Sex allocation is an organism's decision on how much of its reproductive investment should be distributed to male and female functions and/or offspring. Under most conditions, the optimal ratio is 50:50, but that can change under certain circumstances. Sex allocation determines what sexes sequential hermaphrodites should be at each part of their life as well as how simultaneous hermaphrodites should behave. Some species have more control over the sexes of their offspring than others, and adjust the sex ratios of their offspring depending on the environment and conditions.
Stearns, Stephen C. and Rolf Hoekstra. Evolution: An Introduction, chapter 10
February 9, 2009
Professor Stephen Stearns: Okay, today we're going to talk about sex allocation theory, and I would like to begin by reminding you of where we're at in the course. We're in the middle of micro-evolutionary evolutionary biology, the micro part, and we are now applying the ideas that we've developed to try to understand the design of phenotypes for reproductive success.
This portion of the course basically started with the evolution of sex, and then we saw that sexual- the evolution of sex opened up all sorts of possibilities for genomic conflict in evolution, and that gave us the image of the organism as not necessarily being optimized or just adaptive. The organism can be viewed as a composite, and the parts of the composite can be in conflict with each other.
With life history evolution, we've more or less shifted back to a view of the organism as being optimized in some sense. I think we saw that most clearly with the kestrel parental investment and investment in clutch size, and in things like optimal reaction norms for age and size at maturity. Now, when we go to sex allocation, we are looking again at how to optimize the life history. But the issue now is how much should be invested in male function and how much should be invested in female function? And this opens the doorway also to alternative explanations.
Some of these patterns that we're going to be looking at can be seen as the result of more or less an optimality argument, that this is the best way it could be done, given the constraints on the system, but in other places it's possible that there are fundamental conflicts going on and that nobody's winning, that everybody's making the best of a bad job. And I think that you'll see some of that when we get into the frequency dependent parts of sex allocation.
So sex allocation theory is actually a part of evolutionary ecology which has been extremely successful. It predicts the distribution of reproductive effort among male and female offspring, or between male and female function. It makes a lot of successful predictions.
There is a theorem at the heart of this part of biology called the Shaw-Mohler theorem, which is very general in the way it's formulated, and it unites many previously unrelated phenomena. So the successful predictions, and the bringing together in a single explanatory framework of a lot of stuff that was previously seen as unconnected, is a characteristic of any good scientific theory. After all, that's what the Periodic Table does in chemistry; that's what Newton did with his Laws of Motion. So this is a good example of success in evolutionary theory.
In order to get into this field, we need to have a little vocabulary building, just so you can operate in the literature. If you're a botanist, you call organisms that have separate sexes dioecious, and if you're a zoologist you tend to call them gonorchoristic. The default condition in most flowering plants is that they're hermaphrodites and they have both male and female parts in the same flower. But there are some striking exceptions. Papayas have separate male and female sexes; holly have separate male and female plants; and so forth. So there are certainly dioecious plants. The default condition in most animals is that the sexes are separate. So the default condition is different in most flowering plants and most higher animals.
Now if we're dealing with sequential hermaphrodites, then they can be either protandric or protogynous. We call them protandric--so first male, pro andros--if they're born as males and change later to females, and we call them protogynous if they are first females and then change to males. Okay? The only human in mythology, at least in Western mythology, who has done something like this was the Greek sage Tiresias, who was a prophet during the Trojan War and is said to have been, in his lifetime, both male and female, having been changed by the gods, rather than by his hormones, and was able to report on what it's like. You might want to go back and check.
Now for the purposes of sex allocation theory, we define female function in a number of different ways. Okay? It could either be the proportion of offspring that are female; that could be a lot or a little. It could be investment in female versus male offspring; so you have equal numbers of both but you decide to invest more in offspring of one sex than the other. Or in a sequential or simultaneous hermaphrodite, it's the proportion of lifetime reproductive success gained through reproduction as a female. So female function can have to do with timing, with investment and with numbers; male function is defined similarly.
So there are some very basic questions about sex allocation. One is, what's the equilibrium sex ratio? What should we expect to see in a population that has separate sexes? Another is if the species we're dealing with is a sequential hermaphrodite, as what sex should that organism be born, and how old and large should it be when it changes sex? If it's a simultaneous hermaphrodite, then what would be the allocation to male and female function in simultaneous hermaphrodites? We're not going to talk about this very much today, but I would like to give you just a little bit of natural history.
