I was prompted to write this book review after reading Paul Christiano’s post on the evolution of sex and George’s response to Paul Christiano’s post on the evolution of sex. Those two posts are quite interesting! Paul Christiano points out that “sex slightly lowers the average [fitness] but increases the variance”, and argues that increased variance is beneficial over time. George points out that there are lots of ways to increase variance without imposing the same costs as sex. So why sex? George says “I don’t know, nobody really does, that’s why evolution is complex”. Is it really the case that no one knows why sex could evolve?
I recently got a copy of W. D. Hamilton’s book, Narrow Roads of Gene Land Volume 2: The Evolution of Sex, where he attempts to answer the question. I’ll let him introduce the topic: “The main topic of this book is why sexual ways of reproduction are so abundant, when, for natural selection to work and for progressive evolution to occur, much simpler and more efficient ways would seem to suffice”. This seems like exactly what George was asking for, so let’s practice the virtue of scholarship by reading a bunch of papers on the evolution of sex!
The Book
Just like Volume 1 (which I may write a separate book review on), this book alternates between autobiographical accounts and published papers. Each chapter first has Hamilton describing what was happening in his life and research while he was working on the paper, and then the paper. I focused on the three papers most relevant to the parasite theory of sex, out of 18 total papers.
Paper 1: Environmental fluctuation, polymorphism, and the maintenance of sex
This first paper we'll talk about begins by introducing us to some puzzles.
First puzzle: why do all the social species (humans, bees, termites) reproduce sexually? Our best theories of selection for social cooperation relies on the individuals who are cooperating being related to each other. But in clonal populations (like in aphids, armadillo polyembryony, and human monozygotic twins), we don’t observe more social cooperation than in non-clonal populations. This is counter to what we would expect from our kin selection/inclusive fitness theory.
Second puzzle: If relatedness is so important, why would someone choose to have children that are only 50% related to them when they could be having children that are 100% related to them?
Third puzzle: Why do males contribute to raising children? If males don’t help with raising children, females have an incentive to self-fertilize, because they produce the same number of children regardless of whether they mate or not. If males do help with raising children, then females can choose between having N clonal children or 2*N half-related children, giving them an equal amount of their genes in the next generation. But if females can self-fertilize while also receiving help from the males, they would benefit more than either self-fertilizing without help or mating with a male and receiving support. This seems to favor crypto-asexual reproducers which disguise their asexual reproduction while receiving support from the males that think the children they are raising actually share half their genes. (Incidentally, moths get around this in a very cool way. Male moths, when fertilizing female moths, “may contribute importantly to the food reserves of eggs through materials transferred in copulation”. In other words, mating with males provides a fitness advantage for females because the male helps in creating offspring, and the female has no way of gaining this advantage without having the male actually fertilize the eggs.)
These puzzles all present reasons to think that our current models of the evolution of sex are confused. Hamilton shows us a better model, by introducing environmental variation and showing that sex (and thus recombination, and thus faster evolution) can be fitness-enhancing when environments are changing.
The Model
When you have sexual reproduction, your child is only half yours. Your genes are diluted with someone else’s, and so having a child through sexual reproduction nets you only have the genetic fitness of having a child through clonal reproduction. To Hamilton, “[beating] that twofold ‘cost’, or inefficiency of sex as it might equally be called, is the biggest challenge. People who haven’t faced this either through simulation or a mathematical formalism usually don’t realize how awesome of a problem it is”.
Our model will give each species a fitness each generation, and have that species’ size by multiplied by that number per generation. Then, we can look at the long-term geometric mean fitness (LGMF) of each species to determine whether they will persist or die off. Hamilton then points out that for “sex to be ‘stable’, we assume that the LGMF of the sexual species must be higher than the highest LGMF among the clones”. For further discussion, let’s call M the highest such LGMF within clones.
