Darwin himself explored the idea that diversity itself may be selected for, and that phyla that are better at radiating may also be better at flourishing. These questions are deeply complicated by — and may also be critical to — the ongoing discussion of the various levels at which natural selection operates, and the interplay between these levels. Here, we investigate the optimizing role of a mutation parameter in a spirit similar to the three studies described above; however, instead of focusing on individual fitness, we address the optimization of the number of species, represented in our model as clusters of organisms in a simulated morphospace.
The motivation for the design of the present model, implemented in MATLAB, was to incorporate the three fundamental aspects of Darwinian evolution, variability, heritability and overpopulation , in the simplest possible manner. Organisms exist in a two-dimensional morphospace, where each axis represents a hypothetical phenotype. At each time step, a new generation of organisms is produced via an assortative mating algorithm.
The number of new organisms depends on an underlying fitness landscape; the locations of new organisms in the morphospace are determined by the locations of their parent organisms, as well as by the mutation size. We investigate the clustering of organisms, where clusters are defined as reproductively isolated groups and serve as an analogue of species, as a function of maximum mutation size. Simulated organisms exist on a landscape in a two-dimensional morphospace, with the x- and y-coordinates corresponding, respectively, to a given organism's two traits.
This is illustrated in Figure 1 ; diamonds show the locations of organisms within the space. In this implementation of the model, the landscape axes range from 0 to 45; organisms cannot exist beyond the boundaries, i.
Note that the simulation could be performed with a morphospace of variable size and with different boundary conditions; note also that the landscape axis units are arbitrary.
Diamonds show the location of individuals in the morphospace; the color scale indicates the fitness levels corresponding to each location in the morphospace. The model uses assortative mating, whereby, in each generation, every organism picks the nearest other organism in the landscape and mates with it to produce new organisms for the next generation.
The choice of an assortative mating scheme is motivated at once by its simplicity and its realism. Recalling that the organisms exist in a morphospace rather than a physical space, it should be immediately apparent that the simplest realistic mating scheme is one in which phenotypically similar organisms mate with each other rather than with more phenotypically distant organisms.
Assortative mating schemes have been extensively used in various studies, such as investigations of the mechanisms of sympatric [24] and competitive [25] , [26] speciation. Given what de Cara et al. It should be emphasized that clustering of organisms is by no means a given outcome of assortative mating. The conditions under which such clustering occurs are a central focus of the present investigation. The landscape, in addition to having two dimensions indicative of trait values, also has a third dimension, which, when visualized, resembles the elevation of the space see the morphospace color scale in Figure 1.
The elevation at any location on the landscape represents the fitness level available to organisms residing at that location. These fitness levels, ranging from 1 to 4, are realized in the model as the number of offspring an organism will produce.
After the initial distribution of fitness levels is generated, the fitness landscape changes during the simulations in one of two different ways, either 1 shifting gradually or 2 being altered by feedback from the local density of organisms. These operations have the effect of shifting the landscape gradually to the right. For landscapes modulated by feedback, in every generation, the fitness value at each location in the landscape grid was decreased by an amount proportional to the number of organisms living in the region.
For the models implemented here, the proportionality was set at 0. These reactive changes in the landscape symbolize the depletion by over-use of the available resources in a given ecological niche.
The total summation of fitness values available across the entire landscape was conserved in each generation; this was done by adding back the entire subtracted quantity after dividing it equally amongst each of the elements of the fitness landscape matrix before interpolation.
Through this method, areas in the morphospace which were unaffected by the subtraction areas whose resources were not depleted become increasingly advantageous for reproduction. The effects of overpopulation are implemented by setting a distance limit within which only one organism can exist. In all the implementations of the model shown here, the overpopulation limit is set at 0. Clusters, the analog of species in our model, are determined by who mates with whom.
The development of this algorithm was motivated by the concept of biological species , in which species are defined as reproductively isolated groups, i. A similar species definition was also used in another recent computational study, that of de Aguiar et al.
