Can a Hermit Crab Be Rich?

Searching for the Jeff Bezos of Hermit Crabs

Iris Yan

Introduction

To think of animals owning material goods and some of them even being rich, seems bizarre. Animals have no written agreements of ownership, no courts to adjudicate property disputes, and no means of calculating the value of their material possessions. But probably thousands, if not millions, of species across the animal kingdom depend upon material resources for their survival and reproduction. For example, pairs of ospreys return to the same nest year after year to raise their young, clownfish occupy and defend choice spots within the tentacles of sea anemones, and female red squirrels accumulate and guard middens of seed-bearing pinecones.

Even with these examples, the idea of a hermit crab being rich may seem particularly odd. While I am extremely fond of them, I must say that they are relatively simple creatures. Compared to many vertebrate animals, they have limited cognitive abilities, restricted behavioral repertoires, and live mostly as isolated individuals. What could they “own” that could make them rich, or even poor, for that matter?

Unlike regular crabs, hermit crabs are not completely covered by a hard, protective exoskeleton made of chitin. Instead, hermit crabs have soft, vulnerable abdomens, and because of this, they must live in and carry around the shells of dead snails as armor against potential predators and protection from heat and dehydration. To make matters worse, hermit crabs grow throughout their lives and periodically need new and larger shells. Unfortunately for them, they cannot kill snails when they need bigger shells but must wait for predators, disease, or desiccation to kill snails and make their shells available. Consequently, good snail shells are in short supply, especially larger ones. I propose that the size of the snail shell that a hermit crab possesses determines its level of wealth.

In this essay I will do several things. I begin by considering the possibility of wealth in hermit crabs and how you might measure it using the sizes of the snail shells they possess. Then I’ll tell you about a study in which my colleagues and I collected a sample of hermit crabs and determined the distribution of their wealth. We were surprised to discover that the form of the shell distribution in the hermit crabs strongly resembled a typical distribution of wealth in humans. Next, I’ll explore what factors might account for this unexpected similarity between the division of wealth in humans and hermit crabs. I’ll suggest that despite the enormous differences between humans and hermit crabs, there is a reason for why their wealth distributions are similar. Assuming that this is indeed so, I’ll speculate how we might use hermit crabs in lab studies and computer simulations to gain some insight into how human wealth inequality works.       

I’ll develop these points in a talk with my friend Jim. Jim was an academic who worked in theoretical physics before joining a hedge fund. We get together from time to time, and we talk about the hedge fund business and how my research is going. Given his hard science background, he’s not completely convinced that animal behavior and ecology are real sciences, and he usually questions what I report. During the pandemic, Jim started taking long walks along the roads and beaches near where he lives. In general, he’s a keen observer, and he started paying close attention to the plants and animals he noticed during his walks. I think his interest in the local nature made him more open to my research, but he still gives me a hard time when we talk. Perhaps because of working at a hedge fund, Jim has a deep interest in the fundamentals of wealth: he wants to know how it’s generated, how it’s distributed across the members of a society, and what kind of research studies could best investigate his concerns. Not long ago, we ran into one another walking along our street, and I invited him back to my place to catch up.

Comparing Wealth in Humans and Hermit Crabs

Jim: One of our mutual friends said something about you and some colleagues publishing a scientific paper comparing wealth in humans and hermit crabs. No offence, but I can’t even imagine that hermit crabs have something you could call wealth. I don’t have to tell you that hermit crabs are very simple creatures– they don’t have culture or social institutions or anything that constitutes an economy that could produce what I would call wealth.

Even if you weren’t comparing them to humans, I wonder how you could even measure something called wealth in hermit crabs. What would make you say that one hermit crab was richer than another? I can only think of it in a metaphorical way. Maybe you could say that one hermit crab was richer than another if it had more of what it needed to lead a good life than the other. Maybe a rich crab lives in an area where it has a lot of food, a lack of predators, and a good chance to mate and reproduce. And a poor crab must work hard to get enough food, is surrounded by predators, and has fewer chances to mate.

Ivan: What you’re saying reminds me of the Capabilities Approach developed by the philosophers Martha Nussbaum and Amartya Sen. Have you heard of this theory?

Jim: No, I haven’t. What’s the Capabilities Approach?