There is a lovely Caribbean fish called the Hamlet, which is a simultaneous hermaphrodite, and it can make eggs and sperm at the same time, and they mate every day, and when they get together to mate, there's the issue of who should be male and who should be female for this mating? And the eggs are big and expensive, and the sperm is small and cheap, and so you don't want to get cheated by somebody who never wants to be the female and just makes sperm. So what they've come up with is a mating pattern where in order to mate at all, they more or less insist that they trade roles and do it about ten times, so that they equal out. So in the course of twenty minutes, they will switch back and forth from being male to female, and then each of them will have put out roughly the same amount of eggs and the same amount of sperm. So I just wanted you to have that in the background as one of the sort of paradigmatic examples of how simultaneous hermaphrodites have solved that issue.
And then there's the interesting issue--and by the way, this is something I stuck in here this morning, so those of you who have printed out your PDFs, this is new--when should differential investment in offspring of each sex depend on social status? And I stuck this question in here, because in fact the lecture deals with that. We're going to come to the Trivers-Willard hypothesis, and we will see that social status, or physiological status, really does affect sex allocation quite a bit.
So these are all aspects actually of one problem, and that problem arises because of this key fact. Every diploid sexually produced zygote is getting half of its autosomal genes from its father and half from its mother, and that's also true of the sequential and simultaneous hermaphrodites; okay, that's what it means to be a sexual diploid. And that has a consequence. It means that the fitness that's gained by an individual through male function has to be compared with fitness gained by other individuals through male function, and similarly for fitness gained through female function. In other words, male and female function are equivalent paths to fitness.
Now in a number of circumstances in evolutionary biology it is advantageous to use what I call 'the looking backwards ploy' to develop an intuition for why this is true. Think about the genes in your body--you got half from your mom and half from your dad--and look backwards to where they were sitting in grandparents, great-grandparents, great-great-grandparents, and so forth. And if you go through that branching tree, going backwards, you'll see that in each generation half of them were coming down through a female and half of them were coming down through a male, and as they go forward, into the future, it's always going to be, on average, half of them coming down through a male and half of them coming down through a female.
This means essentially that this statement, male and female function are equivalent paths to fitness, is something that you could derive by putting out the whole genealogy of the family tree and just counting the number of times that genes had occurred in male or female ancestors, and you would discover that it was 50:50. Okay? [Request to turn off cell phones]
Okay, we start this kind of analysis with the default condition, which is the 50:50 sex ratio. That's a photo of Ronald Fisher. He came up with this idea. He's one of the people, by the way, who demonstrated that Mendel's laws are consistent with natural selection. He also invented quantitative genetics, and he invented the analysis of variance in statistics. He was a total autistic geek and a nasty father, and his daughter wrote a really fascinating biography of what it was like to grow up with this guy, who was a fulltime, 24/7 biologist, and who kept all kinds of plants and animals around the house and kept breeding them, but was not what you would call a terribly empathetic, emotional person.
And he also was a guy who was nearly blind, but who visualized most problems geometrically. He was very powerful mathematically, but Fisher essentially saw things geometrically that most people see algebraically. So his theoretical writings can be opaque at times. But, this idea is pretty straightforward:
If males and females are equally good at producing male and female offspring, at all ages and sizes--so everybody's pretty much on a level playing field--if mating's at random, in a big, large population, that's thoroughly mixed, then the sex ratio should evolve to 50:50 male/female offspring. Basically the reason that's true is that the rarer sex has an advantage. The sex ratio is adjusted until neither type is rarer than the other, and that's probably the most basic frequency dependent equilibrium in biology.
You can see why that would be true if you imagined that you were a mutation that produced only male offspring in a population that was otherwise producing all female offspring. You would then have the only males in that population, and all of the offspring in the next generation would be carrying your genes. You would increase in frequency.
You can see how it would work in the other direction, if you do this kind of mutation invasion analysis, by asking yourself, what would happen if everybody else in the population was male, or everyone else in the population only produced male offspring, and you're the only one to make female offspring? Well you get--all of the grandchildren are yours. Okay? So you increase from the other direction. So if you imagine populations that are being invaded by these different alternatives, they come together at the middle, and it's only at 50:50 that there's an equilibrium.
