Population Variance

Trying to put down why I think other animals are not as cultural as humans, I think it's important to go off on a little tangent about the importance of variation in traits within populations... It'll take me a little while to get to stuff I consider less appreciated (and therefore more interesting), so please bear with me.

Darwin formulated his theory of evolution while ignorant of genetics. Rather than the atomic inheritance model developed by Mendel and others, Darwin believed in blending inheritance - offspring would tend to be about halfway between each of their parents in any trait. I know R. A. Fisher pointed out that it is very difficult to reconcile blending inheritance with evolution (though I don't believe he was the first to make the point), because blending inheritance naturally reduces the variance of a trait in a population from generation to generation. In fact, I believe variance is supposed to be halved in each generation, when each child is thought to be the mathematical average of the parents. The existence of wide variation in nature, when coupled with blending inheritance, implied an impossible amount of adaptively more-or-less neutral mutation.

Hardy and Weinberg showed that this is not the case for Mendelian inheritance - for each generation reproducing by mixture of atomic genes, in a large enough population, with no selective advantage between genetic variants, and with a couple of other constraints, there will be no change in population variance in genes, or in the traits expressed by these genes. This equilibrium is actually a pretty strong force in a large number of species - in other words, the current gene pool has a lot of inertia, and evolutionary forces will generally act very slowly.

Let's take an example: Peter and Rosemary Grant were able to observe evolution occurring in Darwin's finches through two severe ecological changes - in one case, a drought, and in the other, a flood - and watched the distribution of beak sizes in the population change in response to both events - in the one case, the beaks became shorter and wider to crack open the tougher seeds during the drought, and then longer and narrower after the flood to more efficiently access the softer, smaller seeds that then became abundant. To give a sense of what may be happening evolutionarily, I'll construct a deliberately simplistic genetic model of beak shape: say there are four genes, each with two alleles, that determine the beak shape of a finch. For each gene, one of the alleles will cause the beak to be more stout, and the other will cause the beak to be more lean. We'll call the "stout" allele 0, and the "lean" allele 1, and overall beak shape is determined by how many "stout" and (by definition) "lean" alleles the organism possesses. Any individual in this population will then have K stout alleles, and 4-K lean alleles.

I've set this up to deliberately produce a binomial distribution of beak shapes (though there are complications even here - I note these complications in order to ignore them). In our model, we'll say that after the drought individuals with 3 stout alleles and 1 lean allele will have the optimal beak shape; after the flood, individuals with 3 lean alleles and 1 stout allele will have optimal beak morphology. In neither case should any allele be completely eliminated from the population, which means that there will always be the potential to adapt to the flood after a drought, and to the drought after the flood.

This leads directly to what I think is the core of why culture is not nearly so intensely used in non-human animals as it is in humans: cultural evolution includes a lot of blending of received information, blending inheritance reduces population variance, and reduced variance lowers the ability to respond to ecological change. I may unpack this more later...

Culture and the Central Limit Theorem

James Surowiecki famously applied the Central Limit Theorem of statistics to market behavior in his book The Wisdom of Crowds. I have not read the book, however the wikipedia page seems coherent enough (though I disagree with some of it), and anyone with a background in statistics is probably already familiar with the idea. I do, however, want to point out an irony in his approach already apparent from the title of the book: it is difficult for a "wise" crowd to access the wisdom it generates. I think that unpacking this further may begin to account for why there are no other animals as extensively cultural as humans (but does not explain why we are so cultural).

I don't want to get much into the discussion of the statistics, which are probably valid. Rather, I want to talk about the assumptions required for these statistics to work. The major assumption in the CLT is that the random variables in one's sample are independent and identically distributed. In the sorts of scenarios Surowiecki (apparently) describes (like guessing the number of beans in a jar of jelly beans), these assumptions more-or-less holds until the point when the average is taken. I'll try to make my point more clear by a couple of scenarios:

In both scenarios, we'll place a jar of, say, dollar coins in front of a crowd, and the jar gets awarded to the person who guesses closest to the number of coins in the jar. In the first scenario, everyone makes a private guess about this number; in the second, we'll follow a "Price-is-Right" model, and ask participants in order (and never asking more than once) what they think the number is, while allowing later participants to eavesdrop on earlier. As a further assumption, lets say that everyone in the crowd understands and can use the central limit theorem. There are two questions that immediately arise:

1. What is the best strategy for an individual to choose?
   
2. In which of the two scenarios does the average guess of the crowd come closest to the actual number of coins in the jar?
   

