Size variation, growth strategies, and the evolution of modularity in the mammalian skull

ORIGINAL ARTICLE

doi:10.1111/evo.12177

SIZE VARIATION, GROWTH STRATEGIES,AND THE EVOLUTION OF MODULARITYIN THE MAMMALIAN SKULLArthur Porto,1,2,3 Leila Teruko Shirai,4 Felipe Bandoni de Oliveira,2 and Gabriel Marroig2

1Department of Anatomy and Neurobiology, Washington University in St Louis, St Louis, Missouri2Departamento de Genetica e Biologia Evolutiva, Instituto de Biociencias, Universidade de Sao Paulo, CEP 05508-090, Sao

Paulo, SP, Brasil3E-mail: [email protected]

4Instituto Gulbenkian de Ciencias, Oeiras, Portugal

Received December 9, 2011

Accepted May 15, 2013

Data Archived: Dryad doi:10.5061/dryad.4d236

Allometry is a major determinant of within-population patterns of association among traits and, therefore, a major component

of morphological integration studies. Even so, the influence of size variation over evolutionary change has been largely unap-

preciated. Here, we explore the interplay between allometric size variation, modularity, and life-history strategies in the skull

from representatives of 35 mammalian families. We start by removing size variation from within-species data and analyzing its

influence on integration magnitudes, modularity patterns, and responses to selection. We also carry out a simulation in which we

artificially alter the influence of size variation in within-taxa matrices. Finally, we explore the relationship between size variation

and different growth strategies. We demonstrate that a large portion of the evolution of modularity in the mammalian skull is

associated to the evolution of growth strategies. Lineages with highly altricial neonates have adult variation patterns dominated

by size variation, leading to high correlations among traits regardless of any underlying modular process and impacting directly

their potential to respond to selection. Greater influence of size variation is associated to larger intermodule correlations, less

individualized modules, and less flexible responses to natural selection.

KEY WORDS: Allometry, constraints, flexibility, life-history evolution, morphospace, V/CV matrix.

Living organisms are no longer viewed as an array of discrete

traits, but rather as complex systems in which several characters

interact, sharing genetic, developmental, or functional pathways

(Cheverud 1984; Emerson and Hastings 1998). Under this view,

a trait cannot be considered as evolving independently of others,

and the study of how traits are connected is central to evolution-

ary biology (Steppan et al. 2002). Studies across several levels

of biological organization, from proteins to morphology, have

often found traits to be organized in modules, that is, semiau-

tonomous complexes of highly intercorrelated traits (Schlosser

and Wagner 2004). For studies of morphological evolution, the

importance of such modular architecture relates to the observation

that morphological variation is also modularly organized (e.g.,

Olson and Miller 1958; Berg 1960; Cheverud 1982; 1995; Marroig

and Cheverud 2001; Porto et al. 2009). Such structure of varia-

tion biases the direction, magnitude, and rate of morphological

change, either constraining or facilitating evolution along differ-

ent dimensions of the morphospace (Maynard Smith et al. 1985;

Arnold 1992; Arnold et al. 2001; Marroig and Cheverud 2004a;

2005, 2010). Modularity is, therefore, a central umbrella concept

to understand morphological evolution.

There is a variety of methods available for describing and

quantifying modularity in morphological data. Most methods are

based on correlations or covariances among traits, and modularity

3 3 0 5C© 2013 The Author(s). Evolution C© 2013 The Society for the Study of Evolution.Evolution 67-11: 3305–3322

ARTHUR PORTO ET AL.

is inferred by the analysis of patterns and magnitudes of integra-

tion among morphological elements (e.g., Armbruster et al. 2004;

Badyaev and Foresman 2004; Klingenberg 2004; Monteiro et al.

2005; Porto et al. 2009). However, studies comparing modularity

on a macroevolutionary scale have only recently been addressed,

and many aspects remain unexplored (Chernoff and Magwene

1999; Eble 2004; Porto et al. 2009).

Previous work on the evolution of modularity in the mam-

malian skull pointed to highly conserved integration patterns

across mammals (Porto et al. 2009), indicating that skull diversi-

fication occurred in spite of a relative covariance pattern stasis.

Because theoretical and empirical studies suggest that the evo-

lution of integration patterns can occur relatively fast (Pavlicev

et al. 2007; Delph et al. 2011), we argued that the observed sim-

ilarity can only be explained as a result of stabilizing selection

for structural cohesion within organisms, so that cranial develop-

ment and function are preserved while the average morphology

diversifies (Marroig et al. 2009; Porto et al. 2009). However, mor-

phological integration is not only a consequence of evolutionary

processes, it also plays a significant role influencing the evolution-

ary response to selection. Therefore, we stressed the importance

of another aspect of modularity, namely the differences in inte-

gration magnitudes, for understanding interspecies variation in

the short-term potential for evolutionary responses to selection

(Marroig et al. 2009; Porto et al. 2009). Larger integration magni-

tudes were associated with lower potential to respond in the same

direction of selection (evolutionary flexibility sensu Marroig et al.

2009), and with less apparent modules in the mammalian skull.

Conversely, lower overall integration magnitudes were associated

with higher evolutionary flexibilities and with more distinct cra-

nial modules. We also observed that differences in integration

magnitudes among taxa were strongly correlated with changes

in the proportion of the total variation associated with size varia-

tion (Marroig et al. 2009). By size variation we mean the variation

in the length of one trait that is coupled with variation in all other

traits, in the sense that they increase or decrease together, yielding

variation shared by all traits (isometric or allometric covariation).

Studies have long portrayed size variation as a major deter-

minant of within-population patterns of association among traits,

potentially obscuring underlying modular patterns of integration

(Marroig and Cheverud 2004a; Mitteroecker and Bookstein 2007;

Klingenberg 2009). Most of the approaches to date, however, re-

gard size variation as a methodological concern (e.g., the influence

on the ability to detect modules), rather than address its evolution-

ary meaning. Many studies “correct” for allometric size variation

(e.g., Martinez-Abadias et al. 2011), a tradition that traces back to

Julian Huxley’s work (e.g., Huxley 1932). Although “correcting”

for allometric size is a justifiable approach in some contexts, it

leads to an undesirable side effect: the influence of size variation

on morphological evolution has been largely unappreciated.

This article regards size variation as biologically meaning-

ful because it is directly related to growth variation, which is

an ontogenetic process that potentially affects all traits in an or-

ganism (Nijhout 2011). This is especially true in multicellular

complex organisms, in which adult forms result from continuous

cycles of cell division and differentiation starting from a single

zygotic cell. Variation among individuals emerging from growth

processes imposes some level of correlation among traits, both

within and between modules. Consequently, species that present

larger variation emerging from growth processes (relative to other

sources of variation) will potentially have larger overall integra-

tion among traits (Fig. 1).

