ONE of the ironies of Charles Darwin’s On The Origin of Species is that while it provides ample evidence that new species evolve from existing ones, it doesn’t tell us much about how it happens. It is easy to see that natural selection can cause a species to change as time passes, but it is much less clear why a single species should split into two distinct branches of the evolutionary tree. If some external change makes certain members of a population more able to survive than others, then surely that change will make the whole species evolve in that direction. How could two separate species emerge from one?
Speciation is a complex business, taking place over vastly different scales of size and time. There is no reason to suppose that it is governed by just one force – after all, we know that genetic mutations and sexual recombination of existing genes vie with environmental influences, depletion of resources, parasites, migration and disease. But although many theories and ideas have been offered up to account for speciation, it remains one of the big puzzles in biology.
Within the flurry of activity that surrounds this conundrum there are two very noticeable trends. One is a shift of focus away from theories in which species formation occurs as the direct result of major environmental and geographic differences. The new focus is on situations where speciation takes place without any dramatic changes, in a single interbreeding population of very similar creatures, all in much the same environment. Nearly all publications on speciation in Nature and Science over the past five years or so focus on this undramatic scenario – a complete reversal of what used to be the case.
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The other trend is the growing use of mathematical models, a technique more usually employed to explore aspects of physics. These models are being used by myself and others to describe the natural dynamics of speciation. And when applied to the “undramatic” instances of speciation, they have produced some very interesting results.
The maths indicates that far from being a surprising phenomenon, it would be very odd if speciation didn’t occur. It appears to be a result of exactly the same process that filled the universe with matter, creating subatomic particles, planets, sand dunes and – ultimately – humans. Strange as it may seem, neutrons, narwhals, electrons and elephants in some way seem to owe their diverse characteristics to a principle that dictates much of what happens in the physical world.
That principle is known to physicists and mathematicians as “symmetry-breaking”. An example is the formation of sand dunes. Reducing it to its mathematical ideal, a uniform wind blowing across a uniform desert will produce parallel ridges of sand. The featureless desert had all the symmetries of a flat plane: rotate it through any angle and it will look the same. The wind, however, reduces the level of symmetry: the parallel ridges of the dunes introduce a definite direction, or orientation, into the landscape.
Such symmetry-breaking happens naturally all over the place. For example, if you heat a flat dish of fluid uniformly from below, at a certain critical temperature the uniformity is broken by the onset of a complex pattern of convection cells. They are typically hexagonal, with a few pentagons thrown in, and all much the same size. As with the formation of sand dunes, the symmetry breaks down, in this case reducing to the symmetries of a roughly hexagonal lattice.
Filling the universe
On a far grander scale, physicists believe a type of symmetry-breaking was responsible for the formation of subatomic particles from the fields that filled the primordial universe. These particles are, of course, the building blocks of matter, so you could argue that symmetry-breaking helped create pretty much everything that exists.
But what does symmetry-breaking have to do with speciation? Although the commonest definition of “same species” in sexual populations has been “able to interbreed”, biologists have been seeking an alternative definition for some time, because there are too many cases in which this one just doesn’t fit. In a paper published in BioEssays this year (vol 25, p 596), Massimo Pigliucci of the University of Tennessee in Knoxville analysed nine well-known definitions of “species”, and found serious problems with them all.
So instead of chasing a formal definition of species, biologists are going back to the more intuitive idea that organisms belong to the same species if they are effectively indistinguishable. The degree of similarity can be quantified by listing anatomical or behavioural features and observing how closely they match. And this is where symmetry comes in.
The symmetry of an object or system is simply a transformation that preserves its structure. With speciation, the transformations are not rotations or flips, as with the symmetries of a sphere or a hexagon, but permutations – shufflings of the labels employed in the model to identify the individual organisms.
A group of 10 identical objects possesses a symmetry: line them up and turn your back for a moment, and you wouldn’t know if any or all of them switched position in the line. But if the line were composed of five objects that had one shape followed by five that had another, some of the symmetry is broken: swapping numbers 5 and 6 around, for instance, would produce an obvious change (see Graphic).
