I'm using squared-change parsimony to reconstruct ancestral shapes. The phylogeny has a number of deep nodes, with relatively few recent nodes, and reconstructed shapes in the deep nodes resemble one another - most shape change seems to be concentrated towards the tips. Does squared-change phylogeny allow for delayed or accelerated change?
Squared-change parsimony is the application of a least-squares fit of continuous data to a tree with branch lengths. As such, there is a single best-fit. So unlike a parsimony "fit" of discrete data in which there may be multiple most parsimonious reconstructions (i.e., acctran, deltran and possibly other reconstructions), squared-change parsimony has a single reconstruction.
If you are looking to develop an error estimate at the nodes, there are a number of things you could consider. For example, use squared-change parsimony on a set of trees drawn randomly from the posterior distribution of trees from a Bayesian analysis. Given that there may be trees with different branching orders, this may not be desirable as summarizing the data may be complicated. Alternatively, if your terminals are being coded with a mean value, you could randomly sample (100 or 1000 times) the values used to generate the mean for each of the terminals and use squared-change parsimony to estimate node values on the ML tree. A variance can then be calculated for each of the nodes.
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