This may be why sex chromosomes evolved. Okay? We have sex chromosomes, we have an X and Y chromosome. That guarantees 50:50. But before there were sex chromosomes, there was sex, and there were evolutionary dynamics, and it may be that this is why organisms with sex chromosomes have evolved.
There are many other ways of determining sex. You don't have to have sex chromosomes. Crocodiles and turtles do it with temperature. Sometimes parasites determine what sex you are; Wolbachia will do that. Sometimes sex is determined by a quantitative process of many genes, rather than having a sex chromosome.
So this process, which we find to be almost intuitive because we have sex chromosomes and that's what our population does, in fact is a special case. But it appears that it would have evolved out of this kind of a situation: big populations with fairly equal opportunities for everybody. If these assumptions are violated, we get changes in the optimal sex ratio, and it's the Shaw-Mohler theorem that predicts what would happen when these assumptions don't hold. So let's have a look at it.
A mutation will invade a population if it can increase fitness through one sex more than it decreases fitness through the other. And if we state that as an inequality, the change in male function divided by average male function, plus the change in female function, divided by average female function, needs to be greater than 0. Here, little-m and little-f are the average fitness through male and female function in our resident population. So we're starting just at some starting point in evolution, and there's an average male and female function, and a mutation pops up that changes male and female function.
So its change is the critical thing. Is it changing one of them enough to compensate enough for the other? So if the percent increase in fitness through one sex is greater than the percent decrease through the other sex, this mutation will invade, and that will go on until a new equilibrium is reached. So this is more or less the invasion criterion. We're going to see three cases in which it works pretty well. There are more, but I've just selected three that are fairly dramatic. One is local mate competition; the next is sequential hermaphrodites; and the third is social rank in sex allocation.
So the local mate competition one is one that you're actually already familiar with; I've mentioned it. I will also give a second species, a mite, that does something like this. So what would the sex ratio be if all of the grandchildren stem from matings between brothers and sisters? Well you would make one son and as many daughters as possible. And to get there from a 50:50 sex ratio, basically you can see, I think, that if--we can go stepwise--if the fecundity of this creature--it's a mite usually or sometimes it's a wasp--the fecundity might be say twenty offspring, and if it was at 50:50 sex ratio, then the average mite in the population would be making ten sons and ten daughters.
But if all the sons are only inseminating only those daughters, then anybody that made eleven daughters and nine sons would have more grandchildren; twelve daughters and eight sons would have even more grandchildren; and so forth, until you get down to nineteen daughters and just one son, and that one son inseminates all nineteen daughters, and the nineteen daughters are making almost twice as many grandchildren as the ten daughters would have. So they're just gaining all the way down, to the point where there's just one son.
And that is exactly what Acarophenax does. It's a haplo-diploid parasitic mite--haplo-diploid means that the males are haploid and the females are diploid--and there's incestuous fertilization inside the mother. So the one son inseminates all of the daughters, and then once that's accomplished the son dies and the daughters eat the mother, from the inside. So the curse on the House of Atreus was peanuts, compared to this.
This is what these things look like. This is a straw itch mite, and any of you who have been out in August, cutting the lawn, and then had little bites on your legs, were probably getting bitten by this thing. It makes 98% daughters, and it has that kind of lifecycle. Okay, so that is the case where the Shaw-Mohler theorem works perfectly. A mutation invading this population is increasing the number of grandchildren by increasing female function, and they are not losing anything in male function because that one son is still capable of inseminating all the daughters.
Now if we go to sequential hermaphrodites, it's useful to think of it as--this would be either an age or a size advantage model; the size advantage model is probably the more intuitive way to think about it--and this model is used to answer the question, into what sex should a sequential hermaphrodite be born; so what should the baby be, and then how old and how large should it be when it changes sex?
And the size advantage model basically sketches out lines of fitness, increasing with size, but they increase at different rates, and basically the argument is you should be born into the sex that has higher fitness when you're small and then you should change into the sex that has higher fitness when you're big, and you should change at the point where the lines cross.
And if this line is higher here for females, and higher here for males, we have protogyny, and if it's higher here for males, and higher here for females, we have protandry. So you should be born as a male, if your fitness as a male when you're small is greater, and then change into a female, and you should be born as a female and change if the biology dictates that your fitness is higher when you're big, as a female--as a male.
