Zelditch M.L. (и др.) Geometric Morphometrics for Biologists: a primer

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The relationship between ontogeny

and phylogeny

According to one of the best-known aphorisms in evolutionary developmental biology,

“ontogeny recapitulates phylogeny.” The statement has been discredited numerous times,

but evolutionary biologists remain intrigued by the idea that ontogeny and phylogeny might

be related. Gould proposed an alternative to the theory of recapitulation, one that allows

for the converse phenomenon: rather than a descendant completing and going beyond the

ancestral ontogeny, some fail to complete it (Gould, 1977). In those cases, descendant

adults resemble ancestral juveniles, in direct contradiction to the theory of recapitulation.

However, a broader theory encompasses both cases: parallelism between ontogeny and

phylogeny. According to the theory of parallelism, the descendant’s adult morphology can

be found either in the ancestral ontogeny or by extrapolation of it (Figure 13.1). Either

the descendant adult looks like a subadult ancestor, or it looks like an overgrown one.

Although termed parallelism, the direction of evolutionary change (Figure 13.1, the path

labeled E) actually coincides with the direction of the ancestral ontogeny (Fig. 13.1, the path

labeled O), it does not merely parallel it.

The explanation for parallelism is that species evolve in rates or timings of development,

but otherwise retain the ancestral ontogeny. If development speeds up, or lasts for longer,

the descendant will go further than the ancestor along the ancestor’s ontogeny. Conversely,

if development slows down, or lasts for less time, the descendant will not reach the ances-

tral endpoint. Such changes in developmental rate or timing are called heterochrony, and

Gould (1977) devoted his entire book to the phenomenon. His work stimulated hun-

dreds of studies of heterochrony, but Gould never claimed that heterochrony is a common

phenomenon. Rather, he characterized it as a part of a broader subject, that broader

subject being the relationships between ontogeny and phylogeny. Nevertheless, he found

heterochrony especially interesting, and thus worthy of special attention, for two major

reasons. First, it has an intriguing implication, which is that morphology evolves as an indi-

rect effect of selection on life-history parameters. Should selection favor a younger age at

sexual maturity, the ancestral ontogeny might be truncated so the descendant adult reaches

sexual maturity with a larval morphology. Even though morphology itself is not the target

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322 GEOMETRIC MORPHOMETRICS FOR BIOLOGISTS

Age

Shape

Figure 13.1 Parallelism. The ontogeny of the ancestor (indicated by the circles) and the descendant

(indicated by the squares) begin development having the same shape and follow the same ontogeny

of shape. They differ only in that the descendant’s ontogeny is a truncated version of the ancestral

ontogeny. Consequently, the descendant adult resembles an ancestral juvenile. In cases of parallelism,

the direction of evolutionary change in adult morphology (E) coincides with the direction of the

ancestral ontogeny (O).

of selection, it is nonetheless modified, sometimes dramatically, and those modifications

require no adaptive explanation in their own right. Recognizing that they are simply a cor-

related effect of an evolutionary change in a life-history parameter can temper an excessive

enthusiasm for adaptive explanations. Gould’s logic follows the same line taken by Huxley

(1932) in his discussion of evolutionary allometry – that shape evolves as an indirect effect

of selection on size, so the changes in shape are explained by the changes in size. This con-

nection between heterochrony and allometry is seemingly obvious, but Gould was the first

to recognize and emphasize it.

