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October 27, 2007

R! How can relatedness be negative?

Hamilton's equation for predicting the evolution of altruism is widely misunderstood. A simple diagram from a classic paper can help.
Source: Jesus and Mo

You sank in the opinion of your fellow-men... by leaving your money in a capricious manner without strict regard to degrees of kin...
There wasn't much good i' being so rich... if she'd got none but husband's kin to leave it to.

- The Mill on the Floss

This week I will discuss two classic papers on how relatedness affects the evolution of social behavior. Altruism towards relatives is widely recognized, but W.D. Hamilton was apparently the first to make quantitative predictions of how relatedness would affect the evolution of altruism. In 1964, he published two papers on "The genetical evolution of social behavior"? (J. Theor. Biol. 7:1-52). Hamilton's rule c < r b is now widely known, but also widely misunderstood. The rule states that a gene causing some altruistic behavior (donating blood, say) may spread if the cost of the activity is low enough, and if it preferentially benefits others who carry the same gene, typically because they are genetically related. The cost to the donor and benefit to the recipient are c and b, both measured in fitness units (average increase or decrease in reproduction, due to the altruistic activity). But what is r?

Wikipedia says r is the "coefficient of relatedness."? This is consistent with J.B.S. Haldane's famous joke: "I would lay down my life for two brothers [1/2] or eight cousins [1/8]."? But this definition is not necessarily right. By the correct definition, r can even be negative!

The most intuitive explanation of Hamilton's r that I've seen is in Alan Grafen's "A geometric view of relatedness"? (Oxford Surveys in Evolutionary Biology 2:28). He plotted the frequency of the altruism gene in an actor A, in a group of potential beneficiaries B (each of whom may receive a benefit b, at a cost c to A), and in the population P with which A competes for resources. (The importance of this definition of P will be explained later.) The frequency of the gene in a group or population is the fraction of the group having two copies (one each from mother and father), plus half the fraction having one copy. This frequency can range from 0 to 1. The frequency of the gene in an individual, such as A, is either 0, 0.5 (a copy from one parent only), or 1 (copies from both parents).
Grafen defined Hamilton's r as the fraction of the way along the line from P to A where B is found. In the drawing, B is halfway from P to A , so r is 0.5.

If altruism depends on two or more genes, you can use a two- or three-dimensional version of this graph, but things get complicated if B isn't somewhere on the line connecting P and A.

Does this definition make Hamilton's rule work? If group B produces 10 seeds -- for now, assume we're talking about plants -- that will move the frequency of the altruism gene in the population P in the direction of A. How far? Half as far as if A had produced 10 seeds. B would have to produce 20 seeds to have the same evolutionary effect as A producing 10 seeds. So, a gene that causes A to make 10 fewer seeds (from not shading a neighboring plant B, say) will become more common only if it increases B's seed production by more than 20. Hamilton's rule works with this definition of r. The gene spreads if and only if c < 0.5 b.

Is Grafen's definition of Hamilton's r also consistent with genealogical definitions of relatedness? Sometimes. Suppose group B grew from seeds produced by plant A last year, using a random sample of pollen from the whole population P. In other words, assume mating is random. Each B plant has one copy of each gene from A and one from P. So the frequency of the altruism gene in group B will be halfway between P and A, as graphed above, and therefore r is 0.5. This is the usual relatedness between parent and offspring.

So far so good. But r can take on surprising values, including negative ones, which are inconsistent with our usual understanding of genetic relatedness. For example, suppose mating isn't random. If individuals are more likely to mate with those that are genetically similar, then B could be genetically closer to A than to P, and r would be > 0.5. In that case, the altruism gene would become more common even if the cost c were more than half the benefit b.

Even stranger, an animal might be able to identify some group B -- maybe we should call it V for victim -- that is less similar to them itself than the population as a whole is. Then r is negative, and a gene to spitefully reduce the reproduction of that group, even at some cost to its own reproduction, could spread.

Positive values of r depend on benefits from A going only to a group B that is more likely to share A's altruism gene(s) than the population P does. How might this happen? Animals may recognize kin in various ways and direct help preferentially to them. This may even be true of some plants and microbes.

But is kin recognition essential for r to be >0? Plants that drop seeds on the ground tend to be surrounded by their own seedlings. Bacteria that reproduce by dividing may be surrounded by clonemates. Wouldn't this automatically make potential recipients of altruism more likely to have the same altruism gene(s), relative to the overall population?

