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Piebald rats and selection

Chapter 18: TABLES.
By William E. Castle
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Science - Biology

About This Book

Investigators present a controlled breeding study that tests whether Mendelian determiners remain unchanged during crosses by selecting for increased or decreased pigmentation in piebald coat patterns of laboratory rats. They describe methods for grading dorsal pigmentation, establish parallel plus and minus selection lines, perform return and hybrid crosses with different stocks, and tabulate multigenerational outcomes. Statistical summaries and plates illustrate shifts in pigment distribution and the response to selection. The results are analyzed with respect to the theory of pure gametes and genotype–phenotype distinctions, showing that extracted recessive patterns and selection responses complicate simple notions of gametic purity.

TABLES.

Table 1.—Classification of the first generation of offspring in the plus selection series. At the head of each column is indicated the grade of the individuals recorded in that column. The figures in the body of the table indicate the numbers of offspring of the several grades indicated.

Grade of parents. Grade of offspring. Totals. Means. Regression.
+1 1¼ 1½ 1¾ 2 2¼ 2½ 2¾ 3
1⅞ 1 1 1 1 1 1 1 7 1.82 .05
2 4 1 3 1 4 1 4 18 1.76 .24
2⅛
2¼ 3 1 3 1 6 2 2 2 20 1.87 .38
2⅜
2½ 5 3 1 13 1 8 5 1 37 2.06 .44
2⅝ 1 1 2 1 5 2.15 .47
2¾ 7 3 2 17 1 12 9 51 2.12 .63
2⅞
3 2 3 1 3 3 12 2.35 .65
Totals or means, 2.51 20 3 13 8 44 7 31 10 4 150 2.05 .46

Table 2.—Classification of offspring in generation 2, plus selection series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
-1 -¾ -½ -¼ 0 +¼ ½ ¾ 1 1¼ 1½ 1¾ 2 2¼ 2½ 2¾ 3 3¼ 3½ 3¾
2 1 1 4 2 5 7 3 7 8 2 3 2 1 46 1.70 .30
2⅛ 1 1 2 1 3 5 12 8 5 5 8 2 1 2 56 1.28 .82
2¼ 1 1 3 1 1 1 8 1.87 .38
2⅜ 1 1 4 9 7 8 8 6 1 45 1.92 .45
2½ 4 22 16 19 11 21 13 7 10 9 1 133 1.80 .70
2⅝ 1 2 3 1 6 5 7 9 6 3 1 44 2.11 .51
2¾ 1 3 4 2 6 5 9 6 9 6 1 52 1.92 .83
2⅞ 1 1 3 5 3 9 1 23 2.41 .46
3 1 2 3 2 14 7 4 5 11 6 3 1 59 2.47 .53
3½ 2 1 2 5 2.50 .62
Totals or means, 2.52 1 - 2 1 4 1 5 16 45 37 45 45 77 57 44 48 30 9 3 1 471 1.92 .60

Table 3.—Classification of offspring in generation 3, plus selection series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
¾ 1 1¼ 1½ 1¾ 2 2¼ 2½ 2¾ 3 3¼ 3½ 3¾ 4
2⅛ 1 1 5 6 4 1 3 21 2.06 .06
2¼
2⅜ 5 5 1 4 2 17 2.15 .22
2½ 1 2 1 2 5 5 10 10 9 7 2 54 2.32 .18
2⅝ 2 1 3 9 4 5 15 18 3 1 2 1 64 2.64 -.02
2¾ 2 1 7 10 7 7 7 1 1 43 2.46 .29
2⅞ 1 7 3 7 9 10 9 1 47 2.70 .17
3 2 1 12 14 11 17 11 3 71 2.49 .51
3⅛ 2 5 1 2 10 3.07 .05
3¼ 1 2 1 2 6 3.17 .08
3⅜ 2 1 3 2 8 2.91 .46
Totals or means, 2.73 1 2 5 8 20 51 46 47 66 63 21 6 4 1 341 2.51 .22