And the reasons for this are both physiological and social. The default condition actually is that small things do just fine as males, if there aren't any social dominance interactions, because a small male can still make a lot of sperm. But the fitness advantage switches to being a female when you're large, if there aren't social interactions, because a big female can make a lot of eggs.
A lot of this analysis is done in fish, and the default condition is pretty well described in a lot of fish. Small males do just fine in matings if there aren't complex social interactions, if you don't have to fight in a dominance hierarchy to get to a mating. And big females can make enormous numbers of eggs. A big female codfish, a six-foot long female codfish can make 100,000,000 eggs. A big grouper can make 100,000,000 eggs.
So, let's go through a case of protogyny, and one of the better analyzed cases is the blue-headed wrasse. By the way, for those of you who are snorkelers or divers, all the members of the wrasses and the parrot fish families are sequential hermaphrodites, and they are just about all protogynous--so they're born as females and change to males--and all of the members of the grouper or sea bass family, the Serranidae, are protandrous; so they're born as males and they change to females. So if you see a big lunking grouper, it's going to be a female, and if you see a big parrot fish, it's going to be a male.
And some of them, as you'll see in a minute, look rather radically different when they change sexes, and these are fish families in which figuring out that they were actually just two different sexes of the same species, rather than two different species, took a long time, and some of the changes in morphology and color and behavior are really rather remarkable.
So in Thalassoma, the bluehead wrasse, that's a case where they are born as females and then they change sex and turn into males, and when people first started doing experiments on this, they went out and they pulled the dominant male off of a reef, and the dominant female basically started behaving as a male within twenty-four hours, and within about six weeks she has changed color and she has changed the physiology of her gonads and she's turned into a male and she's functioning and producing sperm and mating perfectly successfully as a male. It takes a little while to change. It doesn't happen right overnight.
And actually it's a little bit more complicated because there are two options. You can actually, in this fish, be born as a female and then turn into a male, or you can be born as a male, as a initial-phase male, and then turn into an adult dominant male. And the initial-phase males are female mimics. They make their living by sneaking fertilizations off of dominant males.
The way that sex works in this species is that that they live on patch reefs, or sometimes they live on a larger reef; and you'll see in a minute that the size of the reef makes a big difference to their lifestyle. They normally swim up to spawn near sunset on the down current side of the reef. When they spawn and their fertilized eggs then are out there, in the ocean, the current will--if they've done it right--the current will carry the eggs away from the reef, because if the eggs settle on the reef, the reef is a forest of open mouths. A coral head is basically a whole bunch of little hydra, just waiting to grab onto anything that falls onto it. And so the fish do their reproduction at a time of day when planktivores will not easily see their eggs, and in a water current that carries the eggs away from the reef.
And the way they do it is that they come up off the reef and they swim up in the water column near the surface, and one of these dominant males will swim up with a whole school of females with him, and he will go through a dance and spawn, and he will release his sperm and they will release their eggs. And if there is an opportunity, one of these initial-phase males will sneak in, and because he looks like a female, he won't get beaten up, by the big male, and he will release his sperm and grab some of the fertilization opportunity. So there's an interesting question: how many should be initial-phase males and how many should be initial-phase females?
Well that's where the ecology and behavior comes in. These big, lunking, dominant, terminal-phase males can actually police a harem, on a small reef, and they can actually police an area which is maybe the size of this piece of furniture up here, or down to about half that size.
If it gets much bigger than that, then the females actually are just wandering around foraging, looking for food, and a female could wander down to this end, and if there was an initial-phase male down at this end, he could grab copulations, because there might be disruptions, as they go up at sunset, and that the number of females would have arisen to the point where the dominant male couldn't control all of the initial-phase males. So basically the idea is that if the reef is small, these guys do well. The bigger the reef gets, the better these do. And you can interpret SF either as success in sneaking fertilizations, or in some slightly less polite terminology.
So this is some field data from Panama, and it shows you what proportion of the males are actually initial-phase males. Remember I said that you would expect them to do better on the large reefs, and you would expect the dominant males to do better on the big reefs. And this axis down here is 1/square root of local population size; so actually populations are getting bigger in that direction, along this axis.
