*Center of Medical Information Science,
Department of Information Science,
Department of Medical Biology,
Medical Research Center, Kochi Medical School, Nankoku, Kochi, Japan;
||Department of Biology, Faculty of Science, Kochi University, Akebono, Kochi, Japan
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Abstract |
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Introduction |
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There exists an original space of vectors whose components are the amino acid sequences of the respective species. However, this space is too abstract for a quantitative analysis of the tree structure, since these components are not digital. If this space can be transformed into the multidimensional vector space (MVS) of Euclidean space without decreasing the degree of freedom of the variables, the tree structure can be directly analyzed by using geometrical quantities such as the distances and angles between the vectors.
In this paper, we first show how the evolutionary process is represented in the MVS. To make lucid our basic idea for this representation, we consider the simplest model of substitutions (hereinafter called the single-substitution model [SSM]), in which the amino acids of any sites can be changed at most once over all the evolutionary processes, and the substitution distances between two species are approximated by the number of different amino acid sites between two sequences. Then, the processes are represented as the developments of branch vectors along the orthogonal coordinate axes in the MVS, and the end points of these vectors correspond to the extant species. The species vectors indicate the specific directions in the MVS, respectively.
Next, to infer the tree structure from the species vectors of the end points, we introduce search vectors to draw out the groups of species, which are distributed around these vectors. A search vector may be a one-species vector or a center-of-gravity vector (CGV) of many species. The drawn-out species stand in line in the nearby order of the topological relationship with the search vectors if the branch vectors are orthogonal. The branching patterns of the tree are analyzed by a scatter diagram which expresses the relationship among the groups of species drawn out by two search vectors. It is shown that the diagram consists of the three parts: the left branch, the right branch, and the central line. The first two include the drawn-out species which are distributed parallel to the x- and y-axes, respectively, while the third represents the other species (outgroup) of the outside branches, which are distributed around the origin of coordinates or along the central line of y = x.
The present theory is meaningless if the spatial positions of the respective species are not obtained. In this paper, their positions in the MVS are determined so that their relative distances may reproduce the substitution distances between species. This can be easily done in simple cases of three and four species. As the number I of species and the dimensional size N increase, however, it is difficult to determine the positions by statistical methods of minimizing or maximizing a quantity, since the number of variables is huge (if I = 150 and N = 100, the number is I x N = 15,000). To remove this difficulty, we introduce the dynamic method of time-dependently solving the equation of motion for the many-body system in physics (David and James 1988
). Here, the species are regarded as particles moving under their mutual interactions. By utilizing the law of physics that the system finally falls into the ground state, irrespective of the initial random distributions of the particles, we can precisely determine the positions of the species in the MVS. Here, the interactions are defined as the sums of two-body potentials, which are expressed so as to be minimum at the points equal to the substitution distances between the two related species. The solution of the equation of motion always converges on the ground state by the (I - 1)-dimensional size. However, when I is larger than the number L of variable sites in amino acid sequences of these species, it is found that the equation of motion can be solved with good accuracy by the L-dimensional size in place of (I - 1). Then, the number of variables in the MVS becomes substantially equal to that in the original abstract space. This means a substantial transformation of the original space into the MVS.
The validity of the present method was examined by using computer simulations of molecular evolution in which any branch patterns could be created by using the Monte Carlo method (Hammersley and Handscomb 1964
) with the weight of the transition probability matrix. Then, it was possible to directly compare the present method with standard ones such as neighbor joining (NJ), maximum likelihood (ML), and parsimony (PA), since all the branch- and end-point sequences were known in advance. The predominance of the present method was demonstrated by using two examples of typical branch patterns in which 100 multiple data sets with a variety of branch lengths were prepared by repeating the simulations.