Table 4.—Classification of offspring, generation 4, plus selection series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
¾ 1 1¼ 1½ 1¾ 2 2¼ 2½ 2¾ 3 3¼ 3½ 3¾
2½ 2 2 4 3 11 2.55 .05
2⅝
2¾ 3 3 2 3 4 3 18 2.65 .10
2⅞ 1 3 3 7 15 4 3 2 37 2.97 .10
3 1 1 7 12 25 19 35 29 9 4 1 143 2.60 .40
3⅛ 1 2 11 14 21 28 30 11 2 2 122 2.69 .43
3¼ 1 1 6 8 13 17 9 8 1 64 2.89 .36
3⅜ 1 6 2 3 9 2 23 2.70 .67
3½ 3 1 2 3 6 2 3 20 3.02 .48
3⅝
3¾ 3 1 1 1 6 2.75 1.00
Totals or means, 3.09 1 1 1 2 12 30 60 58 96 110 45 19 9 444 2.73 .36

Table 5.—Classification of generation 5, plus selection series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
¾ 1 1¼ 1½ 1¾ 2 2¼ 2½ 2¾ 3 3¼ 3½ 3¾ 4 4¼
2¾ 1 2 4 4 1 12 3.00 -.25
2⅞ 4 4 4 2 3 2 2 21 2.87 0
3 1 5 3 2 3 1 15 2.81 .19
3⅛ 1 1 1 1 8 9 14 20 29 18 8 3 1 114 2.81 .31
3¼ 1 1 1 4 12 6 14 24 39 27 7 1 1 138 2.81 .44
3⅜ 1 1 5 14 11 25 36 28 15 7 2 145 2.94 .43
3½ 6 5 10 14 16 8 8 3 69 2.86 .64
3⅝ 3 3 5 7 16 12 11 4 3 64 3.08 .54
3¾ 2 2 4 3 2 1 14 3.07 .68
3⅞ 1 1 1 1 2 2 8 3.35 .52
4 1 1 1 1 2 1 7 3.36 .64
4⅛ 1 1 1 3 3.00 1.12
Totals or means, 3.33 1 2 2 2 6 35 44 66 101 151 107 57 24 11 1 610 2.90 .43

Table 6.—Classification of generation 6, plus selection series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
1½ 1¾ 2 2¼ 2½ 2¾ 3 3¼ 3½ 3¾ 4 4¼ 4½
3 1 1 2
3⅛ 3 4 1 1 4 7 5 3 28 2.84 .28
3¼ 1 3 3 8 26 31 31 24 15 1 143 3.10 .15
3⅜ 1 5 6 13 20 28 30 14 5 123 2.96 .41
3½ 1 9 4 15 29 49 41 43 17 4 212 3.10 .40
3⅝ 4 8 11 24 34 36 37 21 5 1 181 3.16 .46
3¾ 1 1 2 1 3 4 18 13 20 13 2 78 3.22 .53
3⅞ 4 1 3 5 14 15 20 14 4 80 3.26 .61
4 1 2 1 5 4 1 14 3.41 .59
Totals or means, 3.52 3 5 32 24 54 113 183 172 166 90 17 1 861 3.11 .41

Table 7.—Classification of generation 7, plus selection series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
1½ 1¾ 2 2¼ 2½ 2¾ 3 3¼ 3½ 3¾ 4 4¼ 4½ 4¾
3⅛ 2 2 4 5 7 4 3 1 28 2.87 .25
3¼ 1 6 11 7 11 30 19 22 23 1 131 3.09 .16
3⅜ 1 2 10 18 17 21 27 18 21 20 4 1 160 2.97 .40
3½ 6 9 9 21 31 28 35 34 3 1 177 3.18 .32
3⅝ 7 11 13 26 47 53 75 49 7 1 289 3.23 .39
3¾ 2 3 3 16 28 25 58 42 4 3 184 3.35 .40
3⅞ 2 1 2 4 10 12 23 21 6 6 2 1 90 3.49 .38
4 1 1 3 2 4 3 1 15 3.53 .47
4⅛ 1 1 1 3 3.75 .50
Totals or means, 3.56 2 2 35 55 56 105 183 159 240 195 29 12 2 2 1077 3.20 .36

Table 8.—Classification of generation 8, plus series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
1¾ 2 2¼ 2½ 2¾ 3 3¼ 3½ 3¾ 4 4¼ 4½
3¼ 2 2 4 3.25 0
3⅜
3½ 1 4 6 9 18 17 2 2 59 3.46 .04
3⅝ 1 2 9 13 30 69 44 144 149 22 1 484 3.50 .12
3¾ 2 1 9 12 55 39 152 173 23 2 469 3.49 .26
3⅞ 1 2 4 23 18 98 69 19 2 1 238 3.53 .34
4 1 2 3 10 6 34 6 1 1 64 3.31 .69
4⅛ 2 5 2 14 13 14 10 60 3.72 .40
4¼ 1 7 11 2 1 22 3.69 .56
4⅜ 2 5 1 8 3.96 .41
Totals or means, 3.75 1 5 13 25 55 170 119 469 440 88 20 1 1408 3.48 .27

