Squared Change and Linear Parsimony

There are two general types of MP widely used in tracing the evolution of continuous traits: squared-change parsimony and linear parsimony. Squared-change algorithms (Rogers, 1984) seek to minimize the amount of squared change along each branch across the entire tree simultaneously, using a formula in which the cost of a change from state x to y is (x — y)2. Squared-change parsimony assigns a single ancestral value to each internal node to minimize the sum of squares change over the tree (Maddison, 1991). When using squared-change parsimony, the absolute amount of evolution over the whole tree is not necessarily minimized, and some degree of change is forced along most branches. Linear parsimony reconstructs ancestral node values by minimizing total changes (Figure 3). Linear-parsimony algorithms (Kluge and Farris, 1969) seek to minimize the total amount of evolution and consider only the three nearest nodes when calculating the ancestral character states. In linear parsimony the cost of a change from x to y is |x — y|. The result of this local optimization is that changes are inferred on very few or single branches. Linear parsimony therefore permits the accurate reconstruction of discontinuous events, or of large changes in trait values on a tree. Although evolutionary change is often thought of as gradual, large changes on a tree may result from a variety of real biological processes, not the least of which is the extinction of taxa with intermediate trait values (Butler and Losos, 1997).

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