An example: selection in a pentastomid bug

94 individuals were collected along shoreline of Lake Michigan in Parker County, Indiana after a storm. 39 were alive, 55 dead. The means of several characters before selection, the trait correlations, and the selection analysis are presented in Table 1.

Table 1: Selection analysis of pentastomid bugs on the shores of Lake Michigan.

Character	Mean before selection	standard deviation
head	0.880	0.034
thorax	2.038	0.049
scutellum	1.526	0.057
wing	2.337	0.043

	head	thorax	scutellum	wing
head	1.00	0.72	0.50	0.60
thorax		1.00	0.59	0.71
scutellum			1.00	0.62
wing				1.00

Character	$s$	$s'$	$\beta$	$\beta'$
head	-0.004	-0.11	-0.7 $\pm$ 4.9	-0.03 $\pm$ 0.17
thorax	-0.003	-0.06	11.6 $\pm$ 3.9$^{**}$	0.58 $\pm$ 0.19$^{**}$
scutellum	-0.16$^*$	-0.28$^*$	-2.8 $\pm$ 2.7	-0.17 $\pm$ 0.15
wing	-0.019$^{**}$	-0.43$^{**}$	-16.6 $\pm$ 4.0$^{**}$	-0.74 $\pm$ 0.18$^{**}$

The column labeled $s$ is the selective differential for each character. The column labeled $s'$ is the standardized selective differential, i.e., the change measured in units of standard deviation rather than on the original scale.³ A multiple regression analysis of fitness versus phenotype on the original scale gives estimates of $\beta$, the direct effect of selection on that trait. A multiple regression analysis of fitness versus phenotype on the transformed scale gives the standardized direct effect of selection, $\beta'$, on that trait.

Notice that the selective differential⁴ for the thorax measurement is negative, i.e., individuals that survived had larger thoraces than those that died. But the direct effect of selection on thorax is strongly positive, i.e., all other things being equal, an individual with a large was more likely to survive than one with a small thorax. Why the apparent contradiction? Because the thorax measurement is positively correlated with the wing measurement, and there's strong selection for decreased values of the wing measurement.