus of the study are he Turkana. They are a group of Nilotic pastoralists who number between 500,000 and 1 million. They are subdivided into smaller patrilineal units, as well as territorial sections. But the major organizing force among the Turkana in terms of collective action seems to be ‘age group’ cohorts. Basically these are groups of men who come up together as peers. It seems that the Turkana lack institutional religion or formal hereditary leadership. So no kings or warlords of the Turkana who pass their charisma on to the next generation. And the Turkana fight. Or more precisely they raid. As pastoralists they raid for cattle, and they raid for vengeance. Finally, it seems that they do not as a rule raid each other, but rather direct their martial energies outward upon other ethnic groups.

Here’s the abstract, Punishment sustains large-scale cooperation in prestate warfare:

Understanding cooperation and punishment in small-scale societies is crucial for explaining the origins of human cooperation. We studied warfare among the Turkana, a politically uncentralized, egalitarian, nomadic pastoral society in East Africa. Based on a representative sample of 88 recent raids, we show that the Turkana sustain costly cooperation in combat at a remarkably large scale, at least in part, through punishment of free-riders. Raiding parties comprised several hundred warriors and participants are not kin or day-to-day interactants. Warriors incur substantial risk of death and produce collective benefits. Cowardice and desertions occur, and are punished by community-imposed sanctions, including collective corporal punishment and fines. Furthermore, Turkana norms governing warfare benefit the ethnolinguistic group, a population of a half-million people, at the expense of smaller social groupings. These results challenge current views that punishment is unimportant in small-scale societies and that human cooperation evolved in small groups of kin and familiar individuals. Instead, these results suggest that cooperation at the larger scale of ethnolinguistic units enforced by third-party sanctions could have a deep evolutionary history in the human species.

The raw numbers killed proportionally are rather high, but not atypical for many pre-state societies. There are two types of raids. Offensive mass attacks, which seem to be the closest the Turkana and their rivals come to “pitched battle,” and stealth raids with smaller complements of men. I couldn’t but help think of the Cattle Raid of Cooley. Material benefits are real and tangible in many cases, 3 cows per man if victory is theirs. But the costs are real too, the mortality rate is on the order of ~1% per raid. This explains how nearly ~20% of men are dying in their prime years due to violence. Assuming independent probabilities of death you only need 20 raids to have an expected outcome of survival of 0.80. Also, it must be noted that some raids are purely retaliatory and don’t entail any loot, or benefit, to the fighter. These raids of vengeance maintain the honor of the Turkana, and serve as deterrents to future attacks from their enemies. Mass action “tit-for-tat” if you will.

With all the costs and benefits as they are there is naturally free riding. Men beg off on fighting because they can’t find someone to watch their herds, or they’re ill. This might be especially tempting on vengeance raids, where the benefit is a public good which isn’t privately dispersed. Some men avoid being at the tip of the offensive spear during the conflict, and let others take risks so they might live another day. And of course there are stragglers who deviously catch the fleeing cattle first, and secure the best or only portions. If you’ve tread epic myths you know all the varieties of cowardly trickster behavior which might manifest when you are faced with temptations. These raiding parties are numerous, on the order of 250-300 men. They don’t consist of men who are closely related and from the same kin group, but rather a heterogeneous local lot of Turkana, albeit clustered by age group. It seems that the median number of age groups, settlements, and territorial sections, represented in these war parties are around 5 for all of these variables. These war parties are above Dunbar’s number, are not part of some unified group aside from ethnicity and local proximity.

Theory predicts that when you have a diverse lot that diverse interests are going to result in temptation to cheat and let those with whom you’re not close take the fall. How is the problem solved? I’ll quote:

Informally enforced norms allow the Turkana to partially solve the collective action problem in warfare. In 47% of the force raids in which desertions were reported, at least one of the deserters was sanctioned, and in 67% of the force raids in which cowardice was reported, at least one of the cowards was sanctioned (Fig. 7). There are two levels of sanctions. When a warrior’s behavior in a raid deviates from that of his comrades, he is subjected to informal verbal sanctions by his age-mates, women, and seniors. If there is consensus in the community that the act merits more serious sanctions, corporal punishment is initiated. Corporal punishment is severe: the coward or deserter is tied to a tree and beaten by his age-mates. One participant had scars on his torso from being whipped by his age group more than a decade earlier.

This is rather straightforward. In early modern European armies which were involved in set-piece battles there were dragoons stationed at the rear whose role was discourage desertion and retreat through intimidation and force. Obviously the incentive structure here was somewhat different, as defeat in war for a nation-state can have drastic consequences and punishment after the fact may be rendered moot. In the case of these raids documented in this paper it does not seem that the Turkana were involved in existential genocidal conflicts. This may be a function in part of modern norms and the constraining effect of African nation-states in which they’re embedded. Battles between regional warlords in late medieval Europe still occurred, and the monopoly of force accrued to the central government and the monarchy only over time. I would not be surprised if Turkana norms have shifted concomitantly, and non-capital punishment after the raid is an adjustment to the lack of existential urgency in this conflicts.

We know all of the results in this paper in the general verbal sense. How do you fix a free rider problem? You punish them! But the devil is in the details. Here the authors show quantitatively and descriptively that group level dynamics can manifest in a pre-state society above the level of the family band. In fact the unit of organization, the ethno-tribal group, scales up to 500,000 individuals or more! So the social norms were enforced across and beyond kinship groups. Rather it seems that among the Turkana the age groups have a particular power below the level of ethnicity. Presumably what in other contexts might be termed ‘fictive brothers.’ Interestingly these raiding parties were organized and led in an ad hoc and “crowd-sourced” fashion. They illustrate the power of spontaneous dynamics of structured order coming out of a less elaborated and simple social context. And importantly, the violence was directed outward. The rates of murder amongst the Turkana is rather low. Rather, the high risk of death is due to inter-group conflict.

