At a nominal 1km scale, V0.1 provides the spatial distribution of adisaggregated five-class global cropland extent map derived from fourmajor studies: Thenkabail et al. (2009a, 2011), Pittman et al. (2010),Yu et al. (2013), and Friedl et al. (2010). V1.0 is a 5-class product thatprovides information on global cropland extent and irrigated versus rainfedcropping. There is no crop type or crop type dominance information. Croppingintensity (single, double, triple, and continuous crops) can be obtained forevery pixel using time-series remote sensing data. The GFSAD1000 nominal2010 product was created with data from 2007 to 2012.
For a given quantitative trait T, the dominance (h) of allele a relative to allele b was computed using this equation: where Tab, Taa and Tbb represent the average trait values for heterozygotes ab, and homozygotes aa and bb, respectively. Strict dominance of a with respect to b corresponds to h=1 and intermediate values (h0.5) represent co-dominance. The trait T used here to quantify colour pattern variation was derived from the relative proportion of wing area shared between the heterozygote and either homozygote. For a given homozygous genotype, a modal wing pattern was built, calculated by setting each pixel to its modal colour value, that is, shared by the most specimens with this genotype. For each pair of alleles, the trait T was then calculated as the number of pixels in the heterozygotes that were similar to one homozygote modal pattern and different from the other, normalized by the wing surface (in pixels). This calculation could be performed on 93.1% of the wing on average, because a small proportion of the wings of heterozygotes matched neither homozygote modal wing colours. All dominance coefficients measured were normalized so that allele a (equation above) corresponded to the more dominant allele, constraining h values to range between 0.5 and 1. An alternative estimate of the colour pattern trait was computed based on a linear discriminant analysis, and it gave values that were highly correlated with the surface-based estimate used here (Supplementary Figs 7 and 8).
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Dominance heat maps were generated for each heterozygous genotype to visualize how dominance varies across the wing. For each pair of supergene alleles, heat maps represent, on a pixel-by-pixel basis, the proportion of heterozygous individuals for which the colour was identical to one, both or neither homozygote.
To estimate the dominance of one colour to another colour, we computed the probability of expressing the dominant or the recessive colour in heterozygotes throughout all selected pixels for all genotypes. Here the expression of one colour was defined as its probability of being expressed in heterozygotes. Finally, we estimated the proportion of the phenotype of heterozygotes explained by colour hierarchy by computing the overall proportion of pixels conforming to the general hierarchy across the three colours.
A computer sees an image as an array of numbers. The matrix on the right contains numbers between 0 and 255, each of which corresponds to the pixel brightness in the left image. Both are overlaid in the middle image. The source image was downloaded via
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