[R] assessing the fit of a LME model

Federico Calboli f.calboli at ucl.ac.uk
Tue May 13 17:17:11 CEST 2003


Dear All,

I would like to ask a couple of questions on a LME model.

I tested 4 selection lines at 4 food concentrations against a standard
competitor stock. I had 3 replicate cages per selection line. In each cage
I have 10 vials. I counted the number of wild type flies and competitor
stock emerging in each vial. My main question is: is there any difference
between selection lines?

I did fit the following model:

mod1<-lme(wt~selection*food, random=~1|c1/food, competition)

The quantile plot is straight, the plot of residuals looks good, the
standardized residual plot seems ok... BUT if I do a bartlett test for
homogeneity of variance (done by cage*temperature, 48 cages in all) the
variance is NOT homogeneous. Is my model still accettable? if not, what
could I do?

The same model on asin(sqrt(wild type/total)) does not fit anywhere as well.

my dataset (NB *wt* is the number of wild type flies in each vial; *spa* is
the number of comepetitor stock flies in each vial, *p1* is
asin(sqrt(competition$prop)), *c1* is the cage nested in selection using
getGroups...):

    selection cage food wt spa tot       prop        p1   c1
1          25    1  100 21  22  43 0.48837209 0.7737692 25/1
2          25    1  100 21  22  43 0.48837209 0.7737692 25/1
3          25    1  100  5   5  10 0.50000000 0.7853982 25/1
4          25    1  100 21  17  38 0.55263158 0.8381274 25/1
5          25    1  100 13  22  35 0.37142857 0.6553659 25/1
6          25    1  100 24  18  42 0.57142857 0.8570719 25/1
7          25    1  100 22  19  41 0.53658537 0.8220163 25/1
8          25    1  100 15  23  38 0.39473684 0.6793415 25/1
9          25    1  100 19  19  38 0.50000000 0.7853982 25/1
10         25    1  100 18  19  37 0.48648649 0.7718830 25/1
11         25    2  100 21  22  43 0.48837209 0.7737692 25/2
12         25    2  100 24  18  42 0.57142857 0.8570719 25/2
13         25    2  100  9  21  30 0.30000000 0.5796397 25/2
14         25    2  100  2  13  15 0.13333333 0.3737922 25/2
15         25    2  100 10  11  21 0.47619048 0.7615796 25/2
16         25    2  100 26  20  46 0.56521739 0.8508019 25/2
17         25    2  100 11  17  28 0.39285714 0.6774179 25/2
18         25    2  100  9  22  31 0.29032258 0.5690309 25/2
19         25    2  100 15  22  37 0.40540541 0.6902300 25/2
20         25    2  100 19  24  43 0.44186047 0.7271268 25/2
21         25    3  100 22  23  45 0.48888889 0.7742861 25/3
22         25    3  100 13  22  35 0.37142857 0.6553659 25/3
23         25    3  100 18  21  39 0.46153846 0.7468986 25/3
24         25    3  100 12  20  32 0.37500000 0.6590580 25/3
25         25    3  100 17  20  37 0.45945946 0.7448131 25/3
26         25    3  100 15  26  41 0.36585366 0.6495880 25/3
27         25    3  100 19   0  19 1.00000000 1.5707963 25/3
28         25    3  100 25  23  48 0.52083333 0.8062375 25/3
29         25    3  100 15  19  34 0.44117647 0.7264381 25/3
30         25    3  100 12  21  33 0.36363636 0.6472848 25/3
31         18    1  100 30  23  53 0.56603774 0.8516294 18/1
32         18    1  100 18  22  40 0.45000000 0.7353145 18/1
33         18    1  100 20  26  46 0.43478261 0.7199944 18/1
34         18    1  100 21  16  37 0.56756757 0.8531731 18/1
35         18    1  100 17  14  31 0.54838710 0.8338611 18/1
36         18    1  100 26  21  47 0.55319149 0.8386905 18/1
37         18    1  100 19  23  42 0.45238095 0.7377068 18/1
38         18    1  100 24  19  43 0.55813953 0.8436695 18/1
39         18    1  100 25  21  46 0.54347826 0.8289314 18/1
40         18    1  100 14  20  34 0.41176471 0.6966984 18/1
41         18    2  100 18  16  34 0.52941176 0.8148269 18/2
42         18    2  100 23  19  42 0.54761905 0.8330895 18/2
