Modelling speciation: Problems and implications

3.1How do new species originate?

Darwin’s answer to this question was that new species form from a succession of natural variants that breed better (or are fitter) than their parents in a particular environment. Eventually, the changes are sufficient that a new species forms that is unable to breed with its parent species and may well supersede it through natural selection. Evidence to support this answer comes from what are known as ring species. These form when a migrating population meets an inhospitable domain and therefore divides, with some going left and others right, each group undergoing variation over time. In a few cases, the groups eventually meet up forming a ring of distinct variants. An important observation on these is that, while any left- or right-migrating population can successfully mate with its immediate neighbours and so are just subspecies, the terminal left and right populations may not interbreed and thus have to be seen as distinct species. There are several examples of ring species that include the greenish warbler family of birds that surround the Himalayas (Fig. 1), the herring gulls around the Arctic and the Euphorbia plants around the Caribbean (for references, see [10]) and the Wikipedia entry on Ring Species).

Fig. 1

Ring species. The greenish warblers (Phylloscopus trochiloides) were originally present in the region south of the Himalayas. They slowly spread east and west forming a series of distinct species, eventually meeting up in Siberia to form a ring. All neighbouring species will interbreed except for those on either side of the meeting point. This seems to be because theirs songs are too different for the two species to recognise one another [6]. (Main image: Courtesy of G. Ambrus. Inserts: phylloscopus trochiloides: Courtesy of P. Jaganathan. P. t. plumbeitarsus: courtesy of Ayuwat Jearwattanakanok. P. t. viridanus: Courtesy of Dibenu Ash. (Other images published under a CC Attribution -Share Alike 3.0 unported License.)

Although Darwin’s view of speciation is basically correct, it is very thin and says nothing about either how variants arise or how they are propagated within a population under selection. At around the end of the 19th century, the rediscovery of Mendel’s 1866 paper [11], with its basic laws of genetics and the idea that genes underpinned phenotypes, stimulated mathematicians to work through the ways in which these laws could be applied to populations that were evolving. Around 1907, Hardy and Weinberg independently showed that, in the absence of selection or migration, gene frequencies would not change over the generations. A decade later, Fisher had produced a substantial mathematical model of evolutionary population genetics that showed how change could happen in diploid organisms that reproduced sexually. This theory covered selection, the spread of novel alleles and how the effects of several alleles in a gene could explain continuous variation in a phenotypic trait such as height [12]. It was a remarkable and brilliant piece of work.

Over the next few decades, this model was expanded to explain much of how genes spread through populations under selection and other factors such as genetic drift (effects of random gene distributions in small populations –see below). The integration of population genetics and Darwinian selection gave what came to be called the modern evolutionary synthesis [see [13] for a summary of its various components). Its most robust achievement has been to show quantitatively how mutations move through populations and how the details of this movement depend on population size, selection (natural, sexual and kin), immigration and other such factors.

All this remarkable work was of course done in the absence of any knowledge of what a gene was or how it worked, although it was clear that mutations were the basic cause of variation. It also said very little about how speciation was achieved. Enough was however known to pose the two key problems in a far richer context than had previously been possible. The first was how mutations led to changes in the phenotype; the second was how successful variants led to new species. These problems are still not fully answered for the great majority of species, even in the light of contemporary knowledge of molecular and developmental biology. Nevertheless, the quantitative theory still provides a framework for thinking about evolutionary change and is an important component of coalescent analysis, which uses sets of DNA sequences and a model of population breeding behaviour to produce numerical details of ancient populations [14].

