The Continuously Growing CentralNervous System of the Nile Crocodile

(Crocodylus niloticus)AYANDA NGWENYA,1 NINA PATZKE,1 MUHAMMAD A. SPOCTER,1,2

JEAN-LEIGH KRUGER,1 LEIGH-ANNE DELL,1 RICHARD CHAWANA,1

PEDZISAI MAZENGENYA,1 BRENDON K. BILLINGS,1 OLATUNBOSUNOLALEYE,1 SUZANA HERCULANO-HOUZEL,3,4

AND PAUL R. MANGER1*1School of Anatomical Sciences, Faculty of Health Sciences, University of the

Witwatersrand, Parktown 2193, Johannesburg, Republic of South Africa2Department of Anatomy, Des Moines University, Des Moines, Iowa

3Instituto de Ciencias Biom�edicas, Universidade Federal do Rio de Janeiro,21941-590, Rio de Janeiro, Brazil

4Instituto Nacional de Neurociencia Translacional, MCT/CNPq, S~ao Paulo, Brazil

ABSTRACTIt is a central assumption that larger bodies require larger brains,

across species but also possibly within species with continuous growththroughout the lifetime, such as the crocodile. The current study investi-gates the relationships between body growth (length and mass) and therates of growth of various subdivisions of the central nervous system(CNS) (brain, spinal cord, eyes) in Nile crocodiles weighing between 90 gand 90 kg. Although the brain appears to grow in two phases in relationto body mass, initially very rapidly then very slowly, it turns out thatbrain mass increases continuously as a power function of body mass witha small exponent of 0.256, such that a 10-fold increase in body mass isaccompanied by a 1.8-fold in brain mass. Eye volume increases slowlywith increasing body mass, as a power function of the latter with anexponent of 0.37. The spinal cord, however, grows more rapidly in mass,accompanying body mass raised to an exponent of 0.54, and increasing inlength as predicted, with body mass raised to an exponent of 0.32 (closeto the predicted 1/3). While supporting the expectation formulated by Jer-ison that larger bodies require larger brains to operate them, our findingsshow that: (1) the rate of increase in brain size is very small compared tobody growth; and (2) different parts of the CNS grow at different ratesaccompanying continuous body growth, with a faster increase in spinalcord mass and eye volume, than in brain mass. Anat Rec, 00:000–000,2013. VC 2013 Wiley Periodicals, Inc.

Key words: reptile; brain; eye; spinal cord; allometry; reptil-ian; crocodilian; brain size; body size

Grant sponsor: South African National Research Foundation.

*Correspondence to: Paul Manger, School of Anatomical Sci-ences, Faculty of Health Sciences, University of the Witwaters-rand, 7 York Road, Parktown 2193, Johannesburg, Republic ofSouth Africa. E-mail: paul.manger@wits.ac.za

Received 4 March 2013; Accepted 16 April 2013.

DOI 10.1002/ar.22752Published online 00 Month 2013 in Wiley Online Library(wileyonlinelibrary.com).

THE ANATOMICAL RECORD 00:00–00 (2013)

VVC 2013 WILEY PERIODICALS, INC.

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The study of the relationship between body and brainmasses has been guided by the intuitive expectation thatlarger bodies require more neurons, and thus largerbrains, to manage them (Jerison, 1973). It is in this lightthat encephalization quotients—that is, how large abrain is compared to how large it is expected to be for agiven body size—have been calculated and interpretedas meaningful proxies of cognitive capacity across spe-cies: the larger the quotient, the larger the “excess brainmass” available for non-body-related functions, thus pro-moting cognitive flexibility and a richer behavioral rep-ertoire (Jerison, 1973). Despite this, it has been shownthat the number of neurons in the spinal cord, as wellas in the ensemble of brainstem structures directlyrelated to bodily functions, is very small (of the order ofless than 1% of all neurons in the central nervous sys-tem (CNS)), and increases only very slowly with increas-ing brain mass in primates (Burish et al., 2010;Herculano-Houzel, 2011). These findings suggested thatthe neuronal demand imposed by a larger body isactually minimal, with the number of spinal cord neu-rons increasing with body mass raised to an exponent of0.346, or approximately with body length (Burish et al.,2010). Along these same lines, it was recently reportedthat the number of motor neurons in the facial nucleusof marsupials increases very slowly with increasing bodymass across species (Watson et al., 2012), as a powerfunction of body mass with an exponent of 0.184, close tothe exponent of 0.127 reported in primates (Sherwood,2005).