But it seems that the authors are not presenting a simple inter-demic group selection argument. Much of the “action” here operates underneath the level of the group, insofar as group action and cohesiveness is mediated through the regulation of norms of collections of individuals and sub-group entities. This is why I personally find the “group” vs. “individual” dichotomy less than useful. Where do we draw the line from highly elaborated cultural structures built upon atomic units of individual human action to quasi-organismic societies? To a greater extent it seems a matter of taste and convenience, not substance.

One study on the Turkana proves nothing. It may just be part of the bigger puzzle though. For a generation evolutionary psychologists have focused on the model of the hunter-gatherer band during the Pleistocene. Anthropologists working within this tradition have attempted to show that successful hunters and warriors are fecund hunters and warriors. Individual level dynamics then would be validated, as social status is converted into biological currency. From what I have read in the literature (and mind you, I began one theoretically high committed to this hypothesis) the results have been somewhat mixed. This tells us perhaps that one dynamic to explain it all is not going to do the job.

Most of the world’s societies were and are not patrilineal pastoralists. But the Turkana are human, and so they give us a window into the intersection of human psychology and social context, and what that may produce. The intersection is multi-layered, and the product is difficult to distill down to a few broad characterizations. Human social complexity’s raw variety defies broadness of characterization with any economy. But it exists, and it needs explaining, bit by bit.

Citation: Sarah Mathew, & Robert Boyd (2011). Punishment sustains large-scale cooperation in prestate warfare PNAS : 10.1073/pnas.1105604108

* In theory inclusive fitness can obviously be generalized very broadly

Image credit: Wikimedia

(Republished from Discover/GNXP by permission of author or representative)

The original robots

We are haunted by Hamilton. William D. Hamilton specifically, an evolutionary biologist who died before his time in 2000. We are haunted because debates about his ideas are still roiling the intellectual world over a decade after his passing. Last summer there was an enormous controversy over a paper which purported to refute the relevance of standard kin selection theory. You can find out more about the debate in this Boston Globe article, Where does good come from? If you peruse the blogosphere you’ll get a more one-sided treatment. So fair warning (I probably agree more with the loud side which dominates the blogosphere for what it’s worth on the science).

What was Hamilton’s big idea? In short he proposed to tackle the problem of altruism in social organisms. The biographical back story here is very rich. You can hear that story from the “horse’s mouth” in the autobiographical sketches which Hamilton wrote up for his series of books of collected papers, Narrow Roads of Gene Land: Evolution of Social Behaviour and Narrow Roads of Gene Land: Evolution of Sex. For the purposes of the issue at hand the first volume is obviously more important, but the second volume has an enormous amount of personally illuminating material because of Hamilton’s untimely passing in 2000 before it could be edited. In Ullica Segerstrale’s Defenders of the Truth and Oren Harman’s The Price of Altruism Hamilton looms large as a major secondary character in the narrative. The Altruism Equation, A Reason for Everything, and The Darwin Wars, all give him extensive treatment, both his scientific ideas and relevant biographical context. Hamilton’s scientific influence on Richard Dawkins was enormous. There are nearly fifty references to him in both The Selfish Gene and The Extended Phenotype. In writing his obituary Dawkins began: “W. D. Hamilton is a good candidate for the title of most distinguished Darwinian since Darwin.” In terms of the details of his science, Hamilton proposed that genetic relatedness between individuals can explain altruism within groups. In this way Hamilton reduced a phenomenon which had often been explained as a group-level one (e.g., “for the good of the species”) to an individual-level one (e.g., “for the good of the individual/gene”). According to Hamilton when he was a young scientist in the early 1960s most people did not perceive this problem to be a problem at all, and he had difficulty finding support for this line of research, and was in fact warned off it by his superiors. The end culmination of those early years of lonely introspection were two dense, abstruse, and difficult papers (in part due to their peculiar notation), The genetical evolution of social behaviour – I and The genetical evolution of social behaviour – II. But the basic heuristic at the heart of these papers was condensed earlier in a short essay in The American Naturalist as Hamilton’s Rule:

rB > C or rB – C > 0

Where in the context of an altruistic act across two individuals:

r = genetic relatedness between them
C = cost to the individual performing the act
B = benefit to another individual who is the recipient of the act

What the above equation is stating is that when the benefit multiplied by the genetic relatedness exceeds the cost, that is, it is greater than zero, the behavior will spread through natural selection. In contrast, when the cost is greater than the benefit multiplied by the genetic relatedness the behavior will be disfavored.

Here’s a “toy” illustration. Imagine a gene, G, in two variants, G1 and G2. The “ancestral” “wild type” is G1, while G2 is an allele which induces altruistic behavior toward nearby con-specifics. Assume that nearby con-specifics are likely to be genetically close, perhaps siblings. The altruistic behavior induces a cost at no benefit to the individual which is engaging in altruism, but it results in a benefit at no cost to the individual which is a recipient of the act. But here’s the key: nearby kin are much more likely to have the altruistim conferring allele, so G2 is likely increasing its own fitness because recipients of the altruistic behavior may also carry G2. Obviously the details matter here in evaluating exactly whether altruism spreads. What is the magnitude of the cost? What is the magnitude of the benefit? What is the extent of relatedness measured against a basal expectation?

