Of elks and equilibrium

You know when put as clearly as Tim Harford does, the whole elk antler story just doesn’t stack up:

Consider the vast antlers of the north American bull elk: they’re the result of sexual selection balanced by other selective pressures. Elks with big antlers win fights with other elks, and mate with multiple females. However, they also get hunted down and killed by packs of wolves. Elks as a whole would be better off if they could all agree to shrink their antlers by a factor of four or five: the males with the biggest antlers would still get the girls, while only the wolves could object to faster, more agile bull elks. Sadly for the elks and happily for the wolves, that’s not how sexual selection works.

But it is the female elks doing the choosing. So they face the trade-off of choosing someone likely to generate big antlered male offspring whom other females will choose versus getting male offspring more likely to outrun wolves. So that is one equilibrium but is it the only one.

Suppose that females preferred ‘outrun wolve types’ rather than ‘beat up others’ types. Then if one deviated and choose a ‘beat up other’ type with bigger antlers, the chance of reproductive success will go down. So that wouldn’t be profitable and so there is another equilibrium.

So why do we see big antlers all over the place? The answer is likely that there is an actual benefit to offspring of having a big antlered dad. I suspect that it makes them more likely to die earlier and be a wolf target than their offspring; giving their offspring a better chance. Put simply, in mate selection you want mates that will leave the planet quickly.

9 thoughts on “Of elks and equilibrium”

  1. Seriously, though, you’re right – evolution works to maximize the survival of the child’s genes, not their fathers. IIRC, stags only grow their antlers once they’re old enough to compete for breeding privileges, right?

    And once they’ve bred, a few males lagging behind the herd (not necessarily the winner, more likely a wounded competitor) would improve the chances of all pregnant females and their offspring.

    This is pretty much true of any species where the male doesn’t intervene in a positive way after the offspring are born.
    Also, in the case of Elks, is it really true that the antlers are no use against hunting wolves?


  2. Interesting observations, but I’m not sure they address Tim Harford’s point. I believe this is not about how the females select a mate, but about the ineffective genetic arms race between the males: it’s the relative size of the antlers that matters for effective procreation, while it’s the absolute size that affects their eatability by wolves. If a similar differential could be maintained at a smaller antler size then fewer elks would be eaten, and some of the energy going into growing bigger antlers could be diverted to grow bigger, er, organs… 🙂


  3. Here’s another take on the elk antler story which is a critique of Robert Frank’s book The Darwin Economy. Might be a lesson about the hazards of drawing analogies from or speculating about subject content outside your own field.


    I second DavidN’s comments. This comparison relies primarily on the extrapolation of an oversimplified notion of natural selection.
    I think you should be asking ‘what purpose do the elk antlers serve?’. Are they are a signal to females (think peacock feathers) or a tool for combat (walrus tusks)? And if for combat, are they designed to be used on other males or potential predators?
    Although predatory, the relatively small size of wolves discourages them from targeting fully ‘weaponised’ mature elk bucks. Therefore, sick or immature elk are the preferred choice for a wolf pack. So, it is less likely that well-endowed males will be killed off by such predators. Also, as large bucks use their antlers to ‘discourage’ wolves, there is little benefit in being the fastest runner – they need only move as quickly as the lamest herd member. Such pack-herd dynamics are well documented (e.g. lions and buffalo). Males such as elk bucks also fight for mating privileges. However, males of many species (including other ungulates) have evolved highly choreographed routines in place of pitched battle. This minimises each male’s chance of sustaining significant physical harm. To this end, antler size is often considered a proxy for physical strength and many male-male conflicts end without bloodshed.
    Antlers therefore seem to have evolved to fill a variety of roles; from defensive weapons to signals of physical dominance. Simply choosing one role to the exclusion of others can be rather misleading.


  5. “I suspect that it makes them more likely to die earlier and be a wolf target than their offspring; giving their offspring a better chance.”
    I find it hard to believe that parents are significant competitors for offspring. 1) Offspring are mobile if they want to move away from their parents to avoid competition. b) The father is unlikely to compete hard with them for resources or mates as they want them to succeed. c) The population of elk is large enough that the marginal increase in competition from one extra elk – your father – is negligible.
    Though your point about female selection is spot on.


  6. As well various hypotheses involving intra-sex and inter-sex signalling , its been been suggested  large antlers offer a defensive advantage against predators or an advantage in intra-sex combat and that they assist heat regulation. 
    Large antlers are found in a number of cervids so if there is a single explanation it will need to be more ubiquitous than wolves.  Data on predation versus antler size would be good – although maybe your theory is safer kept away from data.


  7. Could the females end up in a bad equilibrium where they only mate with large-antlered males despite their lower survival, because they expect future females to do the same. Therefore there is no benefit to having small antlered children who survive a long time – they won’t be able to find partners!


  8. Sorry Joshua, I don’t think Elks are very PC. Do the Female Elks have a choice when the bigger antlered drive off the smaller antlered?
    BR Richard


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