There are however weaknesses in the mathematical model of evolutionary genetics. First, its emphasis is inevitably on the short-term movement of genes under a constant set of criteria from one equilibrium position to another –it cannot model longer-term events into the future unless conditions remain unaltered over very long periods. Second, its view of the relationship between genotype and phenotype was, and remains, naïve: it assumes that this is direct in that one or at most a few genes that may interact (i.e., show epistasis) are responsible for a particular phenotype and that alleles of those genes underpin alternative phenotypes. This is sometimes true, as Mendel showed for peas, but such Mendelian genes are relatively rare, other than in the case of mutants that lead to genetic disease, and these are unlikely candidates for driving evolutionary change. Modern molecular genetics has shown that most aspects of an organism’s phenotype are underpinned by sets of genes whose proteins cooperate within networks (see below). If the speed of horses was the result of Mendelian genes, racehorse-breeding would be far more reliable than it is! Third, the model requires numerical parameters for its equations, and these can be hard to measure.

3.2The modern view of speciation

Originally, evolutionary population geneticists assumed that, if enough novel and favourable mutations accumulated within a population, a new species would form from the original one. It soon became clear, however, that selection would have to be very strong if a novel mutation was not to be lost in a growing population. During the 1950 s and ‘60 s, a group of geneticists, key members of which were Ernst Mayr and Motoo Kimura, showed that this effect could be overcome in small populations. One reason for this is because genetic drift, which reflects random assortment of gene distributions during breeding, becomes disproportionately important as population numbers decrease ([15] and see below).

When a small population becomes isolated from its parent population, it has a pangenome (the complete set of genes and allelic variants in a population) that is a random, asymmetric subset of the parent profile. Such a small, isolated population that finds itself in a novel environment will frequently die out because it is unfit for the new selection pressures that it encounters. If, however, a subgroup within the small population has an allele distribution that allows it to survive, it will become a new founder population (Fig. 2). In this case, differences between this and the original population will increase more rapidly than might be expected for a series of reasons that are detailed in Box 1. It is also worth noting that, as normal mutation rates are very slow, most new variants derive from novel mixes of existing mutations rather than the formation of new ones (see below).

Fig. 2

The process by which a new species eventually when a small founder population breaks away from a parent population (From [1], with permission).

In an environment with selection pressures different from those of the parent environment, new phenotypic characteristics will slowly appear over time in the descendants of the founder population, mainly as a result of the original asymmetric allele distribution, genetic drift and new mutations; the phenotype distribution of the population will consequently change. As these effects are occurring, larger chromosomal changes will also slowly take place so that the new and the parent organisms would, were they to meet, become increasingly less likely over time to produce fertile offspring. Eventually, all such hybrids would fail, and the two populations will have become different species. The example of mules shows how slow this process is: the very occasional mule is still fertile even though the horse and donkey lines separated some 2 million years ago (Mya), a figure that represents about a million generations [16–18].

While this view of speciation has had major experimental and theoretical successes, it is worth pointing out that some in the field have felt for some time that its broad-brush approach lacks several important features that facilitate novel speciation. They have therefore put forward the Extended evolutionary synthesis that contains mechanisms beyond routine mutation and selection that are not explicitly included in the standard synthesis [19]. These include transgenerational epigenetic inheritance and developmental plasticity to extend the repertoire of novel trait formation and multilevel selection, niche construction and punctuated equilibrium all of which have the general ability to speed up the speciation process. The importance of these factors is obvious and many feel that they are implicitly included in the Modern Synthesis; they are not however considered here partly because their individual contributions to novel speciation are unclear and partly because they cannot yet be quantified.

5.1Normal development

Particular difficulties arise when one considers how the effects of mutation within an organism’s genome work their way upwards to modify its phenotype. This is most obviously seen during embryogenesis as almost all anatomical and physiological changes seen as an adult organism slowly changes have their origins during development (albeit that the effects of developmental plasticity can lead to changes organisms as a result of post-embryonic change [30]). The core problems in understanding the molecular basis of such evolutionary change are that we still have very few details about how normal tissues form and that it is generally impossible on the basis of embryonic anatomy to identify a beneficial change that will eventually improve the fitness of an adult.

