# Also in the Article

Quantifying evolutionary potential in Stylopoma

How colonial animals evolve

Procedure

As noted above, covariances can be calculated as the variance of a traits multiplied by the linear regression of traits. This even works in the case of a single trait, because its variance can be multiplied by the linear regression of the trait on itself. Because a linear regression of a trait with itself will always be equal to 1, the product of a variance value multiplied by 1 is equal to the variance value.

Heritability is of special interest because it is the product of the variance of a trait and its change over generations. This means that the heritability of traits is an efficient feature to investigate because the heritabilities of each trait automatically incorporate a measure of the variance of traits. Thus, we can understand the evolutionary potential of a trait by only looking at its heritability. This is true because there are two ways that heritability can be equal to zero. First, if there is no variation, then heritability will be equal to 0, and as a consequence, the equivalent element of the P matrix will also be equal to 0. The second way heritability will be equal to 0 is if the linear regression of parent and offspring phenotypes is equal to 0.

Measuring heritability. Figure 2 presents the heritability values for traits and pairwise combinations. Heritability is the phenotypic covariance between parent and offspring. Using the algebraic shortcut, we breakdown that covariance into a variance and a linear regression. So, for a single trait, the heritability (h) between parent (ϕp) and offspring (ϕo) is equal to$h=var(ϕo)βϕo,ϕp$()5

In Stylopoma, and all other bryozoans, clonal lineages are aligned in a linear chain. The distal end of a parent is where the offspring buds out and forms. At the growing margin of the colony, there will be many clonal lineages, each contributing a new generation of zooid. For our analysis, we compare phenotypes of zooids along individual clonal chains of parents and offspring.

For our heritability measure, we compare parents to offspring. As a consequence, the offspring in one generation will be the parent in the next. So, the phenotype of many individual zooids will be used twice in the calculation of heritability. For example, the width measurement of the zooid contributes to both PO1 and PO2, first as an offspring and second as a parent. Each comparison, PO(i,j), represents a coordinate on a scatter plot comparing parent to offspring phenotypes (fig. S1). It is from this scatter plot that the heritability is calculated. We then measure the heritability using the linear regression of parent on offspring phenotypes. In fig. S1, this linear component of heritability is shown by the solid regression line. Heritability for colony level traits (fig. S2) was calculated for parent-offspring pairs.

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