One direct manner to evaluate the extent of thedemand possibly imposed by a larger body on the nerv-ous system is to examine how a growing body massrelates to the size of the different divisions of the CNSin species that exhibit continuous growth throughoutlife—one such species is the Nile crocodile (Crocodylusniloticus). The masses of the body and the brain haveonly been reported for a few species of Crocodiliansincluding the Siamese crocodile (Crocodylus siamensis,Chentanez et al., 1983), alligators (Alligator mississip-piensis, Crile and Quiring, 1940), and the caiman (Cai-man crocodilus, Gans, 1980). When these data arecombined, they suggest that there exists an initial post-hatching period of rapid growth of the brain in relationto the body until the Crocodilians reach a body mass ofaround 4 kg, and that this is followed by a long slowgrowth of the brain during a long adult life, where forapproximately every increase of 20 kg in body mass, 1 gof tissue is added to the brain. Unfortunately, the rela-tionship between brain mass and body mass over arange of sizes in the Crocodilians is difficult to deter-mine due to the paucity of data (there are around 80data points from the three species, with the majority ofthese being from the Siamese crocodile with body massesmostly restricted to between 10 and 24 kg). Despite this,the observations in the Crocodilians are interesting, asit appears that the brain continues to grow, albeit slowly,throughout life. In mammals, at around the age of sex-ual maturity, brain growth ceases and body mass andbrain mass remain relatively stable throughout theremainder of life (e.g. Dobbing and Sands, 1973).

This unusual growth relationship between brain andbody was demonstrated in the Siamese crocodile by Che-tanez et al. (1983). “Large” crocodiles (those with a 13.7kg body mass) had a body mass 2,072 times larger than

their brain mass, while “small” crocodiles (those with abody mass of 0.064 kg) had a body mass that was only66.6 times larger than the brain mass, that is the rela-tive brain mass in the “small” crocodiles is considerablyhigher than the relative brain mass of the “large” croco-diles (Chetanez et al., 1983). In an alligator, with a bodymass of 205 kg and brain mass of 14.08 g, the body was14,560 times larger than the brain (Crile and Quiring,1940). The present study aimed to examine growth ratesof the CNS at various stages of post-hatching develop-ment in Nile crocodiles (Crocodylus niloticus) using alarger sample size than was previously used (N 5 70)and a wider range of masses (from 90 g to 90 kg). Withthis dataset we aim to have a clearer understanding ofthe changes in rates of growth of the brain, spinal cord,and eye in relation to increases in the body mass andlength of the Nile crocodile, establishing a baseline forfuture studies in this and other Crocodilian species.

MATERIALS AND METHODS

All Nile crocodiles used in the current study (N 5 70;39 males, 31 females) were bred and raised in captivityat the commercial crocodile farm Thaba Kwena, Bela-Bela, South Africa. Selection of crocodiles was based onbody mass to cover a range from 90 g to 90 kg. Permis-sion to sacrifice the animals and harvest the tissue wasgranted by the University of the Witwatersrand AnimalEthics Committee. The animals were treated and usedaccording to the guidelines of this committee, whichparallel those set down by the NIH for use of animals inscientific experiments. Crocodiles weighing less than10 kg were transported live from the crocodile farm tothe animal facility at the University of the Witwatersrandand were euthanized with an overdose of Euthapent(1 mL/kg i.p. of a 200 mg/mL sodium pentobarbitonesolution). Crocodiles exceeding 10 kg were euthanized onsite, by initially injecting the animal with the musclerelaxant Gallamine triethiodide (a non-depolarizing mus-cle relaxant that blocks the action of acetylcholine at theneuromuscular junction, 2–4 mg/kg, i.m.). Once relaxed,the animals were euthanized with an intracardial injec-tion of Euthapent (0.5–1 mL/kg). All animals were givena dose of Heparin (1–10 mL, i.m. or i.c., depending onanimal size) 5 min prior to overdose to prevent bloodclotting.