In this study, we explore the interplay between size variation,

morphological integration, and their potential evolutionary con-

sequences for the mammalian skull diversification. These aspects

have been preliminarily assayed in two representative groups,

Didelphimorphia and Primates, chosen on the basis of their

extreme integration magnitudes (Shirai and Marroig 2010). Here

we employ a broader phylogenetic framework to account for the

highly variable size variation and its influences on cranial mor-

phology and integration. We also explore whether differences in

life-history traits related to growth processes can explain the dif-

ferences in integration magnitudes we observe across mammals.

The following is an outline of our approach to these questions.

We first extend the analyses of Shirai and Marroig (2010)

to a far broader sample of mammals, including 35 families, and

reassess the following questions: (1) What effect does removal

of size variation have on the magnitude of integration of each

mammal taxon? (2) What effect does removal of size variation

have on the modularity patterns of each taxon? (3) What is the

influence of size variation on the potential ability to respond to

selection?

We also introduce two novel approaches to these questions.

The first is to simulate the evolutionary consequences of dif-

ferences in size variation. We altered the relative proportion of

total variation attributable to size from each taxon matrix, without

changing its structure, and simulated the expected outcomes in

terms of integration magnitudes, modular distinctiveness, and re-

sponses to selection. We then compared these simulated outcomes

to the observed variation found in mammals. If our hypothesis

relating size variation and morphological integration holds, an

increase in allometric size variation would mask modularity be-

cause of the strong between-module correlations associated with

variation along the size dimension. Accordingly, we expect size to

act as a strong “attractor” of evolutionary responses to selection,

reducing overall evolutionary flexibility of a given taxon (sensu

Marroig et al. 2009).

In the second novel approach, we appraise the relationship

between size variation and different growth strategies among

mammals. Differences in the influence of size variation are

3 3 0 6 EVOLUTION NOVEMBER 2013

SIZE VARIATION AND ITS EVOLUTIONARY IMPLICATIONS

P1

G1 G2 G3 G4 G5 G6 G1 G2 G3 G4 G5 G6

P1 P2 P3 P4 P5 P1 P2 P3 P4 P5

V VP1

P2

P2

P3

V

P2

P2

P3

Phenotype

Development

Gene�c factors

Integra�onV

A B

Figure 1. Theoretical expectation regarding the relationship between size variation and overall morphological integration. (A) We have

the situation in which a genetic factor (G3) has global effect over all the phenotypic elements. Plots represent correlations among

characters, which are expected to be high regardless of other modular genetic factors (other Gs). (B) We have a situation in which the

same genetic factor (G3) is not variable (white color) and correlations among characters are only dependent on other modular genetic

factors (other Gs). As can be seen in the plots, correlations among characters from different modules are expected to be low.

expected to emerge throughout ontogeny. Interestingly, mam-

mals possess highly conserved ontogenetic patterns (Moore 1981;

Smith 1996), and intertaxa differences in ontogeny are aligned

across a gradient that involves several life-history traits. On

one side of the gradient, we have species with long gestation,

low metabolism, low growth rate, high survival rate, preco-

cial neonates, and low reproductive output (e.g. primates, bats).

On the other side, we have species with short gestations, high

metabolism, high growth rate, low survival rate, altricial neonates,

and high reproductive output (e.g., rodents, marsupials). This gra-

dient is often referred to as the slow-fast continuum and has of-

ten been thought to influence the evolutionary dynamics of such

groups. They are also considered consequences of selection target-

ing mortality rates (Read and Harvey 1989; Promislow and Harvey

1990). By regressing the proportion of total variation associated

with size on postnatal growth data from life-history databases, we

analyze the relationship between integration magnitudes, growth

strategies, and life-history traits.

Materials and MethodsSAMPLES, LANDMARKS, AND MEASUREMENTS

A total of 3641 skulls were measured. We increased the phyloge-

netic representativeness of our previous studies (Porto et al. 2009;

Marroig et al. 2009), sampling 35 mammalian families belonging

to 18 orders (Table 1). We chose the most common species or

genus available at museum collections for each family, and taxa

will be referred by their family name for simplicity. The taxonomic

arrangement employed in this study follows Wilson and Reeder

(2005). Only adults were measured. A complete list of examined

specimens is available from the authors upon request and visited

collections are listed in the Supporting Information—S.I.1.

Thirty-five skull measurements (Supporting Information—

S.I.2) were calculated as Euclidean distances among 34 land-

marks (Fig. 2). Landmarks were recorded with Microscribe 3DX

and MX digitizers (Microscribe, Chicago, IL) and were defined

at the intersection among sutures and other easily identifiable cra-

nial structures, which reflect important developmental and func-

tional relationships among morphological elements (Cheverud

1982; Marroig and Cheverud 2001). Landmark homology across

mammalian orders followed Cheverud (1982) and Marroig and

Cheverud (2001), and are detailed elsewhere (Porto et al. 2009).

Right–left asymmetries were disregarded by averaging mea-

surements present on both sides of the skull. Skulls damaged

at one side had the other side used as average. All specimens

were measured twice and repeatabilities were estimated to ac-

count for measurement error (Lessels and Boag 1987). Nor-

mality and outlier analyses were also performed to check the

quality of the collected data. Repeatabilities were quite high

for all groups analyzed separately (mean = 0.96) and no sig-

nificant deviations from normality were observed. All subse-

quent analyses were carried out using the average of repeated

measurements.

RAW AND RESIDUAL MATRICES

Pooled within-group phenotypic correlation and variance/

covariance (V/CV) matrices were estimated for each taxon using

SYSTAT 11 (SSPS, Inc. 2004, Chicago, IL) and will be referred

EVOLUTION NOVEMBER 2013 3 3 0 7

ARTHUR PORTO ET AL.

Table 1. Representatives of the 35 mammalian families surveyed in this study, with respective sample sizes (N). Sources of variation

controlled during matrix estimation are presented with the legend in the bottom left corner.

Order Family Genus Controlled variables N

Primates Atelidae Alouatta S,SP,SxSP 384Primates Cebidae Callithrix S,SP 505Primates Cercopithecidae Papio S,SP,SxSP 264Primates Hominidae Homo S,G 267Carnivora Canidae Cerdocyon G 85Carnivora Felidae Leopardus G 66Carnivora Mustelidae Eira S,G 61Carnivora Procyonidae Nasua S,G 87Cetacea Delphinidae Sotalia S,G 80Artiodactyla Cervidae Mazama G 60Artiodactyla Tayassuidae Tayassu S,G 68Chiroptera Molossidae Molossus S,G 63Chiroptera Noctilionidae Noctilio S,G 60Chiroptera Phyllostomidae Artibeus – 54Chiroptera Vespertilionidae Myotis – 74Pilosa Myrmecophagidae Tamandua G 90Rodentia Caviidae Cavia G 71Rodentia Echimyidae Trinomys G 94Rodentia Cuniculidae Cuniculus G 42Rodentia Dasyproctidae Dasyprocta G 84Rodentia Erethizontidae Coendou – 39Rodentia Muridae Rattus G 91Rodentia Cricetidae Wiedomys – 49Rodentia Sciuridae Sciurus S,SP 83Lagomorpha Leporidae Sylvilagus G 86Macroscelidea Macroscelididae Elephantulus – 57Hyracoidea Procaviidae Procavia SSP 41Perissodactyla Tapiridae Tapirus – 42Cingulata Dasypodidae Dasypus G 89Scandentia Tupaiidae Tupaia SSP, SSPxS 58Paucituberculata Caenolestidae Caenolestes S,G 59Dasyuromorphia Dasyuridae Antechinus S,G 54Diprotodontia Macropodidae Macropus SSP 60Peramelimorphia Peramelidae Isoodon SSP 59Didelphimorphia Didelphidae Didelphis S,SP,SxSP 215Total 3641

