TABLE 1. Genetic parameters from which the shell morphology was generated. Parameters 1-10 defined the overall shape of the shell, parameters 11-14 the surface sculpture. The shape of the aperture curve used 8 parameters, see Figure 2.3. For the effect of parameters λ, q, fr and fc, see Figure 3. By reducing parameter a from 1 to 0, the sculptures of the sculptured examples in Figure 3 would be linearly reduced to a smooth surface.
Variable |
Range |
Parameter description |
|
1 |
αh |
[30°, 120°] |
hinge angle |
2 |
rh |
[0, 1] |
hinge radius |
3 |
α3 |
[0°, 360° –αh] |
angle of 3rd control point |
4 |
r3 |
[0, 1] |
radius of 3rd control point |
5 |
α4 |
[0°, 360° –αh] |
angle of 4th control point |
6 |
r4 |
[0, 1] |
radius of 4th control point |
7 |
α5 |
[0°, 360° –αh] |
angle of 5th control point |
8 |
r5 |
[0, 1] |
radius of 5th control point |
9 |
λ |
[1.00339, 1.04086] |
growth scaling factor |
10 |
ϑ |
[0°, 90°] |
shell rotation towards anterior |
11 |
q |
[0, 1] |
radial/commarginal mixture |
12 |
a |
[0, 1] |
sculpture amplitude |
13 |
fr |
[10..100] |
radial ridge frequency |
14 |
fc |
[18..180] |
commarginal ridge frequency |
TABLE 2. Phenotypic (morphometric) parameters. In addition to the parameters listed in Table 1 that were used to generate the shells, we used this set of phenotypic parameters computed from the final shells to find possible correlations with the fitness.
Variable |
Unit/Range |
Parameter description |
|
1 |
L |
[mm] |
length, dimension parallel to hinge axis |
2 |
H |
[mm] |
height, dimension orthogonal to length |
3 |
B |
[mm] |
broadness, dimension orthogonal to burrowing direction |
4 |
T |
[mm] |
tallness, dim. parallel to burrowing direction |
5 |
J |
[mm] |
major axis length, largest diameter |
6 |
N |
[mm] |
minor axis length, dimension orthogonal to major axis |
7 |
W |
[mm] |
width, dimension orthogonal to aperture plane (over both valves) |
8 |
lA |
[mm] |
aperture curve length, circumference of aperture |
9 |
AA |
[mm2] |
aperture area |
10 |
γ |
[0, 1] |
non-convexity, part of aperture area bending inwards |
11 |
pu |
[0, 1] |
relative umbo position (along L) |
12 |
pc |
[0, 1] |
relative centre position (along L) |
13 |
S1 |
[0, 1] |
streamlining, (Watters, 1993, based on L and H) |
14 |
S2 |
[0, 1] |
streamlining, (Watters, 1993, based on B and T) |
15 |
S3 |
[0, 1] |
streamlining, average angle between faces and burrowing direction |
TABLE 3. Correlations of genetic and phenotypic parameters and the burrowing depth D with fitness (original and shift 2, see Figure 6). We computed Pearson and Spearman correlation. The p-values and the correlation coefficients r are given.