Ivan: Very briefly, they proposed that wellbeing in people is based upon their opportunities to achieve things of importance to themselves. Nussbaum also used the approach to describe how we should treat animals –that we should give them the ability to lead good lives. But you’re using the Capabilities Approach to suggest that animals that have the capacity to easily get the things they need are richer than those that don’t.

That’s an intriguing idea, but I’m afraid that our perspective was much less philosophical and much more materialistic. We simply proposed that the larger the snail shell that a crab occupied, the greater its wealth. We approximated the size of shells by their weight.

Lester Lefkowitz

Jim: The weights of their shells? I don’t understand how you could use that to measure what you’re calling wealth. You wouldn’t measure the wealth of people by the sizes of, say, their shirts as they went from infancy to adulthood – so, why would you measure the wealth of hermit crabs by the sizes of their “clothing”?

Ivan: I get your point. For people in developed economies, at least, basic utilitarian clothing is relatively inexpensive. When a child grows larger, parents simply buy the new clothing that the child needs. New clothing is not that hard to come by.

However, besides not having parents that provide for them, it’s not that simple in hermit crabs. They can’t go out and easily get a new, empty snail shell when they have outgrown the one they’re living in. They can’t, for example, find a snail with a shell of the proper size and kill it. And piles of empty shells are not just lying around for the taking. New shells are scarce and obtaining one of the right size takes effort and persistence – as well as a little luck. Even if they are lucky enough to find an empty shell, it may not be of the correct size, and when they do find a good empty shell – neither too big nor too small – they may have to compete with other crabs to acquire it. The result is that most crabs are in undersized small to medium-sized shells, and very few are in large ones.

Occupying an empty snail shell is a matter of life and death to hermit crabs. A crab deprived of a shell becomes a tasty bite to many predators like fish, hard-shelled crabs, and octopuses. Becoming, in my terminology, a rich crab, supplies many benefits beyond just survival. Crabs in bigger shells can develop larger body sizes, and larger sizes convey advantages. Larger males are more successful in mating than smaller ones, and bigger females produce more eggs than smaller ones.

Jim: Okay, for the purposes of this conversation, I’m willing to concede that empty snail shells are a scarce and valuable material resource for hermit crabs and that they could be considered an analogue to wealth in humans. But, as you know, what I’m interested in is wealth in humans. I don’t mean any offense, but why should I care about wealth in hermit crabs?

Are you just trying to extend the efforts of other researchers who have shown that humans aren’t unique in many of their abilities and activities? As I have read, and I’m sure you know, researchers have shown, for example, that many animals use tools: monkeys and chimpanzees employ stones to crack nuts, crows manipulate thorns to fish grubs out of crevices, and ants apply bits of plant debris to soak up sugary solutions for transport back to their nests. Other researchers have written that some animals, like gorillas and chimpanzees are capable of learning language, and the natural communication of others, like whales and dolphins, have some elements in common with human language.

I think it’s great that you and your colleagues have demonstrated that hermit crabs have wealth, but have you and your colleagues done something more than that?

The Study

Ivan: It’s early days yet, but I believe we have. Let me set the stage by telling you a little about our study. We started by collecting a random sample of about 300 hermit crabs at our local beach here in Setauket. After collecting them, we took the crabs back to our lab, immersed them in warm, fresh water, so that they would relax, and we could gently remove them from their snail shells. We then immersed the crabs in cool seawater to revive them, gave them their choices of new snail shells, and returned them to the beach where we collected them. We dried the shells originally occupied by the crabs and then weighed them.

After weighing them, we divided up the shells into weight classes and graphed what percent of the crabs in the sample occupied each weight class. For example, about 5% of the crabs were in shells weighing between 50 and 99 milligrams, and about 16% of the crabs had shells weighing between 150 and 199 milligrams. The species of hermit crabs, Pagurus longicarpus, that we collected is quite small, and you can see that the largest shells occupied by the crabs were just under one gram (1000 milligrams).

Before we graphed the shell weights, we didn’t know what the distribution would look like. We thought of several possibilities. Maybe the graph would resemble a typical distribution of shell sizes from a species of snails, like those that hermit crabs might use, or the sizes of regular, hard-shelled crabs (top figure, below). In snails and hard-shelled crabs, most individuals die young at relatively small sizes, so the bars of the graph diminish very quickly as the sizes of the crabs or snails get larger. Another possibility would be a typical bell-shaped (normal or Gaussian) distribution with many shells of average sizes but very few of very small or very large sizes (middle figure, below). Or – we weren’t counting on this one – it would look like a typical graph for the distribution of wealth in human societies (bottom figure, below). Graphs for human wealth across different societies typically have certain, characteristic features: they have a single mode or peak, are skewed to the right, and have a fat right tail, also to the right.