The basic principles of the development of complex organisms, whether animals or plants, are relatively straightforward [24, 30]. The fertilized egg divides and is then patterned by intrinsic lineage constraints and by a range of mainly short-range signalling interactions. Both may lead to a tissue changing its state, with the latter set of interactions also being able to generate a graded response. Cells generally respond to such instructions by activating protein networks (Fig. 4a) each of whose output is a process that leads to a change in phenotype [31]: they may undergo proliferation (mitosis), they can change their state (differentiation) and they can reorganise themselves through movement, shape change and tissue reorganisation (morphogenesis, Fig. 4b); they can also occasionally undergo programmed cell death (apoptosis). We know a fair amount about some of the signalling interactions and pathways used in the development of the main model organisms (e.g., mouse, Drosophila, C. elegans, zebrafish and Arabidopsis –see the ProteinLounge and KEGG websites) but much less about the process networks. Even where we know their protein constituents, it is hard to see how such networks operate because they are so complex, as Fig. 4 demonstrates.

Fig. 4

Protein networks that play important roles in animal development. a: The Epidermal growth factor (EGF) signalling pathway that often activates cell proliferation but has other roles. b: the Rho-GTPase network that directs morphogenesis through modulating cytoskeletal activity. The reasons why they should be so complicated are not known. (Courtesy of ProteinLounge, with permission).

In the context of evolutionary change, these networks fall into two categories. Changes that eventually lead to novel speciation are particularly driven by changes in tissue patterning, but also in differentiation, morphogenesis and apoptosis –these tend to operate relatively early in development [24]. Changes that lead to variants are primarily due to mutations that modify size and pigmentation –these generally occur in the later stages of development. The human species is a model system here: all human faces are patterned to have the same set of features and the differences across populations and individuals involve modifications in the local growth and in pigmentation networks.

Least understood and most important of these developmental networks are the signalling mechanism that pattern first the early embryo (e.g. the anterior-posterior body axis) and then its constituent tissues such as the vertebrate limbs [24]. More is known about several of the signal-response and process networks. Fig. 4a shows the EGF signalling network that activates mitosis. The input is the presence of a small protein, epidermal growth factor that binds to its receptor; the output is the activation of transcription factors that in turn initiate activity in the mitotic pathway. We have little idea why the EGF network needs to be so complicated although progress is being made on how this network operates [e.g. 32]. The situation is similar in the rho-GTPase network (Fig. 4b) which directs activity within the cytoskeleton and so mediates many of the morphogenetic events that underpin developmental anatomy [e.g. 33].

5.2The effects of mutation on protein networks

Understanding how mutations affect the phenotype of an organism first requires that we appreciate the details of the protein networks whose outputs drive its anatomical development, metabolism and physiological activity. Full analysis of these networks requires understanding the individual protein-protein interactions and the flow of smaller molecules within them. Only when we have a detailed grasp of these can we start to consider the possible effects of mutations that typically modify protein structure and hence their interactions with other proteins and with substrates, so modifying network outputs. This is a difficult but important area of work that is now attracting considerable attention from systems biologists [see [34–36] for reviews). What follows here is a summary of some of the key contemporary approaches and it is worth pointing out that much of the work in this important area is concerned with understanding mutations which lead to diseased states such as cancer rather than those that improve fitness [37].

In the context of novel speciation, we are primarily concerned with mutations that lead to anatomical modifications, and here it is worth pointing out that the options for a successful mutation in the protein networks that drive such change are limited [31]. Many, such as those for differentiation and apoptosis, have outputs that are essentially switches between states. Mutations in these networks are only likely to be successful if the resultant switching is selectable (e.g. [31, 38]). In such cases, the mutation as likely to affect network activation or inhibition as much as its internal dynamics. The developmental mutations most likely to be involved in future speciation are however those in networks involved in tissue patterning [24, 31]. Examples include the production of antero-posterior organisation (i.e. the Hox coding system), the production of a novel bone, changes in tooth morphology and the generation of a new pigment pattern in skin ectoderm.

