Sizing up size ratios

TREE vol. 2, no. 3, March 1987

Sizing up Size Ratios The investigation of the causes of observed size differences between coexisting related animal species re- quires a knowledge of the statistical distributions of size ratios in randomly constructed guilds. Null models can be useful, but are often subject to constraints that severely limit their applicability. New work on the statistics of size distributions may lead to a better understanding of why animals are the sizes they are.

During the past 50 years there has been considerable interest in the sizes of ecologically similar species, and this interest shows little sign of abating. Huxley’ and then Lack* argued that coexisting species using the same types of food must differ in size to reduce competition to toler- able levels. Hutchinson then sug- gested in his influential paper ‘Hom- age to Santa Rosalia or why are there so many kinds of animals?‘3 that coexisting species must differ in size by about 1.3 in linear dimensions. This figure was not based on any theoretical considerations, but rather was a tentative observation of the size differences between two species of corixids (water boatmen) in a Sicil- ian pool, two weasels, two nuthatches, two mice, and five Darwin’s finches. Hutchinson’s paper was en- thusiastically received, and during the next 20 years scores of examples of species appearing to follow ‘Hutchinson’s Rule’ were published. However, in few of these cases was competition, or the lack of it, actually demonstrated in natural conditions.

More recently there has been growing skepticism about the ver- acity of Hutchinson’s Rule, and a general reassessment of the statistical analysis of ecological data. Sim- berloff, Connor and their co-workers have correctly stressed that before we can claim that observed size ratios obey Hutchinson’s Rule, we must know more about the statistical distributions of size ratios of randomly constructed guilds4Z5. If observed size ratios do not differ sufficiently from a random sampling from a source pool of potential colonist species, then we do not need to invoke competitive processes to explain the size pattern; they could just as well have arisen by chance col- onization. Null distributions are generally constructed from one of two types of source pools. Either a list of real species provides the sizes

Erick Greene is at the Department of Biology, Princeton University, Princeton, NJ 08544, USA.

of potential colonists, or real species are replaced by a statistical distribution of sizes (for details on the mechanics of how null models are constructed see Ref. 6).

To illustrate some of these difficulties, Fig. 1 shows three possible null

However, this null model approach is not without difficulties. It is in- creasingly clear that many (often un- stated) biological assumptions are incorporated into null models. For example, how should we construct a null model for Hutchinson’s famous example of the corixids at Santa Rosalia? Should the group of potential colonist species only include species found in Sicily? If corixids have limited dispersal abilities perhaps this is the most realistic. However, if corixids are proficient at dispersing should all Mediteranean species be included, or even all European species? Some species are much more common than others; should we weight a species’ probability of being chosen by its abundance? Also, what is meant by ‘ecologically similar’? Should we consider only the genus Corixa, all members of the family, or even all aquatic inverte- brates that feed primarily on algae? And so on. Another problem arises if competitive interactions have already altered the pool of potential colonist species. Then the resulting null model will not be ‘null’ at all, but will already incorporate the effects being tested for (the Narcissus Effectj7.

Erick Greene distributions of size ratios for the

The same difficulties can arise

corixids at Santa Rosalia. These null distributions were produced by ran-

when a specific statistical distribution

domly selecting 100 pairs of species which occurred within the specified taxonomic and geographic limits, and then tabulating the size ratios for all pairs. The source pools were modified by either expanding the taxonomic limits (Fig. la to lb), or expanding the geographic limits (Fig. lb to tc). All of these general types of null models have been used in other studies. Without more specific ecological knowledge about corixids, we can not assess a priori which of these models is most appropriate. If la is the most valid, we might concede that Hutchinson’s observation was unusual with re- spect to that null distribution. If either lb or Ic is more appropriate, there is no reason to suspect an unusual size ratio. Hence, the answer to the question of whether the Santa Rosalia water boatmen Corixa punctata and C. affinis are more different in size than might be expected by chance may depend critically upon which of the null distributions ap- plies. This exercise is not a true test of the unusualness of Hutchinson’s observation; rather, it is meant to emphasize that null models can be sensitive to the specific biological details which are included. which in turn can influence the answers to the questions we pose.