S = sex, SP = species, SSP = subspecies, G = geography.

as raw (correlation and V/CV) matrices. Sources of variation

that are not directly related to genotype-phenotype map per se

(Wagner and Altenberg 1996) were controlled during matrix

estimation through multivariate analysis of variance tests, models

being chosen based on Wilk’s lambda statistic (considered

significant at P < 0.05). Controlled variables include interspe-

cific variation, subspecies variation, sex, geography, and their

possible interaction (Table 1). This is an important correction

step, because all correlation estimates among variables could

be inflated by differences on trait averages among groups. For

example, if differences between sexes on trait averages are not

controlled, two traits will exhibit a strong correlation due to

sexual dimorphism on the averages even if within each sex there

is no correlation between the two traits.

To test for the impact of size variation on integration mag-

nitudes and modularity patterns, we estimated residual correla-

tion and V/CV matrices. Residual matrices were calculated by

removing the effect of correlations with general size from the

correlations and covariances of raw matrices (Marroig et al. 2004).

A single size eigenvector (V) was obtained from each raw matrix

through the principal component analysis routine implemented in

SYSTAT 11. Eigenvectors were considered size-related whenever



IS

NSL

NA

PMZI

ZS

BR

PTLD

PEAMEAM

ZYGO

TSPAS

IS

PM

ZI

ZYGO

EAMPEAM

PNS

MT

JP

APETTS

OPI

BA

Figure 2. Thirty-four landmarks on the lateral and ventral view

of a dasyproctid skull. Landmarks are placed at the intersection

of cranial sutures and other easily identifiable features considered

relevant cranial anatomies (Cheverud 1996; Marroig and Cheverud

2001; Porto et al. 2009).

all elements presented positive associations with it. The residual

matrix (R) was then obtained from the following relationship:

R = P − V′V,

where P is the raw phenotypic matrix and V’ denotes the trans-

posed size-related eigenvector (V), which is the unstandardized

form of the size-related eigenvector, where the sum of the squares

of the elements is equal to its eigenvalue.

RAW AND RESIDUAL MAGNITUDES OF INTEGRATION

The average coefficient of determination (r2) is an index that rep-

resents the overall magnitude of integration among traits by av-

eraging the squared correlations in correlation matrices. Because

this index is exclusive of correlation matrices, we calculated in-

tegration magnitudes for V/CV matrices by using the coefficient

of variation of the eigenvalues (ICV; Shirai and Marroig 2010),

which is simply the standard deviation of the eigenvalues (σ(λ))

divided by the average of the eigenvalues (λ). This index is appro-

priate for comparisons involving organisms with large differences

in absolute body size, such as those among mammals. Larger or-

ganisms will have larger means and larger variances/covariances

and, therefore, larger σ(λ). Using the coefficient of variation of the

eigenvalues controls for this scale effect.

To evaluate the uncertainty in our integration magnitude esti-

mates, we bootstrapped individuals from the original samples (100

times), calculated ICV values for each resample, and plotted the

distribution of values for each taxon (Supporting Information—

S.I.3). Sampling error of morphological integration indexes (like

ICV) might be correlated to the sampling error of the popula-

tion variance, introducing a significant bias into our estimative

of overall integration magnitude (Young et al. 2010). This po-

tential problem was evaluated (Supporting Information—S.I.4),

and the main result is that original estimates are robust and show

the same pattern depicted by integration indexes when adjusted

using Young et al. (2010) approach. For that reason, integration

magnitudes used hereon are the original ICV values. Even though

we carried out Young et al. (2010) approach, this was done purely

to estimate our confidence in integration magnitudes estimates.

In our view, there is no biological reason that justifies projecting

all species to the same level of morphological variation.

MODULARITY HYPOTHESES AND MODULARITY

INDEX

To test the effect of size variation upon cranial modularity, matrix

correlations were calculated between residual correlation matri-

ces and theoretical matrices based on functional/developmental

relationships among characters (Supporting Information—S.I.2).

These results were later compared to those obtained for raw ma-

trices. Theoretical matrices were constructed as follows: when

two traits belong to the functional/developmental set being tested

(i.e., hypothesized module), a value of 1 is entered in the the-

oretical matrix; if not, a value of 0 is entered. This approach

is equivalent to a t-test where the average of integrated (avg+)

and nonintegrated traits (avg−) are compared for each hypoth-

esis, thus testing for the premise of modularity (i.e., integration

among elements belonging to the hypothesized module should

be higher than those belonging to different modules). Statistical

significance was evaluated through Mantel’s tests (10,000 permu-

tations), which accounts for the nonindependence of correlations

among traits. In spite of recent criticism of using Mantel’s test in

the context of comparative phylogenetic analysis (e.g., Harmon

and Glor 2010), this approach remains an effective ad hoc pro-

cedure for detection of biologically meaningful modules, as the

theoretical hypotheses are strongly anchored on state-of-the-art

literature on mammalian skull development (e.g., Moore 1981;

Cheverud 1995; Smith 1996, 1997, 2001).

A total of nine modularity hypotheses at different hierar-

chical levels were used (Supporting Information—S.I.2). Five of

them test for the existence of functional subregions in the skull:

oral, zygomatic, nasal, cranial base, and cranial vault. Two other


ARTHUR PORTO ET AL.

theoretical matrices test the presence of major developmental

regions: neurocranium and face (Moore 1981). Another theoreti-

cal matrix links all neurocranial traits into a module and all facial

traits into another, testing for neural versus somatic growth. Fi-

nally, we tested an overall connectivity matrix, combining all five

skull subregions in a single structure (total integration matrix).

To measure how much a given module stands out in compar-

ison to all remaining correlations in a matrix, a modularity index

based on the integration hypotheses described earlier was calcu-

lated. Because residual matrices often present negative averages

for nonintegrated (avg−) traits, we could not use the previously

employed index avg+/avg− (Porto et al. 2009). Therefore, the

modularity index was calculated as the absolute difference be-

tween avg+ and avg−, divided by ICV, which is always positive.

Thus, we normalized the absolute differences between averages by

the overall integration magnitude. Although this modularity index

lacks information on modular distinctiveness in terms of percent-

age of increase (as used in Cheverud 1995, Marroig and Cheverud

2001), it is suitable to compare raw and residual matrices.

EVOLUTIONARY FLEXIBILITY AND CONSTRAINTS

Any matrix quantifying modularity and integration in complex

traits has some structure (i.e., non-null correlations among traits)

that imposes a constraint to evolutionary change (Arnold et al.