Here, it is worth noting that developmental networks as a whole (e.g. Fig. 4a,b) seem surprisingly complicated for producing what can be seen as relatively straightforward outputs. One reason for this could be that have evolved to include a fair amount of buffering against the effects of mutation [39], and it may be for this reason that they are conserved to a considerable effect across the animal phyla [see the KEGG database [40]).

It is always possible, in principle at least, to describe networks as a graph of nodes and edges whose dynamics are given by a set of coupled differential equations. A first step in their analysis is to identify the key nodes and an obvious simplification is that all fast reactions will run at equilibrium, with the many slower reactions governing the overall dynamics of the system; however, such is this number that there is unlikely to be a key rate-limiting step. That said, such fast and slow reactions may be hard to identify, while mutations may well change the situation. Moreover, such can be the complexity of these networks that they may contain local domains that represent internal alternative routes through the network. It is currently extremely difficult to work out the full details of how these pathways work and harder still to estimate their dynamic properties. Although it is not yet possible to model in detail the full set of differential equations needed to model the complex protein network shown in Fig. 4a,b, considerable progress is being made, particularly in the study of signalling pathways [e.g. [41]).

The easiest protein networks to investigate and analyse are those that drive metabolism because many can be studied in vitro, as any textbook of biochemistry demonstrates. This is particularly so for the metabolic networks of bacteria such as E. coli since the ability to follow metabolite concentrations in mass cultures allows dynamic variables to be measured. It is much harder to study these networks in eukaryotic organisms, even in simple fungi such as Saccharomyces cerevisiae. This is partly because the quantitative data are much harder to obtain, and partly because it can be hard to identify local interactions within networks. Considerable effort is now being invested in analysing these networks [42–44]. Overton et al. [34] have provided a computational methodology for identifying transcription-factor targets through analysis of protein-interaction databases. Berkhout et al. [45] have developed techniques for analysing such data and shown how networks optimise fitness, while Paulson et al. [46] have considered how inferences may be made about parameter values. Of particular interest here are maximum entropy methods [47] which use statistical models to determine the most likely value of internal network parameters.

In the context of considering evolutionary change during development, a uniquely helpful system has been that of the 2D patterns generated by reaction-diffusion (Turing) kinetics, which essentially produce patterns of high concentration spots on a low concentration background ([48], for review, see [49]). For linear models, small changes in parameters, boundary conditions and timing (i.e. the sorts of changes that can be generated by mutation) can modulate spacing and pattern details (Fig. 5 [50, 51]), while nonlinear models can generate most of the patterns seen in vertebrates from fish to zebras [52, 53]. It has also been suggested that 3D Turing patterns can generate the architecture of complex bone systems such as those in limbs [54]. Although experimental evidence to support pattern formation based on reaction-diffusion kinetics has been hard to obtain, no other mechanism has yet been found capable of generating this range of modulatable patterns.

Fig. 5

The effect of timing on the initiation of zebra striping patterns. 1: Three zebra species. a: Equus quagga burchelli has ∼26 stripes. b; E. zebra as ∼50 stripes. c: E. grevyi has ∼75 stripes. (a: Courtesy of Gusjr; published under a CC Attribution generic 2.0 license. b: Courtesy of Yathin S. Krishnappa; published under a CC Attribution share-alike 4.0 international license. c: Courtesy of Thivier; published under a CC Attribution share-alike 3.0 unported license.) 2a,b c: 3, 3.5 and 5 week horse embryos on which have been drawn stripes of 200um separation such as can be generated by reaction-diffusion kinetics. ai and aii: the effect of normal embryonic growth on stripes laid down at 3 weeks at 3,5 and 5 weeks. (From [51] with permission from John Wiley and sons).

An alternative approach that has been successful in a few cases has been to simplify the situation and to use computational logic rather than differential equations to model networks. The network is formalised as a graph whose nodes are on/off or fast/slow switches and whose edges are Boolean operators [55, 56]. Once the network has been modelled in this way, it is computationally straightforward to test all possible Boolean states and see which produce the expected normal output and how mutation (changes in nodes and edges) affects the output.