There are also some presuppositions within the original theoretical framework of altruism evolving because of gains to inclusive fitness. Hamilton assumed weak selection, additivity of costs and benefits of fitness components, as well as a specific way to frame genetic relatedness. It has long been a question how robust the Hamiltonian framework is to deviations from its assumptions, deviations which are likely to occur empirically. But empirically measuring fitness in the wild as well as genetic relatedness was either impossible or difficult.

So how to get around this? A new paper was published in PLoS Biology does just that with literal a toy model of robots controlled by a simple neural network. The robots seem to mimic foraging behavior, which impacts their fitness in relation to how they replicate their digital genome to the next generation. Remember, Hamilton’s model was very theoretical, so even if there are literal artificialities here it is still an interesting empirical example which moves us closer to concrete reality. A Quantitative Test of Hamilton’s Rule for the Evolution of Altruism:

One of the enduring puzzles in biology and the social sciences is the origin and persistence of altruism, whereby a behavior benefiting another individual incurs a direct cost for the individual performing the altruistic action. This apparent paradox was resolved by Hamilton’s theory, known as kin selection, which states that individuals can transmit copies of their own genes not only directly through their own reproduction but also indirectly by favoring the reproduction of kin, such as siblings or cousins. While many studies have provided qualitative support for kin selection theory, quantitative tests have not yet been possible due to the difficulty of quantifying the costs and benefits of helping acts. In this study, we conduct simulations with the help of a simulated system of foraging robots to manipulate the costs and benefits of altruism and determine the conditions under which altruism evolves. By conducting experimental evolution over hundreds of generations of selection in populations with different costs and benefits of altruistic behavior, we show that kin selection theory always accurately predicts the minimum relatedness necessary for altruism to evolve. This high accuracy is remarkable given the presence of pleiotropic and epistatic effects, as well as mutations with strong effects on behavior and fitness. In addition to providing a quantitative test of kin selection theory in a system with a complex mapping between genotype and phenotype, this study reveals that a fundamental principle of natural selection also applies to synthetic organisms when these have heritable properties.

The science at the heart of this paper isn’t too knotty. There wasn’t a complicated novel derivation or forbidding statistical model. Rather, the authors ingeniously managed to test experimentally the simple insights of the Hamiltonian framework. The results were surprisingly unsurprising.

I reedited the panels below, but they show the consistency of the basic results. Keep in mind that the replicates varied r, B, and C.

Not to be too cute, but the robots followed Hamilton’s Rule in a robotic fashion! When the cost was too great altruism was disfavored and when the benefit was great enough altruism was favored. In a situation of balance there was the sort of stochastic fluctuation about the initial condition you’d expect. One thing to remember is that the authors simulated mutation and recombination, so selection wasn’t the only evolutionary parameter at work. The panel to the left shows how the level of altruism varied as a function of relatedness, with the ratio between cost and benefit held constant. The top left panel shows a situation where c/b = 0.01. That means that the benefit to the recipient is 100 times greater than the cost to the altruist. Even at low levels of relatedness the altruism spreads. As the ratio between cost and benefit converges upon 1, where the cost now equals the benefit, the relatedness threshold for a given level of mean altruism across these groups increases. This is all as you’d expect, boringly thrilling to see a simple model validated.

The authors also tested the impact of switching to a mutation of large effect (so not weak selection) as well as epistatic gene-gene interactions (so introducing nonlinearities which deviate from the assumption of additivity). Basically they seem to have found that both of these impacted behavior and fitness, but not the ultimate outcome. I’ll quote, because honestly I’d have liked to see more of this in the paper, but that’s probably for the future:

To determine whether mutations in our neural network had pleiotropic and epistatic effects and whether there were departures from weak mutations effects , we conducted additional experiments at the last generation in two treatments with intermediate r and c/b values (treatment 1: r = 0.25, c/b = 0.75; treatment 2: r = 0.75, c/b = 0.25). First, for each treatment, we subjected 4,000 individuals (one in each group) to a single mutation of moderate effect…In the first experiment, performance was significantly affected by a much higher proportion of the mutations than the level of altruism…1.36% of the mutations affecting the level of altruism also translated into a significant change in performance, indicating widespread pleiotropic effects. Similar results were obtained in the second experiment with 4.91% of the mutations affecting the level of altruism also significantly affecting performance. Second, we tested for epistatic effects by comparing the effect of a single mutation in 4,000 individuals with two allelic variants at another locus…genetic background significantly influenced the effect of the mutation in 2,371 (59.3%) of the cases in the first treatment and 2,336 (58.4%) of the cases in the second treatment. These results demonstrate that epistatic interactions are also widespread. Finally, our experiments showed frequent departures from weak effects on behavior and fitness. Performance changed by more than 25% for 1,616 (40.4%) of the mutations in the first treatment and 1,776 (44.4%) of the mutations in the second treatment, and the level of altruism changed by more than 25% for 552 (13.8%) and 1,808 (45.2%) of the mutations in the first and second treatment, respectively.

But in the discussion, they note:

Despite the fact that the assumptions mentioned above were not fulfilled, Hamilton’s original 1964 rule always accurately predicted the conditions under which altruism evolved in our system. Whatever the c/b value used, altruism always evolved in populations where r was greater than c/b. This finding is important given that the assumption of weak selection, additivity of costs and benefits of fitness components and absence of pleiotropic and epistatic gene interactions are also likely to be violated in real organisms that also have a complex mapping between genomes and phenotypes.