A second reason for concentrating on the phenomenon of parallelism is that Gould

sought to rehabilitate the concept of recapitulation. Even though he denied that reca-

pitulation is a general rule, he thought the idea had been dismissed unfairly, and for

reasons unrelated to the failure of the theory. Other workers had also attempted to res-

cue the idea of recapitulation, especially Cope (e.g. 1887), by applying it to individual

parts (or measurements). Unlike them, Gould took an organismal, multivariate view of

parallelism. He strongly opposed the trait-by-trait approach to morphology, whereby

each individual organ (or measurement) is accorded its own explanation. Instead of that

approach, which he called “atomistic,” he favored viewing organisms as integrated enti-

ties, bound together by developmental correlations. Accordingly, rather than analyzing

changes in growth rates of individual measurements, he modeled changes in properties of

whole organisms, such as life-history parameters. His models are admittedly informal and

verbal rather than mathematical, so they cannot be considered multivariate in a techni-

cal sense, but formalizing them requires a multivariate mathematical model. Gould did

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THE RELATIONSHIP BETWEEN ONTOGENY AND PHYLOGENY 323

Shape

Figure 13.2 Changes confined to early morphogenesis. This pattern requires using two shape

axes to depict the change; one oriented in the direction of the divergence in early morphogen-

esis, the other depicting the shared direction of subsequent ontogenetic change. The ancestral

ontogeny is depicted by circles, the descendant ontogeny by squares. The two lines differ in

elevation, a difference that is constant throughout ontogeny. Consequently, the direction of evo-

lutionary change in larval morphology (E

) parallels the direction of evolutionary change in adult

morphology (E

). These evolutionary transformations do not parallel the direction of the ancestral

ontogeny.

not provide one, so the assumptions of his theory cannot be examined rigorously, but

a more rigorous model for evolutionary allometry grounded in evolutionary theory was

developed by Lande (1979) and extended to the more general multivariate case by Lande

and Arnold (1983). The important point made by these models is that selection on body

size, or any other life-history trait, will likely have indirect effects, but not necessarily in

the direction anticipated by either Gould or Huxley. Nevertheless, despite that impor-

tant flaw in Gould’s model, he offered a multivariate, organismal view of allometry and

heterochrony.

Gould acknowledged that heterochrony is just a part of a broader subject, deserving

special attention because of its intriguing implications. However, parallelism is neither the

only intriguing nor the only theoretically significant possibility. Another, which is equally

remarkable, is shown in Figure 13.2 – the descendant’s ontogeny is a vertically transposed

version of the ancestral ontogeny. This pattern differs from parallelism because the descen-

dant adult does not lie along the ancestral ontogeny – it lies above or below it. This pattern

is difficult to draw (and perhaps also to read) because we need two shape axes to represent

it: one, the X-axis, is in the direction of their shared ontogeny; the other, the Y-axis, is

in the direction of the difference arising early in development. That the two lines differ

solely in elevation means that the species diverge early in development but thereafter fol-

low the same ontogeny. Consequently, as adults they differ in precisely the same features

that distinguished them very early in development. This pattern is at least as intrigu-

ing as parallelism because of what it implies about the dynamics of evolving ontogenies.

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324 GEOMETRIC MORPHOMETRICS FOR BIOLOGISTS

It means that late development is more conservative than early. Conventionally, embryos

are thought to pass through a “phylotypic period” – the stage at which embryos of all mem-

bers of a phylum look the same (Seidl, 1960; Sander, 1983; Slack et al., 1993). Several

studies have challenged this “hour-glass” model (e.g. Richardson et al., 1997; Bininda-

Emonds et al., 2003) on the grounds that the phylotypic period is not as conservative as

generally thought, but even these critiques do not go so far as to say that morphologies

are more disparate early rather than later. Yet that is precisely the expectation implied

by the two parallel lines. That is not to say that finding this pattern in morphometric

data contradicts the theory of the phylotypic period, because most morphometric studies

encompass far older stages (e.g. postnatal, postlarval). The phylotypic period begins at

onset of neurulation and ends with somitogenesis (see Kimmel et al., 1995), so that is the

phase that must be compared to later stages to test the theory. Nonetheless, it would still be

surprising to find out that all divergence occurs by changes in late embryonic/early larval

development.