There are at least two examples of this approach. The first is the analysis of the Fanconi-anaemia/breast-cancer pathway by Rodríguez et al. [57]. They modelled this as a Boolean network that included checkpoint proteins and DNA repair pathways. Using this model, they were first able to simulate normal behaviour and then to explore the role of repair pathways though simulating mutations. The second, and more important in an evolutionary and developmental context, is the sex determination network for gonad development (GSDN). This determines whether the early human gonad will become a testis (the SRY gene is expressed) or an ovary (the WNT4/β-catenin pathway is activated). Ríos et al. [58] modelled 19 of the key components in the GSDN network as Boolean nodes, each of which could be in an on or an off state, that interacted through the logical operators AND, OR and NOT. The model had 19 nodes and 78 regulatory operations, most of which derived from experimentation, and > 5 million possible initial states. Running all of these alternative showed that there were two major fixed-point attractors (stable states) that reflected male and female gonad development and a minor attractor that reflected a failure to differentiate. Added confidence could be had in this approach because the system could be modified to change node properties, so modelling known mutations. In such cases, the simulations gave the expected abnormal phenotypes.

On this basis, Boolean networks can clearly be used to model switches that direct options such as change state of differentiation or undergo mitosis/apoptosis. It is less clear that they can model the graded responses seen in patterning and morphogenesis or even mitotic rate, which can vary by a factor of five across a developing limb [59]. To approach such problems, more sophisticated approaches are needed. Groß et al. [60] have reviewed the ways in which this can be done and suggested that a particularly useful approach is to use probabilistic rules rather than differential equations to model the interactions between the proteins in a network and demonstrate its use for the Wnt signalling system. An alternative approach is to partition networks using Bond graphs which integrate network dynamics with energy flows [61].

Further insights into network kinetics may come from the analysis of complex medical disorders. Garg et al. [37], for example, explored how drugs altered their properties of the gene-regulatory networks where mutation leads to cancer. Of particular interest here is their analysis of the way in which mutation altered the balance between proliferation and apoptosis. More recently, Béal et al. [62] have devised ways in which models of melanomas and colorectal cancers can be expanded to include experimental data and be tuned to specific sets of mutants.

What this diversity of approaches makes clear is that theoretical progress is being made in this most difficult area of molecular genetics. There is however a long way to go before we can begin to understand the full range of anatomical changes that can occur in response to mutation.

6.1Founder populations

The first step in the formation of new species is the separation from its parent population of a small group with a random sub-pangenome (the complete set of genes and their alleles within a population) of the parent pangenome. This is not a rare event: for any population in a relatively well-defined area, small groups at the periphery are always trying to expand their territory [63, 64], as the example of ring species (Fig. 1) makes clear. Indeed, the dispersal of humans across the world reflects such events.

If this founder group finds itself in a novel environment, either some variants will survive and prosper under the new selection pressures [65, 66], or the whole founder group will die out. Genetic analysis shows that the former will have a disproportionately large number of phenotypic variants. First, there will be a loss of heterozygosity (the Wahlund effect) and, second, genetic drift plays an important role in producing populations that are genetically unbalanced offspring as compared to the parent population. A classic experiment demonstrates this: Rich et al. [67] studied 12 replicates of large (50 M + 50 F) and small (5M+5 F) populations of red flour beetles (Trastaneum castaneum), each of which initially had equal numbers of dominant reds and recessives blacks, with numbers maintained for each generation through random selection. Over time, all large populations increased the proportion of red phenotypes, eventually achieving the expected 3 : 1 ratio. In contrast, the genetics of the small populations was unpredictable to the extent that one ended up being completely black (Fig. 6), with the dominant red gene having been lost.