No. Remember that P is the population with which A competes for resources. This definition isn't arbitrary. Up to this point, we've implicitly assumed no competition. That is, reproduction by B doesn't have any negative effect on reproduction by A. But Imagine a plant A surrounded by its own seedlings. They are closely related, but they are also competing for the same soil resources, and for light. These resources can support only a limited number of plants. Once that limit is reached, any reproduction by B reduces reproduction by A (which is more similar to itself than to B) by the same amount. So, if competition is strictly local, we don't expect altruism to evolve. This requires that r=0 and therefore P=B. This is turn implies that P is the local, competing population, as defined above.

If seeds are widely dispersed by the wind, then P will be more widely distributed, so P will be less similar to A, potentially increasing r. But wind dispersal may also bring less-related seeds into the neighborhood B, decreasing r. These two effects tend to cancel each other, so limited dispersal does not automatically increase r. It depends on the timing of dispersal relative to competition and potential altruism.

Here's one last example. B is the population of rhizobium bacteria in root nodules on a given plant, with a half of the nodules occupied by each of two bacterial strains. Both strains benefit from associating with a healthy plant, but only A has a gene that makes it invest in the expensive process of nitrogen fixation. By helping the plant to photosynthesize, nitrogen fixation indirectly helps all rhizobia infecting that individual plant. The frequency of the beneficial gene in beneficiary group B is 0.5. What is P? Two possible answers are graphed below.
If the bacterial population in the root nodules is a random sample of the population, then P=B and r=0. But what if the beneficial gene is much more common in nodules of this plant than in those of other plants nearby, or in the soil? (Perhaps it's the result of a recent mutation that occurred near this particular plant.) The frequency of the altruism gene in overall population P could be close to 0 and r would be about 0.5. Then, if the cost c of nitrogen fixation is less than 1/2 the benefit b it generates for members of B, the frequency of the gene will increase.

However, B would tend to approach P over time, to the extent that the bacterial population in a given plant is a random sample of the local population. Therefore, we don't think the collective benefits to rhizobia from associating with a healthier plant have much to do with the evolutionary persistence of nitrogen fixation by rhizobia. Instead, we think that rhizobia fix nitrogen to hold off plant sanctions directed at individual nodules that fix little or no nitrogen. With one rhizobium genotype per nodule, B=A, so r=1. The benefits to millions of clonemates from averting host sanctions outweigh the cost to a rhizobium cell of fixing nitrogen instead of using the same resources to reproduce.

There is no evidence that Hamilton associated with pirates.

October 16, 2007

Soybean symbiosis isn't what it used to be

Older soybean varieties benefit more from mixtures of good and bad symbiotic nitrogen-fixing bacteria than modern soybean varieties do. This work has also been
discussed on the Nature website by Heidi Ledford and on the Agricultural Biodiversity Weblog by Jeremy Cherfas.

"variations… profitable to the individuals of a species… will tend to the preservation of such individuals, and will generally be inherited by the offspring. I have called this principle… natural selection, in order to mark its relation to man's power of selection."
-- (Darwin, 1859)
Darwin was rightly impressed by what plant breeders have accomplished. I'm glad that potato breeders have reduced poisonous tomatine concentrations enough that we no longer need to eat absorbent clay with our potatoes, as was necessary with wild potatoes (Johns, 1990 p. 92). But sometimes selecting for a beneficial trait can have negative side effects. This problem applies both to natural selection and to selection by humans. Trade-offs among desirable traits can result from physical linkage between genes, intrinsic constraints (a given amount of sugar can be diluted in a larger strawberry), or random drift in traits not under selection.

This week, Toby Kiers, Mark Hutton, and I are reporting an apparent decrease, over the course of 60 years of soybean breeding, in the ability of plants to benefit from rhizobium bacteria. Our paper “Human selection and the relaxation of legume defences against ineffective rhizobia? is published on-line in Proceedings of the Royal Society.

Rhizobia are soil bacteria best known for infecting legume plants and proliferating inside root nodules, where they typically convert ("fix") atmospheric nitrogen into forms plants can use. Rhizobia in most soils vary in the benefits they provide. A survey of soybean rhizobia in the US found that "25% were highly effective, 50 percent only average, and the rest poor or ineffective" (Erdman, 1950). Soybeans tend to conserve photosynthate by sending more of it to whichever nodules are fixing the most nitrogen (Singleton and Stockinger, 1983). This allows rhizobia that fix more nitrogen to reproduce more inside nodules, relative to those that fix less (Kiers et al., 2003). Without these "host sanctions", rhizobia that allocate more resources to their own reproduction, at the expense of nitrogen fixation, would have displaced more beneficial rhizobium strains over the course of evolution (Denison, 2000; West et al., 2002).

