Measuring resource competition vs. measuring inflation

Welcome to what should probably be a named regular feature here at Dynamic Ecology: Jeremy’s Half-Baked Analogies to Economics!*

I had a thought and I’m not sure what to make of it, or even if it’s original. So I thought I’d share it in the hopes that a reader can enlighten me.

In economics, inflation is a reduction in the purchasing power of a unit of money. It’s often measured as an annualized percentage change in a price index, a weighted average of the prices of a “basket” of goods and services. The contents of the basket obviously need to reflect what consumers actually buy.

Measuring inflation is trickier than you might think. The problem is that consumers react to price changes by changing the quantities they buy. If the price of some good or service rises, consumers often will substitute some other good or service instead. If you ignore this fact, you will badly overstate the extent to which price increases of some goods erode the real purchasing power of a unit of money. But conversely, if you take this fact too seriously, you will understate inflation. Apparently**, economists haven’t come up with a perfect solution to this problem.

I think there’s an analogy here to trying to measure the strength of competition for resources, for instance by measures of resource use overlap. If competition for a given resource (say, a given prey species) gets stronger, so that the resource becomes scarcer on a per-consumer basis, we expect that consumers will respond by substituting other resources instead. That’s the logic of character displacement. Which makes it tricky to summarize the “strength” or “intensity” of competition in terms of a number quantifying how much resource a consumer can “buy” with each unit of foraging effort.

This is why it’s generally a bad idea to use indices of resource use overlap as measures of the strength of competition. Say the abundance of your competitor increases for some reason, causing some of the resources you previously were consuming to become scarce on a per-capita basis. So you move somewhere else, or switch to consuming some other resources instead, thereby reducing or even eliminating overlap with your competitor. But does that mean you’re no longer experiencing competition? If you say yes, isn’t that like saying that there’s no inflation so long as consumers are spending their money on something?

Has anyone else drawn this analogy before, or tried to pursue it further? For instance, has anyone ever looked at whether the price indices economists have developed have applications in ecology? Or is the analogy too loose or half-baked for that?

*Mathematicians are said to be machines for turning coffee into theorems. I’m more of a machine for turning Pepsi into half-baked analogies between ecology and economics. 🙂

**meaning: “as far as I can tell from Wikipedia and a blog post I once read”

16 thoughts on “Measuring resource competition vs. measuring inflation

  1. Peter Buston recently gave a talk here (U. of Mass., Amherst) and pointed out something similar for peacful social systems: sometimes conflict is hidden because the cost of experiencing it is too high, so it functions as a (hidden) threat (pdf). I enjoyed this talk and your comment because it shows just how much behavior and population/group level processes are intertwined. I think I’ve seen papers measuring resources switching, but I’m not sure how often it’s done in the context of measuring competition.

    • Thanks, interesting. Haven’t had a chance to look at the linked pdf, but the basic idea sounds analogous to classical results from applying game theory to understand animal behavior. The reason why you don’t often see animals fighting (over territories, over mates, over food…) is basically that fighting is very risky and costly. You’re right that there are broad issues here relating to the interplay of individual behavior and population- or group-level dynamics and outcomes.

  2. Jeremy: (I only know the basics of index number theory in economics, so don’t take what I say as the gospel truth.)
    “Apparently**, economists haven’t come up with a perfect solution to this problem.”
    That’s roughly right. But if you did know the consumer’s utility function (utility as a function of the quantities of goods consumed) it would be possible in principle to calculate a perfect price index for that individual consumer. It’s the price index such that, if the consumer’s money income was adjusted for inflation as defined by that price index, the consumer’s utility-maximising level of utility would stay constant.

    In biology, something like “reproductive success” would presumably be the counterpart to “utility”. And presumably there exists some function that tells us reproductive success as a function of the vector of resources. If so, it would be possible in principle (with just a little math, duality theory of consumer choice I think to construct an index number that perfectly measures the “price” of resources for any creature that chooses the right mix of those resources to maximise its reproductive success.

    I think your analogy works.

    • As always, you’re spot on, Nick. It hadn’t occurred to me that the consumer’s utility function was a key ingredient here, though perhaps it should have.

      And yes, the biological equivalent would be “fitness” (or in practice, the best index of fitness we can come up with–“lifetime reproductive success” is reasonably good for many purposes).

      It occurs to me that there’s perhaps another post to be written here, on the challenges of precisely defining and measuring fitness in biology, and utility in economics. But I don’t really know enough about either to write that post well. Definition of fitness is a very deep and difficult issue. Alan Grafen at Oxford is one person who’s thought very hard about it. He says you need to use measure theory to get at it, which is rather beyond me. It’s probably fortunate that in practice biologists seem to be able to come up with measurable proxies that work well enough for most purposes, even if we can’t yet be fully precise about *exactly* what they’re proxies of.

      • In practice though, you can define a good approximation to the perfect price index, for a utility-maximising consumer, even if you don’t know the utility function. And you should be able to do the same for a fitness-maximising animal, even if you don’t know the fitness function. We define “utility” as “the thing that consumers maximise”, and you could do likewise with “fitness”.