Pearson correlation |
Spearman correlation |
|||||||
Fitness (orig.) |
Fitness (shift 2) |
Fitness (orig.) |
Fitness (shift 2) |
|||||
Variable |
p-value |
r |
p-value |
r |
p-value |
r |
p-value |
r |
D – T |
3E-40 |
0.92 |
4E-29 |
0.85 |
0 |
0.84 |
6E-08 |
0.52 |
T |
2E-14 |
-0.68 |
0 |
-0.73 |
5E-03 |
-0.28 |
5E-03 |
-0.28 |
L |
3E-10 |
-0.58 |
7E-12 |
-0.62 |
0.14 |
-0.15 |
0.18 |
-0.14 |
S2 |
6E-10 |
-0.57 |
2E-11 |
-0.62 |
9E-03 |
-0.26 |
9E-03 |
-0.26 |
lA |
4E-08 |
-0.52 |
2E-09 |
-0.56 |
2E-04 |
-0.37 |
1E-04 |
-0.38 |
pc |
5E-08 |
0.52 |
8E-10 |
0.57 |
0.3 |
0.11 |
0.3 |
0.1 |
fr |
6E-08 |
0.51 |
6E-09 |
0.55 |
0.55 |
0.06 |
0.93 |
0.01 |
S1 |
9E-07 |
-0.47 |
1E-07 |
-0.5 |
0.19 |
-0.13 |
0.21 |
-0.13 |
α5 |
1E-06 |
-0.47 |
2E-08 |
-0.53 |
0.06 |
-0.19 |
0.03 |
-0.22 |
α4 |
2E-06 |
-0.46 |
2E-08 |
-0.53 |
0.01 |
-0.26 |
2E-03 |
-0.31 |
S3 |
5E-06 |
0.44 |
2E-06 |
0.46 |
0.25 |
0.12 |
0.15 |
0.15 |
r4 |
2E-05 |
0.42 |
7E-07 |
0.48 |
0.38 |
0.09 |
0.17 |
0.14 |
γ |
5E-05 |
-0.4 |
5E-06 |
-0.44 |
0.06 |
0.19 |
0.02 |
0.24 |
rh |
1E-04 |
0.37 |
2E-06 |
0.46 |
2E-03 |
0.31 |
4E-06 |
0.45 |
α3 |
4E-04 |
0.35 |
3E-05 |
0.41 |
0.44 |
-0.08 |
0.37 |
-0.09 |
J |
5E-04 |
-0.35 |
2E-04 |
-0.37 |
3E-03 |
-0.3 |
2E-03 |
-0.31 |
B |
1E-03 |
0.33 |
5E-04 |
0.35 |
0.48 |
0.07 |
0.49 |
0.07 |
H |
1E-03 |
0.33 |
5E-04 |
0.35 |
0.68 |
0.04 |
0.76 |
0.03 |
q |
4E-03 |
-0.29 |
8E-04 |
-0.33 |
0.07 |
0.18 |
3E-03 |
0.3 |
r3 |
6E-03 |
0.28 |
2E-03 |
0.31 |
0.86 |
0.02 |
0.72 |
-0.04 |
λ |
0.02 |
0.24 |
0.01 |
0.25 |
0.45 |
-0.08 |
0.23 |
-0.12 |
D |
0.03 |
0.23 |
0.01 |
0.26 |
7E-07 |
0.48 |
2E-04 |
0.37 |
a |
0.03 |
-0.22 |
0.02 |
-0.24 |
2E-04 |
-0.37 |
1E-06 |
-0.47 |
ϑ |
0.04 |
0.21 |
6E-03 |
0.28 |
0.46 |
-0.08 |
0.39 |
-0.09 |
AA |
0.04 |
-0.21 |
0.04 |
-0.21 |
0.03 |
-0.22 |
0.04 |
-0.2 |
N |
0.08 |
-0.18 |
0.05 |
-0.2 |
0.41 |
-0.08 |
0.41 |
-0.08 |
αh |
0.22 |
-0.13 |
0.3 |
-0.11 |
0.28 |
0.11 |
0.04 |
0.21 |
r5 |
0.24 |
-0.12 |
0.26 |
-0.11 |
0.02 |
-0.23 |
0.03 |
-0.22 |
pu |
0.27 |
0.11 |
0.2 |
0.13 |
0.02 |
-0.24 |
3E-03 |
-0.3 |
fc |
0.38 |
0.09 |
0.18 |
0.14 |
0.2 |
-0.13 |
0.06 |
-0.19 |
W |
0.48 |
-0.07 |
0.42 |
-0.08 |
0.12 |
0.16 |
0.11 |
0.16 |