From this point of view, the definition of a species is simply that it is symmetric, and speciation is then just a form of symmetry-breaking. With this definition in place, mathematicians and physicists can apply their existing theory of symmetry-breaking. This describes how, why and when a given group of symmetries will typically break up into subgroups – species, in this case.
Biologists traditionally recognise two distinct types of speciation. The first is “allopatric” (“different family”) speciation, in which some major geographical change splits a population in two. Once separated, the two groups evolve independently, eventually changing so much that they become two distinct species. Even if reunited, they remain distinct species.
The second is “sympatric”, or same-family speciation, in which new species emerge without separation. You might think that mating between neighbouring animals would encourage “gene flow” – the mixing of “alleles” or gene alternatives that occurs when individuals mate – and would tend to keep the gene pool homogeneous. Classically, this was interpreted as keeping it a single species. But it seems this isn’t always the case. Examples include the recent discovery that there are two species of African elephant, and the 13 species of finch on the Galapagos Islands, which helped set Darwin on the road to what he called “the mutability of species”.
Until around the mid-1990s, allopatric speciation was thought to be by far the most common, but biologists now seem to have begun shifting their view: sympatric speciation, though subtle and counter-intuitive, may be the more important mechanism. The homogenising gene flow within a species can be disrupted by many things: geography is just the most obvious. And that’s exactly what the mathematical analysis of speciation seems to be suggesting.
The mathematical picture of speciation highlights at least three “universal” phenomena – rules, almost. The first is that when a population first speciates, it usually splits into precisely two distinguishable types. To see three or more new species is a rare, mainly transitory phenomenon. The second is that the split occurs very rapidly in the population – much faster than the usual rate of noticeable changes in characteristics, or phenotype. So, for example, a significant change in beak length might happen within a few generations, rather than by tiny increments over many generations. The third phenomenon is that the two new species will evolve in opposite directions: if one evolves larger beaks, the other will evolve smaller ones.
So what causes that initial split? Our knowledge of symmetry-breaking in physics suggests that a key step is the onset of some kind of instability in the population. An example in physics would be a stick being bent by stronger and stronger forces: something suddenly gives way and the stick snaps in two. Why? Because the two-part state is stable, whereas one over-stressed stick is not. The loss of symmetry is rapid – and irreversible.
The symmetry-breaking models for speciation do indeed indicate that instability can be a trigger. To be precise about it, a species is called “stable” if small changes in form or behaviour tend to be damped out in subsequent generations. It is unstable if they grow out of control as new generations shuffle the genes of their parents and natural selection discards combinations that don’t work so well.
Speciation models show that if you subject a population to subtle, gradual changes in environmental or population pressures, it can suddenly cross a threshold from stable to unstable. At that point, all hell breaks loose. As the environment or population size changes, the single-species state may cease to be stable, so that if by chance a few birds diverge from the average phenotype, the divergence grows instead of damping down. The result is that small, random disturbances can lead to big changes (see Graphic).
Thanks to tiny, random variations that occur naturally – in, say, the beak sizes of a population of finches – anything that changes the characteristics of the food supply even slightly can bestow an advantage on birds with slightly above or below average beak size. The mathematical analysis shows that once the balance swings in favour of avoiding the middle ground, there is a collective pressure that rapidly drives the birds into two distinct types that don’t compete directly for food. Instead, they avoid competition by exploiting distinct niches. This demolishes the argument that the whole population ought to evolve in the same direction, and it opens the door to species divergence in a uniform, interbreeding population.
Either of these clumps may split again later, as continuing changes to the environment change the availability of resources. Such a sequence of sympatric splittings is probably how the original single finch species on the Galapagos Islands became 13 (or 14, counting one further species on the Cocos Islands).