The present method was applied to the vector analysis of 185 vertebrate species in the -hemoglobin, and the results were compared with those of the standard methods. The standard methods gave erroneous topologies in the relationship among Artiodactyla, Perissodactyla, and Chiroptera in spite of very high branch resolutions which became lower as the number of species increased. On the other hand, the present approach gave the correct topology, and a larger number of species brought a more stable solution. Encouraged by this success, we challenged recent analyses of topics regarding the reptilian phylogeny. Our results showed that squamates were clearly isolated from the lineage of birds, while the other extant reptilians belonged to the lineage of birds without forming any sister groups. This is in contrast to the traditional phylogeny (Romer 1966
; Benton 1997
) and is also different from recent reports (Gorr, Mable, and Kleinschmidt 1998
; Hedges and Poling 1999
).
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Theory |
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![]() | (1) |
A variety of pairs may be selected for the search points (s, t). For the first pair, s = 31 and t = 16, the SSM gives the following orthogonal relations: R15,1 R15,s, R15,1
R15,30, and R15,s
R15,30, since points 1, 15, 30, and 31 correspond to points 1, 2, 3, and 4, respectively, in figure 1b.
We have Zs,s = Rs,12 and Z15,s = Z30,s. Hence, we obtain Zi,s = C1 for the point (i = 31), Zi,s = C2 for the points (i = 15, 30), Zi,s = C3 for the points (i = 7, 14, 28, 29), Zi,s = C4 for the points (i = 3, 6, 12, 13, 2427), and Zi,t = 0 for the points (i = 3, 6, 7, 1215, 2431), where Cj (C1 > C2 > C3 > C4) are constants. In this way, the four groups of points stand in line on the x-axis according to the nearby order of branches from the search point (s = 31). Similarly, in the upper branches of figure 2
, the point (i = 16) gives the largest value of Zi,t on the y-axis, the points (i = 8, 17) form the second group, the points (i = 4, 9, 18, 19) form the third group, and the points (i = 2, 5, 10, 11, 2023) form the fourth group.
For the second example, the pair (s = 31, t = 24), we have the orthogonal relations Zi,s = Zi,t = 0 for the points (i = 2, 4, 5, 811, 1623), Zi,t = C5 for the point (i = 24), Zi,t = C6 for the points (i = 12, 25), Zi,t = C7 for the points (i = 6, 13, 26, 27), and Zi,s = C8 for the points (i = 3, 7, 14, 15, 2831), since Ri,3 Rj,3 for the two groups of points (i = 6, 12, 13, 2427) and (j = 7, 14, 15, 2831). Here, C5, C6, C7, and C8 are constants (C5 > C6 > C7 > C8). Here, in the x-direction, the point (i = 31) gives the largest value of Zi,s, the points (i = 15, 30) form the second group, the points (i = 7, 14, 28, 29) form the third group, and the points (i = 3, 6, 12, 13, 2427) form the fourth group. In the y-direction, point 24 gives the largest value of Zi,t, the points (i = 12, 25) form the second group, the points (i = 6, 13, 26, 27) form the third group, and the points (i = 3, 7, 14, 15, 2831) form the fourth group. In this way, the scatter diagram for Zi,s and Zi,t gives the groupings of the points which correspond to the nearby orders of branches viewed from the search points (s and t). Also, the regression lines along these plots are orthogonal to each other. However, actual evolutionary processes may include more or less substitutions of higher orders than those in the SSM. Then, the two lines cannot be completely parallel to the x- and y-axes, respectively.
A computer simulation of evolution is a useful tool to check the validity of the vector analysis in terms of Zi,s and Zi,t, since all the sequences of the 31 points of figure 2
are known in advance. The simulation created these sequences on the basis of the Markov process without applying the SSM. An amino acid sequence (141 sites) of the first point (the root) was given by generating white random numbers for the 20 amino acids. We tried to substitute an amino acid at each site of the root sequence by generating a random number with the weight of the transition probability matrix between amino acids. Then, most of the sites remained unchanged, since the diagonal parts of the matrix were much larger than the nondiagonal ones. The sequences of the next two points (2, 3) were fixed after amino acid substitutions of 10 sites in the root sequence, respectively. This procedure was continued to the end points (points 1631). In this simulation, the Dayhoff model was used for both the transition probability matrix and the substitution distances between the sequences of the respective points (Dayhoff, Schwartz, and Orcutt 1978
). The substitution distances between points 131 were calculated in a way equivalent to that of the software package Protdist (Felsenstein 1993
), and used as the input data for the equation of motion.