So in fact if you just--the data's fairly noisy, the transformation down here does tend to squeeze the data together a little bit, but there is a significant effect of reef size. If you're on a small reef, it's mostly terminal males. The larger the reef gets, the bigger the population gets, the more initial-phase males there are.
Now how do they know whether they should be an initial-phase male or an initial-phase female? These guys, remember they go out and they live in the plankton, and then they come back to a reef. And there they are, they're just a tiny little fish, and they're dropping down onto a reef, and from their perspective--after all, if you're just one centimeter long, you don't really know if you're on a reef the size of this room or on a reef the size of this table. So what cues could it use to decide what kind of reef it's on, and is it using a genetic cue or is it a developmental one?
Well, it's really not plausible that this kind of switch would be purely genetic, because if it were purely genetic, then you would be the kind of fish that your parent was, but you might end up in an environment where that way of living was not appropriate, because you're being spread out over hundreds of kilometers out there in the plankton and then coming down on reefs of many different sizes.
So there's some evidence that the larvae are choosing their sex based on density. If you rear them in isolation, the juveniles are almost always differentiated as females. So it's like the first one in on the reef, the default condition is to be a female, and that is regardless of whether they came off a reef with lots of primary males or with a few primary males. So it doesn't appear to be that that's an inherited condition.
But if you have them reared in groups of three, one individual usually differentiates as a primary male. So as the population size, the cues of population size start to accumulate, some of them become primary males rather than primary females.
So this seems to be an environmentally sensitive, developmental strategy, and it's probably evolved in response to variation in reproductive success of primary males and populations of different sizes. That's a fairly stringent logical condition; and again the looking backwards ploy is important.
This would never have evolved if the genes had always been experiencing reefs of the same size, with similar social conditions on each reef. You only get a developmental switch like this evolving if there has been a regular alternation of social conditions for those young male wrasses to encounter, and if that has been the case for long periods of time in the past, then the ones that have been able to adjust appropriately will have left more grandchildren; and that appears to be what's going on here.
So if you would like, if you're interested in this kind of thing, this is a good paper to get you into that literature. And remember, if you're in ISI Web of Science, you can both look backwards and look forwards. You can look at all papers published in 2008 that cite this paper that was published in 2006, for example, and you can do that with any other question that you're asking.
Now, what about a case of protandry? Well this is a case that shows the default condition when there really isn't very much complicated social life. This is a mollusk and it lives on the Connecticut coastline. And if you go out to Hammonasset State Park, which is up by Madison, and you walk down the beach, your shoes are crunching on the shells of Crepidula fornicata; that's basically what the beach consists of is the shells of Crepidula fornicata.
And these guys are born as males and grow up and change over to being females, and they go through a stage where they're both. And, in fact, they have a penis that extends downward, and so the males are actually inseminating the hermaphrodites that are in the middle, and the hermaphrodites in the middle are inseminating the female that's on the bottom. So Crepidula forms a daisy chain as a standard part of its life history. This is how these things live, and you can see the progression just sitting there in one clump, as they go through their life.
Okay, so the Shaw-Mohler theorem actually tells us quite a bit about the main questions of sequential hermaphrodites. Remember they are: as what sex should I be born, and at what age and size should I change sex? And by the way, the existence of sequential hermaphrodites leads us to certain puzzles. There are many, as you'll see in a minute, there are many mammals where it would make a lot of sense to be a sequential hermaphrodite, but evidently we don't have a reproductive system that's flexible enough for that to have evolved. And I think you'll see--but just stick that in your memory for a few minutes, because you're now going to see a few mammals that would make more sense to me as sequential hermaphrodites.
We'll get into that with the Trivers-Willard hypothesis. So again this is Bob Trivers, and with a guy named Willard he came up with the idea that in a polygynous species, a low ranking female, or a female in poor condition, should have female biased litters or clutches, because their daughters can always have offspring. Females in these circumstances are the limiting sex. You do not have to be a highly competitive female in a polygynous species to get inseminated. There's going to be some male that's going to get you pregnant.
On the other hand, high ranking females, or females in good physiological condition, should have male-biased litters or clutches. The reason for that is that their sons can only have offspring if they can dominate. So you're not going to invest in a male offspring unless you're pretty sure that it's going to grow up and be able to actually win competitions. So the examples we'll look at are red deer and chimpanzees, and at the end I'll mention the German farmers. Okay?
