What Links Humans, Hermit Crabs and Possibly Creatures on Mars?
The Distribution of Resources through Vacancy Chains
Introduction
A few years ago, I drove to a beach on the north shore of Long Island, waded into a shallow pool at low tide, sat down on a plastic milk crate, and dropped a small, empty snail shell into the water at my feet. A few minutes later, a hermit crab ran over, grasped that shell, inspected it for size and condition, and then inserted itself into the shell, leaving its old, smaller shell behind. Shortly after that, another crab scurried up to the shell left by the first crab, went through the same inspection procedure, apparently liked the first crab’s old shell, took it, and abandoned its old shell. A third crab eventually occupied the second’s old shell, and this chain of events continued until four crabs had obtained new and larger shells: one getting the shell I had dropped and three gaining the shells left by other crabs.
I really like hermit crabs, but I was not at the beach to improve their welfare by giving them new shells. So, what was I doing? I was documenting a social process called a vacancy chain. It’s a way that certain scarce resources are distributed in groups, but it’s very different from the way in which we usually think about competition over limited resources in humans and animals. In regular competition – often referred to as zero-sum competition – one individual gets something in demand, like a piece of food or a mate, and the other individuals do not. In zero-sum competition, one individual’s gain is another’s loss. But in a vacancy chain, one individual’s success allows several other individuals to also be successful. It’s a case in which individuals depend upon the unintentional kindness of strangers.
Researchers first discovered vacancy chains in humans getting new houses and apartments, cars, and jobs in bureaucracies, such as manufacturing companies, church organizations, and illegal drug distribution networks. My colleagues and I made the first discovery of vacancy chains in a non-human species – hermit crabs gaining new snail shells. Hermit crabs have soft abdomens and, consequently, live in and carry around empty snail shells as protection against predators. These crabs grow throughout their lives and must periodically find new and larger shells. They cannot kill snails to get their shells, but must wait for disease, environmental conditions, or predators to do so. Empty snails are scarce and valuable, so hermit crabs take ones that are abandoned by other crabs thus creating vacancy chains like the one I observed at the beach.
In this essay I try to answer why creatures as different as humans and hermit crabs, and maybe yet undiscovered ones on Earth or other planets, get new possessions through vacancy chains. My answer is in response to a question that my friend Jim raised in my earlier essay asking, “Can a Hermit Crab Be Rich?”. As discussed in that essay, my colleagues and I did a scientific study in which we discovered that the statistical distribution of the sizes of snail shells occupied by a population of hermit crabs closely resembled the typical statistical distribution of wealth in many human populations. Economists have suggested that the transfer of wealth between people in the form of bequests upon a person’s death and gifts while living might help shape the form of human wealth distributions. I suggested that vacancy chains might be an analog to property transfer in humans and could be a possible cause of why the distributions of shells in hermit crabs and wealth in humans might be similar in form. In this conversation, Jim asked why vacancy chains occurred in humans and hermit crabs even though they were otherwise so different.
Several unexpected things come out of my attempt to answer Jim’s question. The first thing is that I suggest that resources distributed through vacancy chains have a common set of abstract qualities. I’ll define what I mean by abstract qualities below. As long as a type of resource has that particular set of abstract qualities, it will necessarily be distributed through vacancy chains and not other processes. The species of creatures that use a resource with these characteristics does not matter, and neither does it matter whether the creature has culture and social institutions like humans, or it does not, like hermit crabs. The second thing is that all vacancy chain systems have a set of identical features: the chains mostly provide upward mobility to bigger and better resource units for individuals, the “careers” of individuals are marked by successes followed by temporary plateaus in advancement, and chains on average involve about the same number of individuals. Again, neither the species nor its level of social development matters. A third thing I suggest is that other resources used by humans and animals have different sets of abstract qualities that dictate that they are distributed through other kinds of social processes than vacancy chains.
Why Are There Vacancy Chains in Humans and Hermit Crabs Despite Their Great Differences?
Jim: The last time we talked, you said we should meet again to discuss why both humans – at least in economically developed societies – and hermit crabs get some of their most important resources through vacancy chains. You know, I wouldn’t have been surprised if you had told me that humans and chimpanzees both obtained resources through vacancy chains. We’re close to chimps evolutionarily, they’re smart animals, and we share around 99% of our genes with them. But hermit crabs? Why not, I don’t know, elephants or kangaroos?
Ivan: I know it must seem strange to say that hermit crabs have something in common with humans in economically developed societies, especially when they are so different in so many other ways. But to answer your question about why we share the use of vacancy chains with hermit crabs, I’m going to ask you to take a very different perspective than you probably do now. I’d like you to temporarily stop thinking about the individuals getting the resources – the humans and the hermit crabs – but instead turn your attention to the resources themselves – the shells, cars, houses, and jobs – that the hermit crabs and people use. These resources have something I call “abstract qualities”.
