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Evolutionary modeling
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Evolutionary parallelisms of pectoral and pelvic network-anatomy from fins to limbs

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We estimated the occurrence of evolutionary shifts in the topological organization of appendages in our phylogenetic tree using a SURFACE (59) analysis of the first two PC components for pectoral and pelvic appendages independently. SURFACE estimates change of evolutionary regimes—i.e., changes in the strength (α) and rate (σ) of evolution and in the optimal mean (θ) in the branches and/or clades of a tree—from multivariate data and a non-ultrametric tree. SURFACE uses an OU stabilizing selection model of evolution, which allows changes in the rate of evolution and optimal means of variables. If present, this method identifies homoplasy: two clades with the same regime. Given the small sample of appendages in our comparisons, we deemed it necessary to calculate the power of the SURFACE analysis as an indicator of reliability in the accuracy of estimated patterns. Because in OU models power is dependent by strength, rate, and optimal mean combined, effect-size measures offer a better prediction of power than sample size (60). We calculated the power of the estimated regimes using the SNR, which is defined as $SNR=2Tαθ/σ2$ where T is the total depth of the phylogeny. High power can be inferred when SNR > 1. To further validate the estimated regimes, the output of SURFACE was then fitted to alternative evolutionary models: a one-rate BM; a multi-rate BM; an OU with fixed strength, rate, and mean; an OU with fixed strength and rate, and multi-mean; and an OU with fixed strength, and multi-rate and multi-mean. Fitted models were compared using AIC. Last, we statistically tested the resulting evolutionary models of evolution with a phylogenetic MANOVA to confirm that the clades identified had a different regime corresponding to different groups with different means. The combination of estimation, fitting, and testing allowed us to build confidence that the evolutionary patterns found were reliable if they converged on the same result. Evolutionary modeling was carried out in R using functions from the packages surface (59), mvMORPH (61), and geiger (62) for the estimation, fitting, and testing, respectively.

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