So in red deer on the Island of Rhum, in Scotland, where Tim Clutton-Brock and Loeske Kruuk and Josephine Pemberton and others--Fiona Guinness--have studied them now for thirty years, they have followed many individuals, from birth to death, and documented their social rank and their reproductive success and many aspects of their behavioral ecology. There is a great deal to be learned from following individual organisms from birth to death, because the variation you then see in their lives tells you a great deal about the selection pressures that are operating on them.
And what they observed was this. Here over here, on the y-axis, you've got lifetime reproductive success of male and female offspring. The closed circles are the sons, and the open circles are the daughters, and this is the social rank of the mother down here--this is subordinate and dominant--and this straight line here is drawn just for the black dots, for the sons. And what you can see is that there is really not very much influence of social rank on the lifetime reproductive success of daughters, but there is an influence of social rank on the lifetime reproductive success of the sons.
Now high ranking females in red deer do give birth to more sons than daughters. They have a distorted sex ratio at birth. So the question is how do the females do that? Well they can be doing it with sperm selection, if they could detect whether the sperm were X or Y bearing sperm. They could do it with selective abortion, if somehow the conflict between mother and offspring has been resolved in favor of the mother.
Just think about it. There you are, you're an embryonic red deer. You happen to be the wrong sex for this particular mother. She has evolved to get rid of you through abortion, if you're the wrong type. You will try to conceal your sex. You will not be expressing whether you're a male or a female in the surface proteins. So there's a puzzle here. How could selective abortion evolve? Because there is a conflict between parent and offspring about whether you should be able to even detect what sex your child is.
We don't know. What we do know is this: Nutrias do this--nutrias are South-American rodents--and if you have a female nutria who is subordinate or in low physiological condition and she should be making mostly female offspring, but she happens to have a mostly male brood, she just aborts the whole thing and tries again. So that's what she does.
The Seychelles warblers--so a great place to go do fieldwork; the Seychelles are just lovely--there's a warbler that lives in the Seychelles Islands and they control the sex of individual eggs, and they do so--in order to have the correct sex, there is a helper at the nest when they--when the baby grows up they actually have helpers at the nest. So whole families of warblers help to feed the next generation, and what the mother is doing is she's making the right kind of egg for her ecological condition. Sometimes it's helpful to have a lot of daughters and sometimes it's not helpful to have a lot of daughters, and they can control the sex. We don't know how they do it.
So there is definitely sex allocation in red deer and in nutrias and in Seychelles warblers where the sex ratio at birth is being changed in terms of social or ecological circumstances, and it seems to be changed appropriately. Now with chimpanzees--chimpanzees are like us. They have a 50:50 sex ratio at birth, and if you don't have selective abortion, you don't have effective sperm selection, it's hard to avoid a 50:50 sex ratio at birth. So sex chromosomes do that for you.
However, you can still make choices after the baby is born. And this is the inter-birth interval in months, over here, and this line here is for dominant mothers, and this line here is for sub-dominant mothers, and this is about five years and this is about seven years, up here. So it's about a two-year difference.
And if a dominant mother gives birth to a daughter, she weans that daughter, when that daughter's about five years of age. But if she gives birth to a son, she keeps him for two more years. That is a high investment. He's getting more and more expensive to take care of and she's losing time that she could put into another child. But because she's dominant and she's got a son, the argument is she'll get more grandchildren if she invests in him and really makes him into a dominant male. On the other hand--and by the way, this is a highly significant result here; this one is marginally insignificant down here--a sub-dominant mother has a bit more of a tendency to rear her daughters longer and her sons shorter and discard the sons earlier.
Look at what happens to them. This is the survivorship. This is the age of the baby here. This is the son of a dominant mother; so these guys over here. They aren't weaned until they're seven-years-old. As soon as they're weaned, 30% of them die, but the rest of them have extremely good survival, and they in fact do better than anybody else. By age 13 they're just the best survivor class that there is up in this diagram.
Look at the sons of a sub-dominant mother. They're these guys here. They are--this square--they are neglected even before they're weaned. They aren't weaned until five years. So before they're weaned, they're already doing worse, and then once they're weaned they only have a 20% probability of becoming 13-years-old; whereas those of a dominant mother have nearly a 70% probability of becoming 13-years-old. You can see that there are similar effects going on with the daughters. That's a very dramatic pattern.