Fig. 6

The effect of genetic drift in 12 large (N = 100) and 12 small (N = 10) populations that originally had equal numbers of red flour beetles (Trastaneum castaneum) with the dominant b⁺ allele and black flour beetles with the recessive genes (b^–/b^–). There was much more variation in the smaller populations and no obvious convergence to the extent that, in one of the small populations, the dominant gene was lost and the whole population ended up black. (From [55], with permission from the Society for the study of evolution (John Wiley Press) and thanks to John Herron for the redrawn and coloured image.)

Genetic drift is important for another reason: because the small group has a diminished and asymmetric pangenome as compared with that of the large original population, unexpected gene combinations can occur with a much higher frequency than might be expected. The resultant phenotypic changes may have a strong selective value and so become established in the normal way. Alternatively, it may have no strong selective effect one way or another and the novel phenotype may become established by chance. A possible example here is variable lung morphology: humans have two lobes in the left and three in the right lung; mice have a single left lobe and four right lobes. There seems to be no obvious physiological explanation for this, and the differences are as likely to have arisen as a result of drift during their long period of separation as for any other reason.

Changes in the phenotypes within a founder group thus result from two very different forms of random process: its limited pangenome and the random effects of genetic drift. Together, these can lead to novel traits that will allow it group to survive and flourish. These events can in principle be modelled using stochastic methodologies provided that key aspects of the genetic or phenotypic data for a population are known [68]. This is however generally difficult, because we have no good molecular model for the genetic basis of the great majority of traits.

6.2Selection and the formation of subspecies

The formal theory of selection is part of evolutionary population genetics [12, 66]. Selection biases the results of random breeding and so affects allele distribution in future populations. It should be emphasised that selection operates only on phenotypic traits, with the key parameter for a particular trait in a particular environment being fitness. This is a measure of the reproductive success of an organism with a particular allele in producing fertile offspring. The fitness coefficient is known as w and the associated selection coefficient s is connected to w by the simple formula

Our practical understanding of fitness comes from experiments done under controlled conditions, mainly studying traits that breed true and that follow Mendelian laws. A classic and well-studied example is the relationship between malaria resistance and sickle-cell anaemia [69]. Analysis of population data shows that there are different traits associated with mutations in the β-globin protein: wild-type proteins afford an individual no protection from malaria, double mutations cause sickle-cell anaemia but protect against malaria; a single mutation substantially diminishes an individual’s chance of getting the disease but does not lead to anaemia. Such special cases where the theoretical modelling is straightforward are however rare and it can be difficult in practice to apply the theory of evolutionary population genetics for a range of reasons that include:

The complexity of fitness away from laboratory conditions means that formal modelling using the classical theory of evolutionary population genetics can only be done when selection primarily operates on one or at the most a few traits, provided that they can be seen as independent [73]. A further limitation is that such studies can generally only examine a change in allele distributions from one stable state to another when all other conditions (e.g. selection pressures) remain constant.

There is however an alternative approach to studying selection which is to simulate it using stochastic methods. This approach is known as evolutionary game theory and dates back to the 1973 work of Maynard Smith and Price [74]. In essence, a model is constructed that includes breeding behaviour associated with individuals that have a range of genetically defined traits, each of which has an associated fitness for the local environment. The model runs for a generation, and this results in a daughter population that will be slightly different from the parent one. This process is then repeated until an equilibrium population is reached, which will usually be one with a stable phenotype distribution [75]. Game theory provides a methodology for testing hypotheses and exploring the implications of possible breeding/trait/environment scenarios as well as demonstrating the process of change.

An oversimple but immediately accessible example of this approach is given by the Primer simulation of natural selection available on Youtube [72]: this models the competing implications of size, speed and food availability in a self-replicating population. It demonstrates that, even for this very simple case, not only are the implications unpredictable because of the trait interactions, but that the final stable state depends on the initial conditions. Complex systems turn out to have final states that are neither expected nor predictable.