43         18    2  100 19  20  39 0.48717949 0.7725762 18/2
44         18    2  100 25  20  45 0.55555556 0.8410687 18/2
45         18    2  100 19  21  40 0.47500000 0.7603877 18/2
46         18    2  100 20  23  43 0.46511628 0.7504861 18/2
47         18    2  100 23  24  47 0.48936170 0.7747591 18/2
48         18    2  100 22  20  42 0.52380952 0.8092167 18/2
49         18    2  100 25  19  44 0.56818182 0.8537931 18/2
50         18    2  100 19  26  45 0.42222222 0.7073032 18/2
51         18    3  100 21  20  41 0.51219512 0.7975945 18/3
52         18    3  100 22  24  46 0.47826087 0.7636522 18/3
53         18    3  100 19  26  45 0.42222222 0.7073032 18/3
54         18    3  100 17  22  39 0.43589744 0.7211187 18/3
55         18    3  100 22  23  45 0.48888889 0.7742861 18/3
56         18    3  100 20  25  45 0.44444444 0.7297277 18/3
57         18    3  100 25  23  48 0.52083333 0.8062375 18/3
58         18    3  100 24  21  45 0.53333333 0.8187562 18/3
59         18    3  100 23  25  48 0.47916667 0.7645588 18/3
60         18    3  100 25  22  47 0.53191489 0.8173348 18/3
61          s    1  100 22  23  45 0.48888889 0.7742861  s/1
62          s    1  100 25  18  43 0.58139535 0.8671574  s/1
63          s    1  100 19  20  39 0.48717949 0.7725762  s/1
64          s    1  100 22  19  41 0.53658537 0.8220163  s/1
65          s    1  100 18  18  36 0.50000000 0.7853982  s/1
66          s    1  100 23  18  41 0.56097561 0.8465259  s/1
67          s    1  100 23  20  43 0.53488372 0.8203102  s/1
68          s    1  100 24  21  45 0.53333333 0.8187562  s/1
69          s    1  100 21  18  39 0.53846154 0.8238977  s/1
70          s    1  100 25  22  47 0.53191489 0.8173348  s/1
71          s    2  100 20  24  44 0.45454545 0.7398808  s/2
72          s    2  100 18  19  37 0.48648649 0.7718830  s/2
73          s    2  100 20  18  38 0.52631579 0.8117261  s/2
74          s    2  100 19  11  30 0.63333333 0.9203646  s/2
75          s    2  100 20  23  43 0.46511628 0.7504861  s/2
76          s    2  100 23  22  45 0.51111111 0.7965102  s/2
77          s    2  100 23  24  47 0.48936170 0.7747591  s/2
78          s    2  100 24  18  42 0.57142857 0.8570719  s/2
79          s    2  100 20  17  37 0.54054054 0.8259833  s/2
80          s    2  100 23  20  43 0.53488372 0.8203102  s/2
81          s    3  100 19  21  40 0.47500000 0.7603877  s/3
82          s    3  100 17  18  35 0.48571429 0.7711105  s/3
83          s    3  100 10  19  29 0.34482759 0.6276203  s/3
84          s    3  100 17  21  38 0.44736842 0.7326689  s/3
85          s    3  100 20  22  42 0.47619048 0.7615796  s/3
86          s    3  100  8  17  25 0.32000000 0.6012642  s/3
87          s    3  100 21  12  33 0.63636364 0.9235115  s/3
88          s    3  100 17  22  39 0.43589744 0.7211187  s/3
89          s    3  100 18  21  39 0.46153846 0.7468986  s/3
90          s    3  100 21  22  43 0.48837209 0.7737692  s/3
91          l    1  100 21  20  41 0.51219512 0.7975945  l/1
92          l    1  100 21  20  41 0.51219512 0.7975945  l/1
93          l    1  100 15  18  33 0.45454545 0.7398808  l/1
94          l    1  100  4   8  12 0.33333333 0.6154797  l/1
95          l    1  100 11  10  21 0.52380952 0.8092167  l/1
96          l    1  100  5  18  23 0.21739130 0.4850498  l/1
97          l    1  100  9  18  27 0.33333333 0.6154797  l/1
98          l    1  100  6  18  24 0.25000000 0.5235988  l/1
99          l    1  100 14   1  15 0.93333333 1.3096389  l/1
100         l    1  100 15  26  41 0.36585366 0.6495880  l/1
101         l    2  100 21  20  41 0.51219512 0.7975945  l/2
102         l    2  100 21  21  42 0.50000000 0.7853982  l/2
103         l    2  100  8  12  20 0.40000000 0.6847192  l/2
104         l    2  100 14   9  23 0.60869565 0.8949687  l/2
105         l    2  100 14  12  26 0.53846154 0.8238977  l/2