Hamilton asks us to assume that asexual species easily arise from sexual species (this assumption is reasonable, because many egg-laying species that aren’t usually self-fertilizing occasionally have eggs that hatch without fertilization, thus confirming that life, uh, finds a way) and that all asexual species have the same long-term mean fitness (this assumption is pretty wild, but the point is to simplify the model into asexual vs sexual competition and ignore competition between different clonal populations).
With our assumptions out of the way, let’s choose an example. Say there are two possible states of the world. In the first, heterozygotic individuals (gG) have a fitness above one, while homozygotic (gg or GG) have a fitness below one. In the second, it’s the opposite. See the payoff table below for a formalization of this idea.
Payoffs for sexual species and clones over the two environments
Now, depending on which environment the population finds itself in, different genes will confer fitness advantages. If you set r=4, the payoffs would be 4 or 0.25. The figure below shows the overall population fitness (thick line) and individual genotype fitness (thin line) in different environments. Only the left half of the figure was printed because it is symmetric around a frequency of 0.5. You can see that when the environments alternate between A and B, the peak fitness value is an even 50/50 split between homo- and heterozygous genomes.
Fitness for species and the population as a function of frequency of G
However, suppose that the environment didn’t alternate between A and B, but instead stayed in one environment for a random number of generations, and then swapped. When the environments are slightly “sticky”, the sexual species is rapidly pushed towards the current optimal genome, while the asexual species have to wait for mutation to happen more slowly. Hamilton shows us some sets of parameters where the sexual species has a fitness of over double the asexual species. This is enough to pay for having children which are only half-related to you, and allow sex to be stable.
The model, in my opinion, only answers the second puzzle – relatedness can be outweighed by the fitness gains in fast evolution. The first is somewhat answered by the understanding that sexual selection and social cooperation are driven by separate forces, so they may be orthogonal to each other – and thus evolve separately. And in my opinion, the third puzzle is still an open question.
Let’s move on to a potential driver of environmental change – parasites!
Paper 2: Sex versus non-sex versus parasite
Hamilton was the first to publish a paper arguing that parasites help stabilize sexual reproduction. This paper points out that parasites evolve much faster than their hosts, and so having a constant cycle of genomes (as a host) can be beneficial, to avoid having whichever genome parasites are most effective against. As the host species becomes more likely to have a certain genome, the parasite evolves to be more effective against that genome, and we can get a cycle.
To quote the conclusion, “frequency-dependent selection acting hardest against the most common genotype easily sets up cyclical processes”. Because the ideal genotype varies quickly over time, based on what the current most common genotype is, sexual reproduction and the corresponding high variance helps sexuals win over asexuals.
There’s a model in this paper, and some computer simulations, but I don’t think we have to get into them too much – all the intuition is in the English, not the math.
If parasites are driving evolution, then rapid mutation is favored. Rapid mutation is easiest to accomplish with sexual recombination, so that is what we get! You can also think of this as an application of the above model, where the different environments are different populations of parasites that are effective against different genomes.
Now that parasites have been introduced as a driver of sex, let’s skip ahead to paper five and look into parasitism in some more detail.
Paper 3: Pathogens as causes of genetic diversity in their host populations
This paper also starts with a puzzle. The puzzle is that elephants have very slow generations, so “on the elephant’s timescale of change, why don’t bacteria of skin or gut, turning over generations a hundred thousand times faster, evolve almost instantly an ability to eat the bast body up?”. Good question!
One answer is that there are a bunch of smaller-scale evolutionary processes happening within the larger organisms. For instance, immune systems have a variety of species of asexual specialists (antibodies!), and the immune system can use mutation and selection among antibodies to quickly find an antibody that works against a pathogen, allowing larger host species to partially match evolution rate of pathogens.
Hamilton’s favorite answer to the parasite problem is sex. He believes that sex is what allows the large creatures to overcome their slow selection processes and prevent parasites from taking over. He also makes sexual reproduction sound quite cool: “sex also creates true species in an otherwise straggling mess of clones: if the idea about parasites is right, species may be seen in essence as guilds of genotypes committed to free fair exchange of biochemical technology for parasite exclusion”.
