EEB 122: Principles of Evolution, Ecology and Behavior?

Lecture 12.?Sex Allocation

https://oyc.yale.edu/ecology-and-evolutionary-biology/eeb-122/lecture-12

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.?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.?

• 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.

• 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.

Now for the purposes of Sex allocation theory, we define female function in a number of different ways. Female function can have to do with timing, with investment and with numbers; male function is defined similarly.?

• 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.

• In a sequential or simultaneous hermaphrodite, it's the proportion of lifetime reproductive success gained through reproduction as a female.?

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?

• When should differential investment in offspring of each Sex depend on social status?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; 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.?This?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.?

We start this kind of analysis with the default condition, which is the 50:50 Sex ratio. Ronald Fisher?came up with this idea. He's one of the people?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.?

• 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 are?the only male?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,?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? All of the grandchildren are yours. So you increase from the other direction.

• If you imagine populations that are being invaded by different?alternatives, they come together at the middle, and it's only at?equilibrium of 50:50.?

This may be why Sex chromosomes evolved. 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?other than?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.?

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.

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.?One is local mate competition; the next is sequential hermaphrodites; and the third is social rank in Sex allocation.?

The local mate competition one is one that you're?already familiar with.?I will also give a second species, a mite.?

• 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.?

• Acarophenax?is?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.

• A?straw itch mite?makes 98% daughters, and it has that kind of lifecycle. It?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.

If we go to sequential hermaphrodites,?it would be either an age or a size advantage model; the size advantage model is probably the more intuitive?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??

• The size advantage model basically sketches out lines of fitness, increasing with size?but 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.

• 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.?

• 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.?

• Let's go through a case of protogyny, and one of the better analyzed cases is the blue-headed wrasse. 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.

• Some of them look rather radically different when they change Sexes.?In Thalassoma, the bluehead wrasse, that's a case where they are born as females and then they change Sex and turn into males. When scientists?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.

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 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.?

• They live on patch reefs, or sometimes they live on a larger reef; and 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 carry the eggs away from the reef, because if the eggs settle on the reef, the reef is a forest of open mouths.?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.

• 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.?

There's an interesting question: how many should be initial-phase males and how many should be initial-phase females??

• 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.?So basically the idea is that if the reef is small, these dominant?guys do well. The bigger the reef gets, the better these?initial-phase males?do.?

So this is some field data from Panama, and it shows you what proportion of the males are actually initial-phase males. 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. 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? 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??

• 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.

• It 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.?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.

Now, what about a case of protandry? This is a case that shows the default condition when there really isn't very much complicated social life. This is a mollusk?called?Crepidula fornicata.?They?are born as males and grow up and change over to being females. 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. The Shaw-Mohler theorem actually tells us quite a bit about the main questions of sequential hermaphrodites: as what Sex should I be born, and at what age and size should I change Sex??We'll get into that with the?Trivers-Willard hypothesis.

• Bob Trivers with?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.

• 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?the German farmers.?

• In red deer on the Island of Rhum?in Scotland, scientists?have followed many individuals, from birth to death, and documented their social rank and their reproductive success and many aspects of their behavioral ecology.

• On the y-axis, you've got lifetime reproductive success of male and female offspring. The closed circles are the sons, and the open ones?are the daughters, and this is the social rank of the mother down here--this is subordinate and dominant on the x-axis--and the?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.

High ranking females in red deer do give birth to more sons than daughters. They have a distorted Sex ratio at birth. Females?can do?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.?The mother?has evolved to get rid of you through abortion, if an embryonic?red deer?happens to be the wrong Sex for this particular mother.?It will try to conceal its?Sex,?not expressing whether it is a?male or a female in the surface proteins.?So?there is a conflict between parent and offspring about whether you should be able to even detect what Sex your child is.?How could selective abortion evolve??We don't know.

• Nutrias are South-American rodents. 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.

• There's a warbler that lives in the Seychelles Islands and they control the Sex of individual eggs. In order to have the correct Sex, there is a helper at the nest when the baby grows up.?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?or effective sperm selection, it's hard to avoid a 50:50 Sex ratio at birth. 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?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.

• If a dominant mother weans?the?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. He's getting more and more expensive to take care of and she's losing time that she could put into another child. Because she's dominant and she's got a son, the argument is she'll get more grandchildren if she invests in him and makes him into a dominant male. On the other hand,?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.

• This is the survivorship of?sons of a dominant mother.?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 are neglected even before they're weaned. They aren't weaned until five years and 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%. You can see that there are similar effects going on with the daughters.

• 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 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.?

The probability that a son or a daughter would survive to maturity was dependent upon the economic cycle, just like?chimpanzees.?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.?

It?is one case where it does look like the Trivers-Willard hypothesis actually works in humans. But there have been large-scale studies in the United States that show that this effect is fairly weak or fairly strong. So the evidence is mixed on this one. However, in humans it might have a cultural rather than an evolutionary explanation.?

There is a shrimp,?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. Then we create a fishery that?starts catching all?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??

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 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.?