106         l    2  100 27  23  50 0.54000000 0.8254410  l/2
107         l    2  100  7  16  23 0.30434783 0.5843739  l/2
108         l    2  100 13  23  36 0.36111111 0.6446581  l/2
109         l    2  100 24  25  49 0.48979592 0.7751934  l/2
110         l    2  100 26  24  50 0.52000000 0.8054035  l/2
111         l    3  100 23  22  45 0.51111111 0.7965102  l/3
112         l    3  100 23  25  48 0.47916667 0.7645588  l/3
113         l    3  100 21  23  44 0.47727273 0.7626631  l/3
114         l    3  100 26  21  47 0.55319149 0.8386905  l/3
115         l    3  100 22  16  38 0.57894737 0.8646773  l/3
116         l    3  100 22  22  44 0.50000000 0.7853982  l/3
117         l    3  100 25  20  45 0.55555556 0.8410687  l/3
118         l    3  100 29  26  55 0.52727273 0.8126844  l/3
119         l    3  100 26  20  46 0.56521739 0.8508019  l/3
120         l    3  100 24  22  46 0.52173913 0.8071441  l/3
121        25    1   50 20  18  38 0.52631579 0.8117261 25/1
122        25    1   50 19  19  38 0.50000000 0.7853982 25/1
123        25    1   50 16  23  39 0.41025641 0.6951656 25/1
124        25    1   50 20  25  45 0.44444444 0.7297277 25/1
125        25    1   50 17  23  40 0.42500000 0.7101140 25/1
126        25    1   50 20  20  40 0.50000000 0.7853982 25/1
127        25    1   50 19  21  40 0.47500000 0.7603877 25/1
128        25    1   50 21  26  47 0.44680851 0.7321058 25/1
129        25    1   50 18  20  38 0.47368421 0.7590702 25/1
130        25    1   50  8  22  30 0.26666667 0.5426391 25/1
131        25    2   50 17  24  41 0.41463415 0.6996120 25/2
132        25    2   50  3  19  22 0.13636364 0.3782282 25/2
133        25    2   50  8  14  22 0.36363636 0.6472848 25/2
134        25    2   50 19  22  41 0.46341463 0.7487801 25/2
135        25    2   50  3  24  27 0.11111111 0.3398369 25/2
136        25    2   50 15  22  37 0.40540541 0.6902300 25/2
137        25    2   50  2   9  11 0.18181818 0.4405107 25/2
138        25    2   50 16  19  35 0.45714286 0.7424884 25/2
139        25    2   50  1  23  24 0.04166667 0.2055689 25/2
140        25    2   50 18  16  34 0.52941176 0.8148269 25/2
141        25    3   50  0  17  17 0.00000000 0.0000000 25/3
142        25    3   50  6  20  26 0.23076923 0.5010930 25/3
143        25    3   50 12  25  37 0.32432432 0.6058911 25/3
144        25    3   50 12  21  33 0.36363636 0.6472848 25/3
145        25    3   50 13  22 145 0.84827586 1.1706883 25/3
146        25    3   50 14  22  36 0.38888889 0.6733516 25/3
147        25    3   50 17  25  42 0.40476190 0.6895746 25/3
148        25    3   50 15  23  38 0.39473684 0.6793415 25/3
149        25    3   50 14  25  39 0.35897436 0.6424324 25/3
150        25    3   50 23  24  47 0.48936170 0.7747591 25/3
151        18    1   50  9  21  30 0.30000000 0.5796397 18/1
152        18    1   50 18  19  37 0.48648649 0.7718830 18/1
153        18    1   50 15  25  40 0.37500000 0.6590580 18/1
154        18    1   50 25  23  48 0.52083333 0.8062375 18/1
155        18    1   50 19  22  41 0.46341463 0.7487801 18/1
156        18    1   50 18  25  43 0.41860465 0.7036390 18/1
157        18    1   50 18  21  39 0.46153846 0.7468986 18/1
158        18    1   50 20  21  41 0.48780488 0.7732018 18/1
159        18    1   50  8  22  30 0.26666667 0.5426391 18/1
160        18    1   50 14  25  39 0.35897436 0.6424324 18/1
161        18    2   50 11  21  32 0.34375000 0.6264863 18/2
162        18    2   50 22  21  43 0.51162791 0.7970271 18/2
163        18    2   50  4  16  20 0.20000000 0.4636476 18/2
164        18    2   50 20  23  43 0.46511628 0.7504861 18/2
165        18    2   50 21  22  43 0.48837209 0.7737692 18/2
166        18    2   50 18  20  38 0.47368421 0.7590702 18/2
167        18    2   50  9  17  26 0.34615385 0.6290148 18/2