2001). To explore those constraints and the influence of size vari-

ation on the ability to respond in the direction of selection, we

carried out a simulation of evolutionary responses to selection on

both raw and residual V/CV matrices of each taxon (see Marroig

et al. 2009 for the original description). This approach is based on

the multivariate response to selection equation (Lande 1979). It

uses P-matrices as surrogate for G-matrices, assuming that struc-

tural similarity is kept in relation to their phenotypic counterparts

(Cheverud 1988). Such premise was tested in a previous study, in

which we found remarkable stability in G- and P-matrices (Porto

et al. 2009) even though matrices were not strictly constant or

proportional. The 10,000 selection vectors were created with a

normal distribution random number generator, and selection vec-

tors were normalized to have a length of one. We subjected each

V/CV matrix to this series of random selection vectors and ob-

tained matrix response vectors. Two indexes were then calculated

based on these response vectors: an evolutionary flexibility and a

constraint index (Marroig et al. 2009). These were directly com-

parable between raw and residual matrices, and between taxa.

Flexibility is the cosine of the angle (i.e., the correlation)

between the selection gradient vector (β) and the evolutionary

response vector (�z; Marroig et al. 2009); or the ratio between

evolvability and respondability (Hansen and Houle 2008). Bio-

logically speaking, flexibility captures the ability of a population

to closely track the direction in which selection acts, indepen-

dently of the magnitude of the evolutionary response (Marroig

et al. 2009). Therefore, it was calculated as the average correla-

tion of response vectors to the selection vectors that generated

them. The lower the correlation, the lower the ability of a given

population to evolve in the direction of selection.

Evolutionary constraints, on the other hand, can be defined

as any limitation or bias on the course of evolution (Arnold 1992;

Marroig et al. 2009). Here, they were calculated based on the

relationship between the response vectors and the first princi-

pal component (pmax) of each matrix. Each of the 10,000 matrix

response vectors was correlated with pmax and the average corre-

lation calculated. Lower values are associated with matrices with

less constrained responses and higher values to more constrained

responses. Note that, for residual matrices, pmax corresponds to the

second principal component of the correspondent raw counterpart

matrix.

To evaluate the uncertainty in our flexibility and constraint

estimates, we bootstrapped individuals from the original sam-

ples (100 times), calculated flexibility/constraints indexes for

each resample, and boxplotted the distributions (Supporting

Information—S.I.3). It is important to notice that flexibility and

constraint indexes are independent of the absolute amount of mor-

phological variation present in a population and in this sense are

easily compared statistics even among lineages with very differ-

ent scales (body sizes). Both respondability (the length of the

response vector) and evolvability (the projection of the response

vector over the selection gradient) are measures that are scale

dependent (see Marroig et al. 2009). Thus, lineages with a larger

body size will have larger respondabilities and evolvabilities sim-

ply because variances (and covariances) are larger due to the

scale of the organisms when compared to small body size lin-

eages. Yet, notice that one obvious solution to the scale problem

would be to compute evolvability and respondability statistics on

mean or variance-standardized matrices (as suggested by Hansen

and Houle 2008). Interestingly, our previous results show that re-

spondability and evolvability calculated with mean-standardized

V/CV matrices still hold a strong relationship with absolute size

of the organism, at least for the mammalian skull (Marroig et al.

2009). Although this association with body size might indicate

another biologically relevant relationship between mammalian

life-history traits and the ability to respond to selection, it also

suggests that flexibility and evolvability could evolve indepen-

dently from one another.

EVOLUTION OF SIZE VARIATION—MODIFICATIONS

IN TAXON MATRICES

Given that changes in the relative influence of size variation on

the total morphological variation might drastically influence the

evolution of modularity, we simulated those changes in each taxon

matrix and then evaluated their consequences on: (1) the overall

integration magnitude (ICV); (2) the level of modular integration



(modularity index); (3) the flexibility index; and (4) the constraint

index.

The simulation decomposed raw V/CV matrices of each

taxon into their eigenvectors and eigenvalues. Each P matrix is

represented by the following equation:

P = VT�V

where P is the V/CV matrix, V is a square matrix with each column

containing a normalized eigenvector, � is a square diagonal ma-

trix with the eigenvalues in the diagonal and zeros as off-diagonal

elements, and the superscript T denotes matrix transpose. We then

multiplied the first eigenvalue by a constant varying from 0.7 to

20 times the original first eigenvalue. To keep the total amount of

variation constant (sum of eigenvalues equal among all matrices),

we multiplied all eigenvalues by the quotient of the original sum

of eigenvalues and the new sum (after multiplying the first eigen-

value by the constant ranging from 0.7 to 20). We then proceeded

to reconstruct each simulated matrix using the equation above,

obtaining V/CV matrices where the relative contribution of size

variation to the total variation has been altered. This allowed us to

tweak the relative contribution of pmax to the total variation with-

out changing the matrix structure. These new V/CV matrices were

then used to calculate the previously described indexes (ICV, mod-

ularity, flexibility, and constraint) under different contributions of

size variation for each taxon. Using this approach, a theoretical ex-

pectation regarding the relationship between size variation, mor-

phological integration, and its evolutionary consequences could

be produced and later compared to observed results in mammals.

It also allowed us to calculate the deviations of the observed val-

ues to their simulated counterparts (scrutinized in the Supporting

Information—S.I.5) and to interpret eventual deviations. Two po-

tential sources of deviations were considered. The first possibility

was that differences in the orientation of pmax among species

would explain deviations from theoretical expectations. The sec-

ond possibility was that other eigenvectors (other than pmax) were

responsible for deviations from theoretical expectations.

POSTNATAL GROWTH

To examine the possibility that differential allocation of morpho-

logical variation in the size axis could be associated with different

growth strategies, we obtained dimensionless postnatal growth

measurements (Em), as described by West et al. (2001), with data

from the panTHERIA database (Jones et al. 2009). This metric

was calculated as:

Em= (m/M)1/4

where m is the newborn mass and M is the adult mass. West

et al. (2001) derived a model of growth based on the bal-

ance of metabolic energy allocation between maintenance of

existing tissue or the production of new biomass. They inter-

pret Em as the proportion of energy devoted to maintenance

and other activities. Similarly, 1 − Em = Eg can be inter-

preted as the proportion of the total metabolic power devoted to

growth (West et al. 2001). These dimensionless growth measure-

ments were then used as independent variable against which the

within-species percentages of variation explained by the size axis

(% Var Pmax), ICV, flexibility, and constraint indexes were re-

gressed on. Since not all species had their neonate body sizes

reported in the panTHERIA database, we occasionally used

neonatal body size information from closely related species or

compiled from other resources (AnAge database; de Magalhaes

and Costa 2009; Hayssen et al. 1993; Lindenfors et al. 2007).

Data estimated from animals raised in captivity were generally

avoided, due to its potential effects over individual body weight.

Caenolestidae was excluded from the analysis due to the lack of

adequate neonate body size information in any of the databases.

The list of studied species is presented in the Supporting

Information—S.I.6.