Table 9.—Classification of generation 9, plus series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
1¾ 2 2¼ 2½ 2¾ 3 3¼ 3½ 3¾ 4 4¼ 4½
3½ 1 1 1 1 4 3.25 .25
3⅝ 1 1 6 12 28 26 96 63 10 1 244 3.43 .19
3¾ 1 2 4 7 19 45 50 224 212 25 2 591 3.50 .25
3⅞ 2 5 25 32 105 177 64 8 6 424 3.65 .22
4 1 2 5 14 15 7 1 45 3.57 .43
4⅛ 2 4 1 7 3.57 .55
4¼ 1 1 2 4 3.75 .50
4⅜ 3 3 3.50 .87
Totals or means, 3.78 1 3 5 17 38 105 110 443 473 109 11 7 1322 3.54 .24

Table 10.—Classification of generation 10, plus series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
2¼ 2½ 2¾ 3 3¼ 3½ 3¾ 4 4¼ 4½ 5
3¾ 1 1 9 13 63 117 44 8 1 257 3.69 .06
3⅞ 1 3 3 16 95 142 62 20 5 347 3.72 .15
4 4 26 61 20 7 2 120 3.76 .24
4⅛ 11 17 7 6 1 2 44 3.87 .25
4¼ 1 4 2 1 8 3.84 .41
Totals or means, 3.88 1 1 4 12 33 196 341 135 42 9 2 776 3.73 .15

Table 11.—Classification of generation 11, plus series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
2¾ 3 3¼ 3½ 3¾ 4 4¼ 4½ 4¾ 5
3¾ 2 7 2 11 3.75 0
3⅞ 2 7 17 87 162 41 11 3 3 333 3.70 .17
4 3 2 25 87 65 24 6 1 1 214 3.87 .13
4⅛ 3 3 16 49 27 8 2 2 110 3.81 .31
4¼ 2 13 5 3 1 1 25 3.91 .34
4⅜ 1 3 4 3.94 .43
Totals or means, 3.97 2 13 22 132 319 143 46 12 7 1 697 3.78 .19

Table 12.—Classification of generation 12, plus series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
2½ 3 3¼ 3½ 3¾ 4 4¼ 4½ 4¾ 5 5¼
3¾ 4 20 7 4 35 3.83 -.08
3⅞ 2 19 17 6 2 2 48 3.96 .09
4 1 1 10 53 59 12 5 1 1 2 145 3.93 .07
4⅛ 1 2 17 86 83 28 6 3 1 227 3.91 .21
4¼ 1 7 19 29 11 3 1 71 3.94 .31
4⅜ 3 6 14 10 7 3 1 1 45 4.13 .24
4½ 1 4 1 1 7 4.14 .36
4⅝ 1 3 4 3 11 3.90 .72
5 1 1 4.75 .25
Totals or means, 4.09 1 3 3 43 207 217 75 23 11 4 3 590 3.94 .17

Table 13.—Classification of generation 13, plus selection series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
2¾ 3¼ 3½ 3¾ 4 4¼ 4½ 4¾
4 4 17 23 19 2 65 3.67 .31
4⅛ 1 8 16 5 1 31 3.97 .15
4¼ 1 5 10 20 6 1 43 3.93 .32
4⅜ 1 5 3 1 10 3.85 .52
4½ 1 14 15 7 3 40 3.98 .52
4⅝ 3 1 1 5 3.95 .80
Totals or means, 4.22 1 4 25 63 74 21 5 1 194 3.88 .34

Table 14.—Summary of the results of thirteen generations of plus selection based on Tables 1-13.