a) Zone 1 - Corlxa only 40 -

-- c

20 -

0 d- III III 1

1 2 3 4 1 2 3 4

SIZE RATIO SIZE RATIO

b) Zone 1 - all Corlxlds

40 7

- c

c) Zone 2 - all Corixlds

20 -

0 I I I I I I

Fig. 1. Three possible null models for the size ratio of two Sicilian corixids. These distrlbutlons were generated by randomly selecting 100 species pairs from a source pool. The geographic and taxonomic limits for including species in the source pool are shown above each histogram. The arrows indicate the sue ratio of Corixa punctata and C. affinis, the two species observed by Hutchinson at Santa Rosalia


100 l-l

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Bill-size ratio

Fig. 2 Size ratio distributions in guilds of sympatric, congeneric birds. Reproduced, with permission, from Ref. 73.

of sizes is used as a source pool instead of a group of real species. Some studies have used a log- uniform distribution as a source pool for species sizes4**. However, random samples from a log-uniform distribution have the property of constant expected values of con- tiguous size ratiosg; the use of this distribution produces a null model which incorporates one of the prime characteristics being tested for (constant size ratios). Other distributions can be used (e.g. Ref. 10; log- normal”), but again the conclusions may not be robust.

Another serious constraint concerns the power of null model tests. There has been very little considera- tion of both type I (a) and type II (8) errors in establishing rejection criteria”. The traditional emphasis upon reducing critical values of ~1, in conjunction with often small sample sizes, necessarily increases 8 (the probability of accepting a false null hypothesis). Although it is certainly better to err on the side of ignorance5, the power of many null model tests (1 - f3 : the ability of the test to determine whether the null hypothesis is false) can be stagger- ingly smallg~‘0~12.

One of the latest additions to this literature may help us out of the statistical mire. Tonkyn and ColeI have investigated the general statistical properties of size ratios which are independent of the underlying source pool distributions. They use two types of statistical distribution as the source of potential colonists (the Uniform and the Weibull distributions). These two broad families of distributions can generate many shapes (depending on their par- ameter values), which describe most plausible distributions for a source pool. Tonkyn and Cole show that the size ratio distributions of randomly- constructed guilds from these pools share three qualitative features: (1) they decrease monotonically from a peak at 1, (2) they are concave upwards, and (3) as the number of species per guild increases the aver-

age value of all ratios decreases. These predictions are independent of the precise details of the underlying source pool.

These three general features of size ratios for randomly constructed, non-competitive guilds stand in sharp contrast to those features we would expect if guilds were assem- bled according to Hutchinson’s Rule. In this latter case, the size ratio distribution should be unimodal with a peak at about 1.3. Also, as the number of species per guild increases, the average size ratio should remain the same, or perhaps even get larger due to increasing levels of diffuse competition.

So how do the distributions of real size ratios compare with the predictions made by these very different models? Tonkyn and Cole examined two large data sets, one for sympatric congeneric birds (Fig. 2), and another for sympatric, insectivorous bats. In both cases, the distributions of size ratios conform to the null expectations; there is no evidence that the size ratios conform to Hutch- inson’s Rule. However, as Tonkyn and Cole point out, this does not necessarily mean that competition in some of these guilds is not occur- ring. There may be some guilds in which the sizes of species are strongly influenced by competition. Also, many congeners occur in different types of habitat, so that their inclu- sion in the analysis may not be war- ranted. It is clear, though, that inter- specific competition has not led to the ubiquitous evolution of constant or minimum size ratios in these groups.

Many other textbook examples of competitively produced size differences do not appear to be valid. In their paper ‘Homage to the Null Weasel’, Harvey and Ralls14 demon- strate that what had once been inter- preted as a simple case of character displacement in North American weasels is a complex geographical size pattern which shows no evidence of competition. Grant” had earlier demonstrated that the bill size differences for the two rock nuthatches also show a rather more complicated pattern of geographic clinal variation, instead of the post- ulated size shift in the zone of sym- patry.

