Tuesday, March 25, 2014

Social Evolution in Structured Populations, Again

First, let me say that I've long been interested in altruism.  What accounts for generosity?  It's a complex behavior that surely has many motivations.  A cynic would say that there are no true acts of generosity.  Perhaps, but I would reply that at least sometimes, altruism is motivated by the pleasure of being altruistic.  We must have evolved to derive pleasure from altruism, at least sometimes and under certain conditions.

Several years ago, I was perplexed when a series of articles were published in which E. O. Wilson expressed his thoughts on eusociality.  Take, for instance, the Slate article Altruism and the New Enlightment:

E. O. Wilson stated: "Eusociality, where some individuals reduce their own reproductive potential to raise others' offspring, is what underpins the most advanced form of social organization and the dominance of social insects and humans. One of the key ideas to explain this has been kin selection theory or inclusive fitness, which argues that individuals cooperate according to how they are related. I have had doubts about it for quite a while. Standard natural selection is simpler and superior. Humans originated by multilevel selection—individual selection interacting with group selection, or tribe competing against tribe."

To me, something seemed off about this.  Perhaps for insects, behavior was rigidly assigned.  However, at least for mammals, it seemed to me that social behavior was fluid.  Mammals, even the same individual mammals, seemed capable of both acts of spite and acts of altruism.  An example of altruism would be polar bears befriending sled dogs.


Yet, these very same polar bears probably also occasionally attack polar bear cubs.

A close observer of dogs and cats would know that they often become fast friends.  Yet, the very same cats would probably viciously claw the nose of a dog it didn't know.

It has always seemed to me that human behavior and human altruism is at least just as fluid and temporal.

With this in mind, I was delighted to see the recent paper Social Evolution in Structured Populations.  The full text of the paper is available for a modest price via Readcube.  (This is the first time I've accessed a paper by way of Readcube and I was quite impressed.)

One of the key points of the paper is that studies of altruism have mostly focused on fecundity.  Yet, the paper points out that survival must also have played a role in the development of altruism:

"In most previous models, the costs and benefits altruism or spite are assumed to affect the fecundity of individuals, and costs and benefits for survival have received much less attention, despite the fact that such effects are equally plausible and should hence be incorporated in general models of social evolution."

"The identities of the individuals who die and reproduce depend on the individuals’ fecundity and survival potential, both being affected by social interactions and by the rules according to which the population is updated."

Another key observation of the paper is that "altruism requires some form of assortment so that altruists interact more often with altruists than defectors."  In other words, altruism can only work when similarly functioning altruists find each other.

In order to account for both fecundity and survival, the paper employs two step updating rules: death-birth and birth-death.  Costs and benefits of social interactions in both steps are considered (both fecundity and survival).

The paper assumes weak selection such that the fitness effects of interactions are small.

The implication of the two step updating is nicely illustrated in Supplementary Figure 1.


"Competition in the first step is among all individuals that are one dispersal step away, while competition in the second step is among all individuals that are two dispersal steps away. These two different competition neighbourhoods are illustrated in Supplementary Fig. 1 in the case of a lattice-structured population. In other words, for both DB and BD updating rules, the first step, which involves choosing a first individual globally among all individuals of the population, results in a narrower competitive radius than the second step, in which another individual is chosen locally among the neighbours of the first individual. Thus, whether social interactions affect the first or the second step results in a difference in the spatial scale over which social interactions affect competition."

Step 1:

"The offspring of an individual are located one dispersal step away, which happens to correspond to the competitive radius during the first step of the Moran process. Individuals are therefore directly competing against their offspring, and the detrimental effects of kin competition exactly cancel the social benefits of living next to related individuals. As a result, population structure barely has any effect on the evolution of social behavior."

Step 2: 

"In contrast, population structure is of crucial importance for the evolution of social behavior whenever social interactions affect the second step of the process. This is because the radius of the competitive circle is wider at the second step (two dispersal steps away): individuals are therefore competing against less related individuals, on average, than at the first step."

The paper considers four classical games: Prisoner’s dilemma, Snowdrift, Stag hunt and Simple Spite. These are illustrated in Figure 3 of the paper (not shown here).  I didn't get around to understanding the rules in each of these games.  The paper points out that altruism (in the case of Prisonner’s dilemma, Snowdrift and Stag hunt) is most favoured if benefits are allocated to the second step of the process, which gives more weight to interactions of individuals of the same type.

In the discussion of the games, the paper described cases where social interactions are of the same type on both steps.  However, the paper then emphasizes that the theoretical framework allows for the consideration of mixed cases.  Evidently, this will be elaborated on in a subsequent publication.

I really like this paper as it moves us toward understanding how both fecundity and survival have driven the development of altruism.  Another strength of the paper is that it permits modeling of strategies where both spite and altruism come into play in the same individual.  I’m looking forward further publications from this group.

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