Clearly, parallelism is not the only theoretically interesting or counterintuitive pattern

that can be imagined. However, rather than seeking out counterintuitive possibilities, we

might do better to look for the most general patterns. Focusing on a rare (albeit inter-

esting) pattern can foster a highly biased view of the evolution of ontogeny. If our aim

is to generalize about the evolution of ontogeny, we need to devote as much attention

to common patterns as to rare ones. Given the enormous literature on the subject, het-

erochrony might seem to be a very common phenomenon, but that impression results

partly from the broadened definition of heterochrony, which obviously increases the

number of cases that satisfy it (see, for example, McKinney and McNamara, 1991). Some-

times, heterochrony is defined so broadly that it means nothing more than that ontogeny

evolves. The theoretical significance of the concept is thereby diluted, and by classify-

ing all the possibilities into a single category we lose the ability to recognize distinctions

among them.

Our objective in this chapter is to describe a variety of patterns that can be found

in comparative studies of ontogeny. To that end, we focus on the patterns amenable

to discovery by comparative studies of ontogenetic allometry. Studies of allometry are

sometimes viewed as a poor substitute for studies of heterochrony, but allometry is not just

something we study when we have no information about age. Rather, comparative studies

of allometry allow for a richer formalism than is feasible in studies of heterochrony because

the formalisms for heterochrony were designed for cases of parallelism. They cannot be

applied more generally without sacrificing a multivariate approach to the evolution of

ontogeny.

Comparative analyses of allometry not only rely on a richer formalism; they also ana-

lyze a phenomenon that is interesting in its own right. Allometry is no less interesting

than heterochrony, an argument we develop below. After motivating the study of ontoge-

netic allometry, we introduce the formalism for analyzing it and discuss the meaning (both

formal and biological) of the coefficients obtained by that formalism. We next discuss meth-

ods for discerning patterns in the relationship between ontogeny and phylogeny, focusing

on the significance of those patterns for our understanding of the evolution of develop-

ment. The first part of this chapter focuses on traditional morphometric data because most

comparative studies of allometry have relied on them. We then briefly review the geomet-

ric analysis of ontogenetic allometry (the subject of Chapter 10) and revisit the patterns

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THE RELATIONSHIP BETWEEN ONTOGENY AND PHYLOGENY 325

introduced in context of traditional allometry, describing how these would appear in

studies of geometric shape data.

Why allometry is interesting in its own right

For purely biomechanical reasons, we expect allometry because we expect organisms to

change shape as they grow. Were they to grow without changing shape, they would likely

decrease their ability to perform such vital functions as respiration, locomotion and feed-

ing. Allometric scaling maintains functional equivalence. However, only certain very basic

physical properties (such as surface area: volume relationships) might be expected to scale

predictably over an entire ontogenetic series because young (small) organisms are often

ecologically very different than older (larger) members of their own species. For that rea-

son, they do not face the same functional demands. Nonetheless, they grow allometrically.

That by itself is interesting; over an individual’s life-time, it is increasing in size, changing

shape, and also experiencing transitions in functional demands. At every age the organ-

ism must be competent, but it is continually changing. How these transformations in

size, shape and function are interrelated is a central question in studies of ontogenetic

allometry.

This focus on related transformations in size, shape and function arises from the percep-

tion that an organism’s morphology is a continuum of shapes. To understand morphology

we must not only understand the relationship between form and function at one age, we

must also understand the entire continuum. That continuum can be described by a vector

that extends from the form of the smallest to that of the largest individual. The optimal

form for any one age might not lie along that vector, because the direction in which the

vector points may represent a compromise among age-specific optima. The adult morphol-

ogy may be especially important for determining the direction of the vector; even though

ontogeny is not just the vector pointing towards an optimal adult, adult morphology could

conceivably matter as much as the pathway. That is because the adult shape may be stable

once it is attained; in organisms that have determinate morphogenesis (whether or not they

also have determinate growth) the adult form persists for much of the life cycle. Yet that

adult shape will never be reached if organisms do not first survive the especially vulnerable

pre-adult phases. Thus, the direction in which the vector points, as well as the rate at which

it develops, may be related, in part, to age-specific mortality rates and to the processes

responsible for mortality. When mortality is largely a result of predation, and predation

rates are particularly high early in life, the ontogenetic vector may be oriented towards

development of anti-predator defenses early in life, with consequences for morphology at

later ages.