168        18    2   50 20  24  44 0.45454545 0.7398808 18/2
169        18    2   50 13  20  33 0.39393939 0.6785256 18/2
170        18    2   50 20  21  41 0.48780488 0.7732018 18/2
171        18    3   50  6  14  20 0.30000000 0.5796397 18/3
172        18    3   50 19  25  44 0.43181818 0.7170032 18/3
173        18    3   50  7  21  28 0.25000000 0.5235988 18/3
174        18    3   50 19  24  43 0.44186047 0.7271268 18/3
175        18    3   50 21  23  44 0.47727273 0.7626631 18/3
176        18    3   50 16  20  36 0.44444444 0.7297277 18/3
177        18    3   50 23  26  49 0.46938776 0.7547668 18/3
178        18    3   50 22  20  42 0.52380952 0.8092167 18/3
179        18    3   50 13  20  33 0.39393939 0.6785256 18/3
180        18    3   50 18  24  42 0.42857143 0.7137244 18/3
181         s    1   50 14  21  35 0.40000000 0.6847192  s/1
182         s    1   50 16  21  37 0.43243243 0.7176232  s/1
183         s    1   50 18  18  36 0.50000000 0.7853982  s/1
184         s    1   50 12  16  28 0.42857143 0.7137244  s/1
185         s    1   50 15  17  32 0.46875000 0.7541278  s/1
186         s    1   50 17  22  39 0.43589744 0.7211187  s/1
187         s    1   50  3  20  23 0.13043478 0.3695089  s/1
188         s    1   50 18  20  38 0.47368421 0.7590702  s/1
189         s    1   50 18  23  41 0.43902439 0.7242704  s/1
190         s    1   50  9  19  28 0.32142857 0.6027946  s/1
191         s    2   50 16  24  40 0.40000000 0.6847192  s/2
192         s    2   50 20  22  42 0.47619048 0.7615796  s/2
193         s    2   50 18  20  38 0.47368421 0.7590702  s/2
194         s    2   50 22  22  44 0.50000000 0.7853982  s/2
195         s    2   50 19  23  42 0.45238095 0.7377068  s/2
196         s    2   50 13  15  28 0.46428571 0.7496534  s/2
197         s    2   50 13  15  28 0.46428571 0.7496534  s/2
198         s    2   50 18  20  38 0.47368421 0.7590702  s/2
199         s    2   50 12  26  38 0.31578947 0.5967431  s/2
200         s    2   50  7  21  28 0.25000000 0.5235988  s/2
201         s    3   50 13  22  35 0.37142857 0.6553659  s/3
202         s    3   50 16  21  37 0.43243243 0.7176232  s/3
203         s    3   50 12  17  29 0.41379310 0.6987583  s/3
204         s    3   50 17  10  27 0.62962963 0.9165257  s/3
205         s    3   50  7  18  25 0.28000000 0.5575988  s/3
206         s    3   50  7   9  16 0.43750000 0.7227342  s/3
207         s    3   50  8  20  28 0.28571429 0.5639426  s/3
208         s    3   50  5  15  20 0.25000000 0.5235988  s/3
209         s    3   50  9  20  29 0.31034483 0.5908728  s/3
210         s    3   50  6  15  21 0.28571429 0.5639426  s/3
211         l    1   50  4  18  22 0.18181818 0.4405107  l/1
212         l    1   50  7  16  23 0.30434783 0.5843739  l/1
213         l    1   50  4  20  24 0.16666667 0.4205343  l/1
214         l    1   50 21  24  45 0.46666667 0.7520401  l/1
215         l    1   50  7  24  31 0.22580645 0.4951811  l/1
216         l    1   50  9  19  28 0.32142857 0.6027946  l/1
217         l    1   50  2  13  15 0.13333333 0.3737922  l/1
218         l    1   50  5  24  29 0.17241379 0.4281928  l/1
219         l    1   50 23  21  44 0.52272727 0.8081333  l/1
220         l    1   50 16  19  35 0.45714286 0.7424884  l/1
221         l    2   50 20  16  36 0.55555556 0.8410687  l/2
222         l    2   50 12   8  20 0.60000000 0.8860771  l/2
223         l    2   50 15  23  38 0.39473684 0.6793415  l/2
224         l    2   50  3  18  21 0.14285714 0.3875967  l/2
225         l    2   50  8  16  24 0.33333333 0.6154797  l/2
226         l    2   50  9  19  28 0.32142857 0.6027946  l/2
227         l    2   50 22  22  44 0.50000000 0.7853982  l/2
228         l    2   50  9  10  19 0.47368421 0.7590702  l/2
229         l    2   50 13  23  36 0.36111111 0.6446581  l/2
230         l    2   50 15  20  35 0.42857143 0.7137244  l/2