Generation. No. of offspring. Mean, parents. Mean, offspring. Standard deviation, parents. Standard deviation, offspring. Correlation, parents-offspring. Absolute regression of offspring on parents. Advance of parents. Advance of offspring.
1 150 2.51 2.05 .313 .541 .298 .46
2 471 2.52 1.92 .307 .732 .317 .60 .01 -.13
3 341 2.73 2.51 .285 .531 .331 .22 .21 .59
4 444 3.09 2.73 .215 .468 .066 .36 .36 .22
5 610 3.33 2.90 .240 .505 .160 .43 .24 .17
6 861 3.52 3.11 .209 .490 .180 .41 .19 .21
7 1,077 3.56 3.20 .212 .555 .215 .36 .04 .09
8 1,408 3.75 3.48 .246 .439 .099 .27 .19 .28
9 1,322 3.78 3.54 .112 .346 .210 .24 .03 .06
10 776 3.88 3.73 .112 .362 .116 .15 .10 .19
11 697 3.98 3.78 .113 .289 .233 .20 .10 .05
12 590 4.09 3.94 .176 .302 .161 .15 .11 .16
13 194 4.22 3.88 .433 .270 .132 .34 .13 -.06
Total 8,941

Table 15.—Mean grade and number of offspring produced by parents of a particular grade in each generation of the plus selection series, based on Tables 1-13. The grade of the parents is indicated at the head of each column. In the body of the table is recorded the grade of the offspring (in light-faced figures) and the number of offspring (in heavy-faced figures).

Generation. Grade of parents; below, grade and number of their offspring. Total number of offspring.
2 2⅛ 2¼ 2⅜ 2½ 2⅝ 2¾ 2⅞ 3 3⅛ 3¼ 3⅜ 3½ 3⅝ 3¾ 3⅞ 4 4⅛ 4¼ 4⅜ 4½ 4⅝ 4¾
1 1.76 1.87 2.06 2.15 2.12 2.35
18 20 37 5 51 12
2 1.70 1.28 1.87 1.92 1.80 2.11 1.92 2.41 2.47 2.50
46 56 8 45 133 44 52 23 59 5
3 2.06 2.15 2.32 2.63 2.46 2.70 2.49 3.07 3.17 2.91
21 17 54 64 43 47 71 10 6 8
4 2.55 2.65 2.97 2.60 2.69 2.89 2.70 3.02 2.75
11 18 37 143 122 64 23 20 6
5 3.00 2.87 2.81 2.81 2.81 2.94 2.87 3.08 3.07 3.35 3.36 3.00
12 21 15 114 138 145 69 64 14 8 7 3
6 3.25 2.84 3.10 2.96 3.10 3.16 3.22 3.26 3.41
2 28 143 123 212 181 78 80 14
7 2.87 3.09 2.97 3.18 3.23 3.35 3.49 3.53 3.75
28 131 160 177 289 184 90 15 3 1,077
8 3.46 3.50 3.49 3.53 3.31 3.72 3.69 3.96
59 484 469 238 64 60 22 8 1,408
9 3.25 3.43 3.50 3.65 3.57 3.57 3.75 3.50
4 244 591 424 45 7 4 3 1,322
10 3.69 3.72 3.76 3.87 3.84
257 347 120 44 8 776
11 3.75 3.70 3.87 3.81 3.91 3.94
11 333 214 110 25 4 697
12 3.82 3.96 3.93 3.91 3.94 4.12 4.14 3.90 4.75
35 48 145 227 71 45 7 11 1 590
13 3.67 3.97 3.93 3.85 3.98 3.95
65 31 43 10 40 5 194
8,941

Table 16.—Classification of the offspring in generation 1 of the minus selection series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
+¼ 0 ¼ ½ ¾ 1 1¼ 1½ 1¾ 2
-1¼ 1 2 3 2 8 1.34 -.09
1⅜ 1 1 3 12 8 3 1 1 1 31 .86 .51
1½ 1 1 1 1 1 1 6 1.37 .13
1⅞ 1 1 2 2 3 1 10 1.05 .82
Totals or means, 1.46 2 1 4 1 15 13 4 8 5 2 55 1.00 .46

Table 17.—Classification of generation 2, minus selection series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
+½ 0 -¼ ½ ¾ 1 1¼ 1½ 1¾ 2
¾ 1 2 2 1 6 2 3 2 19 1.04 -.29
1⅛ 2 2 2 2 3 1 12 1.05 .07
1¼ 4 6 3 3 1 17 1.18 .07
1⅜ 1 1 1 2 5 1.45 -.08
1½ 1 10 13 1 8 4 37 1.11 .39
1⅝ 1 1 1 3 .67 .95
1¾ 1 1 2 14 4 3 1 1 27 1.09 .66
1⅞ 1 1 1 2 3 1 3 12 1.10 .77
Totals or means, 1.41 2 3 6 6 20 44 13 19 14 5 132 1.07 .34