Positions Ri of the 31 points of figure 2
were precisely determined by solving the equation of motion in the 30 dimensions and used for the vector analysis. Figure 3a
shows the scatter diagram for Zi,s and Zi,t (s = 31, t = 16). The scatter plots were clearly classified into the eight groups according to the branching orders from the specific points (s = 31, t = 16), and the regression lines along the plots were almost orthogonal to each other on the x- and y-axes, although the SSM was not applied and the end points were rather far from the root (point 1) (d 35). Figure 3b
shows the scatter diagram for Zi,s and Zi,t (s = 31, t = 24). Here, the points of the upper branches of figure 2 were distributed around the origin of coordinates to compose the outgroup, since their vectors were almost orthogonal to the vectors Rs and Rt. Those of the lower branches were distributed in a pattern quite similar to that shown in figure 3a
and were classified into the seven groups. In this way, a successive change of the search vectors s and t completely resolved the branch pattern of figure 2
.
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Prior to the inference, we determine the origin of coordinates using the positions of the end points. The molecular clock is assumed as the first approximation for this position. We look for the position Rc of the spherical center which is equidistant from all the end points. Let us consider the quantity S defined by the equation
| (2) |
Once the root position is determined, the tree structure can be analyzed in terms of the scattering diagram for Zi,s and Zi,t by using only the end points. By adopting R16 and R31 as the search vectors, we obtain figure 3a without points 215. Then, on the basis of the orthogonal theory presented in the previous section, we know that points 1623 and points 2431 groups that are independent from each other. In the group of points 1623, points 2023 are first separated from the evolution process toward the point 16, points 18 and 19 are separated next, and point 17 is finally separated. On the other hand, in the group of points 2431, points 2427 are first separated from the evolution process toward point 31, points 28 and 29 are separated next, and the point 30 is finally separated. As a result, we obtain the tree inserted in figure 3a. Next, we further resolve points 2427 by taking R24 as the search vector instead of R16. We get figure 3b without points 215. Then, we know that the points 26 and 27 are first separated from the evolution process toward point 24, and point 25 is separated next. As a result, we get a more detailed tree, presented in the insert in figure 3b. By continuing such a procedure, we can obtain the full tree of 16 points.
The vector analysis can be performed without any mathematical approximations. However, the branch lengths of the tree are obliged to be evaluated model-dependently. This can be easily done by using the SSM as follows: In figure 2
, for example, we have the orthogonal relations Ri,4 Rj,4 for the points [i = (16, 17), j = (18, 19)], [i = (1), j = (16, 17)], and [i = (1), j = (18, 19)]. We have R16,42 + R18,42 = R16,182, R1,42 + R16,42 = R16,12, and R1,42 + R18,42 = R18,12. As a result, the branch lengths are given by R1,42 = (R16,12 + R18,12 - R16,182)/2, R16,42 = (R16,12 + R16,182 - R18,12)/2, and R18,42 = (R18,12 + R16,182 - R16,12)/2. We finally note that the scalar product Ui,s = Ri·Rs =
Nn=1 Xi,nXs,n = RiRscos
i,s of the search vector Rs and vector Ri gives the distance from the root to the branch point between the two points (s and i). The scatter diagram may be expressed in terms of Ui,s and Ui,t in place of Zi,s and Zi,t.