As implemented here, the clustering algorithm is carried out as follows. For a given organism in a given generation, a search is performed to find all the organisms that it, as well as its nearest neighbor its mate and its second-nearest neighbor, have mated with. Then a similar search is performed for each of the organisms found during this first search.
This iterative search continues until a closed set — a cluster — is obtained, where all organisms within the set have mated, in that generation, only within the set. This algorithm assigns each organism to one, and only one, cluster, and arrives at a unique solution for each generation. Several points need to be mentioned in this regard. Consider one individual in the cluster, and its mate. A third organism which mates with the mate is also included in the cluster, and therefore the first individual chosen to seed the cluster could presumably mate with this third individual, under an expanded version of our assortative mating criterion.
A second point to be emphasized is that a more explicit implementation of the rigorous definition of biological species would necessitate a top-down definition of clusters for example, specifying that individuals could mate with organisms within a given radius.
Such a top-down definition would undermine the crux of the approach taken here, which is to capture fundamental dynamical features which emerge naturally from a model satisfying certain basic criteria of evolving systems.
After all the parent organisms in a given generation have produced a new generation of organisms and some of the new organisms have been culled, the parent organisms vanish and a new generation begins, with the previous offspring now playing the role of parents. In the implementation of the model used here, the initial generation consisted of individuals randomly placed within the landscape; during subsequent generations the population fluctuated between several hundred and nearly ten thousand organisms.
Over the course of each simulation, various parameters were recorded at each generation, such as the total population size, the number of clusters, the mean distance between individuals in a cluster, etc. The results of a typical simulation after generations are shown in Figure 1. As described above, the shaded background of the landscape corresponds to the fitness level of individuals at that location, with individuals in the darkest regions being the least fit one offspring each , and those in the lightest regions being the most fit four offspring each.
In the first generation, organisms were randomly seeded throughout the landscape with a uniform distribution. By the end of generations, as shown here, organisms occur in clusters throughout the landscape. In this realization of the model discussed in more detail below , there is negative feedback between the population and the fitness levels available on the landscape, so that when many organisms grow in the most advantageous regions, the regions' underlying fitness levels decrease.
This leads to clustering along the boundaries between the regions offering the highest and lowest fitness. In some cases, simulations with identical parameters exhibited a high degree of historical contingency, as illustrated in Figure 2. Figure 2a shows the population for each of the two runs as a function of generation. For one simulation, the population fluctuates and then suddenly plummets nearly to extinction, while the population in the other simulation continues to fluctuate without crashing.
Snapshots of the two simulations at generation are shown in Figures 2b and 2c. In his time, however, no molecular techniques were available to study the evolutionary changes of genes, and therefore his conclusions have remained as conjectures. In this sense, recent molecular studies have provided solid empirical evidence for his theory.
Actually, Oka was aware of the possibility of ancient polyploidization of rice based on the cytogenetic study by Sakai and Nandi At this point, it should be noted that A 1 and B 2 in figure 4 represented lethal mutations but they may also represent the loss of the duplicate genes A 0 and B 0 , respectively, because they have the same effect as that of lethal mutations in generating reproductive isolation.
In fact, the formation of new species in yeasts after the genome duplication in their ancestral species figs. It should also be noted that most authors who studied the duplicate gene mutation hypothesis mistakenly called it the DM model instead of the Oka model e. In the Oka model, lethal mutations or gene losses are the causal factors, and there is no need of interaction between A 1 and B 2.
In the DM model, however, A 1 and B 2 are functional genes and a special form of gene interaction between alleles A 1 and B 2 is assumed to exist, as will be discussed below. In the DM model, the fixation of alleles A 1 and B 2 by positive selection is also often assumed.
Some authors are not enthusiastic about the importance of the Oka model of speciation. Coyne and Orr stated that polyploidization does not occur so often in animal species and this minimizes the importance of this model. As mentioned above, however, recent genomic studies indicate that small-scale gene duplications are abundant, and there is no reason to believe that the Oka model is less important in animals than in plants.
