That doesn’t seem like a stable equilibrium—too much incentive for the rabbits to be “over-cautious” for foxes at the expense of running ability. If they can figure that “being able to notice and turn toward a fox” is just as good as having the energy to escape a fox, then they’ll over-invest in being good at this signal until the foxes realize it’s not a reliable signal of a failed hunt.
Well, let me explain my intuition behind my objection, even if there’s a reason why it might be wrong in this case.
I am, in general, skeptical of claims about Pareto-improvements between agents with fundamentally opposed goals (as distinguished from merely different goals, some of which are opposed). Each side has a chance to defect from this agreement to take utility from the other.
It’s a quite famliar case for two people to recognize that they can submit their disagreement to an arbitrator who will render a verdict and save them the costs of trying to tip the conflict in their favor. But to the extent that one side believes the verdict will favor the other, then that side will start to increase the conflict-resolution costs if it will get a better result at the cost of the other. For if a result favors one side, then a fundamentally opposed other side should see that it wants less of this.
So any such agreement, like the one between foxes and rabbits, presents an opportunity for one side to abuse the other’s concessions to take some of the utility at the cost of total utility. In this case, since the rabbit is getting the benefit of spending the energy of a full chase without spending that energy, the fox has reason to prevent it from being able to make the conversion. The method I originally gave shows one way.
Another way foxes could abuse the strategy is to hunt in packs. Then, when the rabbit spots one of them and plans to run one direction, it will be ill-prepared for if another fox is ready to chase from another direction (optimally, the opposite) -- and gives away its location! (Another fox just has to be ready to spring for any rabbit that stands and looks at something else.)
So even if the “stand and look”/”give up” pattern is observed, I think the situation is more complicated, and there are more factors at play than timtyler listed.
Re “pack hunting”—according to this link, the phenomenon happens with foxes—but not dogs: “Hares did not stand before approaching dogs”. Perhaps they know that dogs pay no attenntion—or perhaps an increased chance of pack hunting is involved.
Okay, thank you, that answers the nagging concern I had about your initial explanation. There are reasons why that equilibrium would be destabilized, but it depends on whether the predator species would find the appropriate (destabilizing) countermeasures, and this doesn’t happen with foxes.
Yes, I’m familiar with stotting. But keep in mind, that doubles as an advertisement of fitness, figuring into sexual selection and thus providing an additional benefit to gazelles. So it’s a case where other factors come into play, which is my point about the rabbit fox example—that it can’t be all that’s going on.
There’s often “other things going on”—but here is a description of the hypothesis:
Pursuit-deterrent signals represent a form of interspecific communication, whereby the prey indicates to a predator that pursuit would be unprofitable because the signaler is prepared to escape (Woodland et al. 1980). Pursuit-deterrent signals provide a benefit to both the signaler and receiver; they prevent the sender from wasting time and energy fleeing, and they prevent the receiver from investing in a costly pursuit that is unlikely to result in capture. Such signals can advertise prey’s ability to escape, and reflect phenotypic condition (quality advertisement, sensu Zahavi 1977; also see Hasson 1991), or can advertise that the prey has detected the predator (perception advertisement, sensu Woodland et al. 1980). Pursuit-deterrent signals have been reported for a wide variety of taxa, including fish (Godin and Davis 1995), lizards (Cooper et al. 2004), ungulates (Caro 1995), rabbits (Holley 1993), primates (Zuberbühler et al. 1997), rodents (Shelley and Blumstein 2005), and birds (Alvarez 1993).
The intuition does make sense, but I don’t think it serves to refute the proposed co-evolved signal in this case. Perhaps the prey also likes to maintain view of its hunter as it slinks through the brush.
Doing things that are costly isn’t the only way to reliably signal. In this case the rabbit reliably communicates awareness of the fox’s presence. It cannot be fake because the rabbit must look in the right direction. The fact that it’s prey is not unaware of its presence is always going to be useful to a fox. It will still attempt to chase aware rabbits some times but the exchange of information will help both creatures in their decision making.
This is an equilibrium that all else being equal will be stable. Speed will still be selected for for exactly the same reason that it always was.
Just to elaborate (for clarity’s sake), by standing up and looking directly at the fox, the rabbit is changing the fox’s expected utility calculation. If the rabbit doesn’t see the fox, the fox will have the advantage of surprise and be able to close some of the distance between itself and the rabbit before the rabbit begins to run. This makes the chase less costly to the fox. If the rabbit does see the fox, when the fox begins the attack the rabbit will see it and be able to react immediately, neutralizing any surprise advantage the fox has. So if the fox knows that the rabbit knows that the fox is nearby, the fox may well not attack because of the amount of extra energy it would take to capture the rabbit.