The likely power of this sort of inclusive fitness does not in my book invalidate other forces which shape social behavior such as reciprocal altruism. Nature is one, how we carve it at its joints is our business. Hopefully we’ll see a lot more tests of social behavior using robots in the future. And, with the rise of cheap typing of individual identity with genotyping there is the possibility for better assessments of relatedness and fitness across generations in nature itself.

Citation: Waibel M, Floreano D, & Keller L (2011). A Quantitative Test of Hamilton’s Rule for the Evolution of Altruism PLoS Biology : 10.1371/journal.pbio.1000615

(Republished from Discover/GNXP by permission of author or representative) With the recent huge furor over the utility of kin selection I’ve been keeping a closer eye on the literature on inclusive fitness. The reason W. D. Hamilton’s original papers in The Journal of Theoretical Biology are highly cited is not some conspiracy, rather, they’re a powerful framework in which one can understand the evolution of social behavior. They are a logic whose basis is firmly rooted in the world of how inheritance and behavior play out concretely. But because of their formality and spareness inclusiveness fitness has also given rise to a large literature derived from simulations “in silico,” that is, evolutionary experiments in the digital domain.

375px-Green_Beard_GeneOne can elucidate inclusive fitness through Hamilton’s Rule, but it is also rather easy to exposit verbally via a “gene’s eye view.” Imagine for example a dominant mutation in a diploid organism which produces the behavior of altruism toward near kin. Initially the altruist will have offspring whose probability of carrying the dominant mutation is 50%, because there is also the probability that they will carry the ancestral non-altruistic variant. Imagine an altruistic behavior which incurs a small, but not trivial, cost to the individual performing the behavior, and a large gain to the individual who is on the receiving end of the altruism. The logic of favoring near kin is such that in the initial generation the parent which behaves altruistically toward near kin is increasing their own “inclusive fitness” because their offspring share 50% of their genes identical-by-descent (in the case of a diploid sexually reproducing organism). But from a gene’s eye perspective what is really occurring is that there is a 50% chance that the gene which fosters altruism is promoting the fitness of a copy of itself. So inclusive fitness operates by modulating the parameters of costs and gains to focal individuals as a function of their relatedness, but it is the genes, the “replicators,” which persist immortally across the generations. We “vehicles” are just the ocean through which genes sail.

But like Darwin’s theory of evolution through natural selection the fruit of these logics are in the details. A new paper in The Proceedings of the Royal Society puts the focus on different means by which inclusive fitness may be maximized. In particular, the paper offers up a reason for why what Richard Dawkins termed the “green-beard effect” is not more common. Selective pressures for accurate altruism targeting: evidence from digital evolution for difficult-to-test aspects of inclusive fitness theory:

Inclusive fitness theory predicts that natural selection will favour altruist genes that are more accurate in targeting altruism only to copies of themselves. In this paper, we provide evidence from digital evolution in support of this prediction by competing multiple altruist-targeting mechanisms that vary in their accuracy in determining whether a potential target for altruism carries a copy of the altruist gene. We compete altruism-targeting mechanisms based on (i) kinship (kin targeting), (ii) genetic similarity at a level greater than that expected of kin (similarity targeting), and (iii) perfect knowledge of the presence of an altruist gene (green beard targeting). Natural selection always favoured the most accurate targeting mechanism available. Our investigations also revealed that evolution did not increase the altruism level when all green beard altruists used the same phenotypic marker. The green beard altruism levels stably increased only when mutations that changed the altruism level also changed the marker (e.g. beard colour), such that beard colour reliably indicated the altruism level. For kin- and similarity-targeting mechanisms, we found that evolution was able to stably adjust altruism levels. Our results confirm that natural selection favours altruist genes that are increasingly accurate in targeting altruism to only their copies. Our work also emphasizes that the concept of targeting accuracy must include both the presence of an altruist gene and the level of altruism it produces.

Using the Avida software platform the researchers ran trials of the evolution of populations of artificial life which varied in fitness, coefficient of relatedness, as well as their phenotypes. In one set of trials the organisms operated through conventional means of kin selection, whereby the heuristic was to favor those to whom an individual was closely related. This will result in a fair amount of “false positives,” as everyone knows that near kin can be selfish and “cheat.” Remember that in the toy example above 50% of the offspring who will gain from altruism will themselves lack the altruism gene. A second set of organisms look to total genetic similarity. This is the sort of thing which humans could engage in if they had immediate knowledge of the genomic sequences of those around them. Even among near relatives genetic similarity is only correlated with, not perfectly correspondent with, coefficients of relatedness. Some full siblings may share more identity-by-descent than others. This is trivially obvious in the initial illustration, as there will be a great deal of intra-familial variance on the gene which produces altruism. To focus on the dynamics of the specific gene, the authors also looked at a green-beard effect, whereby a there is a correlation between altruism, a gene, and a visible phenotype. In other words, you know altruists by a correlated physical trait. If the correlation between a phenotype and a genotype is close enough you don’t need do a typing of their genome because you know the state of their genotype, and so have expectations as to whether they’re truly altruists or not. Presumably using the green-beard effect one could side-step the usage of kinship or relatedness as a proxy. In many cases those more distantly related could be more phenotypically similar on the traits of interest than those who are genetically closer.

What did they find? Figure 1 shows the outcomes of various sets of trials:


Their expectations were that in regards to the evolution of altruism kin selection should be inferior to genetic similarity which should be inferior to the green-beard effect. The reasoning is straightforward, as you progress across these sequence of dynamics the false positive rate of aiding those without the altruism conferring gene should decrease. That is not what they found, at least not initially.