Coyne and Orr also stated that the ultimate fate of duplicate genes is to acquire new gene functions rather than nonfunctionality. Actually, this statement is incorrect. Duplicate genes become pseudogenes much more frequently than gain new functions Lynch and Force ; Nei and Rooney For these reasons, the Oka model may play an important role in speciation in both plants and animals.
In the Oka model of speciation, it is necessary to have duplicate genes. However, reproductive isolation may be developed without duplicate genes if there are two or more genes that interact with each other negatively when they are brought together in hybrids.
One of such models is the so-called DM model Dobzhansky ; Muller , The essence of this model is presented in figure 5A. In this figure, two loci, A and B , are considered, and A 0 A 0 B 0 B 0 represents the genotype for these loci in the foundation stock from which populations 1 and 2 were derived. If these two populations are geographically or ecologically isolated, it is possible that A 0 mutates to A 1 in population 1 and this mutant allele is fixed in the population by natural selection or genetic drift.
Similarly, B 0 may mutate to B 2 in population 2 and the mutant allele may be fixed. However, if there is gene interaction such that any combination of mutant genes A 1 and B 2 in an individual results in inviability or sterility, the hybrids A 0 A 1 B 0 B 2 between the two populations will be inviable or sterile. Theoretically, however, it is possible to assume that the ancestral genotype is A 1 A 1 B 1 B 1 and that this genotype remained unchanged in population 1 but it changed to A 2 A 2 B 2 B 2 in population 2.
DM model of evolution of reproductive isolation. A Diploid model. B Haploid gamete model. In our view, this argument is disputable. It is certainly true that Bateson considered a two-locus model of complementary genes to explain hybrid sterility, but he never considered how such a system can evolve. By contrast, Dobzhansky and Muller spelled out the evolutionary process of hybrid sterility genes, albeit very crudely.
In evolutionary biology, it is important to understand the process of evolution. For this reason, we will refer to the model as the DM model in this paper. However, Dobzhansky and Muller presented only a verbal argument and never explained why only A 1 is fixed in population 1 and B 2 is fixed in population 2. How is then only A 1 fixed in population 1 and only B 2 fixed in population 2? Both Dobzhansky and Muller argued that allele A 1 may affect a secondary character through the pleiotropic effect and this effect may confer a selective advantage for A 1 over A 0 in population 1.
Similarly, B 2 may have a selective advantage over B 0 in population 2 because of the pleiotropic effect. The first mathematical study of this problem was conducted by Nei Here, let us present a summary of his results. For simplicity, we consider the haploid model given in figure 5B instead of the diploid model because essentially the same result is obtained by both models.
Note also that the haploid model directly applies to sperm or egg fertility. In the haploid model, four possible genotypes may be generated for the two alleles at each of loci A and B , and we assign the fitnesses for the four genotypes as given in table 2.
Here, x and y represent the frequencies of alleles A 1 and B 2 , respectively, whereas s A and s B are selective advantages conferred by pleiotropy for alleles A 1 and B 2 , respectively, and t is the selective disadvantage of genotype A 1 B 2 , which becomes 1 when the interpopulational hybrids are completely sterile.
Note that alleles A 0 , A 1 , B 0 , and B 2 are all vitally important in this model. Here, we have assumed no linkage disequilibrium for simplicity. Generally speaking, it is very difficult to identify any character affected by pleiotropic effects of speciation genes A 1 and B 2 , and even if a character is identified, the selection coefficient s A and s B are unlikely to remain constant for the entire process of fixation of alleles A 1 and B 2.
However, even if s A and s B are 0, alleles A 0 and B 0 may be replaced by A 1 and B 2 in populations 1 and 2, respectively, by the effect of genetic drift. Therefore, it will take a long time for alleles A 0 and B 0 to be replaced by A 1 and B 2 , respectively.
Even if A 1 and B 2 are selected with positive values of s A and s B , the replacement time will not be much shorter because it primarily depends on the mutation rate Li and Nei It should also be noted that the mutation rate v refers only to those mutations that enjoy selective advantage because of the pleiotropic effect within populations but generate strong deleterious effects when they are brought together in hybrid individuals.