(He also throws in a side note about how larger animals can just up and move, much further and faster than any single-celled pathogen, to escape areas with parasites that have adapted to them. As usual for a side note from Hamilton, I think this deserves a paper of its own!)
Let’s look at the model introduced in this paper.
The Model
Imagine water splashing around in a bathtub. No, seriously, Hamilton introduces his model by describing “fitness profiles whose shape over the genotypes and over time may be said to resemble the shape and change of water that is kept slopping about in a bath”. Let’s try to figure out what that means.
Hamilton asks us to imagine three spikes poking out of the bottom of the bathtub, each representing one genotype. gg is on the left side of the tub, gG in the middle, and GG on the right. The height of the water on the spike represents current fitness of that genotype. Now, we can sort of see that water splashing around means that each genotype’s fitness is going up and down over time. The waves in the bath must be high, so that selection pressure is high enough to cause fast evolution. The waves must sometimes reverse direction, which will cause trouble for whichever genotype is most common, as the water level will lower on the highest spike. The water level in the middle must occasionally be highest, and occasionally be lowest, such that heterozygotes (gG) have high variation in fitness. Also, we are assuming that the mean of fitness of the two homozygotes (gg and GG) is always higher than the fitness of the heterozygotes (gG).
With this crude mental model in hand, we can start thinking about the ways for water to sloshing in the bathtub that would lead to sex (I’ll leave it to the fluid dynamicists to figure out how sex lead to different ways for water to slosh around in a bathtub).
“Sex thrives on movement”, says Hamilton, and he means to say that dynamic fitness for genotypes leads to sexual reproduction. If the fitness function is relatively static, any individual that stumbled upon the highest-fitness genotype could just produce clones of itself and win against the sexual species.
If the fitness function changes rapidly, then whichever genotype is least fit this generation might be most fit next generation – there may be a negative correlation between parent’s fitness and their offspring’s fitness. In this case, Hamilton suggests that females might be best off picking “the sickest male that looks as though he could still just effect copulation”. However, we don’t observe this behavior. However, you may have heard about vertebrates tending to choose mates with different major histocompatibility complexes (Hamilton cites this relatively old paper, but the effect is still considered real today as far as I know). So, possibly we do try to find mates that would do better against the pathogens affecting our generation.
This model is not very formal, but does make some falsifiable predictions. Let’s look at some of them, and then see whether they are correct!
One prediction: for animals that have slow disease cycles, there will be more effort spent on signaling ability to fight disease. In the next paper, Zuk and Hamilton looked at blood diseases in birds, and found a strong positive correlation between brightness of plumage of a species and the amount of disease within that species. This finding seems to support this theory.
Another prediction: sexual reproduction should be more stable in species that are afflicted by more pathogens. This is true, for example, trees in tropical regions, where there are more parasites, are more sexual than trees in the arctic, where there are far fewer parasites. Also larger, less-fecund organisms such as humans, elephants, and palm trees have very stable sexual characteristics, because of the previously-mentioned slow generations. This is particularly important because many other theories of sex do not explain why less-fecund organisms would have more sexual stability.
There are many other predictions this model makes, but I’ll stop here.
Conclusion
The parasite theory of the evolution of sex has some theoretical and empirical backing. Far from George’s idea that “you’d likely have to simulate evolution “from scratch” in a bunch of Earth-like environments to get an answer with any degree of certainty”, Hamilton provides us a well-grounded theory of the evolution of sex, and backs up his theory by looking at what it predicts and then seeing if those things are actually true, like a good evolutionary biologist ought to.
All in all, I’m currently pretty convinced that parasitism plays a role in the evolution and stability of sex. But only reading papers by one author seems like bad espistemic hygeine, so I don’t want to stop here. I’m going to read some papers by other authors that think Hamilton are wrong, and see what they say! If there’s anything interesting there, I’ll make another post.