Once euthanized, accurate body masses and bodylengths of the animals were measured using appropriatescales and a flexible tape measure. Body length wasmeasured from the anterior tip of the snout to the poste-rior tip of the tail on the ventral aspect of the body. Wemeasured the entire body length, instead of the usualsnout-vent length measured in reptiles, as the spinalcord of the crocodile continued to almost the last verte-brae of the tail. We felt that using the snout-vent lengthmay underestimate the growth of the spinal cord due topotential specific elongation of the tail during growthand thus wanted to eliminate this possible confound inthe study. All animals were perfusion-fixed transcar-dially, initially with a rinse of 0.9% cold saline solution,followed by 4% paraformaldehyde in 0.1 M phosphatebuffer (PB) solution (between 0.5 and 1 L/kg of eachsolution). The eyes were removed and placed in fixativeovernight before being placed in 0.1% sodium azide in0.1 M PB for storage at 4�C. The bones surrounding the

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brain and spinal cord were removed using various sawsand rongeurs, and both parts of the CNS were thenplaced in the fixative solution overnight. The length ofthe spinal cord, in situ, was measured prior to removalfrom the vertebral canal, and was again measured, exsitu, after 24 hr in the fixative solution. Mass of thebrain (including the olfactory bulbs and tract, but notthe remaining cranial nerves which were sectioned atthe exit/entry from/to the brain) and spinal cord (thedorsal and ventral roots were sectioned at the exit/entryfrom/to the spinal cord) separately was only determinedafter 24 hr in the fixative solution. We removed the liv-ers from each animal and these were weighed after 24hr in the fixative solution. Lastly, the volumes of theeyes were measured using the water displacementmethod in graduated cylinders, providing volumes accu-rate to 0.5 mL. For this measurement, the optic nervewas sectioned at its exit from the globe and the eye vol-ume reported is the average of the two eyes for eachindividual animal. Thus, we have data for body mass,body length, brain mass, spinal cord mass, spinal cordlength (in situ and ex situ), liver mass, and eye volumefor most of the animals (TableT1 1). Following post-fixation, the brains were transferred to a solution of 30%sucrose in 0.1 M PB for 3 days at 4�C, by which timethey had equilibrated in this solution. The brains werethen transferred to an antifreeze solution comprised of30% glycerol, 30% ethylene glycol, 30% distilled water,and 10% 0.244 M PB. The brains and spinal cordsremained in this solution at 4�C for a period of �5 daysbefore they equilibrated, and at this stage they wereplaced in a 220�C freezer in this antifreeze solution forstorage. This process of tissue handling allows the main-tenance of antigenicity necessary for immunohistochemi-cal staining procedures (Manger et al., 2009).

The data generated in the current study were ana-lyzed using both linear and non-linear regression mod-els. All regression analyses were run using CurveExpertProfessional Version 1.6.5 (Hyams, 2010). Ordinary leastsquares regressions were calculated and the probabilitiesof using these regressions to correctly predict relation-ships were assessed (Sokal and Rohlf, 1995, p. 469). Inaccordance with earlier findings (Katkowsky, 1990),whenever linear regression models were inadequate torepresent the relationship between variables, nonlinearregression models were applied. Previous studies havedemonstrated the usefulness of nonlinear regression tomodel growth in crocodilians (Chabreck and Joanen,1979; Brisbin, 1989). While we tested several nonlinearfitting models we present only the results from the Wei-bull (a sigmoidal nonlinear growth model) and the Powerfit (a Power family nonlinear model) as these consis-tently ranked highest on Goodness of Fit Criteria (r2;AICC, means square error) and made for more directcomparisons with previously published results of thegrowing CNS and its relationship with body mass(reviewed in Herculano-Houzel, 2011).

RESULTS

The data collected in the current study represents themost comprehensive post-hatching data set of the Croco-dilian CNS in relation to body size parameters of whichthe authors are aware (see introduction for other papersreporting data). Below we present an analysis of the rel-

evant relationships between the measured parameters.No significant differences were found when analyzingmales as distinct to females; therefore all analyses pre-sented below include the pooled data of both sexes.