ResultsRAW AND RESIDUAL MAGNITUDES OF INTEGRATION

To address the question of the integration magnitude changes

once size variation is removed, we calculated ICV values for

raw and residual matrices for all mammal families. In raw

matrices, integration magnitudes were highly variable among

families (mean ICV = 3.0; Fig. 3), with values ranging from 1.57

(hominids) to 4.74 (peramelids). Higher integration magnitudes

were mainly associated with marsupial and half of rodent

families, but also with canids, cervids, tayassuids, delphinids,

myrmecophagids, and cercopithecids. Lower ICV values were

essentially observed for primate and chiropteran families.

Tupaids and macroscelids also presented moderately low values

(Fig. 3). In residual matrices, integration magnitudes were lower

than their raw counterparts and also more similar across groups

(mean ICV = 1.66; Fig. 3). Values ranged from 1.21 (hominids)

to 2.23 (peramelids). Again, marsupials and half of the rodents

emerged as the most integrated taxa; and chiropterans, together

with primates, were the least integrated groups. Although ICV

values were lower in residual matrices in all cases, there was

considerable heterogeneity in the degree of reduction for each

taxon. Many highly integrated families, with regards to raw

matrices, appeared among the lowest integrated in residual matrix

analyses (e.g., Dasyproctidae), and vice versa.

MODULARITY HYPOTHESES AND MODULARITY

INDEX

The second question addressed whether and which modularity

patterns become more evident without size variation. The results


ARTHUR PORTO ET AL.

0.00 1.00 2.00 3.00 4.00

Atelidae

Cebidae

Cercopithecidae

Hominidae

Canidae

Felidae

Mustelidae

Procyonidae

Delphinidae

Cervidae

Tayassuidae

Molossidae

Noc�lionidae

Phyllostomidae

Vesper�lionidae

Myrmecophagidae

Caviidae

Echimyidae

Cuniculidae

Dasyproc�dae

Erethizon�dae

Muridae

Crice�dae

Sciuridae

Leporidae

Macroscelididae

Procaviidae

Tapiridae

Dasypodidae

Tupaiidae

Caenoles�dae

Dasyuridae

Macropodidae

Peramelidae

Didelphidae

ICV

Residual

Raw

Figure 3. Overall integration magnitude, calculated as the coefficient of variation of the eigenvalues of the V/CV matrix (ICV) of each

mammal family, for both raw and residual matrices.

of modularity tests for both raw and residual correlation matrices

are presented in Table 2. Cranial regions exhibiting higher cor-

relations with the theoretical matrices are also those with higher

modularity indexes so that the description of the results will be

primarily focused in the modularity hypothesis tests. One should

keep in mind that the modularity index provides a metric for

the distinctiveness of cranial modules within each taxon, and is

comparable between raw and residual matrices.



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ARTHUR PORTO ET AL.

Ta

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The most noticeable result from these analyses is that mod-

ularity is more evident in residual than on raw matrices, both in

terms of the number of modules detected and in terms of the de-

gree of modularity. This pattern can readily be seen in four of the

hypotheses: total, neural, vault, and zygomatic. In raw matrices,

two thirds of mammal families presented significant correlations

with the total integration matrix. Once size variation was removed,

all sampled mammal families presented positive and significant

correlations with this hypothesis. Similarly, the neural integration

matrix differed sharply between raw and residual matrices, from a

single family presenting significant and positive correlation with

this hypothesis (Hominidae) in raw matrices, to 29 (out of 35)

families in residual ones. Modularity indexes for this hypothesis

greatly increased for almost all groups once size variation was

removed. Changes observed in vault and zygomatic matrices are

also noticeable. Both hypotheses found no support in the raw

matrices, but appeared as highly significant for most families in

residual matrices. They also presented the highest increases in

modularity indexes among all theoretical hypotheses, when com-

paring residual to raw matrices.

EVOLUTIONARY FLEXIBILITY AND CONSTRAINTS

Results regarding the impact of size variation on the ability of a

given matrix to respond to selection are described in Table 3. In

raw matrices, the constraint index ranged from 0.54 (Cebidae) to

0.93 (Peramelidae). It followed the same basic pattern observed

for integration magnitudes, in which the marsupial families to-

gether with half of the rodents, exhibited higher values than all

other groups (Table 3). Variation explained by pmax (% Var Pmax)

was also among the highest in those taxa. The primate and chi-

ropteran families, however, presented the lowest values for both

indexes.

The flexibility index exhibited the opposite pattern: higher

among primate and chiropteran families and lower among most

marsupials and half of the rodents (Table 3). Values ranged

from 0.24 (Peramelidae) to 0.59 (Hominidae). Considerable

variation within orders can be observed for all three indexes.

The cercopithecids (order Primates), for example, presented ex-

tremely high values for both the constraints index and the per-

centage of variation explained by pmax and a relatively low

flexibility.

In residual matrices, constraint indexes ranged from 0.40

(Hominidae and Molossidae) to 0.68 (Peramelidae), and all taxa

presented lower values for these matrices compared to raw ones.

No pattern of taxonomic/phylogenetic structure could be observed

in these indexes; for instance, several marsupial families presented

values as low as primates. The flexibility index followed the in-

verse pattern with all taxa presenting higher values than the ones

observed for the raw matrices, but again with no evidence of taxo-

nomic/phylogenetic structure (Table 3). Mean values ranged from

0.46 (Peramelidae) to 0.66 (Hominidae). Especially noteworthy

is the lower dispersion observed for both indexes (constraints

and flexibility) in residual matrices, when compared to the raw

ones.

EVOLUTION OF SIZE VARIATION—MODIFICATIONS

IN TAXON MATRICES

We explored the consequences of differences in size variation by

comparing evolutionary responses derived from theoretical ex-

pectations with responses derived from observed data collected

on mammalian skulls. The simulations produced by tweaking

size variation on each of the V/CV matrices (see Supporting

Information—S.I.7 for an example) revealed that, on one hand,

V/CV matrices presenting higher percentages of variation asso-

ciated with pmax yielded higher integration magnitudes and lower

modularity indexes. Those were also the matrices with lower

evolutionary flexibility and more constraints. On the other hand,

matrices exhibiting lower percentages of variation associated with

pmax presented lower integration magnitudes, higher modularity

indexes, and more flexibility in terms of evolutionary responses

to selection. These relationships among indexes after altering size

variation in simulated matrices remarkably mirrored the pattern

observed in raw matrices for the mammalian families sampled

(Fig. 4).

It is important to notice that analysis of pairwise similar-

ity of pmax among taxa (Supporting Information—S.I.5) indicates

that, although fairly similar, these vectors are not identical among

taxa. Mustelidae, Delphinidae, and Hominidae stand out as taxa

with particularly divergent pmax. Even so, deviations of the ob-

served statistics (integration magnitudes, flexibility, and modular-

ity) from the ones simulated by tweaking size variation cannot be

explained by dissimilarity among the first principal components

(Supporting Information—S.I.5).

