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| 4 | <TITLE>contchar</TITLE> |
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| 11 | <BODY BGCOLOR="#ccffff"> |
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| 12 | <DIV ALIGN=RIGHT> |
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| 13 | version 3.6 |
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| 14 | </DIV> |
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| 15 | <P> |
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| 16 | <DIV ALIGN=CENTER> |
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| 17 | <H1>CONTRAST -- Computes contrasts for comparative method</H1> |
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| 18 | </DIV> |
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| 19 | <P> |
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| 20 | <PRE> |
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| 21 | </PRE> |
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| 22 | <P> |
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| 23 | © Copyright 1991-2002 by the University of |
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| 24 | Washington. Written by Joseph Felsenstein. Permission is granted to copy |
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| 25 | this document provided that no fee is charged for it and that this copyright |
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| 26 | notice is not removed. |
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| 27 | <P> |
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| 28 | This program implements the contrasts calculation described in my 1985 |
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| 29 | paper on the comparative method (Felsenstein, 1985d). It reads in a |
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| 30 | data set of the standard quantitative characters sort, and also a |
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| 31 | tree from the treefile. It then forms the contrasts between species |
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| 32 | that, according to that tree, are statistically independent. This is |
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| 33 | done for each character. The contrasts are all standardized by |
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| 34 | branch lengths (actually, square roots of branch lengths). |
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| 35 | <P> |
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| 36 | The method is explained in the 1985 paper. It assumes |
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| 37 | a Brownian motion model. This model was introduced by Edwards and |
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| 38 | Cavalli-Sforza (1964; Cavalli-Sforza and Edwards, 1967) |
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| 39 | as an approximation to the evolution of gene frequencies. I have |
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| 40 | discussed (Felsenstein, 1973b, 1981c, 1985d, 1988b) the difficulties |
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| 41 | inherent in using it as a model for the evolution of quantitative |
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| 42 | characters. Chief among these is that the characters do not necessarily evolve |
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| 43 | independently or at equal rates. This program allows one to evaluate this, |
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| 44 | if there is independent information on the phylogeny. You can |
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| 45 | compute the variance of the contrasts for each character, as a measure of |
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| 46 | the variance accumulating per unit branch length. You can also test |
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| 47 | covariances of characters. |
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| 48 | <P> |
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| 49 | The input file is as described in the continuous characters |
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| 50 | documentation file above, for the case of continuous quantitative |
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| 51 | characters (not gene frequencies). Options are selected using a menu: |
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| 52 | <P> |
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| 53 | <TABLE><TR><TD BGCOLOR=white> |
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| 54 | <PRE> |
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| 55 | |
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| 56 | Continuous character comparative analysis, version 3.6a3 |
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| 57 | |
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| 58 | Settings for this run: |
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| 59 | W within-population variation in data? No, species values are means |
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| 60 | R Print out correlations and regressions? Yes |
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| 61 | A LRT test of no phylogenetic component? Yes, with and without VarA |
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| 62 | C Print out contrasts? No |
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| 63 | M Analyze multiple trees? No |
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| 64 | 0 Terminal type (IBM PC, ANSI, none)? (none) |
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| 65 | 1 Print out the data at start of run No |
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| 66 | 2 Print indications of progress of run Yes |
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| 67 | |
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| 68 | Y to accept these or type the letter for one to change |
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| 69 | |
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| 70 | </PRE> |
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| 71 | </TD></TR></TABLE> |
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| 72 | <P> |
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| 73 | Option W makes the program expect not means of the phenotypes in each |
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| 74 | species, but phenotypes of individual specimens. The details of |
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| 75 | the input file format in that case are given below. In that case the |
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| 76 | program estimates the covariances of the phenotypic change, as well as |
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| 77 | covariances of within-species phenotypic variation. The model used is |
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| 78 | similar to (but not identical to) that of Lynch (1990). The |
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| 79 | algorithms used differ from the ones he |
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| 80 | gives in that paper. They will be described in a forthcoming paper by |
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| 81 | me. In the case that has within-species samples contrasts are used by |
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| 82 | the program, but it does not make sense to write them out to an |
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| 83 | output file for direct analysis. They are of two kinds, contrasts |
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| 84 | within species and contrasts between species. The former are |
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| 85 | affected only by the within-species phenotypic covariation, but the |
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| 86 | latter are affected by both within- and between-species covariation. |
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| 87 | CONTRAST infers these two kinds of covariances and writes the |
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| 88 | estimates out. |
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| 89 | <P> |
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| 90 | M is similar to the usual multiple data sets input option, but is used here |
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| 91 | to allow multiple trees to be read from the treefile, not multiple |
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| 92 | data sets to be read from the input file. In this way you can |
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| 93 | use bootstrapping on the data that estimated these trees, get |
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| 94 | multiple bootstrap estimates of the tree, and then use the M |
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| 95 | option to make multiple analyses of the contrasts and the |