Table 18.—Classification of generation 3, minus series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
0 -¼ ½ ¾ 1 1¼ 1½ 1¾ 2
-1⅛ 2 1 1 1 5 .85 .27
1¼ 1 3 6 5 1 2 1 1 20 1.05 .20
1⅜ 1 3 4 11 3 4 2 28 1.03 .34
1½ 1 1 12 1 5 5 3 28 1.31 .19
1⅝ 1 1 1 10 10 5 8 8 4 48 1.22 .40
1¾ 1 2 8 19 9 9 7 8 63 1.26 .49
1⅞ 3 3 1.00 .87
Totals or means, 1.56 1 4 12 30 61 19 29 23 16 195 1.18 .38

Table 19.—Classification of generation 4, minus selection series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
+½ +¼ 0 -¼ ½ ¾ 1 1¼ 1½ 1¾ 2 2¼
-1¼ 1 1 1 1 4 1.56 -.31
1⅜ 2 3 4 8 3 1 2 6 29 1.16 .21
1½ 1 1 3 2 7 7 6 8 16 8 59 1.31 .19
1⅝ 1 4 10 4 8 7 6 40 1.36 .26
1¾ 4 4 6 19 11 16 22 11 93 1.34 .41
1⅞ 2 1 2 6 1 10 19 12 17 19 5 1 95 1.18 .69
2 1 2 3 1 2 9 1.36 .64
Totals or means, 1.69 2 2 3 16 10 32 66 39 51 68 39 1 329 1.28 .41

Table 20.—Classification of generation 5, minus series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
0 -¼ ½ ¾ 1 1¼ 1½ 1¾ 2 2¼ 2½
⅞ 2 1 4 5 3 4 1 20 1.09 -.22
1 2 1 1 4 .99 .01
1⅜ 4 1 1 6 2 10 14 11 2 51 1.50 -.13
1½ 1 3 9 9 11 7 7 5 1 53 1.25 .25
1⅝ 1 1 5 12 4 15 12 4 54 1.35 .27
1¾ 9 14 29 50 30 50 55 24 1 262 1.30 .45
1⅞ 4 11 12 29 50 31 6 143 1.64 .23
2 1 2 11 14 5 19 28 25 4 109 1.52 .48
2⅛ 1 2 2 5 1.80 .32
Totals or means, 1.73 3 18 21 63 108 64 134 172 104 13 1 701 1.41 .32

Table 21.—Classification of generation 6, minus series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
0 -¼ ½ ¾ 1 1¼ 1½ 1¾ 2 2¼ 2½
-1⅛ 1 1 2 1 5 .85 .27
1⅜ 1 1 1 1 4 1.44 -.07
1½ 1 3 4 4 4 6 2 24 1.34 .16
1⅝ 1 1 11 16 3 17 28 17 94 1.45 .17
1¾ 1 1 8 14 39 20 39 77 43 2 244 1.49 .26
1⅞ 1 9 24 61 40 71 156 127 12 1 502 1.59 .28
2 1 3 5 12 32 22 37 89 76 5 1 283 1.58 .42
2⅛ 2 4 4 5 35 31 4 85 1.52 .60
2½ 2 5 3 1 11 1.82 .68
Totals or means, 1.86 3 6 25 66 159 94 177 396 300 22 4 1252 1.56 .30

Table 22.—Classification of generation 7, minus series.

Grade of parents. Grade of offspring. Totals. Means. Regression.
0 ¼ ½ ¾ 1 1¼ 1½ 1¾ 2 2¼ 2½ 2¾
1⅝ 1 1 2 1 5 1.55 .07
1¾ 1 2 1 1 6 11 9 1 32 1.67 .08
1⅞ 2 1 6 4 35 20 47 99 106 6 3 1 330 1.65 .22
2 8 14 51 60 119 368 324 22 3 969 1.72 .28
2⅛ 1 2 3 14 10 30 92 104 4 260 1.74 .38
2¼ 5 10 19 6 1 41 1.93 .32
2⅜ 2 2 4 1.63 .74
2½ 1 4 10 15 1.88 .62
2⅝ 1 3 8 5 1 18 2.28 .09
2¾ 3 3 6 1.87 .88
Totals or means, 2.01 2 2 17 24 101 92 211 594 584 43 8 2 1680 1.73 .28