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July 21, 2008

Evolution and Distribution of Species Body Size

One of the most conspicuous and most important characteristics of any organism is its size [1]: the size basically determines the type of physics it faces, i.e., what kind of world it has to live in. For instance, bacteria live in a very different world from insects, and insects live in a very different world from most mammals. In a bacterium's world, nanometers and micrometers are typical scales and some quantum effects are significant enough to drive some behaviors, but larger-scale effects like surface tension and gravity have a much more indirect effect. For most insects, typical scales are millimeter and centimeters, where quantum effects are negligible, but the surface tension of water matters tremendously. Similarly, for most mammals [2], a typical scale is more like a meter, and surface tension isn't as important as gravity and supporting your own body weight.

And yet despite these vast differences in the basic physical world that different types of species encounter, the distribution of body sizes within a taxonomic group, that is, the relative number of small, medium and large species, seems basically the same regardless of whether we're talking about insects, fish, birds or mammals: a few species in a given group are very small (about 2 grams for mammals), most species are slightly larger (between 20 and 80 grams for mammals), but some species are much (much!) larger (like elephants, which weigh over 1,000,000 times more than the smallest mammal). The ubiquity of this distribution has intrigued biologists since they first began to assemble large data sets in the second-half of the 20th century.

Many ideas have been suggested about what might cause this particular, highly asymmetric distribution, and they basically group into two kinds of theories: optimal body-size and diffusion. My interest in answering this question began last summer, partly as a result of some conversations with Alison Boyer in another context. Happily, the results of this project were published in Science last week [3] and basically show that the diffusion explanation is, when fossil data is taken in account, really quite good. (I won't go into the optimal body-size theories here; suffice to say that it's not as popular a theory as the diffusion explanation.) At its most basic, the paper shows that, while there are many factors that influence whether a species gets bigger or smaller as it evolves over long periods of time, their combined influence can be modeled as a simple random walk [4]. For mammals, the diffusion process is, surprisingly I think, not completely agnostic about the current size of a species. That is, although a species experiences many different pressures to get bigger or smaller, the combined pressure typically favors getting a little bigger (but not always). The result of this slight bias toward larger sizes is that descendent species are, on average, 4% larger than their ancestors.

But, the diffusion itself is not completely free [5], and its limitations turn out to be what cause the relative frequencies of large and small species to be so asymmetric. On the low end of the scale, there are unique problems that small species face that make it hard to be small. For instance, in 1948, O. P. Pearson published a one-page paper in Science reporting work where he, basically, stuck a bunch of small mammals in an incubator and measured their oxygen (O2) consumption. What he discovered is that O2 consumption (a proxy for metabolic rate) goes through the roof near 2 grams, suggesting that (adult) mammals smaller than this size might not be able to find enough high-energy food to survive, and that, effectively, 2 grams is the lower limit on mammalian size [6]. On the upper end, there is an increasingly dire long-term risk of become extinct the bigger a species is. Empirical evidence, both from modern species experiencing stress (mainly from human-related sources) as well as fossil data, suggests that extinction seems to kill off larger species more quickly than smaller species, with the net result being that it's hard to be big, too.

Together, this hard lower-limit and soft upper-limit on the diffusion of species sizes shape distribution of species in an asymmetric way and create the distribution of species sizes we see today [7]. To test this hypothesis in a strong way, we first estimated the details of the diffusion model (such as the location of the lower limit and the strength of the diffusion process) from fossil data on about 1100 extinct mammals from North America that ranged from 100 million years ago to about 50,000 years ago. We then simulated about 60 million years of mammalian evolution (since dinosaurs died out), and discovered that the model produced almost exactly the size distribution of currently living mammals. Also, when we removed any piece of the model, the agreement with the data became significantly worse, suggesting that we really do need all three pieces: the lower limit, the size-dependent extinction risk, and the diffusion process. The only thing that wasn't necessary was, surprisingly, the bias toward slightly larger species in the diffusion itself [8], which I think most people thought was necessary to produce really big species like elephants.

Although this paper answers several questions about why the distribution of species body size is the way it is, there are several questions left unanswered, which I might try to work on a little in the future. In general, one exciting thing is that this model offers some possibilities for connecting macroevolutionary patterns, such as the distribution of species body sizes over evolutionary time, with ecological processes, such as the ones that make larger species become extinct more quickly than small species, in a relatively compact way. That gives me some comfort, since I'm sympathetic to the idea that there are reasons we see such distinct patterns in the aggregate behavior of biology, and that it's possible to understand something about them without having to understand the specific details of every species and every environment.


[1] An organism's size is closely related, but not exactly the same as its mass. For mammals, their density is very close to that of water, but plants and insects, for instance, can be less or more dense than water, depending on the extent of specialized structures.

[2] The typical mammal species weights about 40 grams, which is the size of the Pacific rat. The smallest known mammal species are the Etruscan shrew and the bumblebee bat, both of whom weight about 2 grams. Surprisingly, there are several insect species that are larger, such as the titan beetle which is known to weigh roughly 35 grams as an adult. Amazingly, there are some other species that are larger still. Some evidence suggests that it is the oxygen concentration in the atmosphere that mainly limits the maximum size of insects. So, about 300 million years ago, when the atmospheric oxygen concentrations were much higher, it should be no surprise that the largest insects were also much larger.

[3] A. Clauset and D. H. Erwin, "The evolution and distribution of species body size." Science 321, 399 - 401 (2008).

[4] Actually, in the case of body size variation, the random walk is multiplicative meaning that changes to species size are more like the way your bank balance changes, in which size increases or decreases by some percentage, and less like the way a drunkard wanders, in which size changes by increasing or decreasing by roughly constant amounts (e.g., the length of the drunkard's stride).

[5] If it were a completely free process, with no limits on the upper or lower ends, then the distribution would be a lot more symmetric than it is, with just as many tiny species as enormous species. For instance, with mammals, an elephant weights about 10 million grams, and there are a couple of species in this range of size. A completely free process would thus also generate a species that weighed about 0.000001 grams. So, the fact that the real distribution is asymmetric implies that some constraints much exist.

[6] The point about adult size is actually an important one, because all mammals (indeed, all species) begin life much smaller. My understanding is that we don't really understand very well the differences between adult and juvenile metabolism, how juveniles get away with having a much higher metabolism than their adult counterparts, or what really changes metabolically as a juvenile becomes an adult. If we did, then I suspect we would have a better theoretical explanation for why adult metabolic rate seems to diverge at the lower end of the size spectrum.

[7] Actually, we see fewer large species today than we might have 10,000 - 50,000 years ago, because an increasing number of them have died out. The most recent population collapses are certainly due to human activities such as hunting, habitat destruction, pollution, etc., but even 10,000 years ago, there's some evidence that the disappearnace of the largest species was due to human activities. To control for this anthropic influence, we actually used data on mammal species from about 50,000 years ago as our proxy for the "natural" state.

[8] This bias is what's more popularly known as Cope's rule, the modern reformulation of Edward Drinker Cope's suggesting that species tend to get bigger over evolutionary time.

posted July 21, 2008 03:01 PM in Evolution | permalink