TABLE 1 Sample statistics for simulated walks in Figs. 3 and 4

 

Sample statistics*

 

N

n

D(± SE)

VF

Single-task walks

 

 

 

 

Light interception, E

116

3

5.81 ± 0.152

0.568

Mechanical stability, M

81

3

5.49 ± 0.186

0.335

Reproductive success, R

56

1

4.37 ± 0.130

0.117

± SE

84.3 ± 17.4

2.33 ± 1.15

5.22 ± 0.44

0.34 ± 0.13

Multi-task walks

E-M-R

49

7

14.4 ± 0.58

3.65

E-R

41

5

15.1 ± 1.02

3.53

E-M

40

5

21.6 ± 1.26

10.1

M-R

13

1

13.7 ± 1.63

0.84

± SE

35.8 ± 7.85

4.50 ± 1.26

16.2 ± 1.82

4.52 ± 2.26

*N, number of steps in walk; n, number of phenotypic maxima or optima in landscape; D, mean diameter of steps in walk; VF, volume fraction of morphospace occupied by walk.

of walks are graphic reactions of mathematically more complex features. Every walk proceeds through the same morphospace; walks differ solely as a consequence of differences in fitness topologies. Specifically, walks are shown for three single-task and four multi-task-defined fitness-landscapes. The three individual tasks are light interception E, mechanical stability M, and reproduction R (Figure 3). In turn, these tasks have four combinatorial permutations (Figure 4), three of which give two-task landscape (i.e., E-M, E-R, M-R) and one of which is a three-task landscape (i.e., E-M-R).

The most apparent differences between simulated single- and multi-task walks are the number and magnitude of their phenotypic transformations, on the one hand, and the number of phenotypic maxima and optima they reach within landscapes, on the other (Table 1). Single-task walks have many small phenotypic transformations within landscapes that contain what appear to be comparatively few phenotypic maxima. By contrast, multi-task walks have few, but large, transformations within landscapes that, at first glance, appear to contain comparatively many phenotypic optima. Also, the mean morphospace volume occupied by multi-task walks is greater than that occupied by single-task walks (Table 1). Statistical comparisons indicate that the hypothesis that multi-task walks require significantly larger phenotypic transformations than those of single-task walks can be accepted (Table 2). However, statistical comparisons show that the mean number of phenotypic maxima in single-task landscapes does not significantly differ from that of optima in multi-task landscapes. In part, this is due to the small sample sizes for each of these two categories of fitness-landscape and to



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