ben g: I replied to your comment earlier, but for some reason my reply has not appeared, and it wasn't very good anyway. The points you raised are tricky, and even W. D. Hamilton himself was sometimes unclear on how to deal with them. It is usually tacitly assumed that randomly selected members of a population are unrelated, but this is never strictly true, and sometimes far from true. However, the general level of relatedness between random members acts as a kind of baseline against which any more specific relationship can be measured. So, for example, if the general level of relatedness is equivalent to that of first cousins, then true first cousins will have that degree of relatedness *plus* the normal relatedness of cousins, and brothers will have an even closer relatedness. It is the difference between the total relatedness of two individuals and the average level of relatedness in the relevant population (roughly, the population within which interactions take place) that determines whether 'altruism' is worthwhile. There is a discussion of this issue under point 6 of the article by Dawkins which I linked to in my earlier post.

TGGP: I haven't given it much thought either, but my gut feeling is to go to the opposite extreme: everything placed online should 'expire' after a standard period unless someone (either the author or someone who has found value in it) takes a conscious decision to preserve it. Otherwise, we will be drowned in a rising tide of intellectual garbage. ben g: I didn't really answer your second question, because I wasn't quite sure whether the motivation for altruism is weakened in this situation. But on further reflection I think the answer is as follows. Suppose that in a community the average level of relatedness is equivalent to that of first cousins. Suppose now that A and B are brothers - full siblings with both parents in common. Assuming that their parents have mated at random, then the parents will, on average, be related to each other as closely as first cousins. A and B will therefore be related to each other via their parents' relationship, but in addition they will be related as full siblings. I will call this additional relatedness their 'surplus'. Now the question is, does this surplus give them a motivation to be altruistic to each other, and if so is this motivation stronger, weaker, or equal to that of full siblings whose parents are not related? I think the short answer is that the motivation is equal. If we consider it from the point of view of a gene in A, that gene has a strategic choice between helping A produce more offspring, or inducing A to help B to produce more offspring. In both cases there is some selective advantage for the gene in question, since either A's or B's offspring will have the gene in question with higher probability than in the general population, but the advantage - the 'surplus' probability - is twice as great for A's offspring as for B's. So it will not 'pay' the gene to induce A to be altruistic to B unless, for some reason, the increase in offspring would be twice as great for B as for A. Which is precisely the usual result of Hamilton's Rule. At least, that is what I think at the moment, but these issues are tricky, and I'm open to correction.

Yes, that's it. I have deleted my old text which you included in your comment, because it is (a) very long, and (b) very boring. I think (or hope, anyway) that the point is made more clearly in my new post. It is alarming, incidentally, to find that things you thought had been deleted are still out there somewhere on the net. Sometimes there might be much stronger reasons for wanting to remove something from the public record; e.g. you find that something was inadvertently libellous.

Steve: you have increased the reproductive fitness of your sister. That is a benefit to her. From your own point of view it is (genetically) worthwhile provided you do not reduce your own fitness by half a child! I don't see any fitness benefit to your niece or your nephew, unless conceivably your niece narrowly avoids being strangled by her mother (or, more broadly, benefits from the relief in family stress.) I am thinking about Henry Harpending's comment.