The rabbit standing up and staring at the fox is an effective signal of awareness of the fox because it is difficult to fake (costliness is only one way that a signal can be difficult to fake). The rabbit can stand up and stare in a random direction if it wants to, but the probability of a rabbit doing that and being able to randomly stare directly at the fox is pretty slim. So if the fox sees the rabbit staring at it, then the fox can be pretty certain that the rabbit knows where the fox is at.
So ‘noticing the fox’ signals that the rabbit notices the fox and will run when it sees the fox beginning to chase. The fox uses the signal thus: “If the rabbit notices me it gets a headstart. With such a head start, and the fact that the rabbit runs at a certain minimum speed, I would not be able to catch it”.
Even though the reliability of the signal is independent of the running, its effectiveness/usefulness depends on the rabbit’s speed.
Once we have the free riding rabbits placing resources into noticing and away from running, foxes will realize this, and they will chase even when they have been noticed. So now noticing does not prevent the fox from chasing anymore, so there is less pressure on even fast rabbits to signal it.
And then the signaling collapses?
I admit to being quite confused over this. Waiting for someone to clear it all up!
Once we have the free riding rabbits placing resources into noticing and away from running
Placing emphasis on ‘noticing vs running’ is just confusing you. Noticing helps the rabbit run just as much as it helps it look in the right direction.
And then the signaling collapses?
No. Silas was just wrong. If average rabbit speed become slower then there will be a commensurate change in the threshold at which foxes chase rabbits even when they have been spotted. It will remain useful to show the fox that it has been spotted in all cases in which about 200ms of extra head start is worth sacrificing so that a chase may potentially be avoided.
If you are still confused, consider a situation in which rabbits and foxes always become aware of each other’s presence at a distance of precisely 250m. Would anyone suggest that rabbits would freeload and not bother to be fast themselves in that circumstance? No. In the ‘rabbits standing up’ situation the rabbits will still want to be fast for precisely the same reason. All standing up does is force the mutually acknowledged awareness.
Placing emphasis on ‘noticing vs running’ is just confusing you. Noticing helps the rabbit run just as much as it helps it look in the right direction.
Sorry I wasn’t being clear, previously I had always meant noticing==‘showing the fox you have noticed it’.
If average rabbit speed become slower then there will be a commensurate change in the threshold at which foxes chase rabbits even when they have been spotted.
What threshold? I’m guessing other factors such as the fox’s independent assessment of the rabbit’s speed?
It will remain useful to show the fox that it has been spotted in all cases in which about 200ms of extra head start is worth sacrificing so that a chase may potentially be avoided.
I didnt consider the fact that signaling having noticed required that sacrifice. Does it affect the analysis?
consider a situation in which rabbits and foxes always become aware of each other’s presence at a distance of precisely 250m. Would anyone suggest that rabbits would freeload and not bother to be fast themselves in that circumstance?
What threshold? I’m guessing other factors such as the fox’s independent assessment of the rabbit’s speed?
If the average rabbit becomes slower then the average fox will be more likely to estimate that a given rabbit chase is successful.
I didnt consider the fact that signaling having noticed required that sacrifice. Does it affect the analysis?
Not particularly. We haven’t been quantising anyway and it reasonable to consider the overhead here negligible for our purposes. ′
I don’t understand this part.
You don’t particularly need to. Just observe that rabbits running fast to avoid foxes is a stable equilibrium. Further understand that nothing in this scenario changes the fact that running fast is a stable equilibrium. The whole ‘signalling makes the equilibrium unstable’ idea is a total red herring, a recipe for confusion.
Hypothesis: most rabbits which are in good enough shape to notice are also in good enough shape to escape.
There simply aren’t enough old? sick? rabbits to freeload to make the system break down.
Anyone know whether inexperienced foxes chase noticing rabbits? If so, this make freeloading a risky enough strategy that it wouldn’t be commonly used.
Standing on your hind legs—which is the behaviour under discussion—is costly to rabbits—since it increases the chance of being observed by predators—so they can’t do it all the time.
However, that is not really the point. The signal is not: “look how fast I can run”—it is “look how much of a head my family and I have—given that I can see you now”.
Not all the time of course. I was refering to SilasBarta’s observation that this might not be a stable equilibrium. Because noticing the fox and turning to it is much cheaper than being able to run fast enough such that the fox will not catch you once you notice it. A good noticer but bad runner can take advantage of the good noticer/good runner’s signal and free ride off it. The fox wouldn’t care if you were a good noticer if you weren’t also a good runner, since it can still catch you once you have noticed it.
Maybe. Rabbits go to ground. Escape is not too tricky if they have time to reach their burrow. Running speed is probably a relatively small factor compared to how far away the fox is when the rabbit sees it.
Standing on your hind legs—which is the behaviour under discussion—is costly to rabbits—since it increases the chance of being observed by predators—so they can’t do it all the time.