The model I have talked about is highly simplified: all creatures in the given species are identical. But researchers are working to remove this crude approximation. One approach is simply to add “random noise” to the equations, so that the phenotype (body-plan and behaviour) passes from generation to generation as per the original rules, but plus or minus small random variations. In this scenario, a population corresponds to a cluster of organisms in phenotypic “space” – an abstract space whose “coordinates” might be beak size, wing span, and so on – rather than a single point. Interestingly, we have found that the clumps split up in much the same way that the original points divided, but the noise makes speciation happen a little more easily.
An even more intriguing approach is to use the original noise-free equations but to modify them so that at each generation the creatures mate according to a set of randomly chosen pairings. In this scenario, all variation is caused by mating. Again, what we see is clusters, not single points, but these clumps are tighter than in the random noise model, since the homogenising gene flow pulls the population closer together, just as Harvard zoologist Ernst Mayr has argued it should.
Birds of a feather
But contrary to what Mayr thought, divergent splits can still occur, and when they do a tight clump diverges into two much looser ones. After that, even though the creatures can choose mates from the other group, the clusters tighten up and remain separate from each other. This behaviour is not fully understood even mathematically (though curiously it appears to be related to fractal geometry), but it seems very close to what happens in real populations. All the same, we can see that sympatric speciation is not as surprising as we first thought.
This kind of modelling is still in its infancy. Its main achievement so far is to show that sympatric speciation is entirely reasonable and natural, and to focus attention on the role of instability as a mechanism for speciation. Species become unstable when small but critical changes to their common environment – what food is available, for example – make new gene combinations superior to the existing ones. This alone can cause the phenotypes to rapidly diverge, and contrary to what many textbooks say, it doesn’t require mutations within the DNA code. The population just shuffles its existing genes into new arrangements.
Work is already under way to make the models more biologically realistic in order to give a deeper understanding of the nature of these instabilities. My University of Warwick colleague, mathematician Toby Elmhirst, has modelled finch speciation, for instance. His research follows work done in 1999 by Ulf Dieckmann of the International Institute for Applied Systems Analysis in Laxenburg, Austria, and Michael Doebeli of the University of Basel. The approach may tell us about the effect of non-uniform habitat – allopatry as well as sympatry, or subtle mixtures like patchy environments – and it can model sexual and asexual reproduction. The result may yield new insights into how evolution has occurred in the past by placing more emphasis on the links between phenotype and habitat.
Another major objective is to incorporate genetics explicitly. At the moment, its role is implicit: it simply lets the phenotype change. It would be a huge achievement to establish the link between the detailed genetic changes and the phenotypic ones. Such breakthroughs may come from work being carried out by other groups, such as those of Eva Kisdi and Stefan Geritz of the University of Turku in Finland. Their method, known as “adaptive dynamics”, follows the same general line of thought as ours, but uses markedly different models. It focuses on the genes in very much the same way we focus on phenotype, and their results give insights into the forces behind allopatric speciation (Evolution, vol 53, p 993). The two approaches seem very complementary, and I hope (and expect) that they will join forces as the subject unfolds.
In the meantime, we can at least say that the symmetry-breaking approach puts the whole problem in a new light. Species diverge because of an unmanageable loss of stability. The actual sequence of events – which gene does what, and in what order – determines the precise response to this loss of stability, but it depends on a bewildering variety of accidental factors, such as which birds get the bigger beaks and which get the smaller ones. Broadly speaking, such details are less important than the overall context. They may appear to be the causes of speciation, but actually they are just the effects of a far-reaching instability. An over-stressed stick must break. An over-stressed group of birds must either speciate or die. Speciation is not surprising – it is simply how the world works.
- “Self-organisation in evolution: a mathematical perspective” by Ian Stewart, Philosophical Transactions of the Royal Society A, vol 361, p 1101 (2003)
- “Symmetry-breaking as an origin of species” by Ian Stewart, Toby Elmhirst and Jack Cohen, in Trends in Mathematics: Bifurcations, symmetry and patterns (Birkhauser Verlag)