Other examples, however, have withstood more rigorous analyses. Schoener” has examined the size patterns of all 47 species of bird- eating hawks in the genus Acciprer. He found that the wing lengths (which are good measures of overall body size and are related to prey size) of coexisting Accipter hawks

are less similar than might be expected by chance.

There is certainly good reason to be cautious when making inferences about size ratios. An animal’s size undoubtedly reflects adaptations to many factors, of which competition with other species for food is but one. McMahon and Bonner’s book On Life and Size’7 yields an impress- ive list of biological phenomena that are strongly influenced by body size: metabolic rate (and hence food re- quirements), rates of physiological processes, rates of warming and chilling, the style and economy of transportation, speed of locomotion, longevity, gestation period, fecund- ity, relative body proportions, and the strengths of inter- and intra- sexual selection, just to name a few. Notice that all of these factors may have large consequences for the be- havior and ecology of animals (and therefore may also strongly influence the evolution of body size), and yet none of these mechanisms depend upon the sizes of other species in the community.

In short, there is still much to be learned about why animals are the sizes they are. We can expect progress in two areas. The first concerns pattern finding: further refinements in the statistical approaches used to analyse ecological patterns will allow increased confidence in the conclusions of those tests. The second concerns pattern explana- tion: field and laboratory experi- ments will continue to be important in illuminating the precise mechanisms underlying those patterns.

References 1 Huxley, J. (1942) Evolution: The Modern Synthesis, Harper 2 Lack, 0. (1947) Darwin’s Finches, Cambridge University Press 3 Hutchinson, G.E. (1959) Am. Nat. 93, 145-159 4 Simberloff, D. and Boecklen, W. (1981) Evolution 35, 1206-I 228 5 Connor, E.F. and Simberloff, D. (1986) Am. Sci. 74,155-l 62 6 Strong, D.R., Simberloff, D., Abele, L.G. and Thistle, A.B., eds (1984) Ecological Communities: Conceptual issues and the Evidence, Princeton University Press 7 Colwell, R.K. and Winkler, D.W. (1984) in Ecological Communities: Conceptual issues and the Evidence (Strong, D.R., Simberloff, D., Abele, L.G. and Thistle, A.B., eds), pp. 344-359, Princeton University Press 8 Simberloff, D. (1983) in Coevolution (Futuyma, D.J. and Slatkin, M., eds), pp. 404-430, Sinauer Associates 9 Sinclair, D.F.. Mosimann, J.E. and Meeter, D.A. (1985) Biometrics 41, 835-846 10 Hopf, F.A. and Brown, J.H. (1986) Ecology 67,1139-l 155

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11 Boecklen, W.J. and NeSmith, C. (1983) Evolution 39,695698 12 Tot?, C.A. and Shea, P.J. (1983) Am. Nat. 122,618625 13 Tonkyn, D.W. and Cole, B.J. (1986) Am. Nat. 128,66-81 14 Harvey, P.H. and Rails, K. (1985) in Evolution: Essays in Honour of John MaynardSmith (Greenwood, P.J., Harvey, P.H. and Slatkin, M., eds), pp.

155-171, Cambridge University Press 15 Grant, P.R. (1975) Evol. Biol. 8, 237-337 16 Schoener, T.W. (1984) in Ecological Communities: Conceptual Issues and the Evidence (Strong, D.R., Simberloff, D., Abele, L.G. and Thistle, A.B., eds), pp. 254-281, Princeton University Press 17 McMahon, T.A. and Bonner, J.T. (1983) On Size and Life, Scientific American Library

DARWIN DAWRIN DAWRINS DAWKINS

The Blind Watchmaker

by Richard Dawkins, Longman, 7986. f72.95, hbk (xiii + 332 pages) ISBN 0 582 44694 5

There are all sorts of people on the fringe of evolutionary studies, from molecular biologists to philos- ophers, who are ever ready to show you that natural selection is inad- equate or misconceived or (a popu- lar cry) ‘tautological’. And right within the citadel itself, in recent years, there has been a vociferous group of evolutionists who would replace (much) selection with jumps or ‘saltations’, arguing that the Dar- winian emphasis on adaptation is a throw-back to prescientific, theo- logical times. It is these nay-sayers, particularly the professional ones, that Richard Dawkins takes on in The Blind Watchmaker.