POSTNATAL GROWTH

To understand whether the impact of size variation is associated

with growth strategies, we regressed ICV values on postnatal

growth data gathered from the literature and public databases.

Postnatal growth measurements (Eg) presented a significant rela-

tionship with integration magnitudes and, consequently, with size

variation (regression of Eg on ICV; MSeffect = 10.58, MSerror =0.47, P < 0.001, r2 = 0.41; Fig. 5), with a regression coefficient of

3.58 (SE = 0.75). V/CV matrices presenting higher percentages of

variation associated with pmax (therefore, with higher ICV) were

from species with higher postnatal growth rates, such as marsu-

pials and some rodents. V/CV matrices with lower percentages,

in contrast, were from groups with lower postnatal growth rates,

such as primates and chiropterans. As a consequence, Eg also

presented a significant relationship to flexibility (MSeffect = 0.1,


ARTHUR PORTO ET AL.

Table 3. The overall integration magnitude (ICV) and results of selection simulations: the average correlation of evolutionary responses

and selection gradients (flexibility), the average correlation of evolutionary responses and pmax (constraints), and the percentage of

variation explained by pmax (% Var Pmax). All variables were calculated for raw and residual matrices.

Raw matrices Residual matrices

ICV Flexibility Constraints %Var Pmax ICV Flexibility Constraints %Var Pmax

Atelidae 2.48 0.46 0.76 41.73 1.31 0.63 0.45 16.27Cebidae 1.70 0.54 0.54 22.99 1.53 0.58 0.53 20.65Cercopithecidae 3.82 0.33 0.89 65.16 1.29 0.64 0.44 15.60Hominidae 1.57 0.59 0.59 23.90 1.21 0.66 0.40 13.29Canidae 3.20 0.37 0.82 53.69 1.78 0.53 0.57 25.19Felidae 2.87 0.40 0.79 47.93 1.64 0.54 0.48 20.05Mustelidae 2.37 0.45 0.69 37.36 1.75 0.53 0.60 25.25Procyonidae 3.12 0.37 0.80 51.79 1.91 0.51 0.60 28.20Delphinidae 3.68 0.33 0.87 62.45 1.56 0.57 0.53 21.35Cervidae 3.21 0.36 0.82 53.98 1.75 0.53 0.55 23.83Tayassuidae 3.06 0.39 0.82 51.66 1.52 0.57 0.43 16.66Molossidae 1.61 0.57 0.58 23.60 1.31 0.62 0.40 13.81Noctilionidae 2.76 0.41 0.77 45.82 1.63 0.55 0.51 20.41Phyllostomidae 1.87 0.51 0.60 26.07 1.67 0.55 0.54 22.86Vespertilionidae 1.74 0.54 0.58 25.32 1.45 0.59 0.45 16.32Myrmecophagidae 3.74 0.32 0.86 63.14 1.96 0.50 0.62 28.61Caviidae 4.02 0.30 0.89 68.24 1.81 0.53 0.57 24.79Echimyidae 3.54 0.35 0.87 60.32 1.43 0.60 0.49 17.78Cuniculidae 3.23 0.36 0.80 53.64 2.04 0.49 0.66 31.34Dasyproctidae 3.74 0.33 0.90 63.77 1.36 0.62 0.47 16.64Erethizontidae 2.67 0.40 0.73 42.95 1.92 0.49 0.60 27.39Muridae 4.30 0.28 0.92 73.17 1.65 0.56 0.55 22.92Cricetidae 2.47 0.43 0.70 38.82 1.88 0.50 0.60 26.82Sciuridae 2.13 0.49 0.68 33.60 1.54 0.57 0.55 21.45Leporidae 3.08 0.38 0.81 51.70 1.68 0.54 0.55 22.81Macroscelididae 2.04 0.49 0.62 30.47 1.68 0.55 0.56 23.56Procaviidae 3.97 0.30 0.88 67.35 1.74 0.52 0.55 23.81Tapiridae 2.25 0.47 0.69 36.05 1.56 0.56 0.46 18.45Dasypodidae 3.78 0.32 0.87 63.98 1.80 0.52 0.54 23.94Tupaiidae 2.25 0.44 0.62 32.65 1.99 0.48 0.61 28.01Caenolestidae 3.06 0.38 0.80 51.34 1.65 0.55 0.55 22.69Dasyuridae 3.05 0.39 0.83 51.50 1.47 0.59 0.52 19.25Macropodidae 4.46 0.27 0.91 75.62 1.91 0.49 0.52 22.72Peramelidae 4.74 0.24 0.93 80.30 2.23 0.46 0.68 34.34Didelphidae 4.01 0.30 0.89 68.07 1.74 0.52 0.47 20.22

MSerror = 0.005, r2 = 0.37, P = 0.001) and constraint indexes

(MSeffect = 0.18, MSerror = 0.009, r2 = 0.4, P = 0.001).

DiscussionSize can be regarded as an emergent property of the growth pro-

cess that includes the integration of different modules into a sin-

gle, coherent, functional structure. This integration establishes

correlations among traits on top of local processes, and therefore

potentially obscures the individuality of modules. Module indi-

viduality, in turn, directly impacts the potential for evolutionary

responses to selection of a given structure. Our results point that

the greater the relative influence of size variation over the total

morphological variation, the greater the intermodule correlations,

the less distinct the modules, and the more constrained their po-

tential responses to natural selection.

Evidence supporting this perspective of the evolution of mod-

ularity has been published in four complementary papers (Porto

et al. 2009; Marroig et al. 2009; Shirai and Marroig 2010; and this

article). Our previous studies pointed to the importance of integra-

tion magnitudes in understanding the potential of the evolutionary



1 2 3 4 5 60.1

0.3

0.5

0.7

FLEX

IBIL

ITY

412

2 1514

26 24

3028

7231

2113

632 31

3433

22173527329

1620 918191058

2511

1 2 3 4 5 6ICV

0.4

0.5

0.6

0.7

0.8

0.9

1.0

CONS

TRAI

NTS

412

215

1426

24

30

2872312113

63231

3433

22

173527

3

2916

209

18

19

10582511

1 2 3 4 5 6ICV

0.0

12.5

25.0

37.5

50.0

62.5

75.0

87.5

100.0

% V

ar. P

max

4 12215 1426

2430

287231

2113632 31

343322

173527329

16

20

9181910582511

1 2 3 4 5 6ICV

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

MO

D IN

DEX

12

2

15

14

26

24

30

287

23

1

2113

63231

3433

221735

273291620

9

18

1910

5

8

25

11

ICV1 2 3 4 5 6

ICV

0.1

0.2

0.3

0.4

0.5

0.6

0.7

FLEX

IBIL

ITY

1 2 3 4 5 6ICV

0.40

0.55

0.70

0.85

1.00

CONS

TRAI

NTS

1 2 3 4 5 6ICV

0

25

50

75

100

% V

ar. P

max

1 2 3 4 5 6ICV

0.0000

0.0175

0.0350

0.0525

0.0700

MO

D IN

DEX

Figure 4. Comparison of results obtained for the mammalian families (right column) and the expected under evolution of the influence

of size variation over the total morphological variation (modifications of mammalian V/CV matrices; left column). Plots of the several

indexes (flexibility, constraints, percentage of variation along pmax, and modularity) against the measurement of overall integration

magnitudes are shown for both cases.