Body Mass vs. Body Length

While body mass ranged from 92 g to 90 kg in oursample, body length varied from around 20 cm to over2.5 m (Table 1). For those animals with both data avail-able, the largest body mass was 95 times the smallest,while the longest body length was only 3.8 times theshortest (Table 1). We find that body length increaseswith body mass raised to an exponent of 0.293 6 0.003(95% confidence interval, 0.287–0.299) across threeorders of magnitude of increase in body mass (Fig. F11),such that for every doubling in body mass, body lengthincreased by 1.23 times. The exponent of 0.293 is signifi-cantly smaller than the expected exponent of 0.333 forisometric growth, indicating that not only body mass isgained at a far faster rate than body length in the Nilecrocodile, but at a rate that surpasses isometric growth.Growth over the lifetime of the Nile crocodile, therefore,occurs with a significant change in body shape such thatmass is gained faster than expected for the increase inbody length.

Body Mass vs. Liver Mass

For the subsample above in which body mass varied95 times, liver mass varied 59 times (Table 1), suggest-ing that liver mass increases more slowly than bodymass. Although the relationship between body mass andliver mass can be described by a linear relationship(r2 5 0.98, Puncorr 5 4.52 3 10243; Fig. F22A), the liver rep-resents a significantly decreasing percentage of bodymass with body growth (Spearman correlation,q 5 20.817, P< 0.0001), varying from 2.4% in thesmaller animals to around 1.2% in the largest. Indeed,liver mass is best described as a power function ofbody mass with exponent 0.89 6 0.016 (r2 5 0.98,Puncorr 5 4.52 3 10243, 95% CI 0.788–0.852), which issignificantly different from unity (Fig. 2B). Thus, livermass does not grow isometrically with body mass, butrather significantly more slowly than body mass.

Body Mass vs. Brain Mass

While body mass varied 978.3 times in our sample,brain mass varied only 6.3 times (Table 1 and Fig. F33).The growth of the brain relative to the body was investi-gated using both the Weibull growth model and powerfunctions. Examining the raw data indicated that duringthe post-hatching period there was a rapid increase inthe mass of the brain both absolutely and in relation tobody mass, but after body mass exceeded 2,500 g, thepattern of growth of the brain altered, showing a con-sistent but slow increase in mass throughout the lifeperiod sampled (Figs. 3 and F44). When using the Weibullgrowth model to describe the data the results indicatedthat the pattern that was adopted for the data wasunlikely (AICC 5 2138.14). In contrast, we found thatthe relationship between brain mass and body masswithin Nile crocodiles can be described across the entirerange of masses as a single power function, Mbr 5 0.46 3

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CROCODILE BRAIN GROWTH 3

TABLE 1. Parameters recorded for the Nile crocodiles used in the current analysis

Bodymass (g)

Bodylength(cm) Sex

Brainmass

(g)

Spinalcord mass

(g)

Spinal cordlength

in situ (cm)

Spinal cordlength

ex situ (cm)

Eyevolume

(mL)

Livermass

(g)