Do plants vary in sanctions as much as rhizobia vary in nitrogen fixation? If so, have sanctions evolved differently in agricultural species subject to human selection, relative to wild species with only natural selection? Toby Kiers (my former PhD student, now at Vrije Universiteit Amsterdam) hypothesized that increased availability of nitrogen fertilizer since 1940 may have reduced the importance of nitrogen fixation as a selection criterion in plant breeding programs. (Nitrogen is not usually applied directly to nitrogen-fixing crops, but carryover from previous crops like corn can be significant.) Alternatively, the greater availability of soil nitrogen might raise the bar for rhizobia, allowing plants to shut down all but the best-performing nodules.


To test these hypotheses, we designed a field experiment, which she conducted in Maine with collaborator Mark Hutton. They used fields where soybeans had not been grown before, so she could expose plants to any combination of good and bad rhizobia. When the soil contained a 50:50 mix of fixing and nonfixing rhizobia, older varieties (3 bars at left) yielded at least as well as if only good rhizobia were present (dashed line in figure) but newer varieties did worse. As a result, the yield advantage of newer varieties disappeared with this mix of good and bad rhizobia (lower panel of figure). Although old varieties seemed to do better with the rhizobium mix than with good rhizobia alone, this apparent benefit was not statistically significant.

It seems unlikely that plant breeders and farmers would have failed to notice a lack of progress in soybean yields over decades, so maybe improvements in other genetic traits (better resistance to diseases not present in Maine, for example) have outweighed any deterioration in rhizobium interactions, for most farmers. It is also possible that the rhizobium mix used was worse than what is present in the soil of many commercial fields. Or there may be enough left-over nitrogen in many fields that nitrogen fixation is less critical. Given the high energy cost of nitrogen fertilizer and its contribution to water pollution, however, substituting fertilizer for nitrogen fixation is probably a bad idea.

Are host sanctions in the older varieties optimal? I suspect not. Although natural selection (or human selection based on yield in a low-nitrogen soil with a mixture of good and bad rhizobia) would presumably maintain sanctions against the very worst rhizobia, mediocre strains might be tolerated, if they provide more immediate benefit than immediate cost to the plant. But allowing mediocre strains to reproduce in nodules and escape into the soil means that the next soybean crop will also be plagued with mediocre rhizobia. A better longer-term approach would be to breed legume crops that impose sanctions severe enough to selectively enrich the soil with only the best rhizobium strains. Natural selection is blind to long-term considerations, but we need not be -- budget deficits, over-harvesting of forests and fish, and under-investment in research and education notwithstanding!

Darwin, C.R. 1859. The origin of species (reprinted 1962). Collier, New York.
Denison, R.F. 2000. Legume sanctions and the evolution of symbiotic cooperation by rhizobia. Am. Nat. 156:567-576.
Erdman, L.W. 1950. Legume inoculation. USDA Farmer's Bull. 2003:1-20.
Johns, T. 1990. The origins of human diet and medicine. University of Arizona Press, Tuscon.
Kiers, E.T., R.A. Rousseau, S.A. West and R.F. Denison. 2003. Host sanctions and the legume-rhizobium mutualism. Nature 425:78-81.
Singleton, P.W. and K.R. Stockinger. 1983. Compensation against ineffective nodulation in soybean. Crop Sci. 23:69-72.
West, S.A., E.T. Kiers, E.L. Simms and R.F. Denison. 2002. Sanctions and mutualism stability: Why do rhizobia fix nitrogen? Proc. R. Soc. Lond. B 269:685-694.

October 11, 2007

Evolution of language

Ed Yong beat me again, this time discussing an interesting paper in Nature on the evolution of language, but I'm going to comment anyway. Actually, there are two papers in the same issue, both showing that frequently used words change more slowly. For example, irregular past tenses of rarely-used verbs (bide, delve, etc.) have tended to disappear, but we still say "came and saw" not "goed and seed." Lieberman et al. (Nature 449:713) note that:

It is much rarer for regular verbs to become irregular: for every ‘sneak’ that ‘snuck’ in there are many more ‘flews’ that ‘flied’ out.

I bet this is also true of less-used definitions of words and of collective nouns: a group of football players will still be a "team" long after a "bouquet" of pheasants has become a "flock" and then a "group."

Languages evolve, but analogies with evolution of genes may be misleading. Genes pass only from parent(s) to offspring and their frequency changes over generations. Words and ideas can spread much more rapidly, including from child to parent. Cultural evolution seems more analogous to the spread of viruses, only some of which come from our parents.

Some ideas (e.g., religions) come packaged with explicit instructions to proselytize, like the rabies virus making its victims bite others. But the desire to spread our tastes in music, for example, seems intrinsic to us, not to the music. So cultural evolution seems similar enough to epidemiology that analogies will sometimes be useful, but only sometimes.

October 5, 2007

Faster speciation in the tropics?

