Fig 1.
(a) A map of Japan with zoom-in on Tokyo bay, showing the locations of the three populations from which we have obtained T. sazae shells. Sample shells from each of the three populations: Hayama (b), Jyogashima (c), and Tateyama (d), including close-up image of a spine, and mathematical reconstructions of spines from our modeling framework (see S1 Text Section 7). Maps adapted from mapchart.net.
Fig 2.
A biochemical system, modeling an Activator-Substrate reaction (a), potentially creates a spatial pattern, depending on the choice of six parameters. This biochemical pattern is passed to the tissue scale (b) and defines the rate and width of mantle growth and secretion. From this mechanical process, a spine shape emerges, which is then compared with an image of an actual spine (c). For a given shell, we then seek the biochemical parameters such that the model output best matches the real spine shape, (d).
Fig 3.
(a) At the tissue level, a Gaussian growth profile is input to the mechanical model, defined by two parameters {g1, g2}, for which different values produce different spine shapes that are then compared to a given spine image from a real shell in order to determine a best fit target pair {g1, g2}. (b) At the molecular level, a Quality-Diversity algorithm looks for the full range of {g1, g2} pairs that can be produced by the Activator-Substrate reaction-diffusion system and stores the parameter sets that produced them in a grid. Sets in the grid may be reused by the algorithm, with some added noise (mutation), in an attempt to explore nearby area of the {g1, g2} space. The filled grid is then used as a look-up table that provides parameter sets matching a given {g1, g2} pair from the tissue level.
Table 1.
Model parameters, parameter ranges, and sampling methods.
Table 2.
Algorithm and simulation parameters.
Fig 4.
(a) Morphospace of spine shapes as the growth parameters g1 and g2 are varied. (b) Aggregated sets of biochemical model parameters, plotted with respect to their respective {g1, g2} values. Coloring corresponds to the value of individual parameters, showing a clear global organization for c1, c2, and c3.
Fig 5.
(a) The best-fit values of {g1, g2}, extracted from comparing tissue-model output to images of real shells, separated by population. (b) Relationship between biochemical model parameters for each population, as obtained from the algorithmic parameter exploration. The + symbol represents the average parameter values for the population, highlighting the difference between the Jyogashima population and the other two.