Now, rearing a son at all, if you're a sub-dominant mother, and you're going to kind of neglect him and get rid of him early, is a very expensive thing. So why is it that they haven't evolved screening mechanisms, at the sperm or the zygote stage, that respond to social rank? We don't know. It would be very adaptive for them to do that.
And I'll now tell you about the German farmers. Klaus Voland, in Germany, has analyzed the demographic data sets of a set of Northwestern German farming communities from the seventeenth and eighteenth century, through the nineteenth century. And during this time there were economic cycles. When times were good, it was possible for a son to inherit a farm. When times were bad, the sons couldn't inherit anything, or only one son could inherit the farm, but in bad times daughters could still marry up.
And what Voland showed is that the probability that a son or a daughter would survive to maturity was dependent upon the economic cycle, pretty much in the same way that we just saw for the chimpanzees. In other words, German farmers invested more in sons when sons could inherit, and they invested more in daughters when daughters could marry up, and the degree of investment was actually reflected in the mortality rates of the children. So it had to do with parental neglect.
So that is one case where it does look like the Trivers-Willard hypothesis actually works in humans. To be fair to the data, I want to mention some of the other cases. There have been large-scale studies in the United States that show that this effect is fairly weak, and there have been some other studies in the United States that show that this effect is fairly strong. So the evidence is mixed on this one.
And I would like to emphasize that in humans it could very well be cultural rather than genetic. After all, people generally do talk about issues like this, and they are understood within families. So it's possible that patterns of parenting could be culturally as well as genetically influenced. However, what one can say is that that's perfectly consistent with the Trivers-Willard hypothesis. It's just that it might have a cultural rather than an evolutionary explanation.
So I think that the Shaw-Mohler theorem is a case in which very disparate kinds of information are being brought together and explained in the same theoretical framework. Remember, we've looked today at sex ratios in mites where you have incest and cannibalism going on. We have looked at sex change in hermaphroditic fish, sequentially hermaphroditic fish, and we have looked at the investment in offspring of the two different sexes in red deer and in chimpanzees; and that's really quite a range of biological information.
If you get into the sex allocation literature, you will find hundreds of more cases where the Shaw-Mohler theorem works. So it indicates that it has captured something that's very important about evolutionary biology. And to remind you of that, it's the fact that in a sexually reproducing population every diploid adult is getting half of its genome from its father and half of its genome from its mother, and the consequence of that is that the male and the female paths to fitness are equivalent. So this is a very fundamental structuring fact about much of the sexual biology of organisms.
In sex allocation we've seen that there are really quite strong connections between mating systems, social structure, sexual selection, population structure, life history evolution and genetic systems. Let me test your understanding of what I've said today about male and female function being equivalent paths to fitness, and about the Shaw-Mohler theorem.
There is a shrimp--and you have all probably eaten it in your dinning halls--which is born male and changes to female. And let us suppose that this shrimp, before there was ever a fishery for it, made the sex change when it was three-years-old. So when it was small it was a male, it changed to a female at three years, and then it lived the rest of its life as a female. Male and female function are equivalent paths to fitness. Now, we create a fishery, and the fishery goes in and it starts catching all those nice big fat females, because they're the biggest ones, and the fishery operates long enough for there to be an evolutionary response. What happens to the age at sex change?
Student: It's longer.
Professor Stephen Stearns: What?
Student: It's longer.
Professor Stephen Stearns: No, they do not spend longer as males. So now you know the answer. But I want to know why. What happens is that they change sex at two-years, rather than at three-years. What's happened is that the fishery has been taking away their female function, and evolution wants them to get half of their fitness through male function and half of it through female function.
In order to maintain that equivalency, it has to create more space in the life through the females. The fishery is taking away space in the life to be female, and so the sex ratio, the sex change shifts to an earlier point. This is exactly what's happened, and if you buy fish at A1 Fish Market, or you have them in the dining hall, you will get shrimp in those fish markets that do this, and they have responded to the human selection pressure created by the fishery, and it's changed the age and size at which they change sex.
This is actually one of the reasons why this course is called Principles of Evolution, Ecology and Behavior. It's because there are examples like this where it doesn't make any sense to separate these fields. All of this stuff is going on, in these examples. You have dominant behavior, you have ecology, population density and evolution all interacting with each other. Okay, so next time sexual selection.
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