Allometry is interesting not only because of its implications for form–function rela-

tionships, but also because of the insight it offers into growth and development. Those

processes cause the changes in size and shape recorded in studies of allometry. Often we

know much about the processes causing those changes, especially in studies of vertebrate

skeletal form. In this case, the processes we are studying are the spatiotemporal dynamics

of bone growth. From the coefficients we obtain in studies of allometry, we can learn about

the spatial distribution of relative growth rates. Evolutionary changes in the spatiotemporal

dynamics of growth can be discovered by comparative studies of allometry.

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326 GEOMETRIC MORPHOMETRICS FOR BIOLOGISTS

Formalisms for the analysis of ontogenetic allometry: traditional

morphometric data

The traditional formalism

The traditional formalism for the study of allometry relates the increase in size of one

part (Y) to that of another (X). Often, X is intended to represent the size of the whole

organism. To make our discussion of allometry as concrete as possible, and to ease the

transition from geometric to traditional morphometric data, we will focus on the case

of the piranha, Serrasalmus gouldingi, which we used as our model for the geometric

analyses of ontogenetic allometry. To analyze its ontogenetic allometry we measure a

variety of lengths and depths (Figure 13.3). For our measure of body size we will use the

measurement extending from landmark 1 to landmark 7, which is termed standard length

(SL) and is frequently used as the measurement of body size in studies of teleosts – so,

for our example, X =SL. The other 29 measurements are the measures 2–30, which we

will represent by the vector {Y

, Y

,…Y

}. We first discuss the mathematical analysis

Figure 13.3 Landmarks sampled on Serrasalmus gouldingi, and the traditional morphometric

measurement scheme based on those landmarks.

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THE RELATIONSHIP BETWEEN ONTOGENY AND PHYLOGENY 327

of allometry, then follow this with an interpretation of the coefficients obtained by the

analysis, and then consider their developmental significance.

The mathematical analysis of allometry

The relationship between X and Y often fits a model, the power law (Huxley, 1932):

Y = bX

(13.1)

where k is the rate of growth of part Y relative to X, and b is the size of Y when X is at

unit size. To ease fitting the model to data, it is often rewritten in a linear form:

log(Y) = log(b) +k log(X)(13.2)

Expressed in this form, we can use linear regression to estimate the parameters b and k;

they are the intercept and slope (respectively) of a linear regression of log(Y)onlog(X).

Table 13.1 gives the regression coefficients, b and k, of the variables shown in Figure 13.3

Table 13.1 Allometric coefficients for Serrasalmus gouldingi;

b is the intercept term, k is the slope (measurements are shown

in Figure 13.3)

Variable b k

v2 −0.939 0.806

v3 −0.613 0.885

v4 −1.163 0.850

v5 −2.643 1.225

v6 −1.396 1.042

v7 −1.512 1.002

v8 −1.383 0.928

v9 −1.974 1.104

v10 −1.761 1.220

v11 −1.931 1.198

v12 −1.595 1.136

v13 −2.378 1.186

v14 −2.228 1.116

v15 −1.681 1.210

v16 −1.781 1.225

v17 −1.551 1.171

v18 −2.572 1.170

v19 −1.938 1.085

v20 −1.685 1.104

v21 −1.991 1.225

v22 −1.834 1.217

v23 −1.473 1.072

v24 −1.674 0.939

v25 −2.686 1.120

v26 −1.558 1.129

v27 −1.815 0.898

v28 −1.231 0.811

v29 −1.160 0.751

v30 −0.635 0.903