231         l    3   50 20  21  41 0.48780488 0.7732018  l/3
232         l    3   50  9  18  27 0.33333333 0.6154797  l/3
233         l    3   50 18  18  36 0.50000000 0.7853982  l/3
234         l    3   50  9  16  25 0.36000000 0.6435011  l/3
235         l    3   50 22  26  48 0.45833333 0.7436831  l/3
236         l    3   50 21  17  38 0.55263158 0.8381274  l/3
237         l    3   50 19  23  42 0.45238095 0.7377068  l/3
238         l    3   50 19  20  39 0.48717949 0.7725762  l/3
239         l    3   50 18  21  39 0.46153846 0.7468986  l/3
240         l    3   50 21  22  43 0.48837209 0.7737692  l/3
241        25    1   25 19  23  42 0.45238095 0.7377068 25/1
242        25    1   25  0   7   7 0.00000000 0.0000000 25/1
243        25    1   25 14   9  23 0.60869565 0.8949687 25/1
244        25    1   25  0  14  14 0.00000000 0.0000000 25/1
245        25    1   25 14  22  36 0.38888889 0.6733516 25/1
246        25    1   25  0   3   3 0.00000000 0.0000000 25/1
247        25    1   25 15  23  38 0.39473684 0.6793415 25/1
248        25    1   25 14  20  34 0.41176471 0.6966984 25/1
249        25    1   25  7  13  20 0.35000000 0.6330518 25/1
250        25    1   25 15  20  35 0.42857143 0.7137244 25/1
251        25    2   25  0   9   9 0.00000000 0.0000000 25/2
252        25    2   25 16  23  39 0.41025641 0.6951656 25/2
253        25    2   25 15  25  40 0.37500000 0.6590580 25/2
254        25    2   25 17  19  36 0.47222222 0.7576061 25/2
255        25    2   25  1  10  11 0.09090909 0.3062774 25/2
256        25    2   25  2  20  22 0.09090909 0.3062774 25/2
257        25    2   25  7  15  22 0.31818182 0.5993139 25/2
258        25    2   25  1  18  19 0.05263158 0.2314774 25/2
259        25    2   25  3  22  25 0.12000000 0.3537416 25/2
260        25    2   25  9  21  30 0.30000000 0.5796397 25/2
261        25    3   25  2  23  25 0.08000000 0.2867566 25/3
262        25    3   25  1  19  20 0.05000000 0.2255134 25/3
263        25    3   25  8  21  29 0.27586207 0.5529804 25/3
264        25    3   25 10  20  30 0.33333333 0.6154797 25/3
265        25    3   25  6   6  12 0.50000000 0.7853982 25/3
266        25    3   25  0  15  15 0.00000000 0.0000000 25/3
267        25    3   25  1  17  18 0.05555556 0.2379411 25/3
268        25    3   25  3  24  27 0.11111111 0.3398369 25/3
269        25    3   25  7  19  26 0.26923077 0.5455338 25/3
270        25    3   25  4  22  26 0.15384615 0.4030571 25/3
271        18    1   25  6  18  24 0.25000000 0.5235988 18/1
272        18    1   25  0  14  14 0.00000000 0.0000000 18/1
273        18    1   25  7  19  26 0.26923077 0.5455338 18/1
274        18    1   25  5  22  27 0.18518519 0.4448600 18/1
275        18    1   25  3  10  13 0.23076923 0.5010930 18/1
276        18    1   25 14  24  38 0.36842105 0.6522512 18/1
277        18    1   25 12  21  33 0.36363636 0.6472848 18/1
278        18    1   25  0  23  23 0.00000000 0.0000000 18/1
279        18    1   25 14  17  31 0.45161290 0.7369352 18/1
280        18    1   25  2  12  14 0.14285714 0.3875967 18/1
281        18    2   25  8  19  27 0.29629630 0.5755915 18/2
282        18    2   25 12  20  32 0.37500000 0.6590580 18/2
283        18    2   25 10  18  28 0.35714286 0.6405223 18/2
284        18    2   25  0   6   6 0.00000000 0.0000000 18/2
285        18    2   25  8  16  24 0.33333333 0.6154797 18/2
286        18    2   25  8  21  29 0.27586207 0.5529804 18/2
287        18    2   25  2  18  20 0.10000000 0.3217506 18/2
288        18    2   25  5  17  22 0.22727273 0.4969325 18/2
289        18    2   25  3  20  23 0.13043478 0.3695089 18/2
290        18    2   25  7  17  24 0.29166667 0.5705104 18/2
291        18    3   25 11  20  31 0.35483871 0.6381162 18/3
292        18    3   25  8  19  27 0.29629630 0.5755915 18/3