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| 96 | covariances, correlations, and regressions. In this way (Felsenstein, |
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| 97 | 1988b) you can assess the effect of the inaccuracy of the trees on |
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| 98 | your estimates of these statistics. |
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| 99 | <P> |
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| 100 | R allows you to turn off or on the printing out of the statistics. |
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| 101 | If it is off only the contrasts will be printed out (unless option |
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| 102 | 1 is selected). With only the contrasts printed out, they are in |
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| 103 | a simple array that is in a form that many statistics packages should |
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| 104 | be able to read. The contrasts are rows, and each row has one contrast |
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| 105 | for each character. Any multivariate statistics package should be able |
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| 106 | to analyze these (but keep in mind that the contrasts have, by virtue |
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| 107 | of the way they are generated, expectation zero, so all regressions |
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| 108 | must pass through the origin). If the W option has been set to |
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| 109 | analyze within-species as well as between-species variation, the R |
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| 110 | option does not appear in the menu as the regression and correlation |
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| 111 | statistics should always be computed in that case. |
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| 112 | <P> |
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| 113 | As usual, the tree file has the default name <TT>intree</TT>. It |
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| 114 | should contain the desired tree or trees. These can be |
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| 115 | either in bifurcating form, or may have the bottommost fork be a |
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| 116 | trifurcation (it should not matter which of these ways you present the tree). |
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| 117 | The tree must, of course, have branch lengths. |
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| 118 | <P> |
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| 119 | If you have a molecular data set (for example) and also, on the same |
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| 120 | species, quantitative measurements, here is how you can allow for the |
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| 121 | uncertainty of yor estimate of the tree. Use SEQBOOT to generate multiple |
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| 122 | data sets from your molecular data. Then, whichever method you use to |
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| 123 | analyze it (the relevant ones are those that produce estimates of the |
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| 124 | branch lengths: DNAML, DNAMLK, FITCH, KITSCH, and NEIGHBOR -- the latter |
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| 125 | three require you to use DNADIST to turn the bootstrap data sets into |
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| 126 | multiple distance matrices), you should use the Multiple Data Sets |
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| 127 | option of that program. This will result in a tree file with many |
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| 128 | trees on it. Then use this tree file with the input file containing |
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| 129 | your continuous quantitative characters, choosing the Multiple Trees |
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| 130 | (M) option. You will get one set of contrasts and statistics for each |
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| 131 | tree in the tree file. At the moment there is no overall summary: |
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| 132 | you will have to tabulate these by hand. A similar process can be |
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| 133 | followed if you have restriction sites data (using RESTML) or |
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| 134 | gene frequencies data. |
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| 135 | <P> |
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| 136 | The statistics that are printed out include the covariances between |
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| 137 | all pairs of characters, the regressions of each character on each |
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| 138 | other (column j is regressed on row i), and the correlations between |
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| 139 | all pairs of characters. In assessing degress of freedom it is |
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| 140 | important to realize that each contrast was taken to have |
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| 141 | expectation zero, which is known because each contrast could as |
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| 142 | easily have been computed xi-xj instead of xj-xi. Thus there is no |
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| 143 | loss of a degree of freedom for estimation of a mean. The degrees |
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| 144 | of freedom is thus the same as the number of contrasts, namely one |
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| 145 | less than the number of species (tips). If you feed these contrasts |
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| 146 | into a multivariate statistics program make sure that it knows that |
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| 147 | each variable has expectation exactly zero. |
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| 148 | <P> |
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| 149 | <DIV CENTER> |
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| 150 | <H2>Within-species variation</H2> |
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| 151 | </DIV> |
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| 152 | With the W option selected, CONTRAST analyzes data sets with variation within |
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| 153 | species, using a model like that proposed by Michael Lynch (1990). |
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| 154 | If you select the W option for within-species variation, the data |
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| 155 | set should have this structure (on the left are the data, on the right |
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| 156 | my comments: |
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| 157 | <P> |
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| 158 | <TABLE><TR><TD bgcolor=white> |
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| 159 | <PRE> |
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| 160 | 10 5 |
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| 161 | Alpha 2 |
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| 162 | 2.01 5.3 1.5 -3.41 0.3 |
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| 163 | 1.98 4.3 2.1 -2.98 0.45 |
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| 164 | Gammarus 3 |
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| 165 | 6.57 3.1 2.0 -1.89 0.6 |
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| 166 | 7.62 3.4 1.9 -2.01 0.7 |
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| 167 | 6.02 3.0 1.9 -2.03 0.6 |
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| 168 | ... |
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| 169 | </PRE> |
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| 170 | </TD> |
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| 171 | <TD> |
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| 172 | <PRE> |
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| 173 | number of species, number of characters |
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| 174 | name of 1st species, # of individuals |
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| 175 | data for individual #1 |
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| 176 | data for individual #2 |
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| 177 | name of 2nd species, # of individuals |
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| 178 | data for individual #1 |
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| 179 | data for individual #2 |