Determination of Species Positions Ri in the MVS
To obtain species positions Ri in the MVS, we have to determine a large number of parameters of Xi,n (i = 1, 2, ... , I; n = 1, 2, ... , N), which are the vector components of Ri. We introduce a new method of time-dependently solving the equation of motion for the many-body system. For this purpose, the species are regarded as the particles moving according to the equation of motion. They are initially deposited at random within a volume of the MVS. With time, they continue to move toward lower energy states under the influences of both a viscosity effect and their mutual interactions. They gradually lose their kinetic energies due to the viscosity effect and finally stop falling into the ground state of the system, irrespective of the initial conditions given using random numbers. This falling is one of the most fundamental laws of physics. Therefore, it is quite easy to confirm whether the equation of motion has been correctly solved or not, since the ground state is explicitly known in advance. The interactions are defined as the sum of two-body attractive potentials, which are minimized at the points equal to the square roots of the substitution distances between the two species. The ground state corresponds to the situation in which any pairs of the particles are positioned at the points equal to the square roots of the substitution distances.
The initial positions Ri and velocities Vi of the particles are randomly distributed within the volumes of R0 and V0 by the equations
| (3) |
| (4) |
| (7) |
![]() | (8) |
Equations (4)(8)
are expressed in no dimensions without physical units such as meters, grams, or seconds. If we set µ = 0, these equations are reduced to the well-known "canonical equation," where the total energy E of the system is conserved time-independently. The Runge-Kutta method is applied for the numerical solution, where we set the constant values as follows: V0 = 0.3, M = 900, P0 = -0.5, µ = 8, and A = 20. R0 denotes the range of the initial distribution of the particles and is defined as half of the maximum value of Di,j. P0 is the depth of the potential which confines the particles within the interaction range. The value of µ may be adjusted to be small such that the particles will gradually lose their kinetic energies in time, and µ = 8 was found to be suitable. A time mesh to integrate the differential equations about time is taken as T = 0.3, which is sufficiently small to keep the calculations accurate. The size of dimensions, N, is set equal to (I - 1) if I is smaller than the number of variable sites within the given species, L. If I > L, we may put N = L, since the average error of Ri,j versus Di,j is then negligible. The numerical calculations start with a high-energy state given by a set of the initial distribution of the particles, and they stop at the ground state, whose appearance verifies the correct solution of equations (4)(6)
. This can be easily confirmed in practice, since the ground state is given by E0 = P0I(I - 1)/2, as known from equations (7) and (8)
. In numerical calculations using the interaction potential of equation (8), we do not have any local minimum of the total energy. The calculations were performed by a Fortran program with double precision.
Comparison with Other Methods by Computer Simulations of Molecular Evolution
The efficacy of the present theory was demonstrated by using computer simulations of molecular evolutions in which all of the branch- and end-point sequences were known in advance. Once an initial sequence of amino acids is given, a series of sequences of the following evolutionary process are determined by using Monte Carlo method (Hammersley and Handscomb 1964
) with the weight of the transition probability matrix t(p, q) for the Dayhoff model. The amino acid transition at each site is determined by generating a random number F between 0 and 1: if a given F satisfies the condition T(p, q - 1) < F
T(p, q), the transition from the pth amino acid to the qth one occurs. Here, T(p, q) =
qr=1 T(p, r)/
20r=1 T(p, r), T(p, 0) = 0, and T(p, p) means no transition. An operation of the transitions is performed from the first site to the last, so that the first sequence is created. The second sequence is created by the next operation. The (i + 1)-th sequence is given by using the ith sequence. Two sequences are created at each branch point. In this way, we can simulate any branch patterns of molecular evolution based on the stochastic (Markov) process. The number of operations is proportional to evolutionary time.