No one has measured the mutation rate for this type of mutations, but the rate must be very low because only special mutations would be able to produce such dual gene effects. We know that the DM model is currently very popular e. In reality, he assumed the validity of the model from the beginning and simply studied the possibility of continuous accumulation of incompatibility genes.
He conceived that reproductive isolation is developed by positive Darwinian selection caused by their pleiotropic effects. This is in contrast to the Oka model, where reproductive isolation is assumed to occur due to deleterious mutations in duplicate genes. Let us now examine some recent experimental data that have been regarded to support the DM model.
The first data set we consider is that of Presgraves et al. Nuclear pores are large protein complexes that cross the nuclear envelope and allow the transport of water-soluble molecules such as RNAs, DNA polymerases, and carbohydrates between the nucleus and the cytoplasm. This nuclear pore is composed of a large molecular structure called the nuclear pore complex, which contains about 30 different protein components, each with multiple copies Presgraves and Stephan One of the proteins is the nucleoporin Nup96, and Presgraves et al.
This hybrid inviability occurred only when the D. They therefore assumed that the hybrid inviability occurs when the D. They then concluded that their observations support the DM model of speciation, and the hybrid inviability is a consequence of adaptive evolution at the Nup96 locus. A similar study was conducted by Tang and Presgraves , who identified another nucleoporin gene, Nup , involved in the hybrid male inviability between the two Drosophila species. This gene in D. However, there are a few problems with their conclusions.
First, they have not really identified the D. This identification is critical because otherwise we do not know how the interaction between the two genes leads to hybrid male inviability. Theoretically, the X chromosome genes may not be protein-coding genes but the heterochromatin that is often involved in hybrid inviability e.
Second, Presgraves and his colleagues obtained a signature of positive selection for the increase in frequency of Nup96 and Nup by using the MK test. However, the MK test depends on a number of simplifying assumptions, and it may give erroneous conclusions when these assumptions are not satisfied Nei et al. We therefore examined the extent of positive selection by using the modified Nei-Gojobori method Zhang et al.
In addition, this analysis tells us whether the nucleoporin genes evolve more rapidly than other genes as often claimed by Presgraves and others. When we computed this ratio for Nup96 and Nup using the D. These values indicate that the two genes have not evolved particularly fast among the 5, genes examined 0.
A total of 5, protein-coding genes having one-to-one orthologs among 12 Drosophila species were used. However, what is important here is not to know whether positive selection has occurred for the new alleles but to understand how these genes generate hybrid inviability.
Some may argue that positive selection is important because it would speed up the speciation process. In reality, there is no need for any organism to have fast speciation. Reproductive isolation occurs merely as a consequence of a more general evolutionary change of morphological or physiological characters, and therefore, it must be a passive process, as was emphasized by Darwin , p. However, there are a few data sets that apparently support the DM model.
Long et al. Gene SaF encodes an F-box protein involved in protein degradation, whereas SaM produces a small ubiquitin-like modifier E3 ligase-like protein. It hybridizes both with Indica and Japonica without any problem fig.
However, the molecular basis of the gene interaction to generate the hybrid sterility is still unknown. Male sterility caused by different combinations of alleles at the SaF and SaM loci in rice. Modified from Long et al. Another data set that supports the DM model is that of Chou et al.
This mutation is most likely to have been neutral because the loss of intron did not affect the gene or protein function of COX1. Subsequently, the MRS1 lost its splicing function, which also seems to have been neutral.
However, the hybrids between the two species show sterility because the MRS1 protein in S. This scheme of evolution of reproductive isolation is consistent with the DM model, and in this case, it is likely that the evolutionary changes of the genes have occurred primarily by mutation and genetic drift. There are many other papers that have claimed to support the DM model Coyne and Orr ; Wu and Ting , see table 1. However, close examination of the papers indicates that the authors often misunderstood the concept of the model or the demonstration is incomplete.