Tom O’Brien

When we plotted the shell sizes occupied by the crabs (figure below), we could hardly believe it, but it really did look a lot like a distribution of wealth in human groups! The graph for the hermit crabs also had a single, major mode, was skewed to the right, and had a fat tail (but it did also have a small, secondary mode). As you know, Jim, in a graph with a fat right tail, the bars at the right end of the graph – the right-hand tail – are higher, have higher percents of the population, than many other kinds of graphs. Our graph showed that there were greater percentages of rich hermit crab than there would have been if the graph had taken the form of a bell curve or of the distribution that is typical of snails or regular, hard-shelled crabs. So, the graphs show that there are more rich hermit crabs and humans than you would get if the distributions were not fat-tailed and skewed to the right.

Tom O’Brien

How Much Wealth Inequality Is There in Hermit Crabs Compared to Humans?

Jim: That’s not something I would have expected. But I wonder about the level of inequality in the hermit crabs compared to humans. Were there some extraordinarily rich crabs like many of my colleagues in the hedge fund business?

Ivan: We did try to answer these questions. One of the things that we looked at was the Gini index in the hermit crabs as compared to that in human societies. It’s a measure of the amount of inequality in a population, and it can go from 0 to nearly 1. When the index is 0, everyone has the same amount of wealth. When the index is at its maximum value, nearly 1, one individual in the population has all the wealth. In human societies the Gini index varies widely from estimates of a little over 0.10 to around 0.40 for ancient farming societies in Mesoamerica and the Middle East, 0.17 to 0.36 for hunter-gatherers, 0.35 to 0.69 for pastoralists, and 0.85 for the present-day United States. In other developed countries, like Japan and France, the Gini is lower at about 0.63 and 0.70, respectively. The Gini for the hermit crabs was 0.32 which put it above some of the ancient agricultural groups and around the level of hunter-gatherers. The extent of wealth inequality in the hermit crabs was moderate compared to a range of human groups and not nearly as extreme as in economically developed societies.

We also measured the size of something called the tail exponent and how much of the total wealth in shells the richest 1% of the crabs owned. Both the tail exponent and the amount of the total shell wealth owned by the richest 1% of the crabs were small compared to the United States today. In particular, the richest 1% of the crabs only owned about 3.2% of the total shell wealth compared to about 32% for the richest 1% of people in the United States (some estimates suggest that the richest 1% own about 40% of the total wealth in the United States). Some crabs were richer than others, but there wasn’t a Jeff Bezos among them!

Why Do Human and Hermit Crab Wealth Distributions Look Similar?

Jim: That’s also very interesting. It seems to me that differences in the “economic” systems of humans and hermit crabs might explain your findings. Hermit crabs can’t hoard, or should I say, to be more neutral, can’t collect more than one shell. They can only carry around one shell at a time. But of course, humans are a little different. It’s perfectly within their abilities – not to mention their desires – to stockpile extra dollars, stocks, or houses if they can.

But I want to go back to the question I raised earlier: The resemblance between your graph and the one for humans is remarkable, but maybe it’s just a curiosity, a delightful, but random finding. What does it really tell us? Do you think that the resemblance really means that human and hermit crab wealth systems are alike in some way?

As I am sure you know, many processes in the natural and human-made worlds can produce distributions that have single modes, are skewed to the right, and show fat tails. Perhaps the similarity between the human and hermit crab distributions is just a coincidence – one kind of process generates wealth in humans and another in hermit crabs. Isn’t that a possibility?

Ivan: I do think it’s a possibility. And it’s also a possibility that different processes could be at work in different human groups, say, one kind of wealth distribution process for pastoralists on the plains of East Africa and another kind for economically developed societies. And our research needs to be repeated in other populations of hermit crabs to test whether they have a similar form of shell wealth distribution to the one we observed in the crabs we studied.

But I’m going to take the liberty to speculate that analogous factors in both hermit crabs and humans generate the similarity in their wealth distributions. These factors would have to be of the most basic sort, since as we agree, hermit crabs are otherwise so very different from humans. Looking at the literature on inequality, I can see two possibilities for the analogous factors: individual differences and wealth transfer.