To compare the present method with the standard ones, we formed the branch patterns of figure 4a and b. Here, the end points (points 59) correspond to the 100 operations. Branch points 2, 3, and 4 in figure 4a are the positions of the 50, 70, and 70 operations, respectively. Those in figure 4b are the positions of the 40, 60, and 80 operations, respectively. To make the simulation realistic, we assumed that the initial point (point 1) was the consensus sequence of eutherians. We also assumed that the 64 sites could be substituted, since the other 77 sites were known to almost freeze in eutherians.
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Applications to Vertebrates in the ![]() |
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For the search vectors in the vector analysis, we introduced the CGV Rs to express the representative direction of a group (s) of species in the MVS. It was defined by Rs = 'i Ri/Is, where the prime sign of
'i denotes the summation about the species of the group s and Is is their total number. Consequently, the scatter diagram for the two groups s and t was expressed in terms of the quantities Zi,s and Zi,t, which are the projection components of the species vectors Ri to the two CGVs of Rs and Rt, respectively.
Relationship Among Artiodactyla, Perissodactyla, and Chiroptera
First, the present theory was applied to a typical problem in which it is difficult to get the correct branch patterns by using standard methods such as the ML, NJ, and PA methods. We picked up eight species of Artiodactyla and Perissodactyla and used a rat as the outgroup. It is well known that the consensus topology is [rat, {(Tylopoda, Ruminantia), (Ceratomorpha, Hippomorpha)}] (Novacek 1992
; Benton 1997
). The standard methods gave an erroneous pattern, [Tylopoda, {Ruminantia, (Ceratomorpha, Hippomorpha)}], with high branch resolutions (see fig. 10
). Especially, the ML method gave this strange pattern with 100% confidence (fig. 10a
), although this method gave the correct pattern with 100% confidence in the case of the ß-hemoglobin (data not shown). Additional inclusions of other orders resulted in another problem with the topology. As shown in figure 11
, by adding Chiroptera, Tylopoda still made the first clade of the tree in a way similar to that in figure 10
, and furthermore, Chiroptera were included inside of the ungulate branches. Here, the branch resolutions were rather high for the NJ method (fig. 11b
), while they were very low for the ML method (fig. 11a
). It is well known that Chiroptera are located outside the ungulate branches, since it is rather close to Primates (Novacek 1992
; Benton 1997
).
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Drawing Out of Lineage of Mammals and Birds
The positions Ri of 185 vertebrates were determined in the 110-dimensional size in which the average error of Ri,j versus Di,j was sufficiently small, i.e., 0.08%. The spherical center Rc of vertebrates was obtained by using equation (2)
and defined as the origin of coordinates, from which the species vectors Ri were measured. The CGVs Rm and Rb of mammals and birds were calculated and regarded as their representative directions in the MVS, respectively. Figure 13
shows the angular distribution of the vectors Ri around the CGV Rm. Here, the x-axis denotes the projection components Wi,m = (Zi,m)1/2 of the species vectors Ri to the vector Rm. The angles show roughly a chronological order of evolution of the species, since the branching events of the tree at earlier stages of evolution yield larger angles. The distribution was well fitted to the dotted curve (given by W = R cos() with a constant radius R = 8.5, which is the average value of |Ri|.
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| (9) |
Figure 14 gives the scatter diagram (with C = 0.2) consisting of the three parts: the central line, the left branch, and the right branch. This figure showed a clear splitting into three groups of the central line and the left and right branches. The central line included fishes, amphibians, and squamates to form the outgroup. Fishes began with a coelacanth, a carp, and a dragonfish and ended with a goldfish. The central line included fishes, newts, frogs, and squamates. The left branch represented the lineage of birds. Crocodilians, turtles, and tuataras belonged to this lineage. In this way, the extant reptilians were clearly classified into the two groups of squamates and others. On the other hand, the right branch represented the mammalian lineage, which began with Monotremata (a platypus and an echidna) and Marsupialia (an opossum) at the base of the branch. They were followed by a guinea pig, a hedgehog, a manatee, and a whale, which are considered to be the core member species of the mammalian radiation. Primates were located at the uppermost part of the right branch.