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| 180 | data for individual #3 |
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| 181 | (and so on) |
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| 182 | </PRE> |
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| 183 | </TD></TR></TABLE> |
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| 184 | <P> |
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| 185 | The covariances, correlations, and regressions for the "additive" |
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| 186 | (between-species evolutionary variation) and "environmental" (within-species |
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| 187 | phenotypic variation) are |
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| 188 | printed out (the maximum likelihood estimates of each). |
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| 189 | The program also estimates the within-species phenotypic variation in the |
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| 190 | case where the between-species evolutionary covariances are forced to be |
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| 191 | zero. The log-likelihoods of these two cases are compared and a |
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| 192 | likelihood ratio test (LRT) is carried out. The program prints the result |
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| 193 | of this test as a chi-square variate, and gives the number of degrees of |
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| 194 | freedom of the LRT. You have to look up the chi-square variable on a |
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| 195 | table of the chi-square distribution. |
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| 196 | <P> |
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| 197 | The log-likelihood of the data under the models with and without |
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| 198 | between-species For the moment the program cannot handle the case where |
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| 199 | within-species variation is to be taken into account but where only species |
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| 200 | means are available. (It can handle cases where some species have only one |
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| 201 | member in their sample). |
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| 202 | <P> |
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| 203 | We hope to fix this soon. We are also on our way to |
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| 204 | incorporating full-sib, half-sib, or clonal groups within species, so as |
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| 205 | to do one analysis for within-species genetic and between-species |
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| 206 | phylogenetic variation. |
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| 207 | <P> |
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| 208 | The data set used as an example below is the example from a |
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| 209 | paper by Michael Lynch (1990), his characters having been log-transformed. |
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| 210 | In the case where there is only one specimen per species, Lynch's model |
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| 211 | is identical to our model of within-species variation (for |
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| 212 | multiple individuals per species it is not a subcase of his model). |
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| 213 | <P> |
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| 214 | <HR> |
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| 215 | <P> |
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| 216 | <H3>TEST SET INPUT</H3> |
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| 217 | <P> |
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| 218 | <TABLE><TR><TD BGCOLOR=white> |
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| 219 | <PRE> |
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| 220 | 5 2 |
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| 221 | Homo 4.09434 4.74493 |
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| 222 | Pongo 3.61092 3.33220 |
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| 223 | Macaca 2.37024 3.36730 |
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| 224 | Ateles 2.02815 2.89037 |
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| 225 | Galago -1.46968 2.30259 |
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| 226 | </PRE> |
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| 227 | <P> |
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| 228 | </TD></TR></TABLE> |
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| 229 | <HR> |
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| 230 | <P> |
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| 231 | <H3>TEST SET INPUT TREEFILE</H3> |
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| 232 | <P> |
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| 233 | <TABLE><TR><TD BGCOLOR=white> |
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| 234 | <PRE> |
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| 235 | ((((Homo:0.21,Pongo:0.21):0.28,Macaca:0.49):0.13,Ateles:0.62):0.38,Galago:1.00); |
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| 236 | </PRE> |
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| 237 | </TD></TR></TABLE> |
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| 238 | <P> |
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| 239 | <HR> |
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| 240 | <P> |
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| 241 | <H3>TEST SET OUTPUT (with all numerical options on )<H3> |
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| 242 | <P> |
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| 243 | <TABLE><TR><TD BGCOLOR=white> |
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| 244 | <PRE> |
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| 245 | |
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| 246 | Continuous character contrasts analysis, version 3.6a3 |
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| 247 | |
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| 248 | 5 Populations, 2 Characters |
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| 249 | |
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| 250 | Name Phenotypes |
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| 251 | ---- ---------- |
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| 252 | |
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| 253 | Homo 4.09434 4.74493 |
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| 254 | Pongo 3.61092 3.33220 |
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| 255 | Macaca 2.37024 3.36730 |
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| 256 | Ateles 2.02815 2.89037 |
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| 257 | Galago -1.46968 2.30259 |
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| 258 | |
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| 259 | |
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| 260 | Covariance matrix |
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| 261 | ---------- ------ |
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| 262 | |
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| 263 | 4.1991 1.3844 |
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| 264 | 1.3844 0.7125 |
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| 265 | |
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| 266 | Regressions (columns on rows) |
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| 267 | ----------- -------- -- ----- |
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| 268 | |
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| 269 | 1.0000 0.3297 |
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| 270 | 1.9430 1.0000 |
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| 271 | |
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| 272 | Correlations |
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| 273 | ------------ |
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| 274 | |
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| 275 | 1.0000 0.8004 |
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| 276 | 0.8004 1.0000 |
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| 277 | |
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| 278 | </PRE> |
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| 279 | </TD></TR></TABLE> |
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| 280 | </BODY> |
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| 281 | </HTML> |
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