At this time in the United States, as well as other parts of the world, there is enormous interest in the characteristics of individuals that might help them achieve great levels of wealth: “Here is what sets Elon Musk apart.” Both academic and popular writers have explored the correlation between individual qualities like IQ scores, effort, and various personality traits and the levels of wealth that people amass. Some people working in this area claim that differences in individual attributes do explain levels of wealth, while others propose that “luck” – being in the right place at the right time when economic opportunities present themselves – is more important. Perhaps in the future, you and I could explore this controversy of luck versus talent by discussing some of my research on animals.

Some economists have used individual characteristics in another way – through what is known as “human capital” theory – to try to explain the shape of human income distributions. The idea is that people gain income in relation to their levels of human capital – their training, work habits, education, health, etc. Human income distributions are similar in form to wealth distributions: one mode, skewed to the right, and fat tailed. But there is not as much inequality in income as there is in wealth, e.g., income distributions have lower Gini indexes. Some economists have suggested that human capital should be included in models of wealth distribution, but I am not aware of any work that has yet done this.

You could certainly adapt ideas about individual differences and wealth in humans to hermit crabs. So, for example, instead of human capital, you could have hermit crab capital based upon differences in strength, competitive ability, skill in finding empty snail shells, etc. But I don’t think this would work. 

Jim, I know that you were kind enough to read my first essay on Substack. As you probably remember, in that essay I asked if differences among individuals, like those in aggressiveness or genetics, could explain the top-to-bottom structure of pecking orders. On the face of it, pecking orders seem to be a social structure where this explanation has its best chance. Many dominance researchers do believe that this explanation is correct. But in the essay, I presented experimental and mathematical evidence to show that differences among individuals do not account for the structure of pecking orders. Based upon that work, my best guess is that individual difference approaches, like human and hermit crab capital theories, are not good candidates for explaining the shape of either human or crab wealth distributions.

But I think that the second factor I mentioned above, wealth transfer, in hermit crabs might account for why their inequality in shells has a form that resembles human wealth distributions. Economists have proposed that the transfer of resources between individuals, especially those related to one another, helps structure the forms of human wealth distributions. Resource transfers in the form, for example, of gifts and inheritances are common across most, if not all, human groups. These transfers occur when individuals die and their children or other close kin receive inheritances or when living people bestow gifts on others, again, usually close kin. For example, pastoralists transfer livestock, farmers pass on land, and people in economically developed societies convey homes and other material goods as well as cash in bank accounts.

Wealth Transfer in Hermit Crabs?

Jim: I’ve got to stop you there. With all due respect, how can hermit crabs have wealth transfer? Correct me if I’m wrong, but I don’t believe that hermit crabs make sure that when they die, their children get their now-vacant shells, or that a living hermit crab – one with a death wish –gives its shell to its children or other relatives. I don’t believe that they live in family groups, so shell transfer couldn’t even happen by chance, much less intention.

Ivan: Of course, you’re right, Jim. Hermit crabs don’t live in family groups, and they don’t pass on or give their shells, either on purpose or by chance, to their relatives. But hermit crabs have something called vacancy chains that as a vehicle for the transfer of resources. A vacancy chain occurs when a hermit crab dies, leaving its shell behind, or a new snail shell becomes available, for example, when a predator kills a snail. In both cases, a first crab takes the vacant shell, a second crab takes the old shell of the first crab, and so on. This process gets its name from the successive “moves” of the vacancy from the first shell to the later ones. Researchers first described vacancy chains for people getting houses and apartments, moving to new jobs, and buying cars. A colleague and I were the first to discover vacancy chains in non-humans – hermit crabs getting new snail shells.

Jim: That’s very clever. I didn’t know about vacancy chains in either humans or hermit crabs, and I never imagined that property transfer could occur in hermit crabs and that it might – at least in theory – influence the form of their wealth distributions.

But now I’ve got more questions: First, humans and hermit crabs are so different, why do they both have vacancy chains? Second, I find the idea of vacancy chains intriguing, but what can we do with them? And third, how could you show that property transfer through vacancy chains influences shell wealth in hermit crabs to make it look like a human wealth distribution?

Hermit Crabs as a Model of Wealth in Humans?