        A price index is a weighted average of prices. If we use current period’s quantities as weights, we get a Paasche index, and if we use the previous period’s quantities as weights, we get a Laspeyres index. One is biased up, and the other is biased down. By taking a geometric average of the two indexes, we get a bias that’s small enough for government work (Fisher “ideal” chain index).

        The same procedure could work fine in biology. “Price” becomes “deer/mice/whatever eaten per hour of hunting”, and “quantity” becomes “total amount of deer/mice/whatever eaten”. Both of those are observable (in principle).

      • I think you should take this idea a bit further, I always thought that the tension between absolute and relative utility/fitness is where much of the interesting things in econ and biology are.

        To give an econ-y example: should you pay 5$ to print 100$ to yourself and all your friends? Probably, because you will be 95$ richer and the amount of inflation your money printing will cause will not devalue your other capital enough to offset this increase. However, should you pay 5% of your net wealth to double the wealth of every single participant in the global market place (including yourself)? Now the answer is an obvious no because everybody will have 200%of their wealth, and so all prices will increase by ~200%, but you will only have 190% of your wealth and so will be able to buy fewer goods than before. The question becomes more complicated, if you make things additive and global: should you pay $5 to give every single market participant $200? I am not quiet sure that the answer is as obvious here, since an additive change will reduce Gini index, so maybe you can benefit from it.

        Now lets move on to biology and see what it can teach econ. The equivalent of money in biology is (maybe up to a log transform) fecundity, the equivalent of money normalized for inflation (or maybe for purchasing power parity(?)) is fitness. However, biology has a 3rd and very important thing: inclusive fitness. What is the economic equivalent of inclusive fitness? It might not exist if we define everybody as purely rational… however, even if it does, it is something like ‘externalities’ and can be incorporated into the private utility function (see last paragraph of this post).

        I think resources (in the resource competition sense) enter into this only as a proxy for biology, and might be distracting. However, resource competition is a good way to introduce non-trivial externalities.

      • Hmm…isn’t what you’re getting at here just the fallacy of composition–the fallacy of thinking that whatever’s true of some part of a system must (or even can) be true of every part? I have some old posts on this in an ecological context, which unfortunately have never really grabbed the attention of readers. Here are two:

      • Also, do you have a reference for the Grafen + measure theory meditation? I am always a little bit unhappy with how hand-wavy the concept of fitness is and would like to see a serious attempt at pinning it down.

      • Wow, I took a quick look around, and that work is very appealing to me. Looks like a blog post that I’ll need to write up. Do you know much about the reception of this work in the wider biology community? Is it seen as foundational and important, or just some guy trying to mathematize things?

      • ” Is it seen as foundational and important, or just some guy trying to mathematize things?”

        I don’t really know. But my vague sense is more the latter. It’s difficult stuff and hard to read. I think a small circle of cognoscenti see it as important work, but probably a lot of evolutionary biologists either aren’t aware of it or see it as somebody using elaborate math to prove stuff that’s intuitively obvious.

        To his credit, Alan Grafen’s aware of this, I think. I saw him give a seminar on this work back when I was a postdoc, and I think I remember him joking about how since he was an Oxford don he was free to pursue his own obscure obsessions or something like that. And he does talk in some of his papers about how his results shed new light on more concrete issues, such as what “bet hedging” is, or whether “superorganisms” like honeybee colonies can be said to maximize colony fitness in the way that individual organisms can be said to maximize fitness.

    • There might or might not be such a function. Bassett Maguire says there is (1973, Am Nat 107:213-246), and calls it the niche response structure. Large parts of ecology depend on the assumption that he’s right. But there can’t be such a function if the internal state of an organism matters (because then for a given resource vector, more than one possible value of reproductive success is possible). Ginzburg and Kooijman, for example, have argued that internal states matter a lot. The answer in practice depends on the extent to which internal states are quantitatively important for the particular problem you want to solve.

  3. I’ve never been thrilled with using resource overlap as a measure of the strength of competition, at least when you have no other lines of evidence to suggest that one population is in some way limiting another via competition for that resource. At least in my own subfield, I can’t help but feel that the abundance of available prey relative to the foraging requirements of a species is often underemphasized.

    If you lock two people in a room with a pile of money in the floor, and tell them to start collecting the money for five minutes, competition will certainly be greater if there is two hundred dollars on the floor, relative to (say) two hundred million dollars on the floor. Too often we treat the two scenarios as equivalent.

    • To extend this metaphor further, in the two hundred million dollar scenario, factors other than the gathering of the second person are likely to limit the amount of money you can take in. For example, you need somewhere to store the money, and after a certain point you will run out of storage capacity. Furthermore, money weighs a lot, and you may not be able to carry anymore. If the resource is abundant enough, the second person gathering money is irrelevant, because numerous other factors will limit your ability to continue gathering (increasing in population size) before the second person’s activities are relevant (access to mating resources, home ranges requirements, etc.).

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