Added source Matlab code for reference
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Waldir Leoncio
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matlab/graph/seqNeighJoin.m
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matlab/graph/seqNeighJoin.m
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function t = seqNeighJoin(D, method, names, varargin)
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%SEQNEIGHJOIN neighbor-joining method for phylogenetic tree reconstruction.
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%
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% TREE = SEQNEIGHJOIN(DIST) computes a phylogenetic tree object from the
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% pairwise distances DIST between the species or products applying the
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% neighbor-joining method. The input DIST is a matrix (or vector) such as
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% is generated by SEQPDIST.
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%
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% TREE = SEQNEIGHJOIN(DIST,METHOD) selects the method to compute the
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% distances of the new nodes to all other nodes at every iteration. The
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% general expression to calculate the distances between the new node (n)
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% (after joining i and j) and all others nodes (k) is given by:
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%
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% D(n,k) = a*D(i,k) + (1-a)*D(j,k) - a*D(n,i) - (1-a)*D(n,j)
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%
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% This expression guarantees to find the correct tree with additive data
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% (a.k.a. minimum variance reduction). The options for METHOD are:
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%
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% 'equivar' --- Assumes equal variance and independence of
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% (default) evolutionary distance estimates (a = 1/2). Such as
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% in Studier and Keppler, JMBE (1988).
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% 'firstorder' --- Assumes a first order model of the variances and
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% covariances of evolutionary distance estimates, 'a'
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% is adjusted at every iteration to a value between 0
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% and 1. Such as in Gascuel, JMBE (1997).
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% 'average' --- New distances are the weighted average of previous
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% distances, the branch distances are ignored:
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% D(n,k) = [ D(i,k) + D(j,k) ] /2
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% As in the original neighbor-joining algorithm by
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% Saitou and Nei, JMBE (1987)
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%
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% TREE = SEQNEIGHJOIN(DIST,METHOD,NAMES) passes a list of names to label
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% the leaf nodes (e.g. species or products) in the phylogenetic tree
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% object. NAMES can be a vector of structures with the fields 'Header' or
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% 'Name' or a cell array of strings. In both cases the number of elements
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% provided must comply with the number of samples used to generate the
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% pairwise distances in DIST.
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%
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% TREE = SEQNEIGHJOIN(...,'REROOT',false) excludes rerooting the resulting
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% tree. This is useful to observe the original linkage order followed by
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% the algorithm. By default SEQNEIGHJOIN reroots the resulting tree using
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% the mid-point method.
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%
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% Example:
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%
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% % Load a multiple alignment of amino acids:
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% seqs = fastaread('pf00002.fa');
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%
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% % Measure the 'Jukes-Cantor' pairwise distances:
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% dist = seqpdist(seqs,'method','jukes-cantor','indels','pair');
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%
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% % Build the phylogenetic using the neighbor-joining algorithm
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% tree = seqneighjoin(dist,'equivar',seqs)
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% view(tree)
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%
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% See also MULTIALIGN, PHYTREE, PHYTREE/REROOT, PHYTREE/VIEW, SEQLINKAGE,
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% SEQPDIST.
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% References:
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% [1] Saitou N, Nei M.The neighbor-joining method: a new method for
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% reconstructing phylogenetic trees. Mol Biol Evol.(1987) 4(4):406-25
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% [2] Gascuel O. BIONJ: An improved version of the NJ algorithm based on a
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% simple model of sequence data. Mol. Biol. Evol. (1997) 14:685-695
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% [3] Studier JA, Keppler KJ. A note on the neighbor-joining algorithm of
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% Saitou and Nei. Mol Biol Evol. (1988) 5(6):729-31.
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% Copyright 2003-2006 The MathWorks, Inc.
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% $Revision: 1.1.8.2 $ $Date: 2006/05/17 20:48:43 $
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rerootTree = true;
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checkForNames = true;
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% check the input distances
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if isnumeric(D)
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[m, n] = size(D);
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if isvector(D)
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n = numel(D);
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m = (1+sqrt(1+8*n))/2; % number of leaves
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if m ~= fix(m)
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error('Bioinfo:seqneighjoin:DbadSize',...
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'Size of DIST not compatible with the output of the SEQPDIST function.');
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end
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D = squareform(D);
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elseif m~=n
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error('Bioinfo:seqneighjoin:DnotSquare',...
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'Size of DIST not compatible with the output of the SEQPDIST function.');
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end
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else
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error('Bioinfo:seqneighjoin:DnotNumeric',...
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'DIST must be a numeric vector compatible with the output of the SEQPDIST function.');
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end
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% Selects appropiate method
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if nargin == 1
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method = 'e'; % set default method
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checkForNames = false;
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else
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okmethods = {'equivar','firstorder','average','reroot'};
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methodkeys = {'e','f','a'};
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k = find(strncmpi(method,okmethods,numel(method)));
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if isempty(k)
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error('Bioinfo:seqneighjoin:UnknownMethod',...
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'Unknown method name: %s.',method);
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elseif length(k)>1
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error('Bioinfo:seqneighjoin:IncorrectMethod',...
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'Ambiguous method name: %s.',method);
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elseif k<4
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method = methodkeys{k};
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else % case that second and third input are optional paired inputs
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if numel(varargin) || nargin==2
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error('Bioinfo:seqneighjoin:IncorrectInputArguments',...
