Mathematics of Life (2011)

Chapter 3. Long List of Life

This is a short chapter about a long list.

Early biologists studied life on a human level, considering an animal or a plant as a whole. They might dissect one, to see how it was arranged inside, but mostly they investigated life’s diversity.

We all discover, as children, that a simple category like ‘butterfly’ fails to reflect the gaudy reality, with blue butterflies, red ones, brown ones, yellow ones, white ones, butterflies with spots, big butterflies, small butterflies, and so on. Even on a human scale, biology is huge. In order to grasp it, we have to cut it down into manageable chunks. It is too big and complicated for our villagelevel minds; we have to organise it. One way to handle the problem is to make a list. This was the second revolution.

The extraordinary diversity of life on Earth is a relatively recent discovery, made only after intrepid scientists acquired the courage and the means to explore the furthest reaches of our planet and bring back specimens of what they had found.

I recently acquired a facsimile copy of the first edition of Encyclopaedia Britannica, which dates to 1771. About two-thirds of the way through Volume I (there are three altogether) is an entry for ARK. This includes a discussion of how many creatures Noah’s Ark had to hold:

The dimensions of the ark, as given by Moses, are 300 cubits in length, 50 in breadth, and 30 in height, which some have thought too scanty, considering the number of things it was to contain; and hence an argument has been drawn against the authority of the relation. To solve this difficulty many of the ancient fathers, and their modern critics, have been put to very miserable shifts: But Buteo and Kircher have proved geometrically that, taking the common cubit of a foot and a half, the ark was abundantly sufficient for all the animals supposed to be lodged in it. Snellius computes the ark to have been above half an acre in area, and ... Dr Arbuthnot computes it to have been 81062 tuns.

The things contained in it were, besides eight persons of Noah’s family, one pair of every species of unclean animals, and seven pair of every species of clean animals, with provisions for them all during the whole year. The former appears, at first view, almost infinite; but if we come to a calculation, the number of species of animals will be found to be much less than is generally imagined, not amounting to an hundred species of quadrupeds, nor two hundred of birds; out of which, in this case, are excepted such animals as can live in the water. Zoologists usually reckon but an hundred and seventy-two of the quadruped kind needed a place in the ark.

The article goes on to provide details of what sort of food would be needed for various animals, especially domestic ones, and to suggest a possible layout for the animal stalls and storage areas. It offers a startling insight into the thought processes of the period, and it makes some kind of sense given what was then known about the diversity of the species that live on our planet. But, without wishing to offend any sensibilities, the calculations were over-optimistic.

The Book of Genesis tells us that the Ark contained every species on the planet, though there is some ambiguity about creatures that live in water. However, an influx of enough fresh water to submerge the highest mountains would make the sea far less salty, hence unsuitable for sea creatures; conversely the extra salt in previously fresh water would kill off all the fresh water creatures. So everything would have to have gone into the Ark.

We now know that there are millions of species, not just a few hundred. Each would need its own special habitat, and food – which would often be other species. Even a common lion would need a five-month supply of gazelles. Then there’s the leopard, the cheetah, the tiger, the jaguar, the serval, the lynx, the snow leopard, the fishing cat . . . a total of 41 known species, and that’s just cats.

I’m not trying to poke fun at the Noah tale, which is a charming moral fable derived from an earlier Babylonian flood story found in the Epic of Gilgamesh. My point is that less than 250 years ago, even the wisest scholars greatly underestimated the diversity of life on Earth, and let their personal beliefs blind them to the diversity in their own back garden, where a virtually endless parade of butterflies, moths and beetles – especially beetles – passed before their eyes every day.

Some thinkers, however, were ahead of their time, and aware of the enormous diversity of nature. It was so diverse, in fact, that someone had to bring order to it if humans were ever to be able to understand it.

The first systematic approach to the classification of living organisms was the brainchild of a Swedish botanist, zoologist and doctor: Carl Linnaeus. To him we owe the standard system for naming organisms in terms of species, genus and more extensive groupings, using Latin (or Latinised) terms, a programme that he first put into practice in the 1740s – thirty years before that first edition of Britannica. In fact, the encyclopaedia has an extensive discussion of Linnaeus’s classification of plants under BOTANY, and a shorter one for animals under NATURAL HISTORY. Linnaeus initially intended to include minerals, plants and animals in his classification, but it soon became clear that minerals were so different from living things that it was inappropriate to shoehorn them all into the same grand scheme. However, plants and animals are both forms of life, and although they have major differences they also have more in common than a quick glance might suggest. Many of the details of Linnaeus’s scheme have changed considerably over the years, but the basic organisational principles remain the same.