I was prompted to write this book review after reading Paul Christiano’s post on the evolution of sex and George’s response to Paul Christiano’s post on the evolution of sex. Those two posts are quite interesting! Paul Christiano points out that “sex slightly lowers the average [fitness] but increases the variance”, and argues that increased variance is beneficial over time. George points out that there are lots of ways to increase variance without imposing the same costs as sex. So why sex? George says “I don’t know, nobody really does, that’s why evolution is complex”. Is it really the case that no one knows why sex could evolve?
I recently got a copy of W. D. Hamilton’s book, Narrow Roads of Gene Land Volume 2: The Evolution of Sex, where he attempts to answer the question. I’ll let him introduce the topic: “The main topic of this book is why sexual ways of reproduction are so abundant, when, for natural selection to work and for progressive evolution to occur, much simpler and more efficient ways would seem to suffice”. This seems like exactly what George was asking for, so let’s practice the virtue of scholarship by reading a bunch of papers on the evolution of sex!
The Book
Just like Volume 1 (which I may write a separate book review on), this book alternates between autobiographical accounts and published papers. Each chapter first has Hamilton describing what was happening in his life and research while he was working on the paper, and then the paper. I focused on the three papers most relevant to the parasite theory of sex, out of 18 total papers.
Paper 1: Environmental fluctuation, polymorphism, and the maintenance of sex
This first paper we'll talk about begins by introducing us to some puzzles.
First puzzle: why do all the social species (humans, bees, termites) reproduce sexually? Our best theories of selection for social cooperation relies on the individuals who are cooperating being related to each other. But in clonal populations (like in aphids, armadillo polyembryony, and human monozygotic twins), we don’t observe more social cooperation than in non-clonal populations. This is counter to what we would expect from our kin selection/inclusive fitness theory.
Second puzzle: If relatedness is so important, why would someone choose to have children that are only 50% related to them when they could be having children that are 100% related to them?
Third puzzle: Why do males contribute to raising children? If males don’t help with raising children, females have an incentive to self-fertilize, because they produce the same number of children regardless of whether they mate or not. If males do help with raising children, then females can choose between having N clonal children or 2*N half-related children, giving them an equal amount of their genes in the next generation. But if females can self-fertilize while also receiving help from the males, they would benefit more than either self-fertilizing without help or mating with a male and receiving support. This seems to favor crypto-asexual reproducers which disguise their asexual reproduction while receiving support from the males that think the children they are raising actually share half their genes. (Incidentally, moths get around this in a very cool way. Male moths, when fertilizing female moths, “may contribute importantly to the food reserves of eggs through materials transferred in copulation”. In other words, mating with males provides a fitness advantage for females because the male helps in creating offspring, and the female has no way of gaining this advantage without having the male actually fertilize the eggs.)
These puzzles all present reasons to think that our current models of the evolution of sex are confused. Hamilton shows us a better model, by introducing environmental variation and showing that sex (and thus recombination, and thus faster evolution) can be fitness-enhancing when environments are changing.
The Model
When you have sexual reproduction, your child is only half yours. Your genes are diluted with someone else’s, and so having a child through sexual reproduction nets you only have the genetic fitness of having a child through clonal reproduction. To Hamilton, “[beating] that twofold ‘cost’, or inefficiency of sex as it might equally be called, is the biggest challenge. People who haven’t faced this either through simulation or a mathematical formalism usually don’t realize how awesome of a problem it is”.
Our model will give each species a fitness each generation, and have that species’ size by multiplied by that number per generation. Then, we can look at the long-term geometric mean fitness (LGMF) of each species to determine whether they will persist or die off. Hamilton then points out that for “sex to be ‘stable’, we assume that the LGMF of the sexual species must be higher than the highest LGMF among the clones”. For further discussion, let’s call M the highest such LGMF within clones.