Abstract Qualities of Resources
Jim: You’ve got to stop for a second. What in the world do you mean by the abstract qualities of a resource? I’m used to thinking about abstraction in mathematics, but not for resources – not for the physical objects – that we and animals use.
Ivan: Okay, fair enough. Let me give you an example that is mathematical, from geometry to be specific, that we can apply to physical objects. In Euclidean geometry, all triangles have two abstract qualities: they have three sides and the (internal) angles where these three sides meet sum up to 180 degrees. We don’t care if the triangles are red or blue, made from sticks or rods of gold, or if astronauts on the moon or school children in Sudan draw them, they still have those two abstract qualities. The particular instantiations of a triangle make no difference.
I think you can see, like my triangles example, when it comes to resources, abstract qualities are features that don’t depend upon the resources themselves. That may still sound mysterious but let me give you some of the abstract qualities of resources that dictate distribution through vacancy chains. The first quality is that individuals or family units can’t take over a new resource unit just because they want to. The individual or family unit can’t eject the present occupant but must wait for the unit to become vacant. Forcible ejections, like car and shell jacking do occur, but at a rate that is very low compared to moves into units that are vacant.
The second abstract quality is that most of the individuals or families in a group already have units that they can leave vacant when they get a new one. Of course, there are always some individuals or families, like first-time home buyers or people entering the job market, who do not have units to leave behind. But usually these are far fewer in number than people or crabs that already have units.
The third quality is that vacant units are scarce, there aren’t large numbers of empty units just lying around that can be taken by crabs or people who want one. If there were many unoccupied units, individuals or families could take one and not have to wait for a unit provided by a vacancy chain. There are other abstract qualities needed for vacancy chains, but I think you get the idea.
What About Social Institutions?
Jim: You’re right, it does sound strange to think about different kinds of resources, or resource units as you call them, as having abstract qualities. I’ve thought about the abstract qualities of mathematical objects, like the triangles from your example, and of theories for explaining things from my time as a physicist, but never resources that we or animals might use. I mostly follow what you’re saying about the abstract qualities of the resources used in vacancy chains, but something still troubles me. In human groups, some of those abstract qualities are based upon social institutions like laws and customary practices and groups that are set up to enforce those institutions and practices, like police forces and courts of law. Even in northern California, it’s still against the law to rip a Silicon Valley entrepreneur out of his fancy new Ferrari, just because you want to. I think it would be great if there were a hermit crab police force protecting against forcible shell evictions, but, as far as I know, there isn’t. And they don’t have any other social institutions set up, I believe, to prohibit the forced appropriations of shells. So, I have to ask you, how can you really say that the snail shells used by hermit crabs have the same abstract qualities as various resources that we use when the hermit crabs don’t have the same institutions and enforcement groups that we do?
Ivan: I understand your objection, and I think you’re raising an important question about what I mean by an abstract quality of a resource. The point that I’m trying to make is that resources can have certain properties, but how they get those properties is of no concern in this case. Let’s take the example of the first abstract quality I mentioned – that a resource unit must be vacant before it is taken by a new occupant. As you have just said, for human resources like cars, houses, and jobs, that quality arises from things like laws, police forces, and courts. But in hermit crabs, the physicality of the snail shell and its crab occupant do the trick. Crabs usually fit snugly in their snail shells and withdraw into them and brace themselves securely when another crab tries to pull them out.
I’m saying that the abstract qualities of resources distributed through vacancy chains may arise from many different causes, and the same abstract qualities may derive from one set of factors in one species and from a different set in another species. But the factors that produce an abstract quality do not matter. As long as the resource has the right set of abstract characteristics, the creatures using that resource have to get them through vacancy chains.
Are Vacancy Chains Just a Choice?
Jim: I think I get your idea that it doesn’t matter how the abstract qualities are produced, just as long as they are produced. It still seems a little strange to me, but I think I understand it. But there’s another thing that bothers me. Are you saying that in some sense people and hermit crabs “choose” to use vacancy chains for resources that have the right set of abstract characteristics? In other words, are vacancy chains optional, just a convenient custom for the distribution of certain resources in humans and hermit crabs?
Ivan: I think it’s just the opposite. When a group depends upon a resource that has the right set of abstract qualities, they must get new ones through vacancy chains. The group is compelled to live in a vacancy chain system. There may be some exceptional resource transfers here and there, like car and shell jacking, but nearly all individuals, nearly all the time, get new units through chains.
Vacancy Chains on Mars?
Jim: Just to make sure you really mean what you just said, let me give you this scenario: Elon Musk finally gets his wish, and he and a group of followers land on Mars and set up a colony. After they have been there for a while, they discover a group of creatures that live beneath the surface of the planet. These creatures occupy some resources – maybe caves or jobs in a complex bureaucratic system – that have the abstract qualities that you say are necessary for distribution through vacancy chains. Are you willing to predict, without knowing anything else about them – their economy, if they have one; their cognitive ability; their culture and social practices, if they have them; and so on – that they get new caves or bureaucratic positions through vacancy chains?