ARTHUR PORTO ET AL.

1 2 3 4 5ICV

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

EG

Hominidae

Molossidae

Cebidae

VespertilionidaePhyllostomidae Macroscelididae

Sciuridae

Tupaiidae

TapiridaeMustelidae

Cricetidae

Atelidae

Erethizontidae

Noctilionidae

Felidae

Dasyuridae

Tayassuidae

PeramelidaeMacropodidae

Muridae

Caviidae

Didelphidae

ProcaviiddaeCercopithecidae

Dasypodidae

Myrmecophagidae

Dasyproctidae

Delphinidae

Echimyidae

Cuniculidae

Cervidae

Canidae

ProcyonidaeLeporidae

Figure 5. Plot of the proportion of the total metabolic power

devoted to growth (Eg) against the overall integration magnitude

(ICV) calculated for each mammal family. The regression line is

shown in gray.

responses to selection produced by different species, because, as

a rule, covariation patterns remained very similar among mam-

mals while integration magnitudes changed rapidly (Marroig and

Cheverud 2001; Oliveira et al. 2009; Porto et al. 2009). Higher

integration magnitudes were associated with lower evolutionary

flexibilities and less distinct developmental/functional modules in

the skull, and vice versa (Marroig et al. 2009). This pattern was

consistently observed here in several mammal orders, including

taxa that diverged more than 130 million years ago (Bininda-

Emonds et al. 2007).

This study goes further and analyzes the relationship between

size variation, growth strategies, and integration/modularity in the

mammalian skull. The data set used is by far the largest of its kind

in terms of phylogenetic breadth, spanning a total of 35 mammal

families. We used three main analytical methods: (1) removed

size variation from within-species data and evaluated the conse-

quences of it; (2) simulated changes in the influence of size vari-

ation in each species matrix and compared expectations derived

from this manipulation to observed results; and (3) regressed in-

tegration magnitudes on postnatal growth measurements. Results

from these three lines of evidence support each other and paint a

common picture, detailed later.

Much of the overall magnitude of integration among mor-

phological elements can be attributed to size variation. This is

consistent with what was previously observed in a much smaller

data set in terms of phylogenetic scope (neotropical marsupials

and primates) but with a fairly good representativeness of within-

clade diversity (Shirai and Marroig 2010). Once size variation

was removed, integration magnitudes lowered, and became more

similar among groups than previously observed. The effect of size

removal was particularly dramatic in taxa exhibiting higher inte-

gration magnitudes in raw data (e.g., marsupials). In such groups,

integration magnitudes dropped to values more than 50% lower

than their raw counterparts. Concomitantly, modularity patterns

became more evident and modules that could not be detected in

raw matrices (see also Porto et al. 2009) were consistently detected

in all groups. Neurocranial traits, for example, only presented

significant integration in hominid’s raw matrices. In residual ma-

trices, significant neurocranial integration was detected in most

groups. A similar pattern was observed for the cranial vault and zy-

gomatic hypotheses. All families presented significant total inte-

gration in residual matrices, indicating that the failure to detect it in

raw matrices was due to the impact of size variation in integration.

The theoretical simulations involving modifications on the

first eigenvalue of V/CV matrices clearly showed that altering

the relative amount of variation along the pmax of V/CV matrices

leads to results that closely mirror those observed for all mam-

mal families (Fig. 4). Similarly, V/CV matrices exhibiting high

percentages of variation associated with the pmax yielded higher

overall integration magnitudes and less distinct modular patterns.

Results from both approaches support the notion that size acts

as a strong and general integration factor that blurs the largest

part of the modularity signal in morphological variation patterns.

Our results also corroborate the suggestion that studies of mod-

ularity will probably be more successful in detecting modules

once variation induced by global factors, such as size, is mini-

mized compared to variation due to local factors (Mitteroecker

and Bookstein 2007).

Our data further indicate that size variation cannot be con-

sidered a nuisance. Size variation is a genetically variable, bi-

ologically meaningful, and a major component of within-group

variation patterns and magnitudes. Moreover, we have shown that

removing size variation discloses hidden modularity, but not in

the same degree for all groups, nor equally among modules. This

implies that corrections for size variation cannot be treated ho-

mogeneously across taxa because each lineage will behave in

different ways according to how its evolution has been shaped

by size variation. We hope to encourage other researchers to con-

sider the impact and implications of removing size variation when

addressing evolutionary questions, especially in groups like mam-

mals, where growth is determinate and age classes can be estab-

lished with reasonable accuracy. When removing size variation,

a researcher might be neglecting a substantial part of the within

population morphological variation. Given that size variation has

important evolutionary and ecological implications, if size is

removed a priori without further consideration, one might miss



the role and impact of size on the evolution of the taxon under

study. The removal of the main axis of variation also leads to the

undesirable consequence of increasing the proportion of variance

due to error (Marroig et al. 2012). In marsupials, for example, size

removal could increase the proportion of variance due to error to

values above 20%, even when measurement repeatabilities are

higher than 0.95.

Before discussing the impact of size variation on evolution,

it is important to consider that the ability of a population to

evolve in the direction of selection has two aspects: one is the

response vector’s alignment with the direction of selection (flex-

ibility); the other is the amount of change in the direction of

selection (evolvability sensu Hansen and Houle 2008). Our previ-

ous studies found a scaling effect on evolvability among mammals

(Marroig et al. 2009) and a lack of association with integration

and modularity. Although these two aspects are mathematically

and biologically related (flexibility is the ratio between evolvabil-

ity and respondability; Hansen and Houle 2008), we focus here

on the relationship between flexibility and other life-history and

integration/modularity statistics.

The impact of size variation within a population can be

easily captured by the flexibility index. As mentioned earlier,

this metric was employed to represent the capacity of a given

structure to respond in the direction of selection (Marroig

et al. 2009). Thus, if evolutionary responses are closely aligned to

the selection gradient that generated them, one can argue that the

structure under concern is flexible to respond in that direction of

the morphospace. Although flexibility and constraints are obvi-

ously inversely related concepts capturing the overall evolutionary

consequence of modularity/integration, it is important to keep in

mind that flexibility and constraints are calculated through very

different procedures. Constraints are defined as the correlation

between the evolutionary response and pmax. Thus, if selection is

pushing along pmax, both flexibility and constraints should be high

in a strongly integrated matrix. In any case, once size variation

was removed, flexibility values increased in all groups, indicating

higher capacity of closely tracking selection, and also the poten-

tial for broader exploration of the morphospace. This potential

is constrained by the association among morphological elements

induced by size variation, as shown by the constraints index.