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'Incorrect format of input arguments.')
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end
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varargin = {method,names};
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checkForNames = false;
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method = 'e'; % set default method
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end
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end
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% detects the names
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if checkForNames && (nargin >2) % names were supplied, check validity
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if iscell(names) || isfield(names,'Header') || isfield(names,'Name') || isfield(names,'LocusName')
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if isfield(names,'Header') % if struct put them in a cell
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names = {names(:).Header};
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elseif isfield(names,'Name') % if struct put them in a cell
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names = {names(:).Name};
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elseif isfield(names,'LocusName') % if struct put them in a cell
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names = {names(:).LocusName};
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end
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names = names(:);
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namesSupplied = true;
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if numel(names)~=m
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error('Bioinfo:seqneighjoin:IncorrectSize',...
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'NAMES must have the same size as number of leaves in the tree')
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end
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elseif strncmpi(names,{'reroot'},numel(names))
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varargin = {names varargin{:}};
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namesSupplied = false;
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else
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error('Bioinfo:seqneighjoin:IncorrectInputType',...
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'NAMES must be a cell with char arrays or a vector of structures.')
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end
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else
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namesSupplied = false;
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end
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% check optional input arguments
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nvarargin = numel(varargin);
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if nvarargin
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if rem(nvarargin,2)
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error('Bioinfo:seqneighjoin:IncorrectNumberOfArguments',...
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'Incorrect number of arguments to %s.',mfilename);
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end
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okargs = {'reroot',''};
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for j=1:2:nvarargin
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pname = varargin{j};
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pval = varargin{j+1};
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k = find(strncmpi(pname,okargs,numel(pname)));
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if isempty(k)
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error('Bioinfo:seqneighjoin:UnknownParameterName',...
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'Unknown parameter name: %s.',pname);
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elseif length(k)>1
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error('Bioinfo:seqneighjoin:AmbiguousParameterName',...
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'Ambiguous parameter name: %s.',pname);
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else
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rerootTree = opttf(pval);
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if isempty(rerootTree)
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error('Bioinfo:seqneighjoin:rerootInputOptionNotLogical',...
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'%s must be a logical value, true or false.',...
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upper(char(okargs(k))));
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end
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end
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end
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end
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% ------------------------------------------------------------------------
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% Algorithm starts here:
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%
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% D - pairwise distance matrix (full form)
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% method - 'a' for Saitou & Nei, 'e' for Studier & Keppler, and 'f' for
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% Gascuel
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% names - labels for leaf nodes
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N = size(D,1);
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Z = zeros(N-1,2);
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bd = zeros(N*2-1,1);
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p = 1:N; % pointers in matrix
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bc=1; % branch counter
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if method=='f'
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V=D; %initialize the variance matrix for Gascuel method
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end
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for n = N:-1:3
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R = sum(D)/(n-2); % sums of columns
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Q = D-repmat(R,n,1)-repmat(R',1,n)+diag(inf(n,1)); %Studier & Keppler optimized
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% S = (sum(sum(D))/(n-2)+Q)/2 % original total sum in Saitou & Nei
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[m,g] = min(Q(:)); %#ok
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[i,j] = ind2sub(n,g); % find minimum
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if i>j
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k=i;i=j;j=k; % j>i always
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end
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pp = p([i j]); % pointers to join
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bl = (R([i j])*[1 -1;-1 1] + D(j,i))/2; % branch lengths
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bl = max(bl,0);
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bd(pp) = bl; % save branch lengths
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Z(bc,:) = pp; % save pointers
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h = [1:i-1 i+1:j-1 j+1:n];
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switch method % distances to new node
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case 'a' % Saitou & Nei method
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d = (sum(D(h,[i j]),2))/2;
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D = [[D(h,h) d];[d' 0]]; % update distance matrix
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case 'e' % Studier & Keppler method
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d = (sum(D(h,[i j]),2)-D(j,i))/2;
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if any(d<0)
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d = max(d,0);
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end
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D = [[D(h,h) d];[d' 0]]; % update distance matrix
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case 'f' % Gascuel method
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if V(i,j)
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lambda = max(0,min(1,(1+sum(V(h,i)-V(h,j))/(n-2)/V(i,j))/2));
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else
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lambda = 1/2;
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end
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d = D(h,[i j])*[lambda;1-lambda] - bl*[lambda;1-lambda];
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if any(d<0)
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d = max(d,0);
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end
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D = [[D(h,h) d];[d' 0]]; % update distance matrix
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v = V(h,[i j])*[lambda;1-lambda] - V(i,j)*lambda*(1-lambda);
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if any(v<0)
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v = max(v,0);
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end
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V = [[V(h,h) v];[v' 0]]; % update variance matrix
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end
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p = [p(h),N+bc]; % update pointers
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bc = bc+1; % update branch counter
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end
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Z(bc,:) = p; % pointers of last branch
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bd(p) = D(2)/2; % lengths of last branch
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% convert data to a phylogenetic tree object
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if namesSupplied
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t = phyTree(Z,bd,names);
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else
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t = phyTree(Z,bd);
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end
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if rerootTree
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t = reRoot(t); % reroot with mid-point method
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end
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