In scenario 1, the answer to the first question is obvious: the respondent should make the guess that matches his or her internal idea about the number of coins in the jar. The responses will be independent, and probably have pretty similar distribution centered around the actual contents of the jar, so the CLT ought to be able to characterize the answer to the second question quite well.

In scenario 2, the answer is much less obvious. Each person's answer will depend on both what that person believes the true answer to be, and on the circumstances in which he or she answers the question; If I know I'm the last to answer the question, but my internal idea about the count is widely larger from what all others have answered so far, the best guess to make is *not* what I believe the number is, but rather the guess which seems likely to be closer to the true value than the others, rather than that which will be closest. An epsilon greater than the largest value picked by previous guessers. The upshot is that the best strategy is no longer independent of the actions of other participants, and the CLT can not be applied.

This is likely to be true of any game with eavesdropping. Early guesses may be relatively independent, but later participants who know this will also know that they can make a better guess by taking the mean of those early, independent guesses. The obvious danger is that maybe you've sampled the guess of someone else playing the exact same strategy as you have, without knowing it - now you've increased the number of samples, and decreased the variance within the population of the parameter you've attempted to guess. After several iterations of this strategy, the sample variance is now smaller than the population variance, and the variance of the sampling distribution of the mean rapidly approaches 0. It appears, statistically, like there is a very narrow confidence interval for the population parameter, but it's an illusion - there's no more information added to the system when later samples are describable as functions of earlier samples. The result roughly approximates mobbing behavior, like we see in the market.

Later I'll try to argue why I think this makes culture a generally losing proposition across species...

I'd just like to appropriate this...

I noticed the Atlantic had a new blog by Jeffrey Goldberg, who wrote one of the best articles I've recently read on Israel. I don't know how well the blog will turn out, but I wanted to align myself with this sentiment from his opening post:

This is almost certainly a mistake.

Friends tell me that I will take naturally to blogging because I am in possession of many poorly considered opinions about issues I understand only marginally. I am dubious, however.

Yup.

Evolution of institutions

One of the themes from the post on religion below is that institutions can profitably be regarded as evolved entities in their own right. This echoes group selection theory, but I don't really intend it that way. An evolutionary theory to account for modern human behavior needs to include the concept that individual humans are (or can be) members of several communities at once, which may have conflicting hierarchies. It is not clear to me that the usual formulations of group selection consider humans in this way. Besides which, the success of an institution is not necessarily linked to its ability to create copies of itself - often, stability over a long time period is intuitively a better measure of an institution's success. The generally declining marginal contribution of additional group members to group success (which is an assumption frequently made in economics to describe why firms eventually stop growing or shrinking) suggests that group selection theory must ultimately favor the creation of new groups. This is not necessarily true of institutions.

Institutions, to me, can be described more or less as basins of attraction. I say this with some reservation, because I'm not well enough versed in the mathematics to be precise. I understand a basin of attraction as a concept in dynamical systems, used to describe more-or-less regular trajectories through the space under consideration. For example, the trajectory of astronomical bodies (planets, stars, etc.) are well described by differential equations - astral body acceleration at any instant depends on the body's position and mass, and the position and mass of any other astral bodies nearby. Without getting too deep into it, this dependence of acceleration on the positions of several mobile bodies makes modeling the motion of the planets actually quite a bit more complex than one might naïvely expect (see the N-body problem for details). The orbits of the planets within the solar system are regular to the extent that they are caught within the solar system's basin of attraction. (I'm happy to be corrected on this.) Incidentally, "adaptive peaks" on Sewall Wright's "fitness landscape" are themselves essentially basins of attraction... As are other evolutionary scenarios, such as rock-paper-scissors games described by Maynard-Smith (in which an individual is committed to a strategy at birth - in this case, there is no ESS. nevertheless, the path through time is quite regular: scissors is replaced by rock is replaced by paper is replaced by scissors. I've wondered if this scenario perhaps accounts for nuptial-gift patterns in insects, which I may expand on later).

This sounds excessively complicated, it probably is excessively complicated. But that doesn't mean that this sort of thinking isn't useful. Ecology in general is considered by those who study it as a very complicated dynamic system. Adaptation is considered to follow a trajectory on a fitness landscape defined by the entities in the ecosphere, which is a very complicated beast. Studies of biological adaptation, however, greatly simplify this picture by considering a denuded subset of the ecosphere, and model but a few variables of interest.