The history of Linnaean classification, and the many changes that have occurred, is fascinating, but what matters for us is where it led. Today’s taxonomists – biologists whose speciality is the classification of living organisms into species and related groupings – organise the living kingdom into an eight-tier hierarchy:

• life splits into three domains;

• each domain splits into kingdoms;

• each kingdom splits into phyla (plural of phylum);

• each phylum splits into classes;

• each class splits into orders;

• each order splits into families;

• each family splits into genera (plural of genus);

• each genus splits into species.

There are further divisions into subspecies and so on, but these are the eight main taxonomic ranks.

Looking at this list from the bottom up, species represent the different animals, birds, fish, plants, and so on. To a great extent they agree with our gut instinct that, say, all blue tits are basically the same type of bird, but thrushes are different. A few years ago some taxonomists compared the names used by natives of New Guinea for various birds to the names in the Linnaean classification, and both made exactly the same distinctions. The next level up, the genus, similarly corresponds to the view that blue tits and great tits and coal tits and so on are all variations on the theme of ‘tit’, whereas song thrushes and mistle thrushes are variations on the theme of ‘thrush’, but blue tits aren’t. However, the genus on the whole makes finer distinctions than that: ducks, for example, fall into more than one genus. Families often reflect our instinctive opinions more closely.

More precisely, the blue tit is classified as in Table 1 (see over). This complete classification places the blue tit in a very specific relation to all other organisms – for example, the frog is also a chordate but not a bird, whereas the dandelion is a eukaryote but not an animal. (Eukaryotes have cells with nuclei; chordates develop a notochord, a precursor of the spinal column, as an embryo.) However, the full list is a bit of a mouthful, and for most purposes the final two groups suffice, the famous binomial (double-barrelled) classification, in which the blue tit is Cyanistes caeruleus, written like that in italics, with a capital letter for the genus but not for the species.¹ After the first mention the genus is usually abbreviated: C. caeruleus.

Table 1 Classification of the blue tit.

Classification, however, is just the start of the complexity of biology – it is mere ‘butterfly collecting’ (which for lepidopterists it literally is). There is more to biology than just listing creatures and giving them fancy names. And the complexity of life is not just a matter of the quantity of different life forms, gigantic though that number is. Each individual organism, even the simplest, has enormous internal complexity. And when it comes to organisms interacting with each other in ‘the environment’ ... well, the magnitude of the task becomes almost overwhelming.

Nevertheless, classification is a sensible first step: it pins down the area of discourse and provides a basis for deeper comparisons and the search for general patterns. Many sciences could not have arisen without an initial stage of ‘butterfly collecting’; a clear example is crystallography.

Taxonomists have so far listed just over one and a half million distinct species. They range in size from viruses to blue whales; they live in virtually every region of the planet, from boiling-hot vents in the ocean floor to clouds high in the stratosphere; they can be found in equatorial rainforests, deserts, rivers, lakes, seas, caves . . . even miles underground in minute cracks in the rocks. About the only place where life has not yet turned up is in the molten magma of volcanoes – and given all the unlikely places where life has been found, in flat contradiction to what most scientists had previously thought was possible, it wouldn’t be too surprising to find some exotic life form there as well. It would have to be a kind of life never before detected on Earth, and I doubt that anyone would lose their shirt betting against it.

Taxonomists currently recognise about 300,000 species of plants, 30,000 fungi and other non-animals, and 1.25 million animals. Of these animals, 1.2 million are invertebrates – creatures lacking a backbone, such as snails and shrimps, of which some 400,000 are beetles. The geneticist and evolutionary biologist J.B.S. Haldane, asked by a lady what his studies had taught him about God, allegedly replied, ‘That he has an inordinate fondness for beetles, madam.’ Vertebrates account for a mere 60,000 species: 30,000 fish, 6,000 amphibians, 800 reptiles, 10,000 birds and 5,000-plus mammals. Among the mammals, about 630 species are primates, the order of animals that includes monkeys, lemurs, apes ... and humans. In the last decade, 53 new species of primates have been discovered: 40 in Madagascar, two in Africa, three in Asia, and eight in Central and South America. Such discoveries are surprising in a world so thoroughly explored, but living creatures can be very elusive: they’ve evolved to be.

Out of all this enormous number of species, just one has developed reading, writing, religion, science, technology and language: Homo sapiens, human beings. Rudiments of most human attributes can be found in other creatures, and many of the more intelligent animals – such as chimpanzees and dolphins – are much smarter than we used to think even a few years ago. For that matter, so are crows.