Dawkins is preeminently suited for this task. Love it or hate it (and a good many hate it), can you ever again think of natural selection in the same way since you first heard the metaphor ‘selfish gene’? In The Blind Watchmaker, Richard Dawkins looks at the broader questions and suc- ceeds quite brilliantly. In his own words: ‘You can explain something so that your reader understands the words; and you can explain something so that the reader feels it in the marrow of his bones’. It is the marrow that Dawkins works on.

How is this done? By bringing the metaphors and paradigms and machines of the 20th century to bear on the problems and concepts and suggestions of the 19th century. On Dawkins’ own admission, some of his chapters are more profound, and less tied contingently to the ideas of his fellow scientists, than others, Let me therefore concentrate on what I believe to be his deepest analysis: ‘Accumulating Small Change’.

What worries everybody about Darwinism is the randomness. How can it be that small, quite undirected, chance jumps in one direction or another add, cumulatively, to the in- tricately functioning organisms we see around us today and of which we ourselves are a wonderful exemplar? Creationists invoke God’s design. Non-Darwinians like Stephen Jay Gould refer to macromutations or saltations. Dawkins takes that quin- tessential invention and symbol of the late 20th century, the home computer, and shows just how it is, and why it is, that natural selection really can generate order out of randomness. The modern, the familiar, the now virtually commonplace is used to show and make comfortable the paradoxical, the threatening, the heretical. Just like Galileo did nearly 400 years ago for the ideas of Coper- nicus.

Consider the sceptics’ favourite anti-Darwinian intuition picture: a monkey attempting to type Shakespeare. The brute strikes away randomly at the keys. In theory, it could produce Ham/et, and all of the other plays. In reality, we know that it never will. Surely, evolution through natural selection is akin to the typing monkey? In theory, selection could produce Ham/et. In reality, we know that it never will. Enter Dawkins with his computer. How easily can one produce, relying on a random creat- ing mechanism, the phrase:

METHINKS IT IS LIKE A WEASEL

Without help, given that the sen- tence has 28 characters (including spaces) one needs to hit upon the correct answer from a total of 2728 alternatives. Your chances are 1 in 10 000 million million million million million million! No wonder people are not Darwinians! But now pro- gramme the computer so that it ‘breeds’ from its first random try:

WOLMNLT DTJBRWIRZREZLMQCO P

It generates many variants on the original phrase, and chooses that

which is closest to the target. The similarity is not great. The second generation produces:

WDLTMNLT DTJESWlFi2REZLMQCO P

But things change (and improve) rapidly. By generation 30 we have:

METHINGS IT ISWLIKE B WECSEL

And after 43 generations we are there.

Nor is this a fluke. A second try took 64 generations. A third try only 41. The secret lies in the fact that the computer, like natural selection, can (in the famous words of Sir Karl Popper) ‘learn from its mistakes’. The point is that the computer does not have to go back to the beginning each time. Like organisms, it picks up from the point where it is, and goes on from there. A W rather than a T is small beer, but if you add them together in a cumulative way, Shakespeare emerges from disorder.

Dawkins goes on to do more wonderful things with his computer, showing how all sorts of animal- and plant-like shapes emerge from randomness. But let me pause and (for a change) pick up on a point where my intuitions differ from Dawkins’. As a Darwinian (especially as a Dar- winian) I want to deny progress. I believe that evolution is going no- where, rather slowly. Yet, I know only too well that the chain of being, from lesser to greater, from blob to organism, from microbe to man, dies hard. Even the most orthodox of evolutionists have hankerings this way. Look again at E. 0. Wilson’s Sociobiology: The New Synthesis. The wonder, a decade later, is not that he talked of humans. As a Dar- winian, he was bound to. What does astound is the incredibly progressive vision that Wilson has of nature. He talks explicitly of humankind as one of the ‘pinnacles’ of evolution.

Dawkins has yearnings for pro gress. In a fascinating chapter on ‘arms races’ and the coevolution of predators and prey he acknowledges explicitly that he sees meaningful

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Sizing up size ratios