What was happening is that they were focusing on the wrong parameters in framing their expectations. That’s why you run the model: human intuition often fails. Green-bearding is very precise as a dichotomous indicator of whether an individual carries a particular gene identical-by-descent, but mutation could produce variation in levels of altruism. What they found was that when green-bearding was dichotomous the levels of altruism tended to converge upon a lower equilibrium as individuals were focused on being just altruistic enough to count as real altruists and so gain advantages from those who were more generous. A concrete example of this would be an “affinity con”. An individual is a member of a group, and they leverage the trust which comes from being a member of the group to exploit the group. Baked into the cake of the original model is that altruists who also had a green-beard had to have donated at least once, and that is the target which green-beards converged upon. In contrast the strategy of genetic similarity resulted in greater donations, and because the model had non-zero sum dynamics (altruism increased everyone’s fitness greatly, though cheaters could exploit this to “free-ride”) the strategy which maximized donations was more successful. The researchers made green-bearding more competitive by simply increasing the donation threshold to match the equilibrium which emerged with the other strategies. So making all things equal the intuition about green-bearding was then vindicated.

Instead of setting a specific threshold there was another way that green-bearding could beat the other strategies to maximize inclusive fitness: vary the green-bearding trait and altruism continuously in a correlated fashion. In other words, the greener the beard, the more altruistic. This is a classic way that one could beat the cheaters: develop detection and discernment mechanisms. Why doesn’t this matter for the two other more “primitive” techniques? Kin selection and genetic similarity are more robust because they’re not fine-tuned, organisms with similar genome content are likely to have similar altruism levels. The genetic relatedness of altruists in green-bearding populations is going to be lower because they’re looking for a very specific genotype and its correlation with a phenotype. Green-bearding is more precise, but it’s also somewhat more complicated, and as a more precisely engineered solution it may not always be as robust.

And that necessity of fine-tuned intelligence in design may be why green-bearding is not more common. The authors note that in theory one could imagine mutations leading to concomitant variations of the magnitude of green-bearding and altruism in the same direction, but in a real evolutionary genetic context with normal parameters of mutation and effective population sizes this may not be plausible. Many people would argue that evolution is littered with kludges because natural selection makes recourse to “quick and dirty” solutions which are simple but effective, and kin selection and genetic similarity are closer to that than green-bearding. In theory selection may lead to a world of green-beards with infinite population sizes and generations, and persistent and consistent selection, but the world may be too protean for this optimal equilibrium to ever arise. So until then, we’ll make do with social evolution’s duct-tape: “I against my brother; my brother and I against my cousin; I, my brother, and my cousin against the stranger.”

Citation: Clune J, Goldsby HJ, Ofria C, & Pennock RT (2010). Selective pressures for accurate altruism targeting: evidence from digital evolution for difficult-to-test aspects of inclusive fitness theory. Proceedings. Biological sciences / The Royal Society PMID: 20843843

Image Credit: Burningrey

(Republished from Discover/GNXP by permission of author or representative)

There is a new paper in Nature which is a full frontal attack on the utility of William D. Hamilton’s inclusive fitness framework in explaining eusociality. Martin A. Nowak, Corina E. Tarnita, & Edward O. Wilson are the authors. Wilson is famous in large part for his authorship of Sociobiology: The New Synthesis, and is arguably the doyen of American organismic biology. He is both an active scientist, and, a premier public intellectual. So with that in mind, I notice that Dienekes Pontikos alludes to “E.O. Wilson’s change of mind about group selection.” This is conventional wisdom, but it is I think wrong (though from what I can tell Wilson has not done much to disabuse the press of the notion). In Defenders of the Truth Ullica Segerstrale notes that Wilson did not expunge group selection thinking even in Sociobiology. In Evolution for Everyone David Sloan Wilson recounts that it was in fact E. O. Wilson who pointed out a group selective interpretation of data he was presenting at a conference, helping to push him early on in a rather unfashionable direction. From what I have heard Wilson always believed that the empirical data was not adequately explained by a pure inclusive fitness model, and simply waited until things shook out before pushing back with more theoretically trained colleagues who had the same skepticism.

From page 30 of Sociobiology:

…….Nevertheless, Williams’ distaste for group-selection hypotheses wrongly lead him to urge the loading of the dice in favor of individual selection. As we shall see in chapter 5, group selection and higher levels of organization, however intuitively improbable they may seem, are at least theoretically possible under a wide range of conditions. The goal of the investigation should not be to advocate the simplest explanation, but rather to enumerate all of the possible explanations, improbable as well as likely, and then to devise tests to eliminate some of them.

And page 129, the last paragraph in the chapter on group selection (quoted in full so there’ll be no confusions as to whether I’m pulling it out of context):

In conclusion, although the theory of group selection is still rudimentary, it has already providd insights into some of the least understood and most disturbing qualities of social behavior. Like Arjuna faltering on the Field of Righteousness, the individual is forcd to make imperfect choices based on irreconcilable loyalties-between the “rights” and “duties” of self and those of family, tribe, and other units of selection, each of which evolves its own code of honor. No wonder the human spirit is in constant turmoil. Arjuna agonized, “Restless is the mind, O Krishna, turbulent, forceful, and stubbon. I think it is no more aesily to be controlled than is the wind.” And Krishna replied, “For one who is uncontrolled, I agree the Rule is hard to attain, but by the obedient spirits who will strive for it, it may be won by following the proper way.” In the opening chapter of this book, I suggested that the science of sociobiology, if coupled with neurophysiology, might transform the insights of ancient religions into a precise account of the evolutionary origin of ethics and hence explain the reasons why we make certain moral choices instead of others at particlar times. Whether such understanding will then produce the Rule remains to be seen. For the moment, perhaps it is enough to establish that a single strong thread does indeed run from the conduct of terminte colonies and turkey brotherhoods to the social behavior of man.