Hamilton asks us to assume that asexual species easily arise from sexual species (this assumption is reasonable, because many egg-laying species that aren’t usually self-fertilizing occasionally have eggs that hatch without fertilization, thus confirming that life, uh, finds a way) and that all asexual species have the same long-term mean fitness (this assumption is pretty wild, but the point is to simplify the model into asexual vs sexual competition and ignore competition between different clonal populations).
With our assumptions out of the way, let’s choose an example. Say there are two possible states of the world. In the first, heterozygotic individuals (gG) have a fitness above one, while homozygotic (gg or GG) have a fitness below one. In the second, it’s the opposite. See the payoff table below for a formalization of this idea.
Now, depending on which environment the population finds itself in, different genes will confer fitness advantages. If you set r=4, the payoffs would be 4 or 0.25. The figure below shows the overall population fitness (thick line) and individual genotype fitness (thin line) in different environments. Only the left half of the figure was printed because it is symmetric around a frequency of 0.5. You can see that when the environments alternate between A and B, the peak fitness value is an even 50/50 split between homo- and heterozygous genomes.
However, suppose that the environment didn’t alternate between A and B, but instead stayed in one environment for a random number of generations, and then swapped. When the environments are slightly “sticky”, the sexual species is rapidly pushed towards the current optimal genome, while the asexual species have to wait for mutation to happen more slowly. Hamilton shows us some sets of parameters where the sexual species has a fitness of over double the asexual species. This is enough to pay for having children which are only half-related to you, and allow sex to be stable.
The model, in my opinion, only answers the second puzzle – relatedness can be outweighed by the fitness gains in fast evolution. The first is somewhat answered by the understanding that sexual selection and social cooperation are driven by separate forces, so they may be orthogonal to each other – and thus evolve separately. And in my opinion, the third puzzle is still an open question.
Let’s move on to a potential driver of environmental change – parasites!
Paper 2: Sex versus non-sex versus parasite
Hamilton was the first to publish a paper arguing that parasites help stabilize sexual reproduction. This paper points out that parasites evolve much faster than their hosts, and so having a constant cycle of genomes (as a host) can be beneficial, to avoid having whichever genome parasites are most effective against. As the host species becomes more likely to have a certain genome, the parasite evolves to be more effective against that genome, and we can get a cycle.
To quote the conclusion, “frequency-dependent selection acting hardest against the most common genotype easily sets up cyclical processes”. Because the ideal genotype varies quickly over time, based on what the current most common genotype is, sexual reproduction and the corresponding high variance helps sexuals win over asexuals.
There’s a model in this paper, and some computer simulations, but I don’t think we have to get into them too much – all the intuition is in the English, not the math.
If parasites are driving evolution, then rapid mutation is favored. Rapid mutation is easiest to accomplish with sexual recombination, so that is what we get! You can also think of this as an application of the above model, where the different environments are different populations of parasites that are effective against different genomes.
Now that parasites have been introduced as a driver of sex, let’s skip ahead to paper five and look into parasitism in some more detail.
Paper 3: Pathogens as causes of genetic diversity in their host populations
This paper also starts with a puzzle. The puzzle is that elephants have very slow generations, so “on the elephant’s timescale of change, why don’t bacteria of skin or gut, turning over generations a hundred thousand times faster, evolve almost instantly an ability to eat the bast body up?”. Good question!
One answer is that there are a bunch of smaller-scale evolutionary processes happening within the larger organisms. For instance, immune systems have a variety of species of asexual specialists (antibodies!), and the immune system can use mutation and selection among antibodies to quickly find an antibody that works against a pathogen, allowing larger host species to partially match evolution rate of pathogens.
Hamilton’s favorite answer to the parasite problem is sex. He believes that sex is what allows the large creatures to overcome their slow selection processes and prevent parasites from taking over. He also makes sexual reproduction sound quite cool: “sex also creates true species in an otherwise straggling mess of clones: if the idea about parasites is right, species may be seen in essence as guilds of genotypes committed to free fair exchange of biochemical technology for parasite exclusion”.