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There appeared to be a vacuum at the base of the two branches of birds and mammals. This is regarded as the result of the extinction of reptilians. Finally, it is noted that the line along the plots of the bird lineage is not orthogonal to that of the mammalian lineage (see the solid lines of fig. 14
). This suggests that substitutions of higher orders than the SSM may exist in the sequences between birds and mammals. The effect of these substitutions may be related to the well known underestimation of the molecular clock between mammals and birds (Zuckerkandl and Pauling 1965
). This problem will be discussed in detail elsewhere.
Relationship Among Birds, Squamates, and Other Extant Reptilians
The phylogeny of reptilians has been one of the most important problems in vertebrate evolution. From a morphological point of view, the number of temporal openings in the skull has been used as an important clue to the classification of species (Romer 1966
; Benton 1997
): mammals have a single opening, the turtle lacks a temporal opening, and the other extant reptilians have two openings. In this way, birds and crocodilians formed one group, tuataras and squamates formed another group, and the turtle was placed at the base of the tree (fig. 15a
). On the other hand, the concept of a sister group of birds and mammals was proposed (Gardiner 1982
; Løvtrup 1985
) and was supported by molecular analyses using the sequences of the myoglobin and ß-hemoglobin (Goodman, Miyamoto, and Czelusniak 1987
; Bishop and Friday 1988
). In recent molecular analyses (Gorr, Mable, and Kleinschmidt 1998
; Hedges and Poling 1999
), however, the turtle was joined with crocodilians, and squamates were placed at the base of the reptilian tree. If these results are accurate, the traditional classification based on the number of temporal openings becomes meaningless for phylogeny, and the morphological and paleontological evidence then remains unclear.
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Discussion |
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The MVS was shown to be useful for phylogeny inference by the vector analysis based on the orthogonal relation, in contrast to the multidimensional space (Grantham et al. 1981
) which is directly expressed in terms of the amino acid or codon frequencies. The solution of the kinetic equation for the MVS always converges on the ground state by the N = (I - 1)-dimensional size. However, when I was larger than L, we found that the equation of motion could be solved with good accuracy by the L-dimensional size in place of (I - 1). In fact, the L values for 113 eutherians and 185 vertebrates were 80 and 110, respectively, and the former values were much smaller than the latter. In this way, the degree of freedom of variables in the MVS became equal to that in the original space of vectors having the amino acid sequences as their components. This means that the MVS is a transformation of the original space, although the components of the vectors are quite different from each other. In this way, we have to analyze a large number of species compared with that of variable sites in order to get a reliable topology. In fact, in the case of 27 species of ungulates, Chiroptera, and rat of figure 12a,
a part of the outside species (Chiroptera) slightly fluctuated upward on the y-axis (toward the CGV of Perissodactyla). This fluctuation may be connected with reason that the size of dimensions (26) was smaller than the number of variable sites (35), since the results (figs. 12b, 14, and 16
) with the larger numbers of species did not bring such a fluctuation.
The standard methods gave a strange topology in the relationship among the four suborders of Perissodactyla and Artiodactyla in spite of high branch resolutions (fig. 10
). Table 3
gives the distance matrix for a tapir, a horse, a bovine, an alpaca, and a rat. In this matrix, it is natural that the distance between the tapir and the horse (10.1) is the shortest. However, the distance between the bovine and the alpaca of the same order (17.3) is larger than that between the bovine and horse of different orders (14.1). Such a complicated relationship among these four species seems phenomenologically to be a main reason for the strange topology of figure 10
. As another possible reason, the number of eight species sampled in figure 10
might be too small to obtain the correct topology. To explain this reason, let us consider a simple case of three species with the grouping {1, (2, 3)}. Then, we have a possibility of getting the opposite coupling, {(1, 2), 3}, by additionally including another species (4) which is located intermediate between points 1 and 2. It was therefore expected that the correct topology might be obtained by increasing the number of species. However, the situation became worse, since Chiroptera were furthermore included in the inside of the ungulate branches and the branch resolutions became very low (fig. 11
). Another example of the strange topology was reported in the ML analysis of the relationship among primates, ferungulates, and rodents with use of the ND1 mitochondrial protein by Cao et al. (1998a)
, who suggested the possibility of convergent or parallel evolution. We investigated this relationship in the
-hemoglobin by using the ML and NJ methods, which gave the same strange pattern, {ungulates, (rodents, primates)} with the ND1, although the branch resolutions were very poor. Therefore, phenomena similar to the ND1 may exist in the
-hemoglobin.
