We present a new model for seed banks, where direct ancestors of individuals may have lived in the near as well as the very far past. The classical Wright‒Fisher model, as well as a seed bank model with bounded age distribution considered in Kaj, Krone and Lascoux (2001) are special cases of our model. We discern three parameter regimes of the seed bank age distribution, which lead to substantially different behaviour in terms of genetic variability, in particular with respect to fixation of types and time to the most recent common ancestor. We prove that, for age distributions with finite mean, the ancestral process converges to a time-changed Kingman coalescent, while in the case of infinite mean, ancestral lineages might not merge at all with positive probability. Furthermore, we present a construction of the forward-in-time process in equilibrium. The mathematical methods are based on renewal theory, the urn process introduced in Kaj, Krone and Lascoux (2001) as well as on a paper by Hammond and Sheffield (2013).

Color induction was measured using a matching method for two spatial patterns, each composed of double contours. In one pattern (the standard), the contours had sharp edges to induce the Watercolor Effect (WCE); in the other, the two contours had a spatial taper so that the overall profile produced a sawtooth edge, or ramped stimulus. These patterns were chosen based on our previous study demonstrating that the strength of the chromatic WCE depends on a luminance difference between the two contours. Low-pass chromatic mechanisms, unlike bandpass luminance mechanisms, may be expected to be insensitive to the difference between the two spatial profiles. The strength of the watercolor spreading was similar for the two patterns at narrow widths of the contour possibly because of chromatic aberration, but with wider contours, the standard stimulus produced stronger assimilation than the ramped stimulus. This research suggests that luminance-dependent chromatic mechanisms mediate the WCE and that these mechanisms are sensitive to differences in the two spatial profiles of the pattern contours only when they are wide.