(Republished from Discover/GNXP by permission of author or representative)

Sometimes in a narrative you have secondary characters who you want to revisit. What do to do after the story is complete? An convenient “work-around” to this problem is to find the story rewritten from the perspective of the secondary character. In broad strokes the picture is unchanged, but in the finer grained shadings different details come into sharper relief. Though the exterior action may be unaltered, it gains different context, and the interior motive may radically alter, as the nature of subjective perspective matters so greatly in the last instance. In many ways Oren Harman’s The Price of Altruism reads to me like a narrative rewritten from the perspective of a character who was a supporting protagonist in other stories. George Price, almost a novelty act elsewhere, now becomes the primary point of view character.

I could almost say that Harman, a historian of science, has given us a novel from a “shared universe” of stories. That universe is the real world. The other stories are the lives of great scientists, and the plot consists of the working out of their ideas. In the acknowledgments Harman alludes to the wide range of works where fragments of George Price’s life filters through. I have read many of the mentioned works, The Darwin Wars, Defenders of the Truth, and Narrow Roads of Gene Land. In all of these George Price cuts a quixotic figure, mercurial, brilliant and exceedingly eccentric. His plain biography already peculiar. Price began his career as a chemist, shifted to journalism and became what we today would term a professional “skeptic,” then entered into a period of productivity as an evolutionary theorist of some major impact, and finally spent his last years attempting to live the life of a serious Christian who followed God’s commands to the best of his abilities. He died tragically, committing suicide in his early 50s in 1975, homeless, destitute, and serious ill.

Much of what I already know comes through the memories of William Hamilton in his collections of papers, titled Narrow Roads of Gene Land. In Narrow Roads of Gene Land Hamilton admits that he did not perceive in totality the implications of Price’s eponymous equation when he first encountered it (in particular, he did not initially comprehend that the two elements within the Price equation allowed for the possibility of group selection as you move up the nested hierarchies of organization and reassign the elements to ascending levels). In The Price of Altruism Oren Harman reiterates this reality, but, importantly he emphasizes that Price felt that it was Hamilton alone in all the world who had perceived the equation’s nature upon first encountering it. The back story, which is told in Narrow Roads of Gene Land, is that George Price had difficulty in getting his papers in this area published because the referees simply did not see the implications. Hamilton, perceiving the importance of Price’s ideas, connived to gain publication by making his own work conditional on the acceptance of Price’s paper (which he cited). As Hamilton already had a reputation the game worked.

The necessity of these strategies makes more sense in light of Price’s unconventional background and affect. In evolutionary biology Price was self-taught, and he entered the field in large part because he was interested in the topic, and perceived that he was going to make some difference in the world. He arrived in London in the late 1960s, impressed people at the Galton Laboratory and managed to obtain a research grant and desk, and became an important stimulator of and collaborator with both William Hamilton and John Maynard Smith, arguably Britain’s two most prominent theoretical evolutionary biologists at the time. Price’s relationship to John Maynard Smith is referenced in Hamilton’s own biography, as well as third person narratives such as The Darwin Wars and Defenders of the Truth, but The Price of Altruism fleshes out many of the details. While Price extended Hamilton’s original work on inclusive fitness, for Maynard Smith he served more as a prod and collaborator as they explored the intersection of game theory and biology which eventually led to the ideas outlined in Evolution and Theory of Games. The “hawk” and “dove” morphs made famous by Richard Dawkins in The Selfish Gene go back to Maynard Smith’s work, but the terms themselves were of Price’s invention according to Harman. If I read Harman’s chronology correctly Price was already a fervent Christian by this time, having left atheism in the same period as he launched his career as an evolutionary biologist, and there is some hint that the term “dove” may have been influenced by his particular religious leanings. This possibility seems all the more amusing in light of Dawkins’ later career as an atheist polemicist. Price’s last contribution to evolutionary biology was an explication of Fisher’s fundamental theorem of natural selection. This formalism has been the subject of so much deep analysis, such that I think Price’s interest in it prefigured his later stab at Biblical textual analysis!

The Price of Altruism is a biography of a scientist, so naturally there’s a great deal of science. The meat and heart of the work is George Price’s life trajectory, with all its travails (many) and triumphs (few, but lasting and of importance). Yet the story begins with an exploration of the lives and opinions of men who seem of a different age, Thomas Huxley and Peter Kropotkin. Huxley and Kropotkin were archetypes, who anticipated two streams of evolutionary ecology and social theory which battled it out through the 20th century. Huxley was a man who saw nature as “red in tooth and claw,” the working out of amoral competitive forces, and human virtue as having emerged out and above nature, just as he had risen up from his working class origins to eminence. Kropotkin reflected a Russian viewpoint which saw cooperation as the norm, and competition as the deviation. For him virtue emerged from our natural tendencies. Lee Alan Dugatkin covers much of the same ground in The Altruism Equation. Great men who you meet elsewhere inevitably make cameo appearances in Harman’s narrative; R. A. Fisher, the brilliant cipher, J. B. S. Haldane, the hereditarian Marxist, and Sewall Wright, the American (also see The Origins of Theoretical Population Genetics). The bright lights of Price’s generation also make prominent appearances; William Hamilton and John Maynard Smith, their characters manifesting no great surprises, but also the schizophrenic genius Robert Trivers, with whom Price perhaps shares a great deal excepting his dark ending, as well as E. O. Wilson.