How many species are there altogether? Estimates range from 2 million to 100 million, though a figure of 5 to 10 million is probable. A recent article plumped for 5.5 million, suggesting that previous estimates may have exaggerated the level of diversity.

Species are becoming extinct faster than they can be discovered. It is not entirely clear how we should define ‘species’; in fact, it is not entirely clear that ‘species’ is a biologically meaningful concept at all. In my schooldays I was taught that there were two species of elephant, African and Indian. Today zoologists recognise five. In ten years’ time . . . who knows?

Linnaeus’s classification scheme has brought a degree of order into the apparently chaotic world of life on Earth today. As an unexpected bonus, its hierarchical structure also hints at the evolutionary ancestry of today’s organisms.

Nothing, however, is sacred in science, and a vocal minority of taxonomists feel that the world of living creatures is not as neat and tidy as Linnaeus’s artificial scheme suggests. More than a dozen alternatives have been proposed, in which Homo sapiens becomes Homo-sapiens, homo.sapiens, homosapiens, sapiens1, sapiens0127654, and so on. The advantages claimed for such systems are that they reflect the complex reality of life, instead of shoehorning it into rigid, tidy categories.

Although these criticisms have some validity, Linnaeus’s scheme – in its modern form – is convenient for the human mind, and has been in use for so long now that changing it would be extremely inconvenient. The widespread resistance to new, allegedly more rational systems is not just scientific conservatism: it is based on the realisation of how much effort would be needed to make the change. Many of the new schemes have flaws of their own, in any case. But in the long run, a scheme invented in the eighteenth century, when evolution, DNA and modern classification techniques did not exist, may well turn out not to be appropriate for the twenty-first century.

Linnaeus’s ideas made zoologists and botanists think more carefully about characters: the features that distinguish one species from another. Which characters are best suited for classifying organisms? Tigers and zebras are both striped, but that doesn’t imply that they are closely related. In fact, tigers and zebras do not belong to the same genus, to the same family or even to the same order. Tigers are in the order Carnivora (carnivores), but zebras are in the order Perissodactyla (odd-toed hoofed animals). The two species come together only on the level of their class: both are mammals. So characters that strike the eye, like the tiger’s stripes, are often less significant than subtler ones, such as how many toes the creature possesses.

The more widely a feature is shared, the higher the level of the corresponding taxonomic rank is likely to be, in the sense that classes are higher than orders and orders are higher than families. Higher ranks are more comprehensive. Many different animals produce milk and suckle their young. This is a key feature of all mammals, and because it is so widespread it takes precedence over more superficial characters such as coloration and markings. So what matters most about a tiger is that it is an animal, not a plant (kingdom); among animals it is a chordate (phylum); among chordates it is a mammal (class); then it is a carnivore (order), then a cat (family), then a big cat (genus). Only then, at the species level, do its iconic stripes enter the picture. Correspondingly, what matters most about a zebra is that it, too, is a mammal, but instead of being a carnivore it has hooves with an odd number of toes (order), is horse-like (family) and is very horse-like (genus). Stripes are shared by three distinct zebra species, and further characters are required to separate them.

Taxonomists quickly learned that the most important features for classification were seldom those that immediately attracted the attention of a human observer. Apparently minor features were particularly significant in flowering plants: a gigantic tree and a diminutive weed might be closely related, but two huge trees in the same forest might be totally different. What mattered most was often the tiny details of the reproductive organs of the plant – pistils, stamens, sepals and petals.

Initially, in his Systema Sexuale, Linnaeus grouped flowering plants according to how many of these various organs it had. He named the classes of plants Monandria, Diandria, Triandria, Tetrandria, and so on. He mainly did this for convenience: it was easy to count how many stamens or petals a flower had, and that made the system useful for identification. This classification was still popular in the mid-nineteenth century, for that purpose, but by then taxonomists had replaced it by a scheme that reflected the relationships among plants more faithfully. However, reproduction is a fundamental feature of plants, so the structure and number of reproductive organs are still important in the classification of plants.

Counting plant organs gave rise to one of the first extensive applications of mathematics to a problem in biology: striking patterns of numbers and shapes observed in the leaves and flowers of plants. The next chapter outlines the story, first using the kind of mathematics that was available in the nineteenth century and the early twentieth, then moving ahead to the modern era to see how the viewpoint has changed as new biological discoveries have motivated new questions for mathematicians to answer.