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In this paper, we tried to obtain statistical confidence by increasing the number of species. Another approach is to fluctuate the distances themselves. In the present examples of applications, however, the groupings of species in the scatter diagrams were very clear. When a grouping pattern is complicated, a more quantitative analysis will be necessary for phylogeny inference. This problem will be discussed elsewhere.
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Conclusions |
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Supplementary Material |
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Acknowledgements |
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Footnotes |
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1 Keywords: phylogeny inference
multidimensional space
equation of motion
vector analysis
hemoglobin
vertebrates
2 Address for correspondence and reprints: Yasuhiro Kitazoe, Center of Medical Information Science, Kochi Medical School, Nankoku, Kochi 783-8505, Japan. kitazoey{at}med.kochi-ms.ac.jp
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literature cited |
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---|
Adachi, J., and M. Hasegawa. 1996. MOLPHY version 2.3: programs for molecular phylogenetics based on maximum likelihood. Comput. Sci. Monogr. 28:1150.
Benton, M. J. 1997. Vertebrate paleontology. 2nd edition. Chapman and Hall, New York.
Bishop, M. J., and A. E. Friday. 1988. Estimating the interrelationships of tetrapod groups on the basis of molecular sequence data. Pp. 3358 in M. J. Benton, ed. The phylogeny and classification of the tetrapods. Clarendon Press, Oxford.
Cao, Y., J. Adachi, A. Janke, S. Pääbo, and M. Hasegawa. 1994. Phylogenetic relationships among eutherian orders estimated from inferred sequences of mitochondrial proteins: instability of a tree based on a single gene. J. Mol. Evol. 39:519527.[ISI][Medline]
Cao, Y., A. Janke, P. J. Wadell, M. Westerman, O. Takenaka, S. Murata, N. Okada, S. Pääbo, and M. Hasegawa. 1998a. Conflict among individual mitochondrial proteins in resolving the phylogeny of eutherian orders. J. Mol. Evol. 47:307314.
Cao, Y., P. J. Waddel, N. Okada, and M. Hasegawa. 1998b. The complete mitochondrial DNA sequence of the shark Mustelus manazo: evaluating rooting contradictions to living bony vertebrates. Mol. Biol. Evol. 15:16371646.
David, H. B., and N. G. James. 1988. Quasiparticle model for nuclear dynamics studies: ground-state properties. Phys. Rev. C 38:18701878.
Dayhoff, M. O., R. M. Schwartz, and B. C. Orcutt. 1978. A model of evolutionary change in proteins. Pp. 345352 in M. O. Dayhoff, ed. Atlas of protein sequence and structure, Vol. 5. National Biomedical Research Foundation, Washington, DC.
Eck, R. V., and M. O. Dayhoff. 1966. Atlas of protein sequence and structure. National Biomedical Research Foundation, Silver Spring, Md.
Felsenstein, J. 1993. PHYLIP (phylogeny inference package). Version 3.5c. Distributed by the author, Department of Genetics, University of Washington, Seattle.
Fitch, W. M., and E. Margoliash. 1967. Construction of phylogenetic trees. Science 155:279284.