All of these individuals have an interest in evolutionary biology, but biology of a behavioral sort. Though molecular evolutionists such as Richard Lewontin and Motoo Kimura are references in The Price of Altruism, they’re ancillary to the thrust of the book’s central idea (though Lewontin seems to serve as a type, the brilliant scientist who saw the import of Price’s equation too late to engage in a productive exchange with George Price himself). Evolution, like theoretical physics, spans may domains of subject, from the aggregations of millions of individual life forms, to evolution of elements within individual genomes! The Price equation’s generality is such that it does speak to the phenomena which bubble just above the level of organizations of the substrate, DNA itself. But George Price’s focus was on higher, not lower, levels of organizations, human societies. Oren Harman makes this clear, for he brings to light Price’s correspondence with Paul Samuelson, one of the greatest economists of the 20th century. Before Price left for London and began his collaboration with Hamilton and Maynard Smith on altruism, he fancied reconstructing the basis of 20th century economics. By the end of his life Price suggested that he was going to go back to this initial impulse, and attempted to renew his correspondence with Samuelson in the hopes of obtaining a research fellowship of some sort. Price also engaged with the behavioral psychologist B. F. Skinner, though as with many of his encounters it seems that the two soured on each other, in part due to Price’s impolitic tendencies.

George Price’s aim was to explain human cooperation, altruism. In short, goodness. This is the domain of angels, but his analytical bent mean that he could not let the phenomenon lay. He had to break it down, reconstruct its fundamentals, and elaborate on how and why goodness, altruism, manifested itself in the world. From the details reported in The Price of Altruism I would have to admit that Price himself was a Janus-like figure, often being in a manifestly selfish fashion, abandoning his family to follow his intellectual bliss, and yet also radically altruistic, allowing himself to be exploited by the dregs of the London underclass near the end of his life because scripture told him so (or his reading of scripture). What I had previous read did not emphasize Price’s selfishness, his need to satisfy his own wants, and place his own elective priorities ahead of the mandatory ones which decency bound him to honor (e.g., supporting his wife and daughters). Harman has a rich catalog of George Price’s selfish actions and the small vendettas which wracked his soul. No saint was he. Much of what Harmon recounts was simply not evident from other sources. Perhaps in Hamilton’s case he wished to highlight the positive aspects of a good friend who had died tragically. More plausibly I suspect that Hamilton was simply not aware of the selfish sequence of acts which led George Price to the Galton Laboratory in the late 1960s. And it was during this period that George Price became a zealous Christian and a radical altruist. Hamilton’s perceptions may simply have been colored by the slice of Price’s life to which he was privy.

Oren Harman wonders at the end of the book if George Price may have been rather far along the asperger’s spectrum. If so, combined with his fierce intelligence, one is not surprised that Price exhibited a fixation on why and how humans behaved, and why and how it came to be that humans did not seem to be rational psychopaths. Though I do not know if, and honestly do not believe, that George Price was a rational psychopath, in The Price of Altruism Oren Harman paints a picture of a man with immediate urges and impulses, earthy hedonic priorities, and a strong tendency to discount the costs which his choices may have for those close to him. George Price was not the first man to not be a good father, but he was one who perhaps wondered why there were good fathers and bad fathers, those who followed their bliss despite the consequences to their progeny, and those who sacrificed so that their children could enjoy the comforts and pleasures which they elected to forgo. The science is well elucidated in works such as Unto Others, The Origins of Virtue and The Evolution of Cooperation. The Price of Altruism is rather a case study not of the theory of altruism, but of the concrete embodied human experience which eventually gave fruit to an important slice of the theory of altruism. From the small details of his day-t0-day actions, to the arc of his life, George Price played out some of the implications of his own intellectual edifice, both through contradiction and confirmation.

Recommended Reading: The Darwin Wars, The Evolutionists, A Reason for Everything, Narrow Roads of Gene Land, Natural Selection and Social Theory, The Origins of Theoretical Population Genetics, Sewall Wright and Evolutionary Biology, R.A. Fisher: The Life of a Scientist, Defenders of the Truth, Unto Others and The Selfish Gene.

(Republished from Discover/GNXP by permission of author or representative)

If you have even a marginal interest in evolutionary biology you will probably have heard of Hamilton’s Rule, a simple formal representation of the logic whereby a gene which favors altruism may spread through a population: rB > C, where r = coefficient of relatedness on the gene in question, B = benefit to those related, and C = cost to oneself. The idea is almost trivially obvious. Consider that you are in a situation where you are faced with the possibility of aiding your full sibling at a cost to yourself. Now imagine that you carry a single allele which favors altruism toward close relations. Your sibling has a 50% probability of carrying that allele identical by descent (let’s stay haploid for simplicity). From a “gene’s eye view” it benefits the allele to predispose you to helping your kin in direct proportion to the probability that your kin carry that allele. In other words the logic underlying inclusive fitness isn’t really that abstract, it is ordered around the benefits and costs to the theoretical genes which manipulate social behavior over the long term. This explains why the evolutionary biologist J. B. S. Haldane responded “…I would to save two brothers or eight cousins,” when asked if he would save his brother from drowning. The genetically relatedness to a sibling is 1/2, to a cousin 1/8. 2 X 1/2 = 1 and 8 X 1/8 = 1, basically equivalent to yourself. Evolutionary altruism is obviously somewhat different from common sense altruism, because you’re averaging out the behavior of many individuals over a time window.