Therefore, more careful studies are necessary about the genes reported in these papers table 1. Note that even when some genes completely follow the DM model, they may have nothing to do with speciation but they just became incompatible simply as a by-product of species divergence. Nei et al. As a concrete example, let us consider the evolutionary changes of sperm protein lysin and its egg receptor VERL in abalone species.
In abalone, the eggs are enclosed by a vitelline envelope, and sperm must penetrate this envelope to fertilize the egg Shaw et al. The receptor VERL for lysin is a long acidic glycoprotein composed of 22 tandem repeats of amino acids and about 40 molecules of lysin bind to one molecule of VERL Galindo et al. The interaction between lysin and VERL is species-specific, and therefore, this pair of proteins apparently controls species-specific mating.
Figure 8 shows a genetic model explaining the species specificity between the lysin and VERL genes. Within a species species 1 or 2 , the lysin and VERL genes are compatible, so that mating occurs freely.
However, if species 1 and 2 are hybridized, lysin and VERL are incompatible, and therefore, the fertilization is blocked. This guarantees the species-specific mating when the two species are mixed. A model of species specificity of gamete recognition between lysin and VERL in abalone. Modified from Nei and Zhang Therefore, these mutations would not increase in frequency in the population. However, the chance that these mutants meet with each other in a large population would be very small.
For this reason, Nei et al. If A j is compatible with B i , B j , and B k and if B j is compatible with A i , A j , and A k , then it is possible to generate the species-specific combination of alleles at the lysin and VERL loci in each species i and k , respectively by means of mutation and genetic drift without positive selection that is often assumed by the DM model.
There are several other examples of ligand and receptor gene incompatibilities involved in fertilization or reproduction. For example, sea urchin protein bindin mediates the fertilization of a sperm to an egg. The receptor of bindin is called EBR1, and its interaction with bindin is species specific Kamei and Glabe The protein—protein interaction in various biochemical processes required for development and physiology is also often complementary.
Similarly, the control of expression of protein-coding genes by cis -regulatory elements is complementary by nature. They considered both one-locus and two-locus models. Mutation was assumed to occur following either the stepwise or the infinite-allele model Kimura , and the fitness of a genotype was assumed to be either 1 or 0 depending on the mutation model and the genotype generated fig.
Premating and postmating isolations were also considered. Their conclusions are summarized in the following way. Stepwise mutation model for hybrid sterility or inviability genes. A In the stepwise mutation model, the forward and backward mutation may occur. B The fertilities for various haplotypes for loci A and B two-locus model and genotypes for locus A one-locus model are given by 0 infertile or 1 fertile.
Distantly related haplotypes or genotypes are infertile. However, these results are model dependent, and we cannot apply the results to natural populations without qualifications. For example, the single-locus model, which will be considered below, may be applicable only to certain characters such as the flowering time in plants and developmental time in animals. At present, we also do not know which of the stepwise and infinite-allele models is more realistic than the other, though we believe that the latter model is more realistic because reproductive isolation is controlled by a large number of genes controlling different phenotypic characters.
Our results imply that speciation occur more rapidly through bottlenecks. However, Nei et al. This would also means that self-fertilizing organisms may undergo more rapid evolution than random mating populations. In general, however, speciation occurs very slowly, and it takes millions to tens of millions of years for well-established species to be developed Coyne and Orr , pp. Chromosomal aberrations are larger-scale mutations that can occur during meiosis in unequal crossing over events, slippage during DNA recombination or due to the activities of transposable events.
Genes and even whole chromosomes can be substituted, duplicated, or deleted due to these errors Figure 1. Point substitutions are in red, and the yellow box with dashes indicates a deletion of 12 bases. Mutations can have a range of effects. They can often be harmful. Others have little or no detrimental effect. And sometimes, although very rarely, the change in DNA sequence may even turn out to be beneficial to the organism.
A mutation that occurs in body cells that are not passed along to subsequent generations is a somatic mutation. A mutation that occurs in a gamete or in a cell that gives rise to gametes are special because they impact the next generation and may not affect the adult at all. Such changes are called germ-line mutations because they occur in a cell used in reproduction germ cell , giving the change a chance to become more numerous over time.
