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Patterning the insect eye: From stochastic to deterministic mechanisms
Fig 4
The mean horizontal correlation coefficient 〈Rh〉 diagram for a set of situations mimicking various fly eyes according to Eq 9 in S1 Text.
The left half of the main diagram corresponds to β < 0 (Eq 5) while the right half corresponds to β > 0 (Eq 6). The horizontal axis shows the value of α which varies from 0 to 1 to the right and left of the y-axis. The vertical axis indicates the value of 
. The chromatic pink indicates 〈Rh〉 = −1, while the gray pixels show 〈Rh〉 = 0. Some examples of the simulated eye configurations are shown (panels (A)-(I)) for the following parameter values: (A) β > 0, α = 1. A value of β > 0 (Eq 6) indicates the Doli striped region, α = 1 makes the second term (
)on the right hand side of Eq 6 vanish, so that it becomes independent of 
. We thus have a pure Doli configuration. (B) β > 0, α = 0.9 and 
. This configuration deviates slightly from a perfect Doli eye by introducing some randomness via the Drosophila component. (C) β > 0, α = 0.65 and P0 = 0.9. As the value of α is reduced, the effect of the ordered Doli wanes, giving way to patterns that more closely resemble Drosophila. (D) β > 0, α = 0.65 and P0 = 0.1 Here we see Drosophila-like patterns, where the spatial distributions are random, although the ratio of the two colors is fixed. (E) α nearly zero, 
and (F) α nearly zero, 
: In both cases, a Drosophila dominant behavior is observed, with the different percentages of reds and greens corresponding to the different values of 
. Note that for β < 0, i.e. the left half of the phase diagram, the effect of the so-called Uniform Fly increases as α increases at the expense of the Drosophila effect. The extreme case of this is at α = 1 when the configurations are a homogeneous green (or red). (G), (H) and (I): α = 0.9. with 
(G), 
(I) and 
(H). The dominant behaviour is that of the Uniform Fly, which gives rise to a nearly uniform green(red) color. As 
increases, red gives way increasingly to green.
doi: https://doi.org/10.1371/journal.pcbi.1006363.g004