293        18    3   25  6  14  20 0.30000000 0.5796397 18/3
294        18    3   25 19  19  38 0.50000000 0.7853982 18/3
295        18    3   25  8  21  29 0.27586207 0.5529804 18/3
296        18    3   25  3  21  24 0.12500000 0.3613671 18/3
297        18    3   25  4  22  26 0.15384615 0.4030571 18/3
298        18    3   25  5  18  23 0.21739130 0.4850498 18/3
299        18    3   25  6  17  23 0.26086957 0.5360615 18/3
300        18    3   25 19  22  41 0.46341463 0.7487801 18/3
301         s    1   25  9  19  28 0.32142857 0.6027946  s/1
302         s    1   25  2  17  19 0.10526316 0.3304226  s/1
303         s    1   25  9  22  31 0.29032258 0.5690309  s/1
304         s    1   25  9  19  28 0.32142857 0.6027946  s/1
305         s    1   25 12  19  31 0.38709677 0.6715128  s/1
306         s    1   25  5  19  24 0.20833333 0.4739849  s/1
307         s    1   25  2  15  17 0.11764706 0.3501058  s/1
308         s    1   25 12  22  34 0.35294118 0.6361321  s/1
309         s    1   25  0   8   8 0.00000000 0.0000000  s/1
310         s    1   25 15  23  38 0.39473684 0.6793415  s/1
311         s    2   25  9  15  24 0.37500000 0.6590580  s/2
312         s    2   25 17  19  36 0.47222222 0.7576061  s/2
313         s    2   25 17  17  34 0.50000000 0.7853982  s/2
314         s    2   25 12  16  28 0.42857143 0.7137244  s/2
315         s    2   25  6  21  27 0.22222222 0.4908827  s/2
316         s    2   25 13  27  40 0.32500000 0.6066126  s/2
317         s    2   25  7  16  23 0.30434783 0.5843739  s/2
318         s    2   25  0   9   9 0.00000000 0.0000000  s/2
319         s    2   25 11  18  29 0.37931034 0.6635047  s/2
320         s    2   25  5  19  24 0.20833333 0.4739849  s/2
321         s    3   25 11  18  29 0.37931034 0.6635047  s/3
322         s    3   25 12  16  28 0.42857143 0.7137244  s/3
323         s    3   25  2  15  17 0.11764706 0.3501058  s/3
324         s    3   25 12  16  28 0.42857143 0.7137244  s/3
325         s    3   25 13  20  33 0.39393939 0.6785256  s/3
326         s    3   25  9  23  32 0.28125000 0.5589899  s/3
327         s    3   25  2  18  20 0.10000000 0.3217506  s/3
328         s    3   25  0  11  11 0.00000000 0.0000000  s/3
329         s    3   25  1   5   6 0.16666667 0.4205343  s/3
330         s    3   25  6  19  25 0.24000000 0.5119727  s/3
331         l    1   25  1  16  17 0.05882353 0.2449787  l/1
332         l    1   25 16  17  33 0.48484848 0.7702443  l/1
333         l    1   25  1  14  15 0.06666667 0.2611574  l/1
334         l    1   25  4  21  25 0.16000000 0.4115168  l/1
335         l    1   25  5  20  25 0.20000000 0.4636476  l/1
336         l    1   25  4  20  24 0.16666667 0.4205343  l/1
337         l    1   25  4  14  18 0.22222222 0.4908827  l/1
338         l    1   25  1  15  16 0.06250000 0.2526803  l/1
339         l    1   25 12  22  34 0.35294118 0.6361321  l/1
340         l    1   25  4  20  24 0.16666667 0.4205343  l/1
341         l    2   25 19  24  43 0.44186047 0.7271268  l/2
342         l    2   25  4  22  26 0.15384615 0.4030571  l/2
343         l    2   25  3  18  21 0.14285714 0.3875967  l/2
344         l    2   25  1  17  18 0.05555556 0.2379411  l/2
345         l    2   25  1  16  17 0.05882353 0.2449787  l/2
346         l    2   25 19  20  39 0.48717949 0.7725762  l/2
347         l    2   25  0  16  16 0.00000000 0.0000000  l/2
348         l    2   25  1  10  11 0.09090909 0.3062774  l/2
349         l    2   25  0   4   4 0.00000000 0.0000000  l/2
350         l    2   25  8  19  27 0.29629630 0.5755915  l/2
351         l    3   25 11  16  27 0.40740741 0.6922680  l/3
352         l    3   25 10  15  25 0.40000000 0.6847192  l/3
353         l    3   25  6  12  18 0.33333333 0.6154797  l/3
354         l    3   25 16  18  34 0.47058824 0.7559694  l/3
355         l    3   25 14  21  35 0.40000000 0.6847192  l/3