Selection in the wild adds two further complications. First, we cannot assume that selection coefficients remain constant over the long periods of time required for novel speciation to occur, as both traits and the environment may change (one would expect more stability in aqueous than land environments). Second, these coefficients are generally impossible to determine with accuracy because the limited amounts of experimental data available have to be used both to calculate selection constants and to test their implications. Perhaps the best that one can do here is a series of simulations using different subsets of the data for constant calculation and for verification. This approach is of course similar to the jackknife resampling techniques once used to test the quality of molecular phylogenies [76].

In summary, one can use modelling to explore hypotheses about selection, but it is not generally possible to make predictions about it for reasons that go beyond the difficulty of obtaining data. These include the random genetic profile of founder populations, the lack of understanding of how such profiles result in a spectrum of traits and the lack of a good theory of selection for multiple and complex traits.

6.3Chromosomal changes and the formation of new species

Once separated and in different environments, parent and founder populations will become increasingly distinct to the extent that that they will eventually be recognised as anatomically different. A classic example here is the hundreds of anatomically distinct populations of cichlid fish in Lake Victoria that descended from an initial population of perhaps a few species that was probably present ∼300 ka [77]. Today, many of these species can still interbreed, albeit that hybrid fertility may be limited [78]. In general, however, relatively minor anatomical differences alone say little about whether two homologous populations are subspecies that can interbreed or are distinct species whose eggs, even if fertilised, are incapable of producing fertile adults. Successful breeding has both phenotypic and genetic aspects.

There are several bars to successful interbreeding between two related groups. The earliest to occur reflects visual or behavioural traits that lead to a lack of interest in cross-mating in animals [20, 78]. There are also a few incompatibility genes whose expression make intergroup breeding essentially sterile, although the reasons are not always clear [79–81]. The most common cause of species separation however is chromosome mismatching. Normal, large, diploid population include a range of chromosomal rearrangements such as translocations, inversions, duplications, joinings and splittings [82, 83], albeit that each is rare.

Over time, different sets of minor chromosomal changes slowly accumulate in the parent and founder populations. Initially, their cumulative effect is to reduce hybrid fertility, but, as their chromosomes become more different, non-disjunction between the germ cells of the two populations becomes more likely. At this stage, hybrids first become sterile and eventually fail to develop. Here, it is worth noting that the bar to mitosis being possible is much higher than that for meiosis as crossover during meiosis may lead to the loss of genetic material [84].

Three examples demonstrate this and indicate the time scale of the process. The lion and tiger clades separated > 10 Ma [85] but can still interbreed to produce female “liger” offspring that are fertile (male offspring are sterile; see [86]). The borderline between fertility and infertility in hybrids is shown by mules, the hybrid offspring of horses and donkeys, which separated ∼2 Ma: although the very great majority are sterile, the occasional fertile example has been recorded [17, 18]. The reason for the difference is, of course, that lions and tigers both have 19 pairs of chromosomes whereas horses and donkeys respectively have 32 and 31 pairs. Third, most of the diverse Canis genus that includes wolves, dogs, grey wolves, dingoes, coyotes and golden jackals can interbreed and produce fertile hybrids They all have 39 pairs of chromosomes and any minor differences are reproductively insignificant. Other members of the wider Canidae family, such as foxes, which separated off the main line > 10 Ma now have 34 main chromosomes and some additional small ones; they are thus unable to breed with members of the Canis genus [87].

The key to irreversible species separation in general is thus the accumulation of differences in chromosome organisation and number between the two populations. The initial formation and subsequent spread of such changes through a population is, as the examples given above demonstrate, rare, slow and stochastic. It is impossible to predict where changes to chromosome structure will occur because there are no constraints on these complex changes, neither are there any endpoints or equilibria. The structural differences continue to accumulate with there being no criteria for determining when numbers are sufficient to lead to non-disjunction. We just know that, given enough time, the accumulation of chromosomal differences will result in this happening.