Ivan: Yes, I am! I do believe that the Martians will have vacancy chains, and I am also willing, sight unseen, to forecast some other aspects of their lives.
Jim: Well, that’s a heck of a statement. Aren’t you worried about being wrong? Remember, you really don’t know much about them. But let me guess, you think you can predict these things because you’ve noticed that human and hermit crab vacancy chain systems here on Earth all share the kinds of features that you foresee for the Martians.
Ivan: Of course, I am making an extravagant claim, and I could very well be wrong. And yes, you’re correct that I am extrapolating from what other researchers and I have observed about vacancy chain systems here on Earth to what I believe would be the case on Mars and for any other vacancy chain system anywhere else, for that matter.
Jim: I think you’re being reckless, but I like it! This may be the start of the interplanetary or maybe even the intergalactic study of social systems. Please tell me more.
Ivan: The first feature that I think the Martian vacancy chain system will have is that chains will start in larger or higher-status units and move down to smaller, lower-status ones as the Martians themselves move up to bigger and better resource units. Moves to new resource units can be risky, stressful, and sometimes costly, so humans and hermit crabs typically only take a new unit in a chain if it’s “worth their while” in terms of a job paying a higher salary, a shell offering more room for growing, or a car that is newer and in better mechanical condition.
A second feature is that the career advancement patterns of the Martians will resemble an irregular stairway. On Earth, this stairway traces the path of an individual or family as they get different resource units through the course of their life. They begin their career by getting a relatively small or low-status unit. After they stay in that unit for a while, they grow large enough, gain enough borrowing power to get a mortgage, or acquire enough experience to get a larger shell, house, or job by participating in another vacancy chain. Below is a figure that helps to illustrate the typical career path in a vacancy chain system. Not every individual or family in a vacancy chain system will have exactly the career path I have illustrated. Some couples, for example, might move to smaller houses or apartments when they leave the work force or their children have left home. But the figure depicts what I think will be the most common career path in all vacancy systems here on Earth and in the ones on Mars that we may discover. The stacks of money represent the increases in salary, size, or condition associated with the new resource unit that an individual gains when they participate in a vacancy chain.
A third feature is that vacancy chains on Mars will, on average, be about three or so individuals long. That is, about three individuals will get new resource units in the typical vacancy chain. Three may seem like an odd number, but it’s the typical vacancy chain length that researchers have found for hermit crabs getting new shells and for humans getting houses, apartments, cars, and jobs. However, chains that start in very large or very high-status resource units can be longer than three, and chains that start in very small or low-status units can be shorter.
I think it’s amazing that average chain length is about the same across such different kinds of resources and species. Although I have a few ideas, it’s still a mystery to me why chain lengths are so similar in different vacancy chain systems. I’m guessing that there are some deep, but not yet obvious, similarities in those systems.
A Strange Thought
Jim: If individuals in vacancy chain systems take new resource units voluntarily, I can understand why you are predicting that aspects one and two – individuals trade up to better resource units and careers look like stairs – will occur in any vacancy chain system. And I appreciate why you find aspect three – the average vacancy chain involves about three individuals – so mysterious. I can’t for the life of me figure out why that might be so. Perhaps that computer simulation of hermit crabs getting shells that we talked about in our last conversation might offer some clues.
When you were talking about resource units having a set of abstract qualities that determined that they would be distributed through vacancy chains, a strange thought came to me. Do you think that resources can have other sets of abstract qualities, and that if they do, they will be allocated through processes other than vacancy chains?
Ivan: Yes, I do. Vacancy chains are probably only one of many kinds of resource distribution processes. I think that resources have many different sets of abstract qualities and that those that share a set of qualities will be allocated through a common process. I also think, like in vacancy chain systems, a particular kind of resource distribution system will have similar implications for all the creatures that use it – no matter how different otherwise.
Perhaps as an illustration of this idea, we could talk about another type of distribution system based upon resources with a different set of abstract qualities. The one I’m thinking about occurs, for example, in both farming families in 19th century Ireland and Florida scrub jays, a species of bird that lives in extended family groups. These groups have some remarkable parallels in their lives that they do not share with other groups of farmers or birds using different resource distribution processes.
Jim: I look forward to that. I have to say that I didn’t expect this conversation to go the way that it did. I just wanted to know something about what I thought was a small, obscure topic: why humans and hermit crabs both used vacancy chains. Not exactly a question for the front page of the New York Times. But I didn’t expect to hear about vacancy chains on Mars, the abstract qualities of resources, and how using resources with the same set of abstract qualities caused similarities in the lives of creatures as different as humans and hermit crabs. Thanks for this conversation, Ivan.
Ivan: My pleasure, Jim.