Not only that, you can only look in one direction at a time. You do need to know where the fox is. The rabbit only loses a couple of hundred milliseconds if the fox decides to make a dash for it anyway.
You’ve described how a scenario in which the rabbits use this behaviour might be unstable, but so what? For any kind of behaviour whatsoever one can dream up a scenario where animals over or underuse it and subsequently have to change.
Prima facie there’s nothing at all implausible about a stable situation where rabbits use that behaviour some of the time and it makes the foxes give up some of the time.
That doesn’t seem like a stable equilibrium—too much incentive for the rabbits to be “over-cautious” for foxes at the expense of running ability. If they can figure that “being able to notice and turn toward a fox” is just as good as having the energy to escape a fox, then they’ll over-invest in being good at this signal until the foxes realize it’s not a reliable signal of a failed hunt.
Note that this type of signalling to predators is well established in many other creatures:
http://en.wikipedia.org/wiki/Stotting
Stotting is awesome. Thanks for that. I’m puzzled at the controversy over the original point, which is so plausible it’s hard not to believe.
Well, let me explain my intuition behind my objection, even if there’s a reason why it might be wrong in this case.
I am, in general, skeptical of claims about Pareto-improvements between agents with fundamentally opposed goals (as distinguished from merely different goals, some of which are opposed). Each side has a chance to defect from this agreement to take utility from the other.
It’s a quite famliar case for two people to recognize that they can submit their disagreement to an arbitrator who will render a verdict and save them the costs of trying to tip the conflict in their favor. But to the extent that one side believes the verdict will favor the other, then that side will start to increase the conflict-resolution costs if it will get a better result at the cost of the other. For if a result favors one side, then a fundamentally opposed other side should see that it wants less of this.
So any such agreement, like the one between foxes and rabbits, presents an opportunity for one side to abuse the other’s concessions to take some of the utility at the cost of total utility. In this case, since the rabbit is getting the benefit of spending the energy of a full chase without spending that energy, the fox has reason to prevent it from being able to make the conversion. The method I originally gave shows one way.
Another way foxes could abuse the strategy is to hunt in packs. Then, when the rabbit spots one of them and plans to run one direction, it will be ill-prepared for if another fox is ready to chase from another direction (optimally, the opposite) -- and gives away its location! (Another fox just has to be ready to spring for any rabbit that stands and looks at something else.)
So even if the “stand and look”/”give up” pattern is observed, I think the situation is more complicated, and there are more factors at play than timtyler listed.
Re “pack hunting”—according to this link, the phenomenon happens with foxes—but not dogs: “Hares did not stand before approaching dogs”. Perhaps they know that dogs pay no attenntion—or perhaps an increased chance of pack hunting is involved.
Okay, thank you, that answers the nagging concern I had about your initial explanation. There are reasons why that equilibrium would be destabilized, but it depends on whether the predator species would find the appropriate (destabilizing) countermeasures, and this doesn’t happen with foxes.
Confusion extinguished!
The basic idea is that both parties have a shared interest in avoiding futile chases—see the stotting phenomenon. Cooperation can arise out of that.
Yes, I’m familiar with stotting. But keep in mind, that doubles as an advertisement of fitness, figuring into sexual selection and thus providing an additional benefit to gazelles. So it’s a case where other factors come into play, which is my point about the rabbit fox example—that it can’t be all that’s going on.
There’s often “other things going on”—but here is a description of the hypothesis:
http://beheco.oxfordjournals.org/cgi/content/full/17/4/547
Another example of signalling from prey to predator is the striped pattern on wasps.
The intuition does make sense, but I don’t think it serves to refute the proposed co-evolved signal in this case. Perhaps the prey also likes to maintain view of its hunter as it slinks through the brush.
Stotting is costly, hence reliable. ‘Noticing and turning to the fox’ is not.
Doing things that are costly isn’t the only way to reliably signal. In this case the rabbit reliably communicates awareness of the fox’s presence. It cannot be fake because the rabbit must look in the right direction. The fact that it’s prey is not unaware of its presence is always going to be useful to a fox. It will still attempt to chase aware rabbits some times but the exchange of information will help both creatures in their decision making.
This is an equilibrium that all else being equal will be stable. Speed will still be selected for for exactly the same reason that it always was.
Just to elaborate (for clarity’s sake), by standing up and looking directly at the fox, the rabbit is changing the fox’s expected utility calculation. If the rabbit doesn’t see the fox, the fox will have the advantage of surprise and be able to close some of the distance between itself and the rabbit before the rabbit begins to run. This makes the chase less costly to the fox. If the rabbit does see the fox, when the fox begins the attack the rabbit will see it and be able to react immediately, neutralizing any surprise advantage the fox has. So if the fox knows that the rabbit knows that the fox is nearby, the fox may well not attack because of the amount of extra energy it would take to capture the rabbit.
