The Trivers-Willard hypothesis and embryonic diapause

"Dan Willard was a graduate student in mathematics at Harvard University, and he wanted to meet some women." -- Robert Trivers

Before Ronald Fisher, there was Charles Darwin. He invented the study of sexual selection and wondered in The Descent of Man why is it the case that men and women are born at quite similar rates. He knew males and females had different fitness distributions—males are more likely to have more offspring than females, and also fewer, but why does natural selection not act to exploit the asymmetry in their fitnesses and produce an uneven sex ratio?

The old boy was not great with numbers, as he himself noted, and never could quite see the final logic. Fisher finished the argument for why a 1:1 ratio is maintained. Remarkably, it involved a synthesis of two ideas that hadn’t been invented yet: frequency-dependent selection and game-theoretic stability.

Fisher reasoned that if individuals produced an excess of male offspring, the frequency itself of those excess males relative to female offspring would be self-defeating because the glut of males would be confronted with a paucity of mates. The same logic works in reverse for females. At conception, only 2 sets of genes can make it into a zygote. Regardless of how many more (or fewer) offspring males could have the evolutionary logic works to sustain the stable 1:1 equilibrium.

Everything in science is obvious after someone explains it.

Was Fisher really correct?

If the lore is believed, Trivers states that Dan Willard approached him after a lecture on this subject and pointed out that individuals might bias the sex ratios of their offspring and as long as the opposite bias occurred in other individuals in the population, Fisher’s 1:1 equilibrium would be maintained. Why might they do that?Trivers and Willard, 1973 explain.

Having read the primary documents for this poast, I’m pretty sure Fisher did not consider this point at all, and it really does detract from his work on the subject. He notes that different sex-determination mechanism could flout the logic, but that’s partial credit. What’s interesting is that I believe Darwin, to his enduring credit and humility, probably did consider it but in Descent he knows his own limitations and demurs.

I formerly thought that when a tendency to produce the two sexes in equal numbers was advantageous to the species it would follow from natural selection, but I now see that the whole problem is so intricate that it is safer to leave its solution to the future.

Trivers and Willard is a compact paper, and I’ll briefly summarize the argument. If a population has differential maternal condition (that can mean health, vigor, or whatever other resources she has) and if a mother’s condition is correlated with the condition of her offspring, and if such condition differentially effects the evolutionary fitness of males and females, mothers in relatively good condition would be biased to produce male offspring and mothers in poor condition would be biased to females.

Think of it like this: a son in good condition is more likely to have many more offspring than a female in similar condition especially in a polygynous population with multiple matings by a dominant male. To best propagate her genes, mothers who are themselves in good condition capable of investing in sons should prefer to do so over daughters. The exact opposite is true of mothers in poor condition who’d rather take a chance on a daughter while in poor condition rather than a son in such condition. If the slope of a condition-fitness plot for males is steeper than such a plot for females, Trivers and Willard predict this pattern of sex biased investment.

Were Trivers and Willard really correct?

It’s notable that the genesis of the paper wasn’t mainly in consideration of deer, or rodents, or pinnipeds, or any other highly polygynous species that have come to dominate the literature on this subject, but in humans. Trivers thought that hypergamy (the tendency of women to marry up the socioeconomic ladder) represented a bias for investment in sons, and they cite some evidence that sex ratios are skewed male in some high SES populations.

In fact, the human application of the hypothesis that Trivers and Willard advance is probably a complete folly. Clark and Cummins, 2023 have assembled an absolutely gigantic dataset of 67M people and half as many marriages spread out over centuries in England and conclude hypergamy simply isn’t a thing, and probably never has been. In datasets with sufficient resolution, it seems men and women match quite strongly on social status, though the reasons for this remain mysterious.

As an aside, note that practically every human adult has some sort of experience searching for partners and pair-bonding but even with that universal experiential base, no one seems possessing of the self-knowledge about why they pick partners who are socially like themselves.

Diapause

I never took a varmints, critters, and living things class in college, so my knowledge can be somewhat unsystematic, but I watch a lot of Planet Earth and am curious. I read Trivers and Willard years ago, but I only pretty recently learned that after mating and conception, some mammal species can delay the mitotic development of blastocysts for an amount of time that varies species to species, and it probably has to do with ensuring good environmental conditions for raising young.

Although the idea of a long term dormancy in animals has been understood since Aristotle noticed honeybees overwinter, this type of embryonic diapause in mammals was not understood at all until the mid-19th century, which is actually earlier than I suspected when I researched this. I don’t claim to have read the original Ziegler paper on European deer in German, but he’s cited by Deanesly, 1943 who was studying this in mustelids so congrats to her for her German language skills.

Maybe I’ll email him, but I don’t think Trivers knew about embryonic diapause when he wrote this paper. Willard obviously didn’t because he was busy studying silly math stuff. It’s not in the paper and nothing referenced seems to mention it either. What’s extraordinary about this is that the mammalian groups singled out as supporting evidence in the paper are the exact ones where diapause is now known to occur. Deer, rodents, mustelids, and seals. The paper is quite terse and maybe Trivers suspected embryonic diapause had some interesting relation to the effect he and Willard were describing, but it’s not on offer if so.

Can it really be a coincidence that the same mammalian groups that have the most time and internal control over the circumstances of their offspring’s development are the ones most likely to sex-vary their investment by maternal conditions?

Discussion

There’s some work that looks at this question obliquely, but I couldn’t find any that handles it straightforwardly. Cameron, 2004, reviews evidence for the Trivers-Willard hypothesis and notes how uninformed everyone is about potential causes.

The lack of a known mechanism for sex-ratio adjustment magnifies the problem of interpreting results. Most studies on sex-ratio manipulation mention that there is no known mechanism by which sex ratios could be adjusted (e.g. Cockburn et al. 2002), although several hypotheses have been proposed (e.g. Krackow 1995a,b; James 1996; Forchhammer 2000; Krackow et al. 2003). Many of these mechanisms focus on differences around conception or are related to early development (e.g. Krackow 1995a; Krackow & Burgoyne 1998; Forchhammer 2000).

So Krackow is the guy to ask about this, and diapause is not included in any of these papers mentioned.

There are different ways diapause could be used by the mother to influence investment. Males embryos in poor condition mothers could be aborted to wait for better times, or in the species that exhibit facilitative rather than obligate diapause, the implantation timing could be extended to wait out bad times until the mother’s condition improves. The point is that the diapause offers a unique window of maternal control that can be gamed to help her improve her fitness, which is probably why this mechanism evolved in the first place. A Trivers-Willard effect would just be downstream of that.

Parent-Offspring conflict

I want to tie this off with another part of Trivers’ work, which was parent-offspring conflict.

He reasoned that parents and offspring have an evolutionary conflict of interest: offspring are fully related to themselves, but only half related to their siblings. When parents care for children with finite resources, they’re indifferent to investment between their children under some not too severe assumptions, but the children will try to bogart parental resources at their siblings’ expense.

During diapause, it’s quite likely that the mother has the upper hand over the embryo in determining when and how implantation occurs, but the conflict of interest still exists. From the embryo’s perspective, it might be better to be implanted earlier rather than later even though it might tax the mother (and her future offspring) too much, and she’d prefer later implantation or none at all. There could be a situation where a tiny blastocyst is selected to figure out a way to fool the mother’s body into earlier implantation!

Coda

The connection between diapause and maternal investment decisions seems sort of underexplored. A subsequent poast might look at some empirical ways to test whether the former is causally upstream of the latter.