Pygmy salamander, Desmognathus wrighti, from the southern Appalachian Mountains (photo by Matt Chatfield)

This week's paper "Climatic zonation drives latitudinal variation in speciation mechanisms" is by Ken Kozak, a new member of my department, and John Wiens of Stony Brook University, published in Proceedings of the Royal Society. They used data on salamanders to test an old hypothesis to explain why there is so much species diversity in the tropics.

The hypothesis goes back to a 1967 paper by the eminent ecologist Dan Janzen, with the provocative title, "Why are mountain passes higher in the tropics?" They aren't, of course, but he suggested a pass at the same elevation may be more of a barrier in the tropics than in temperate regions. This seems odd, because it is presumably warmer at the top of a 2-km-high pass in the tropics than in Alaska, say.

Enter evolution. Tropical regions have less seasonal difference in temperature, at a given location, over the course of a year. Therefore, there is less selection for tolerance of a wide temperature range. Therefore, the top of a mountain pass may be colder than anything a tropical species has been exposed to over its recent evolutionary history. Therefore, tropical species can't usually cross even low mountain passes without dying. Therefore, two populations of the same species, on opposite sides of a pass -- maybe they were carried by migrating swallows, or crossed during a warm spell -- can't get together to interbreed. Without interbreeding, they diverge into separate species. In temperature regions, on the other hand, the temperature at the top of a mountain pass, in summer, is no colder than the temperature in the adjacent valleys, in winter. No problem. A potential date who is "geographically undesirable" for a tropical salamander with a narrow temperature range might be "just down the road" for a salamander whose ancestors had survived snowy winters.

Narrow climatic tolerance could lead to new species in at least two different ways, however. Under the "refuge/niche conservatism" hypothesis, species don't easily evolve tolerance to different climates. A species might move to higher elevations as climate warms, ending up split into isolated populations (which diverge into separate species) on different mountain tops. Alternatively, a species might spread up or down a mountain, evolving different, but still narrow, temperature tolerance as it goes. Limited temperature tolerance would prevent interbreeding up and down slope, leading to high- and low-elevation species. This is the niche divergence hypothesis.

Kozak and WIens used data on the distribution of salamanders in temperate and tropical America to test these hypotheses. They concentrated on pairs of "sister species", shown by DNA analysis to be adjacent twigs in the salamander family tree. They used distribution data and climate maps to determine the temperature tolerance of each species.

Consistent with Janzen's hypothesis, there was more temperature range overlap between sister species from temperate regions than from the tropics. Pairs of temperate species were usually separated by zones outside their temperature range, consistent with niche conservatism.

sister species in the temperate zone show much greater temperature overlap with each other than they do with their intervening absence locations, a pattern that supports the hypothesis that niche conservatism underlies their past and present isolation

This was also true of two of six species pairs in the tropics, but mostly sister species in the tropics were found in zones that differed in temperature at least as much as intervening zones did. They couldn't tell whether tropical species diverged while in contact with each other (parapatric speciation) or whether they were separated for a time, then came back into contact after they had so little in common they might as well be separate species.

Also this week
Has anyone noticed that I have never reviewed a paper in any of the 30+ journals in our library with "evolution" in the name of the journal? I've mostly stuck to general-interest journals for two reasons. First, this is supposed to be a general-interest blog. Second, I wanted to make the point that evolution is central to biology. I'm doing fine without my appendix, and junk DNA can be deleted without affecting fitness, but biology without evolution would be like chemistry without atoms. Even limiting myself to a few general-interest journals, I have several interesting papers to choose from each week. Here are some of this week's runners-up:
Human cooperation in social dilemmas: comparing the Snowdrift game with the Prisoner's Dilemma

Producing sons reduces lifetime reproductive success of subsequent offspring in pre-industrial Finns

Wasp Gene Expression Supports an Evolutionary Link Between Maternal Behavior and Eusociality

Sex Chromosome-Linked Species Recognition and Evolution of Reproductive Isolation in Flycatchers

October 2, 2007

Grad school as an epic quest

I thought this analogy between grad school and Lord of the Rings was pretty funny, but what about Monty Python and the Holy Grail? I'm really tempted to start my next oral exam with:

What is your name?
What is your quest?
What is the long-range dispersal mechanism of Cocos nucifera?

According to Wikipedia:

[Coconut] fruits collected from the sea as far north as Norway have been found to be viable (and subsequently germinated under the right conditions).

So coconuts are migratory.

Menopause in whales

Someone who visited my recent blog on evolutionary aspects of menopause in humans led me to this short article in TREE (briefly discussed in the blog Gene Expression), which notes that, in many whales, female "reproduction ceases at approximately 40 years of age, although females routinely live on for several more decades." It's suggested that they help their daughters by providing wisdom.