(He also throws in a side note about how larger animals can just up and move, much further and faster than any single-celled pathogen, to escape areas with parasites that have adapted to them. As usual for a side note from Hamilton, I think this deserves a paper of its own!)
Let’s look at the model introduced in this paper.
The Model
Imagine water splashing around in a bathtub. No, seriously, Hamilton introduces his model by describing “fitness profiles whose shape over the genotypes and over time may be said to resemble the shape and change of water that is kept slopping about in a bath”. Let’s try to figure out what that means.
Hamilton asks us to imagine three spikes poking out of the bottom of the bathtub, each representing one genotype. gg is on the left side of the tub, gG in the middle, and GG on the right. The height of the water on the spike represents current fitness of that genotype. Now, we can sort of see that water splashing around means that each genotype’s fitness is going up and down over time. The waves in the bath must be high, so that selection pressure is high enough to cause fast evolution. The waves must sometimes reverse direction, which will cause trouble for whichever genotype is most common, as the water level will lower on the highest spike. The water level in the middle must occasionally be highest, and occasionally be lowest, such that heterozygotes (gG) have high variation in fitness. Also, we are assuming that the mean of fitness of the two homozygotes (gg and GG) is always higher than the fitness of the heterozygotes (gG).
With this crude mental model in hand, we can start thinking about the ways for water to sloshing in the bathtub that would lead to sex (I’ll leave it to the fluid dynamicists to figure out how sex lead to different ways for water to slosh around in a bathtub).
“Sex thrives on movement”, says Hamilton, and he means to say that dynamic fitness for genotypes leads to sexual reproduction. If the fitness function is relatively static, any individual that stumbled upon the highest-fitness genotype could just produce clones of itself and win against the sexual species.
If the fitness function changes rapidly, then whichever genotype is least fit this generation might be most fit next generation – there may be a negative correlation between parent’s fitness and their offspring’s fitness. In this case, Hamilton suggests that females might be best off picking “the sickest male that looks as though he could still just effect copulation”. However, we don’t observe this behavior. However, you may have heard about vertebrates tending to choose mates with different major histocompatibility complexes (Hamilton cites this relatively old paper, but the effect is still considered real today as far as I know). So, possibly we do try to find mates that would do better against the pathogens affecting our generation.
This model is not very formal, but does make some falsifiable predictions. Let’s look at some of them, and then see whether they are correct!
One prediction: for animals that have slow disease cycles, there will be more effort spent on signaling ability to fight disease. In the next paper, Zuk and Hamilton looked at blood diseases in birds, and found a strong positive correlation between brightness of plumage of a species and the amount of disease within that species. This finding seems to support this theory.
Another prediction: sexual reproduction should be more stable in species that are afflicted by more pathogens. This is true, for example, trees in tropical regions, where there are more parasites, are more sexual than trees in the arctic, where there are far fewer parasites. Also larger, less-fecund organisms such as humans, elephants, and palm trees have very stable sexual characteristics, because of the previously-mentioned slow generations. This is particularly important because many other theories of sex do not explain why less-fecund organisms would have more sexual stability.
There are many other predictions this model makes, but I’ll stop here.
Conclusion
The parasite theory of the evolution of sex has some theoretical and empirical backing. Far from George’s idea that “you’d likely have to simulate evolution “from scratch” in a bunch of Earth-like environments to get an answer with any degree of certainty”, Hamilton provides us a well-grounded theory of the evolution of sex, and backs up his theory by looking at what it predicts and then seeing if those things are actually true, like a good evolutionary biologist ought to.
All in all, I’m currently pretty convinced that parasitism plays a role in the evolution and stability of sex. But only reading papers by one author seems like bad espistemic hygeine, so I don’t want to stop here. I’m going to read some papers by other authors that think Hamilton are wrong, and see what they say! If there’s anything interesting there, I’ll make another post.