Ivan: Those are great questions, but I think it would be better to discuss the first two at another time. Before I try to answer your third question about how I might investigate the influence of vacancy chains on the form of the shell wealth distribution, I want to say a few things more generally about using hermit crabs as a model species to explore economic activities in humans.   

The shell economy in hermit crabs is of course much simpler than the money economy in economically developed human societies or the more materially based resource economies in small-scale human groups like pastoralists or hunter-gatherers. But that very simplicity may be to our advantage. I believe that we already know the main factors responsible for the distribution of shells in hermit crabs. The first factor is the demography of the snail shells used by the crabs. Snail shells are “born” when snails are killed, and their shells enter the hermit crab population – once crabs occupy them. The shells “die” when they wear out from being dragged across the ocean bottom by their crab occupants or when they are degraded by organisms like boring sponges that live in and slowly destroy the shells occupied by crabs. Crabs will abandon worn out and degraded shells when they have an opportunity to get new and better ones. The second factor is also demographic. Hermit crabs are “born” into the population of those using shells after they go through various immature stages, settle on the ocean bottom, and obtain their first shells, and hermit crabs, like snails, eventually die. The third factor is the transfer of shells among the hermit crabs through vacancy chains. As I said earlier, vacancy chains occur when a shell is born into a group of crabs, or a crab dies leaving its shell behind.

My point is that because we know the main factors in the distribution of snail shells, hermit crabs could be a good model organism for studying wealth distribution and maybe other economic processes. Historically, there are a great many cases in which scientists began research on a phenomenon occurring in humans by first studying non-human species. Two examples that come to mind are the use of garden peas and fruit flies in the development of genetics and of mice and rats to gain understanding of various disease processes. The use of models like these has allowed researchers to discover what kinds of data and methods are needed in an area of research and to develop concepts and hypotheses that can be evaluated in studies of humans. Although animals haven’t been widely used for models of social phenomena in humans, I believe that field work and laboratory experiments on hermit crabs could give us insight into how human inequality works.

To go back to your question, Jim, about how to investigate the possible effect of vacancy chains on the form of the shell wealth distribution, I could do lab experiments in which I introduce new snail shells into two groups of hermit crabs. In one group I could allow vacancy chains to occur by letting the crabs take the old shells of the crabs obtaining the shells I introduced. In the other group, I could prohibit vacancy chains by removing the old shells of the crabs getting new ones. After running this experiment for a while, I could compare the shell distribution in each group and decide whether the occurrence of vacancy chains had an influence on the forms of those shell distributions. When I think about this experiment, I have a fantasy that brings me great joy: economics departments at major universities scrambling to set up hermit crab experiments to test the latest conjectures about wealth inequality in humans.

Another way to investigate the possible effects of vacancy chains on the distribution of shell wealth would be through computer simulation. As far as I know, there are no existing computer programs to do something like this, and for that reason I am learning the Python computer programming language so that I can write my own programs. In the simulations, I could examine how variation in the demography of snail shells and hermit crabs, as well as the parameters of vacancy chains, affect the distribution of shell wealth.

Jim: It’s still a little unsettling, since I’m most comfortable with more orthodox economic views, but I can acknowledge now that individual animals of various species can “own” material resources of varying sizes and qualities. And if I acknowledge that, I can understand how you could consider some individual animals – particularly in hermit crabs – to be rich.

But I have some problems with the experiments you described and the computer simulation you want to work on. I wonder whether you’ll be able to show how the factors you mentioned can actually produce the shape of the shell wealth distribution you found in your hermit crabs and that we also see in humans.

Ivan: I’m glad to hear that you’ve begun to accept the idea of wealth in animals and that some hermit crabs can indeed be rich. From my perspective, Jim, that’s a big step forward. As for the experiments and simulation, I understand that they’re risky. I don’t know whether either will advance our understanding of the distribution of wealth. But of course, I think they have a good chance to do so and that I could learn many interesting things if I did them. In any event, I’ll let you know what happens.

Jim: That would be great. The next time I walk on the beach, I’ll look at the hermit crabs with a lot more respect.

Thanks to Keyan Kaplan, Lester Lefkowitz, Dianna Padilla, and Andrew Sutter for reading drafts and for suggestions and to Lester Lefkowitz, Tom O’Brien, and Iris Yan for illustrations.