The same general pattern can be seen in the simulations alter-

ing the influence of size variation. Matrices with low percentages

of variation associated with pmax yielded lower overall integration

magnitudes, more distinct modular patterns, and more flexibility

in terms of evolutionary responses to selection. The observed pat-

tern for the evolution of the influence of size on morphological

variation of mammals is thus consistent with theoretical expecta-

tions (Fig. 4). These results clearly indicate that size variation can

act as a powerful constraint for evolutionary change in mammals,

which would bias evolutionary responses to selection along the

so-called line of least resistance (Schluter 1996), at least on a

short-term scale if the adaptive landscape is not changing through

time (Arnold et al. 2001). Even when selection gradients are not

strictly aligned with size, taxa with some size variation usually re-

spond along the size dimension (except if selection is orthogonal

to the size variation axis, see Marroig and Cheverud 2010). Large

portions of variation aligned with the size axis, therefore, greatly

reduce the flexibility of a population. In our sample of mammals,

within-population size variation ranged from 20% to almost 81%

of all phenotypic variation (Table 3). Accordingly, those lineages

with a smaller relative amount of size variation (like hominids

and bats) are far less constrained, more modular and flexible with

regard to the potential for selection responses than those lineages

for which the major part of the total variation is associated with

size (like marsupials). It is important to notice that pmax vectors are

not identical across taxa. Pairwise comparisons between the pmax

of different taxa indicate they are not perfectly aligned (Support-

ing Information—S.I.5). In other words, allometric size vectors

do evolve, to some extent, in mammals. However, their effect over

morphological integration is basically the same. Furthermore, al-

though we have been emphasizing this “attractor effect” of size

variation (pmax) with regard to the potential selection response,

other axes of the morphospace also represent lines of least re-

sistance. As long as the within-population variance is unequally

distributed, usually in the form of a negative exponential distribu-

tion of eigenvalues, some axes would present more variance than

others, and would act as attractors of evolutionary responses to

selection (e.g., Hansen and Voje 2011).

All these results lead to the question: which factors could

modify within-population size variation? Part of the answer might

be related to life-history differences among lineages, particularly

related to the growth process. Considering that multicellular com-

plex organisms are built from a single zygotic cell that undergoes

proliferation and differentiation that finally assemble a multi-

cellular integrated adult, one could argue that differential adult

size variation among lineages is a result of differences in the

growth process. Growth affects, to some extent, all traits in an

organism, bringing together modules into a higher hierarchical

structure, like a glue holding parts in a Francois Jacob bricolage

(Jacob 1977). The immediate consequence is that differences in

the growth processes will lead to differences in variance along

the size dimension within a population, with consequences for

modularity and for the evolutionary potential of a population to

respond to natural selection.

The postnatal growth data strongly suggests that the relative

amount of size variation and skull modularity are tightly asso-

ciated with the evolution of life-history strategies in mammals.

Those lineages with altricial neonates, such as marsupials and

rodents, allocate higher portion of the energy budget to growth,

have relatively more variation in size, higher integration, lower


ARTHUR PORTO ET AL.

flexibility, and are highly constrained. Conversely, those lineages

with precocial neonates, such as hominids and bats, allocate a

smaller portion of energy to growth, have a smaller portion of the

total variation in size and are less integrated, more flexible, and

less constrained in its evolutionary potential. This also suggests

that different growth strategies existent in different species have a

fundamental impact on their evolutionary flexibility and potential

for the exploration of the morphospace.

Although certainly speculative at this point, the genetic basis

for the evolution of size variation is clearly an important aspect

to be considered. Particular attention has been paid recently to

genetic variation in pleiotropy caused by differential epistatic in-

teractions (e.g., Pavlicev et al. 2011), mainly because genetic

variation in pleiotropy is necessary for it to evolve (Pavlicev

et al. 2007). The presence of relationship QTLs (r-QTL) has al-

ready been demonstrated to play important roles on long bone

growth, with an effect on body size variance (and its allometric

effects) that resembles the effects described here (see Pavlicev

et al. 2007). Differential epistasis causes differential canalization

of single traits and trait combinations, leading to varying grades

of integration among genotypes and allowing for the evolution of

modularity (Pavlicev et al. 2007).

Finally, it is clear from our results that understanding the

connection between life-history strategies, the genetic architec-

ture, and the influence of size variation will be fundamental to

understand how different mammal species respond to evolution-

ary processes at least on a microevolutionary scale. Depending

on the potentially complex relationship of the history of adaptive

peaks and G-matrix orientation in mammals, such dominance of

size variation in modularity might even extend its consequence to

a macroevolutionary scale as already show in New World mon-

keys (Marroig and Cheverud 2001, 2005, 2010). We showed that

mammal species differ in their apportionment of variation in the

morphospace and that these differences are associated with their

life-history strategies. In altricial species, most of the total mor-

phological variation is concentrated in a single size axis (pmax).

In those species, modularity is masked by the strong between-

module correlations associated with variation along the allometric

pmax. Furthermore, this masking effect upon modularity is not ex-

plained by differences in orientation of the allometric vectors but

instead it is a product of the relative length (norm or the relative

amount of variation) of these vectors. Those lineages with a larger

portion of the morphological variation associated with pmax tend to

be more integrated. Accordingly, pmax acts as a strong “attractor”

of evolutionary responses to selection, potentially constraining

their morphological diversification. In precocial species, varia-

tion is more homogeneously apportioned in the morphospace.

Modularity is evident and evolutionary responses more flexible.

As a consequence, we expect those species to be less constrained

in their short-term morphological diversification.

ACKNOWLEDGMENTSThe authors are grateful to A. Templeton and two anonymous review-ers for careful revision of previous drafts of this manuscript, and to J.Cheverud for helpful discussions. The authors are also grateful to peopleand institutions that provided generous help and access to museum col-lections (Supporting Information). This research was supported by grantsand fellowships from FAPESP, CAPES, CNPq, an American Museumof Natural History Collections Study Grant, and by the Department ofBiology from Washington University in St Louis.

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Associate Editor: P. Lindenfors


ARTHUR PORTO ET AL.

Supporting InformationAdditional Supporting Information may be found in the online version of this article at the publisher’s website:

Figure S1. (A) Plot of the distribution of resampled ICV values for each mammalian family. Range of the distribution is

proportional to the degree of uncertainty in the ICV estimate. Results are shown for 100 resamplings. (B) Plot of the distribution

of resampled ICV values for each mammalian family after the adjustment suggested by Young et al. (2010).

Figure S2. Plot of the distribution of resampled Flexibility and Constraints indexes for each mammalian family.

Figure S3. Distribution of pairwise vector correlations among the pmax of the different mammalian families.

Figure S4. (A) Average vector correlation between each family pmax and that of other families plotted against the deviations of the

observed flexibility values from theoretical expectations. (B) Flexibility index calculated from residual matrices plotted against

the deviations of the observed flexibility values from theoretical expectations.

Table S1. Skull measurements (see Fig. 2 for acronyms) and their association with the theoretical modularity hypotheses for each

order.

Table S2. Variables measured for the simulation involving the V/CV matrix of each taxon with altered proportions of size variation.


Size variation, growth strategies, and the evolution of modularity in the mammalian skull

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