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NON-HOMOGENEOUS EDDIES. “The sensitivity of the neural network to perturbations means that small, gradual evolutionary shifts in one or a few parameters of the neural network can shift a shell from one pattern regime into an entirely dissimilar one.” https://lnkd.in/dwfZQzE View in LinkedIn

BIFURCATION BOUNDARIES. “This limitation does not apply to pigmentation patterns. Although the same averaging procedure is being used on each parameter of the neural-network model, it is possible, and even likely, that a set of estimated parameters will be in a region of parameter space not inhabited by any living species.” https://lnkd.in/dwfZQzE View in LinkedIn

BINARY OUTCOMES. “The role of bifurcation boundaries in evolution was recognized in earlier studies of limb morphogenesis. This feature of our results is quite different from what is usually found when inferring ancestral states of continuously variable characters. A well known limitation of methods for estimating ancestral states is that it is impossible for estimates to fall outside the range of the living species analyzed.” https://lnkd.in/dwfZQzE View in LinkedIn

STEPWISE PATTERNINGS. “The patterns generated by the neural-network model are not necessarily smooth functions of the parameter values. Instead, they can vary discontinuously when parameter values move into a different bifurcation region that produces qualitatively different patterns.” https://lnkd.in/dwfZQzE View in LinkedIn

DISCONNECT OVER GENERATIONS. “A unique feature of our results is that the inferred pigmentation patterns of ancestors may be quite different from the patterns of their descendants.” https://lnkd.in/dwfZQzE View in LinkedIn