Evolution, 4th Edition

372 CHAPTER 15

Such changes account for a great deal of morphological evolution. For example, an

increased rate of elongation of the digits accounts for the shape of a bat’s wing com-

pared with the forelimbs of other mammals (see Fig ure 2.9); an elephant’s tusks are

incisor teeth that have grown faster and for a longer time than the other teeth.

Allometric growth is often described by the equation y = bxa, where y and x

are two measurements, such as the height and width of a tooth or the size of the

head and the body. In many studies, x is a measure of body size, such as weight,

because many structures change disproportionately with overall size. An allo-

metric relationship is often represented logarithmically as log y = log b + a log x.

The coefficient a describes the relative growth rates of features y and x (FIGURE

15.2). If y increases faster than x, as for human leg length relative to body size,

a > 1 (positive allometry); if y increases more slowly than x, as for human head size,

a < 1 (negative allometry). Allometric variation is seen both within species (as the

beetles in Figure 15.2 illustrate) and among species. For example, species of deer

show positive allometry between antler size and body mass; the largest deer, the

extinct Irish elk (Megaloceros giganteus), had spectacular antlers (see Fig ure 1.9).

Heterochrony [22, 45] is broadly defined as an evolutionary change in the timing

or rate of developmental events. One of the best known instances is an evolutionary

change called paedomorphosis, in which some characteristics of the adult of a

species may have a more juvenile form than in the species’ ancestor. One way

paedomorphosis can happen, called neoteny, is seen in the axolotl, a salamander

that grows to full size but does not undergo metamorphosis, as most salamanders

do. Instead, it reproduces while retaining most of its larval (juvenile) characteristics

(FIGURE 15.3).

Heterotopy is an evolutionary change in the spatial position of a feature within

an organism. Often, it is expressed at an additional, novel position. As we will see,

this can result from the expression of specific genes in novel parts of the developing

Futuyma Kirkpatrick Evolution, 4e

Sinauer Associates

Troutt Visual Services

Evolution4e_15.02.ai Date 02-02-2017

1

3

0

20 40 60 80 100

(2) b = 2, a = 1

(3) b = 0.32,

a = 3/2

(4) b = 2.2, a = 2/3

(1) b = 1, a = 1

50

100

150

200

250

300

0

x

y

(A) Arithmetic plots

1 2

(1)

(2)

(3)

(4)

2

Log 10 x Female Males

Log

10

y

(B) Logarithmic plots

y = bxa

FIGURE 15.2 Hypothetical curves showing various allometric growth relationships

between two body measurements, y and x, according to the equation y = bxa.

(A) Arithmetic plots. The curves 1 and 2 show isometric growth (a = 1), in which y is a

constant multiple (b) of x. Curves 3 and 4 show positive (a > 1) and negative (a < 1)

allometry, respectively. (B) Logarithmic plots of the same curves have a linear form. The

slope differences depend on a. Curves 1 and 2 have slopes equal to 1. When a >1, y

increases faster than x. The male stag beetles (Cyclommatus metallifer) at right show

positive allometry of mandibles, relative to body length. (Photos from [21].)

15_EVOL4E_CH15.indd 372 3/22/17 1:30 PM