If the mutation has a deleterious affect on the phenotype of the offspring, the mutation is referred to as a genetic disorder. Alternately, if the mutation has a positive affect on the fitness of the offspring, it is called an adaptation. Thus, all mutations that affect the fitness of future generations are agents of evolution. Mutations are essential to evolution. Every genetic feature in every organism was, initially, the result of a mutation.
The new genetic variant allele spreads via reproduction, and differential reproduction is a defining aspect of evolution. It is easy to understand how a mutation that allows an organism to feed, grow or reproduce more effectively could cause the mutant allele to become more abundant over time.
Even deleterious mutations can cause evolutionary change, especially in small populations, by removing individuals that might be carrying adaptive alleles at other genes. Hyla versicolor , is an example of mutation and its potential effects. When an ancestral Hyla chrysocelis gray treefrog failed to sort its 24 chromosomes during meiosis, the result was H.
This treefrog is identical in size, shape and color to H. All rights reserved. Most mutations occur at single points in a gene, changing perhaps a single protein, and thus could appear unimportant. For instance, genes control the structure and effectiveness of digestive enzymes in your and all other vertebrate salivary glands.
At first glance, mutations to salivary enzymes might appear to have little potential for impacting survival. Yet it is precisely the accumulation of slight mutations to saliva that is responsible for snake venom and therefore much of snake evolution. Natural selection in some ancestral snakes has favored enzymes with increasingly more aggressive properties, but the mutations themselves have been random, creating different venoms in different groups of snakes. Snake venoms are actually a cocktail of different proteins with different effects, so genetically related species have a different mixture from other venomous snake families.
The ancestors of sea snakes, coral snakes, and cobras family Elapidae evolved venom that attacks the nervous system while the venom of vipers family Viperidae; including rattlesnakes and the bushmaster acts upon the cardiovascular system.
Both families have many different species that inherited a slight advantage in venom power from their ancestors, and as mutations accumulate the diversity of venoms and diversity of species increased over time. In addition, large populations usually contain more alleles because they experience less genetic drift. Genetic drift leads to a reduction in the number of alleles in a population. Finally, the diversity of alleles at a locus will be affected by the length of time a population occupies a particular area.
Over thousands of generations, many mutations will be introduced into a population and some of these will increase to a detectable frequency as a result of selection or genetic drift. Both of these processes may take a long time to make a measurable increase in allele diversity. This concept of a "center of genetic diversity" is used to identify the center of origin of a host plant and its pathogens. The center of genetic diversity is usually the center of origin for both host and parasite and it marks the place where coevolution has likely occurred for the longest period of time.
As a result of coevolution, the center of origin is expected to have the largest diversity of plant resistance alleles, as well as the largest diversity of pathogen virulence and avirulence alleles.
Consider the effects of creating resistance gene pyramids. If two new resistance genes are introduced simultaneously into a host genotype, then the pathogen will need two simultaneous or sequential mutations from avirulence to virulence to overcome those two resistance genes.
So in the theoretical mildew population described earlier, only about 10 double mutants would be produced each day. If three resistance genes were pyramided into the same host genotype, then the pathogen would require three mutations, at a probability of 10 , to overcome the resistance gene pyramid.
In this case, we expect to find one triple mutant per 10 5 hectares of host. This is why plant breeders are interested in utilizing resistance gene pyramids. Our theoretical prediction is that R-gene pyramids are likely to be very effective for asexual pathogens like bacteria and some asexual fungi, such as Fusarium spp.
Mundt But given this scenario, and knowing that it is relatively common to find 10 6 hectares of a plant host planted in a region for some cereals, you should wonder why resistance gene pyramids don't break down immediately since most "pyramids" include only 2 or 3 resistance genes. The answer is that the very rare mutant spore is extremely unlikely to land on a suitable host plant and then encounter favorable conditions for infection. The majority probably Thus most of the rare mutants never have an opportunity to infect and reproduce.
This highlights the fact that both epidemiology in this case spore numbers and population genetics allele frequencies are needed to explain observed phenomena in plant pathology.
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