356         l    3   25 14  20  34 0.41176471 0.6966984  l/3
357         l    3   25 18  21  39 0.46153846 0.7468986  l/3
358         l    3   25  4   8  12 0.33333333 0.6154797  l/3
359         l    3   25  7  18  25 0.28000000 0.5575988  l/3
360         l    3   25  9  19  28 0.32142857 0.6027946  l/3
361        25    1   10  3  16  19 0.15789474 0.4086379 25/1
362        25    1   10  7  11  18 0.38888889 0.6733516 25/1
363        25    1   10  4   0   4 1.00000000 1.5707963 25/1
364        25    1   10  0   5   5 0.00000000 0.0000000 25/1
365        25    1   10  4   4   8 0.50000000 0.7853982 25/1
366        25    1   10  3   1   4 0.75000000 1.0471976 25/1
367        25    1   10 10  12  22 0.45454545 0.7398808 25/1
368        25    1   10  3   0   3 1.00000000 1.5707963 25/1
369        25    1   10  9  14  23 0.39130435 0.6758276 25/1
370        25    1   10  5   6  11 0.45454545 0.7398808 25/1
371        25    2   10  0   2   2 0.00000000 0.0000000 25/2
372        25    2   10  2  13  15 0.13333333 0.3737922 25/2
373        25    2   10  4  16  20 0.20000000 0.4636476 25/2
374        25    2   10  9  11  20 0.45000000 0.7353145 25/2
375        25    2   10  0   4   4 0.00000000 0.0000000 25/2
376        25    2   10  1  20  21 0.04761905 0.2199880 25/2
377        25    2   10  8   7  15 0.53333333 0.8187562 25/2
378        25    2   10  2  17  19 0.10526316 0.3304226 25/2
379        25    2   10  0  14  14 0.00000000 0.0000000 25/2
380        25    2   10  8  12  20 0.40000000 0.6847192 25/2
381        25    3   10  0   6   6 0.00000000 0.0000000 25/3
382        25    3   10  3   8  11 0.27272727 0.5494672 25/3
383        25    3   10  2   6   8 0.25000000 0.5235988 25/3
384        25    3   10  3  17  20 0.15000000 0.3976994 25/3
385        25    3   10  7   5  12 0.58333333 0.8691222 25/3
386        25    3   10  9  15  24 0.37500000 0.6590580 25/3
387        25    3   10  4  19  23 0.17391304 0.4301739 25/3
388        25    3   10  4  20  24 0.16666667 0.4205343 25/3
389        18    1   10  5   7  12 0.41666667 0.7016741 18/1
390        18    1   10  4  17  21 0.19047619 0.4516334 18/1
391        18    1   10  1   6   7 0.14285714 0.3875967 18/1
392        18    1   10  9  22  31 0.29032258 0.5690309 18/1
393        18    1   10  1  11  12 0.08333333 0.2928428 18/1
394        18    1   10  5  16  21 0.23809524 0.5097397 18/1
395        18    1   10  9  20  29 0.31034483 0.5908728 18/1
396        18    1   10  6  21  27 0.22222222 0.4908827 18/1
397        18    1   10  2   8  10 0.20000000 0.4636476 18/1
398        18    1   10  1   5   6 0.16666667 0.4205343 18/1
399        18    2   10  0   3   3 0.00000000 0.0000000 18/2
400        18    2   10  4  19  23 0.17391304 0.4301739 18/2
401        18    2   10  8  18  26 0.30769231 0.5880026 18/2
402        18    2   10  8  16  24 0.33333333 0.6154797 18/2
403        18    2   10  3   3   6 0.50000000 0.7853982 18/2
404        18    2   10  8  13  21 0.38095238 0.6651961 18/2
405        18    2   10  0  15  15 0.00000000 0.0000000 18/2
406        18    2   10  9  11  20 0.45000000 0.7353145 18/2
407        18    2   10  2  13  15 0.13333333 0.3737922 18/2
408        18    3   10  1  13  14 0.07142857 0.2705498 18/3
409        18    3   10  2   3   5 0.40000000 0.6847192 18/3
410        18    3   10 12  22  34 0.35294118 0.6361321 18/3
411        18    3   10  5  23  28 0.17857143 0.4362869 18/3
412        18    3   10  4   7  11 0.36363636 0.6472848 18/3
413        18    3   10  5  11  16 0.31250000 0.5931998 18/3
414        18    3   10 11  17  28 0.39285714 0.6774179 18/3
415        18    3   10  7  12  19 0.36842105 0.6522512 18/3
416        18    3   10  6   7  13 0.46153846 0.7468986 18/3
417        18    3   10  4  16  20 0.20000000 0.4636476 18/3