Re Henry Harpending's comments: I am not sure if we disagree on matters of substance or just on methods and terminology. Hamilton's Rule still seems to me to provide the best conceptual framework for analysing these problems, despite the various complications that have been raised (many of them by Hamilton himself). "There is no such thing as ‘true’ relationship." I agree that the relatedness between the members of a population will vary according to how the base population is defined, but in addressing any specific evolutionary problem the choice of base population is not arbitrary. For some purposes it may legitimately be the entire global population of a species, but for others it will be more limited. If what we want to know is whether altruism will evolve, it will be limited to those individuals who are capable of influencing each other's fitness by social interaction or competition for resources. Presumably in general the relevant population will be quite localised. An individual will interact and compete mainly with local population members, to a lesser extent with nearby populations, and to a very limited extent with more distant members of the species. Ideally I suppose one should calculate a weighted average which takes account of the frequency and nature of interactions. Individuals outside the range of interaction and competition can be disregarded. "If I help my brother in a highly inbred population, it doesn’t help him as much _with respect to that population_ as it would if in a population of random people." This brings us back to ben_g's question about altruism in a highly inbred population. My own gut feeling was originally that inbreeding must weaken the benefit of altruism towards close relatives, since the contrast between 'related' and 'unrelated' members of the population is flattened out. But on further reflection this makes no difference to the key question, which is whether it is better to give resources to a relative or to keep them for oneself. In a sense it is true that the 'worth' of a relative is reduced if the surrounding population is genetically similar, but for the same reason the 'worth' of one's own offspring is also reduced. On working through the algebra, the balance of advantage between helping oneself (i.e. creating more offspring) and helping a relative is unaffected. Hamilton's Rule still applies, even in an inbred population. "Relationship as Hamilton used it is not very well defined anywhere, and thinking about it in terms of pedigree relationship has not helped much. " It is unfortunate that in his original formulation W. D. Hamilton referred simply to 'related' and 'unrelated' members of a population, without (I think) defining what he meant by 'unrelated'. But on a sympathetic reading of the context, it is fairly clear that what he meant by 'unrelated' members of the population was that they are no more (or less) likely to share the allele of interest than indi
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gnome: I agree with some of what you say, from a common-sense point of view, but with one major difference: no-one argues that individuals 'calculate' their genetic relatedness and decide whether to be altruistic on that basis. This is one of Dawkins's '12 Misunderstandings of Kin Selection'. The theory of kin selection applies not just to animals but to plants and bacteria, which are presumably not even conscious. Altruistic behaviour, if it exists, would be based on non-conscious factors such as chemical similarity (e.g. pheromones) or mere proximity.

Steve: If your sister uses the resources herself she can make more nephews. If her son (your nephew) uses the resources, you only get more great-nephews, who are genetically worth half as much as nephews. Of course, 'other things being equal' may come into play: e.g. if your sister is past child-bearing, the nephew may be the best investment. (I'm not sure if 'great-nephew' is a recognised term, like great-aunt and great-uncle. I wonder why we have grand-fathers but not grand-uncles?)

gnome: I agree that pro-social behaviour often has advantages of its own, and that the appearance of kin selection may be just a side effect of that. But I think you may be thinking too much in terms of social mammals (including humans), which have relatively sophisticated intelligence, memory, communication, etc. The theory of kin selection (or inclusive fitness) is applicable to the whole range of organisms, including insects, plants, bacteria, slime moulds, etc. In many of these a general 'pro-social' strategy is not very plausible. For example, it would hardly explain why most bees or termites are non-reproductive. [I am still mulling over Henry Harpending's comments.]

Not that I recall. The science in the series is faily superficial. It is more interesting for the personalities involved. BTW, not sure who you mean by 'she'. The series is written and directed by Adam Curtis, who is presumably a person with testicles (not that I've checked!)

As I've mentioned before, there is a problem in the way TFRs are calculated. If women are delaying having babies - say, having them in their 30s rather than their 20s - there will be a transitional period during which TFRs will underestimate completed birth numbers. Eventually (assuming that the new fertility pattern is permanent) the TFRs will catch up, and appear to increase. So at least part of this increase is likely to be spurious.

Thanks for commenting. Personally I don't think the Fletcher-Zwick model is likely to be important in nature, for the reasons I have sketched at the end of my post, but it is theoretically interesting because it had been widely if rather loosely assumed that strong altruism cannot evolve in randomly formed groups. If a physicist showed that water can sometimes flow up hill, you would be interested even if in practice it turns out to be a very rare event. (Actually, I think it could happen, with water on a very gentle slope next to a very high mountain. The local gravity anomaly could - in theory - pull the water up the slope.) As to Axelrod, Fletcher and Zwick do reference a paper by Axelrod and Hamilton, but don't say much about it. I can't really offer an informed opinion about the game-theoretical approach, I just have a gut feeling that it has got detached from biological reality, especially since the death of Maynard Smith. The models get more and more elaborate, but not more robust to changes in the assumptions.