The fascinating back story behind the development of this sort of formal thinking is recounted in W. D. Hamilton’s first collection of papers, Narrow Roads of Gene Land: Evolution of Social Behaviour. An elaboration upon the core logic of Hamilton’s Rule in two seminal papers revolutionized our understanding of the evolution of sociality in the 1960s; Hamilton was proud of how widely cited his original papers were. John Maynard Smith’s evolutionary game theory and Robert Trivers reciprocal altruism emerged out of the same ferment (Trivers’ acknowledges the debt to Hamilton in Natural Selection and Social Theory). More recently E. O. Wilson and David Sloan Wilson have been arguing for a rehabilitation of more complex models of the origins of sociality through multilevel selection theory.

But what about Hamilton’s original ideas, the core elements of inclusive fitness? Their spareness rendered them analytically tractable, but like all models the original formalism made some simplifying assumptions. Relatively weak selection pressures, as well as additivity of fitness effects, were two major axioms, and ones which Hamilton defended in Narrow Roads of Gene Land. A new paper in Science argues that the assumptions rendered the model too simple to be of more than qualitative or heuristic utility in most cases. They modify the Hamiltonian framework by including nonlinear fitness distributions as well as stronger selection coefficients in the context of microbes. A Generalization of Hamilton’s Rule for the Evolution of Microbial Cooperation:

Hamilton’s rule states that cooperation will evolve if the fitness cost to actors is less than the benefit to recipients multiplied by their genetic relatedness. This rule makes many simplifying assumptions, however, and does not accurately describe social evolution in organisms such as microbes where selection is both strong and nonadditive. We derived a generalization of Hamilton’s rule and measured its parameters in Myxococcus xanthus bacteria. Nonadditivity made cooperative sporulation remarkably resistant to exploitation by cheater strains. Selection was driven by higher-order moments of population structure, not relatedness. These results provide an empirically testable cooperation principle applicable to both microbes and multicellular organisms and show how nonlinear interactions among cells insulate bacteria against cheaters.

The bottom line here is that the authors are indicating that a simple framework with the parameters of Hamilton’s original formalism can not explain the various forms of altruism found among microbes, even ubiquitous ones such as biofilms. One should not be surprised, as the problem of altruism was not solved by inclusive fitness in its details, though many use it in a hand-waving manner, i.e., “…everyone knows….” To correct this impasse the authors modify Hamilton’s Rule:


Some of the parameters are now bold. That means they’re vectors, not scalars. Basically lists of variables. First in the list for r is the original coefficient of relatedness, with subsequent elements representing higher orders of relatedness. b represents the benefits to noncooperating morphs as a function of social environment, the frequencies of cooperators and noncooperators. The cost to the focal individual remains the same. Finally, m are the moments for the cooperators (measuring distributions of fitness in terms of their shape) and d represents the difference between cooperators and noncooperators of the distribution. When fitness effects are totally additive, that is there are no nonlinearities and conditionalities of genotype fitness on environment, the second part of the equation falls away, and r and b reduced to their first elements, so you have a classical form of Hamilton’s Rule.

Figure 1 illustrates the aspects differentiating a classical vs. modified Hamiltonian model:


Basically the simplifying assumptions in Hamilton’s original model is illustrated by panel A. The authors claim that the assumptions allow for no quantitative prediction of real structured altruism which we see. Figure 2 has some experimental data:


Here’s the text:

Parameters of the generalized Hamilton’s rule measured in an experimental population of sporulating Myxococcus bacteria. (A) Absolute fitness of a cooperator strain (blue circles) and a cheater strain (red diamonds) as a function of their frequency within groups. Data points are independent experimental replicates; lines, regression model fit to data. (B) Fitness terms in Eq. (1), calculated from the data shown in (A). Green diamonds, benefit vector b; purple circles, genotype-dependence vector d. Points show best-fit model (±SD from bootstrapped data). (C) Initial distribution of cooperators among groups for a specific experimental population. (D) Social structure terms in Eq. (1) were calculated for the population shown in (C). Blue, cooperator moments m; red, noncooperator moments mnon; black, relatedness vector r.

As you can see in panel A there’s frequency dependence going on here. Cooperators run up against a wall, but the frequencies at which they’re fitter than the noncooperators is rather high. Panel B is important because it shows that the benefits really accrue at the higher moments, now the lower additive one. This means that higher level population structure and nonlinearities when viewed on an individual scale are very important. Figure 3 illustrates the nature of frequency dependence, and the conditions where cooperators flourish and cheaters can persist:


Since higher order structure is critical parameters such as migration between groups are important to keep track of us. More experiments obviously need to be done here, I’m not convinced that one model can explain-it-all. But, there are obvious limitations to the classical Hamiltonian framework in many situations. One of the major points in this paper which jumped out at me was the following: “…increasing-returns nonadditivity allows cooperation to evolve at levels of population structure comparable to that seen among social insect colonies.” Increasing returns is a concept which is important in economics in understanding how technological innovation has allowed for productivity gains over the past two centuries. Human social systems are complex, almost baroque to a fault, and their byzantine structure can easily be dismissed as random acts of contingency. But increasing returns to cooperation may explain the ubiquity of more complex orders than we would expect. And yet here we see it on the scale of bacteria! The logic of non-zero sum is deeply rooted in the nature of life, but the next stage is to flesh out how it produces such rich behavioral phenomena. Endless behaviors most ornate!

Smith J, Van Dyken JD, & Zee PC (2010). A generalization of Hamilton’s rule for the evolution of microbial cooperation. Science (New York, N.Y.), 328 (5986), 1700-3 PMID: 20576891

(Republished from Discover/GNXP by permission of author or representative)
Razib Khan
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