What I am trying to get at can be expressed much more simply: a successful institution will select for (that is, recruit and/or develop) the individual or individuals best suited to carry out a role in that institution. The method of selection is a property of the institution, and of the available "talent pool", and will also reflect interactions with other institutions in the cultural web. Understanding the evolution of institutions is a question of how these institutions' mechanisms for selecting or cultivating new individuals in different roles change over time, and understanding the adaptations of institutions will mean describing the circumstances under which different forms of selection or cultivation tend to be more or less successful.

It's probably hubris, but I suspect that research following such a program would do better describing behavior on a global scale than any approach which treats institutions as mere epiphenomena.

I hope to unpack some of this discussion later.

Religion doesn't matter... (updated)

About a year ago, a grad student at my college gave a lecture for one of my classes in which she went over some of the scientific hypotheses proposed to account for why people have religion. At the beginning of the lecture, she described how there does not exist a commonly accepted definition of religion: every proposed definition had some significant problem she was able to point out with very little effort. As study of religion must include some conception of what religion is, this actually poses quite a problem for the discipline, which she side-stepped by focusing on phenomena agreed to be religious.

The fact that, in her preparation, she failed to discover a definition of religion that she found satisfying suggested to me that there was something seriously wrong in the approach of trying to account for religion, and that a different approach might be required.

Since that lecture, I've had reason to read more literature in the area, and there seems to be a pattern. When authors attempt to offer a definition of the term, they always seem much better at tearing down previous attempts than at constructing reliable definitions of their own. I'll quote Pascal Boyer,

If people tell you "Religion is faith in a doctrine that teaches us how to save our souls by obeying a wise and eternal Creator of the universe," these people probably have not travelled or read widely enough. In many cultures people think the dead come back to haunt the living, but this is not universal. In some places people think that some special individuals can communicate with gods or dead people, but that idea is not found everywhere. In some places people assume that people have a soul that survives after death, but that assumption also is not universal. When we put forward general explanations of religion, we had better make sure that they apply outside our parish.

(from Religion Explained)

One is left to wonder if there is anything considered universal across religions! Even the distinct concept of "religion" is not universally held, as it requires some understanding that there are different, incompatible, belief-systems. These difficulties notwithstanding, "religion" is still considered to play a direct and powerful role in most of the great undertakings of most or all human societies.

I am reminded of Popper's criticism of Marxism, which was related to his introduction of the doctrine of falsifiability. Popper noted that Marxists, when presented with evidence that contradicted the implications of their theory, were always quite ready to make post-hoc modifications to the theory so that it would fit the new data. It's worth noting that everyone probably does this, to an extent: new evidence much more often causes refinements to theory, rather than wholesale rejection. But when theory is usually incompatible with the results of observed phenomena at the time of observation, well, you can have...

This is the Turn of a Plausible Phrase
That thickened the Erudite Verbal Haze
Cloaking Constant K
That save the Summary
Based on the Mummery
Hiding the Flaw
That lay in the Theory that Jack Built.

(from The Space Child's Mother Goose, by Frederick Winsor)

...but the flaw in the theory is still there. At some point, it's best to forget your assumptions and try something else. The generally agreed importance of religion in human affairs is probably, at least partially, achieved by constraining the definition of religion so that it can always account for things of importance in human affairs. The accepted transcendent role of religion in the Christian cultures from which our current empirical scientific culture first became established (and, we should remember, the old Catholic Church in Europe used to have power to rival or exceed that of kings - the "transcendent" importance of religion may have followed from this) may have lead to the belief that religion everywhere is transcendentally important.

I want to end with the constructive point that we can still make major progress in understanding religious behavior. I suspect that the major redirection of effort involved will be to stop focusing on why people have religion, and start focusing on the structure of the religious institutions with which they interact. Answering questions about the role of ritual, generally, will help explain religious institutions, but can also help explain fraternity hazing, military cohesion, cooperation in athletics, etc. Understanding why people evangelize will help to understand many religions, but can also explain the invasiveness of neoliberal economic policy, or of advertising and marketing. [UPDATE 3/23/03:There is also a valid question about whether a single, general explanation for religion can account for people's susceptibility to religious ideology within all cultures.] There is so much more understanding we can gain if we stop accepting the framing that dictates that "religion" is what must be explained, as opposed to the structure of religious institutions and of people's behavior within them.

-l

Welcome

Welcome to the blog. I can't promise when or if there'll be something here worth seeing, or, indeed, anything at all.
-l