I wonder about the case of Evelyn Glennie, the British classical percussionist who is described as being deaf. She claims that she can somehow 'feel' the sounds through her body. But I remember a documentary where it was said that she had hearing as a child, but gradually lost her hearing for no known physical reason. So I wonder if at some level she still has hearing, but cannot access it consciously?

Thanks. Very interesting. I looked at some of the early search results (pre-1920) and of course a lot of them are uses of the phrase 'group selection' with quite a different meaning (e.g. apparently it had some use in mathematics). Also, there are some misdated results, e.g. later volumes of the journal Nature all indexed under the date when the journal started! But there are also some genuinely relevant results, e.g. from James Mark Baldwin and William McDougall. I will take a closer look at these.

Let's set up the simplest possible numerical example. Haploid asexual organisms, 2 individuals (A and B) in the population. The gene of interest is marked X. Case 1: Individual A has the gene X and has 2 offspring which also have the gene X. Individual B does not have the gene X and has no offspring. Result: frequency of the gene X increases from 50% to 100%. Case 2: Individual A has the gene X and has 1 offspring with the gene X. Individual B does not have the gene X but has 1 offspring with the gene X (due to a mutation). Result: frequency of the gene X increases from 50% to 100%. In case 1 the increase in the frequency of X is entirely due to the 'covariance' term of the equation. In case 2 it is entirely due to the other term.

"I have often heard that the second law of thermodynamics is just a result of math" Only in the sense that it follows mathematically from certain empirical facts, such as the quasi-random behaviour of gas molecules. These empirical facts are not logically necessary: e.g. we could perfectly well imagine a world in which certain bodies were 'heat attractors' which absorbed heat from surrounding bodies even though these were colder, which would violate the SLT.

Can I restate it in different words? Not sure that I can do it any better, but let me try a slightly different approach. The frequency of a gene in a population can change for two reasons. First, individuals who have the gene in question (or maybe more than one copy of it) may have more or fewer offspring than those who do not. Technically, this means there is a covariance (positive or negative) between the number of copies of the gene possessed by an individual and their number of offspring. If the covariance is positive, then other things being equal the frequency of the gene in the population will increase; if it is negative it will decrease. Second, the frequency of the gene may change between parents and their own offspring. E.g. the parents may each have one copy of the gene but their offspring may have two, or they may have none. Price's Equation provides a framework for quantifying these two ways in which gene frequency in the population may change.

Mutation is indeed rare in genetic inheritance, but remember that Price wasn't just interested in that. Apart from mutation, anything that causes an offspring to differ from its parents would affect the 'transmission' term of the equation. Segregation distortion would be one example. In segregation distortion the offspring do not get a random sample of the parents' genes. But even with random sampling the offspring dont't always get exactly the same proportions of genes as their parents, so for example two AB parents may have offspring who are all AA. In a large population these fluctuations of random sampling tend to cancel out, which is why the 'transmission' term of the equation is often negligible.

I will be commenting on group selection in my final post.

The author sounds suspiciously *French*. For reasons of national pride, neo-Lamarckism had holdouts among French biologists long after it had (almost) died out elsewhere. 'Lamarckist' findings keep cropping up from time to time, but usually they fail on attempts to replicate them. I remember that some time ago there was great excitement when flatworms could apparently 'learn' by being fed on the mashed-up bodies of other flatworms that had been habituated on some task. Ingenious hypotheses were put forward to explain it. Of course, the whole thing was a crock.

There is no point in 'addressing empirical data' if the empirical data are false. When 'data' are a priori improbable (like finding birdshit in a cuckoo clock), the first step is to see if they can be independently replicated. Nine times out of ten in the past 'Lamarckist' claims have failed the replication test, from Brown-Sequard in the 1880s to Steele in the 1990s. In the light of a long history of false, fraudulent, and misinterpreted data (like McDougall's tests on rats in the 1930s), a sceptic is entitled simply to ignore any new claims until they have been independently replicated several times.