Gardiner, B. G. 1982. Tetrapod classification. Zool. Linn. Soc. 74:207232.[ISI]
Gemmell, N. J., and M. Westerman. 1994. Phylogenetic relationships within the class Mammalia: a study using mitochondrial 12S RNA sequences. J. Mamm. Evol. 2:323.
Goodman, M. 1963. Serological analysis of the systematics of recent hominoids. Hum. Biol. 35:377436.[ISI][Medline]
Goodman, M., M. M. Miyamoto, and J. Czelusniak. 1987. Pattern and process in vertebrate phylogeny revealed by coevolution of molecules and morphologies. Pp. 141176 in C. Patterson, ed. Molecules and morphology in evolution: conflict or compromise? Cambridge University Press, Cambridge, England.
Gorr, T. A., B. K. Mable, and T. Kleinschmidt. 1998. Phylogenetic analysis of reptilians: trees, rates, and divergences. J. Mol. Evol. 47:471485.[ISI][Medline]
Grantham, R., C. Gautier, M. Jacobzone, and R. Mercier. 1981. Codon catalog usage is a genome strategy modulated for gene expressivity. Nucleic Acids Res. 9:43r74r.
Hammersley, J. M., and D. C. Handscomb. 1964. Monte Carlo methods. Methuen, London.
Hedges, S. B. 1994. Molecular evidence for the origin of birds. Proc. Natl. Acad. Sci. USA 91:26212614.
Hedges, S. B., and L. L. Poling. 1999. A molecular phylogeny of reptiles. Science 283:9981001.
Janke, A., G. Feldmaier-Fuchs, W. K. Thomas, A. von Haeseler, and S. Pääbo. 1994. The marsupial mitochondrial genome and the evolution of placental mammals. Genetics 137:243256.
Janke, A., N. J. Gemmell, G. Feldmaier-Fuchs, A. von Haeseler, and S. Pääbo. 1996. The complete mitochondrial genome of a monotreme, the platypus (Ornithorhynchus anatinus). J. Mol. Evol. 42:153159.[ISI][Medline]
Jones, D. T., W. R. Taylor, and J. M. Thornton. 1992. The rapid generation of mutation data matrices from protein sequences. Comput. Appl. Biosci. 8: 275282.
Kumar, S., and S. B. Hedges. 1998. A molecular timescale for vertebrate evolution. Nature 392:917920.
Løvtrup, S. 1985. On the classification of the taxon Tetrapoda. Syst. Zool. 4:463470.
Novacek, M. J. 1992. Mammalian phylogeny: shaking the tree. Nature 356:121125.
Romer, A. S. 1966. Vertebrate paleontology. University of Chicago Press, Chicago.
Saitou, N., and M. Nei. 1987. The neighbor-joining method: a new method for reconstructing phylogenetic trees. Mol. Biol. Evol. 4:406425.[Abstract]
Sarich, V. M., and A. C. Wilson. 1967. Immunological time scale for hominid evolution. Science 158:12001203.
Sokal, R. R., and C. D. Michener. 1958. A statistical method for evaluating systematic relationship. Univ. Kans. Sci. Bull. 28:14091438.
Sokal, R. R., and F. J. Rohlf. 1981. Biometry. 2nd edition. Freeman, San Francisco.
Springer, M. S., G. C. Gregory, O. Madsen, W. W. DeJong, V. G. Waddell, H. M. Amrine, and M. J. Stanhope. 1997. Endemic African mammals shake the phylogenetic tree. Nature 388:6164.
Strimmer, K., and A. von Haeseler. 1996. A quartet maximum-likelihood method for reconstructing tree structure. Mol. Biol. Evol. 13:964969.
Swofford, D. L. 1998. PAUP. Version 4. Sinauer, Sunderland, Mass.
Zukerkandl, E., and L. Pauling. 1965. Evolutionary divergence and convergence in proteins. Pp. 97166 in V. Bryson and H. J. Vogel, eds. Evolving genes and proteins. Academic Press, New York.