The rabbit standing up and staring at the fox is an effective signal of awareness of the fox because it is difficult to fake (costliness is only one way that a signal can be difficult to fake). The rabbit can stand up and stare in a random direction if it wants to, but the probability of a rabbit doing that and being able to randomly stare directly at the fox is pretty slim. So if the fox sees the rabbit staring at it, then the fox can be pretty certain that the rabbit knows where the fox is at.
Very clear. Thanks.
So ‘noticing the fox’ signals that the rabbit notices the fox and will run when it sees the fox beginning to chase. The fox uses the signal thus: “If the rabbit notices me it gets a headstart. With such a head start, and the fact that the rabbit runs at a certain minimum speed, I would not be able to catch it”.
Even though the reliability of the signal is independent of the running, its effectiveness/usefulness depends on the rabbit’s speed.
Once we have the free riding rabbits placing resources into noticing and away from running, foxes will realize this, and they will chase even when they have been noticed. So now noticing does not prevent the fox from chasing anymore, so there is less pressure on even fast rabbits to signal it.
And then the signaling collapses?
I admit to being quite confused over this. Waiting for someone to clear it all up!
Placing emphasis on ‘noticing vs running’ is just confusing you. Noticing helps the rabbit run just as much as it helps it look in the right direction.
No. Silas was just wrong. If average rabbit speed become slower then there will be a commensurate change in the threshold at which foxes chase rabbits even when they have been spotted. It will remain useful to show the fox that it has been spotted in all cases in which about 200ms of extra head start is worth sacrificing so that a chase may potentially be avoided.
If you are still confused, consider a situation in which rabbits and foxes always become aware of each other’s presence at a distance of precisely 250m. Would anyone suggest that rabbits would freeload and not bother to be fast themselves in that circumstance? No. In the ‘rabbits standing up’ situation the rabbits will still want to be fast for precisely the same reason. All standing up does is force the mutually acknowledged awareness.
Sorry I wasn’t being clear, previously I had always meant noticing==‘showing the fox you have noticed it’.
What threshold? I’m guessing other factors such as the fox’s independent assessment of the rabbit’s speed?
I didnt consider the fact that signaling having noticed required that sacrifice. Does it affect the analysis?
I don’t understand this part.
If the average rabbit becomes slower then the average fox will be more likely to estimate that a given rabbit chase is successful.
Not particularly. We haven’t been quantising anyway and it reasonable to consider the overhead here negligible for our purposes. ′
You don’t particularly need to. Just observe that rabbits running fast to avoid foxes is a stable equilibrium. Further understand that nothing in this scenario changes the fact that running fast is a stable equilibrium. The whole ‘signalling makes the equilibrium unstable’ idea is a total red herring, a recipe for confusion.
Hypothesis: most rabbits which are in good enough shape to notice are also in good enough shape to escape.
There simply aren’t enough old? sick? rabbits to freeload to make the system break down.
Anyone know whether inexperienced foxes chase noticing rabbits? If so, this make freeloading a risky enough strategy that it wouldn’t be commonly used.
I expected the devil would be in the details! But yeah, your hypothesis sounds plausible, and freeloading seems risky.
That correlation can not (and need not) be counted on to make the equilibrium stable over a large number of generations.
Standing on your hind legs—which is the behaviour under discussion—is costly to rabbits—since it increases the chance of being observed by predators—so they can’t do it all the time.
However, that is not really the point. The signal is not: “look how fast I can run”—it is “look how much of a head my family and I have—given that I can see you now”.
Not all the time of course. I was refering to SilasBarta’s observation that this might not be a stable equilibrium. Because noticing the fox and turning to it is much cheaper than being able to run fast enough such that the fox will not catch you once you notice it. A good noticer but bad runner can take advantage of the good noticer/good runner’s signal and free ride off it. The fox wouldn’t care if you were a good noticer if you weren’t also a good runner, since it can still catch you once you have noticed it.
Maybe. Rabbits go to ground. Escape is not too tricky if they have time to reach their burrow. Running speed is probably a relatively small factor compared to how far away the fox is when the rabbit sees it.
Yeah, running speed may not be such an important factor.
Not only that, you can only look in one direction at a time. You do need to know where the fox is. The rabbit only loses a couple of hundred milliseconds if the fox decides to make a dash for it anyway.
You’ve described how a scenario in which the rabbits use this behaviour might be unstable, but so what? For any kind of behaviour whatsoever one can dream up a scenario where animals over or underuse it and subsequently have to change.
Prima facie there’s nothing at all implausible about a stable situation where rabbits use that behaviour some of the time and it makes the foxes give up some of the time.