418         s    1   10  0  14  14 0.00000000 0.0000000  s/1
419         s    1   10  2   9  11 0.18181818 0.4405107  s/1
420         s    1   10 10  14  24 0.41666667 0.7016741  s/1
421         s    1   10  8  22  30 0.26666667 0.5426391  s/1
422         s    1   10  5  24  29 0.17241379 0.4281928  s/1
423         s    1   10  6  18  24 0.25000000 0.5235988  s/1
424         s    1   10  4   4   8 0.50000000 0.7853982  s/1
425         s    1   10  6  21  27 0.22222222 0.4908827  s/1
426         s    1   10  5  14  19 0.26315789 0.5386635  s/1
427         s    1   10 15  16  31 0.48387097 0.7692663  s/1
428         s    2   10  7   9  16 0.43750000 0.7227342  s/2
429         s    2   10  5   5  10 0.50000000 0.7853982  s/2
430         s    2   10  0   5   5 0.00000000 0.0000000  s/2
431         s    2   10  8   4  12 0.66666667 0.9553166  s/2
432         s    2   10  8   1   9 0.88888889 1.2309594  s/2
433         s    2   10  3  22  25 0.12000000 0.3537416  s/2
434         s    2   10  5  21  26 0.19230769 0.4539613  s/2
435         s    2   10  6   4  10 0.60000000 0.8860771  s/2
436         s    2   10  6  11  17 0.35294118 0.6361321  s/2
437         s    3   10  3   4   7 0.42857143 0.7137244  s/3
438         s    3   10  5  14  19 0.26315789 0.5386635  s/3
439         s    3   10 10   4  14 0.71428571 1.0068537  s/3
440         s    3   10  3  16  19 0.15789474 0.4086379  s/3
441         s    3   10  5  14  19 0.26315789 0.5386635  s/3
442         s    3   10 14  18  32 0.43750000 0.7227342  s/3
443         s    3   10  0   6   6 0.00000000 0.0000000  s/3
444         s    3   10 10  16  26 0.38461538 0.6689641  s/3
445         s    3   10  7   9  16 0.43750000 0.7227342  s/3
446         l    1   10  0   2   2 0.00000000 0.0000000  l/1
447         l    1   10  0   4   4 0.00000000 0.0000000  l/1
448         l    1   10  2  19  21 0.09523810 0.3137279  l/1
449         l    1   10  2  14  16 0.12500000 0.3613671  l/1
450         l    1   10  0  17  17 0.00000000 0.0000000  l/1
451         l    1   10  9  13  22 0.40909091 0.6939806  l/1
452         l    1   10  4   8  12 0.33333333 0.6154797  l/1
453         l    1   10  3  13  16 0.18750000 0.4478324  l/1
454         l    1   10 10  16  26 0.38461538 0.6689641  l/1
455         l    1   10  3  11  14 0.21428571 0.4812754  l/1
456         l    2   10  6   7  13 0.46153846 0.7468986  l/2
457         l    2   10  1  11  12 0.08333333 0.2928428  l/2
458         l    2   10  1  15  16 0.06250000 0.2526803  l/2
459         l    2   10  2  17  19 0.10526316 0.3304226  l/2
460         l    2   10  2  15  17 0.11764706 0.3501058  l/2
461         l    2   10  2   2   4 0.50000000 0.7853982  l/2
462         l    2   10  5  14  19 0.26315789 0.5386635  l/2
463         l    2   10 17  14  31 0.54838710 0.8338611  l/2
464         l    2   10 10  11  21 0.47619048 0.7615796  l/2
465         l    2   10  9  14  23 0.39130435 0.6758276  l/2
466         l    3   10  4   5   9 0.44444444 0.7297277  l/3
467         l    3   10  1   3   4 0.25000000 0.5235988  l/3
468         l    3   10 13   9  22 0.59090909 0.8768157  l/3
469         l    3   10  3  20  23 0.13043478 0.3695089  l/3
470         l    3   10 12  13  25 0.48000000 0.7653928  l/3
471         l    3   10  0   7   7 0.00000000 0.0000000  l/3
472         l    3   10  6   7  13 0.46153846 0.7468986  l/3
473         l    3   10 10   6  16 0.62500000 0.9117383  l/3
474         l    3   10  1   1   2 0.50000000 0.7853982  l/3
475         l    3   10  3  10  13 0.23076923 0.5010930  l/3
 

=========================

Federico C.F. Calboli

Department of Biology
University College London
Room 327
Darwin Building
Gower Street
London
WClE 6BT

Tel: (+44) 020 7679 4395 
Fax (+44) 020 7679 7096
f.calboli at ucl.ac.uk




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