92.0 – M 1.440 0.660 – – 1.00 –111.0 – F 1.640 0.940 – – 1.00 –148.0 – M 1.600 0.740 – – 1.00 –156.5 – M 1.690 0.950 – – 1.00 –160.5 – F 1.790 0.750 – – 1.00 –175.0 – M 1.690 1.060 – – 1.00 –184.0 – F 1.780 0.890 – – 1.00 –190.5 – M 1.850 0.880 – – 1.00 –194.5 – M 1.750 0.800 – – 1.00 –326.5 – M 2.060 1.440 – – 1.00 –336.5 – M 2.120 1.290 – – 1.00 –343.5 – F 1.990 1.340 – – 1.00 –363.0 – M 2.060 1.320 – – 1.00 –365.5 – F 2.120 1.280 – – 1.00 –370.0 – F 1.980 1.050 – – 1.00 –371.0 – M 1.980 1.070 – – 1.00 –636.5 – F 2.180 1.710 – – 1.00 –675.5 – F 2.200 1.720 – – 1.00 –691.5 – F 2.460 1.800 – – 1.00 –950.0 68.10 M 2.382 2.197 – 34.0 1.50 18.81,100.0 71.70 M 2.422 2.120 – 31.2 1.50 27.41,100.0 69.40 F 2.542 2.502 – 33.1 1.50 24.41,200.0 76.00 M 2.763 2.715 – 35.0 1.50 28.31,400.0 77.30 M 2.520 2.684 – 40.5 1.50 32.71,650.0 78.40 F 2.990 3.096 – 37.3 1.50 39.41,700.0 85.00 F 2.908 3.527 – 40.3 1.50 38.11,750.0 82.80 F 2.648 3.353 – 47.0 1.50 47.02,000.0 82.40 F 3.039 3.513 – 37.7 1.50 43.22,150.0 88.20 F 3.108 4.269 53.2 42.5 1.50 42.52,880 95.60 M 4.159 5.886 72.8 51.4 2 51.43,260 96.50 M 4.168 6.159 74.3 60.0 2 61.93,800 101.50 F 4.421 6.272 74.6 56.5 2.5 72.84,120 106.70 M 4.820 7.663 78.5 64.7 2 77.64,180 106.00 F 4.547 7.226 89.3 63.5 2 119.25,340 118.70 F 4.611 7.600 93.6 72.0 2.5 80.06,100 115.50 F 4.788 8.090 91.4 70.8 2 112.36,220 116.00 F 4.509 8.225 93.4 68.0 3 109.46,300 110.30 M 4.066 7.220 88.1 67.3 2.5 127.47,380 119.00 F 4.223 7.916 102.7 73.5 3 126.97,720 125.90 M 4.728 10.387 106.1 72.1 2 170.98,000 117.00 F 4.516 9.103 98.8 78.7 2.5 152.28,520 136.00 M 4.780 11.042 107.4 88.5 3 88.58,860 127.50 F 4.807 10.920 111.5 78.8 2.5 162.910,060 135.00 M 5.355 12.034 115.6 87.8 3 190.712,700 153.00 F 4.800 11.261 121.8 94.5 3 175.313,500 145.00 M 4.783 11.396 116.2 86.5 3 165.313,500 157.50 M 5.077 11.844 126.0 96.8 3.5 180.515,700 150.10 M 5.117 11.962 121.0 93.2 3.5 173.417,020 153.00 M 4.635 11.793 128.6 92.0 3 176.817,100 156.00 F 5.044 12.765 131.0 95.0 4 193.318,840 167.50 F 5.514 14.790 133.5 111.5 3 272.119,140 165.00 M 5.508 15.118 129.0 98.5 3.5 256.620,200 166.70 M 5.706 15.546 132.0 103.0 4 236.622,700 169.00 F 5.643 16.308 138.0 110.0 3.5 252.325,090 180.50 M 5.675 15.228 145.1 117.0 3 309.025,100 180.10 F 5.708 16.587 151.0 120.5 3.5 380.328,080 190.00 M 5.908 17.476 167.5 128.7 5 388.929,500 195.50 M 6.757 20.073 158.0 128.5 4 387.136,900 197.00 M 7.041 21.160 166.0 130.0 5 526.538,100 199.00 M 7.625 24.402 168.8 130.5 4.5 497.938,500 194.60 M 6.450 21.461 169.5 130.8 4.5 458.938,600 200.10 F 6.530 19.845 167.0 132.0 5 557.755,000 226 M 7.614 24.467 188 145 6 719.755,000 226.5 M 7.621 25.435 194 138.9 5 641.470,000 236.5 F 7.886 27.471 196.5 149 7 706.571,000 248.5 M 8.565 33.068 212.5 158 6 839.772,000 249.5 M 7.862 30.388 206.5 161 7 744.775,000 245 F 7.705 30.267 206.5 159 7 913.686,000 250 M 7.902 28.365 200.5 155 5.5 1,052.590,000 261 M 9.114 33.87 220.5 169.5 7 1,117.8

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Mbd0.256 (SE 0.005, Puncorr 5 2.84 3 10257, r2 5 0.97;

AICC 5 2142.55) (Fig. 4). This indicates that whilegrowth proceeds at different rates over the life-periodsampled in the current study, brain mass maintains asingle relationship to body mass as both changetogether. Moreover, the small exponent of 0.256 indicatesthat body growth is accompanied by a very slow increasein brain mass over time. Indeed, while the brain repre-sents 1.5% of body mass in the smallest animals in oursample, its relative size drops to 0.01% of body mass inthe largest animals.

Body Mass vs. Spinal Cord Mass

Spinal cord mass varied 51.3 times in our sample, anintermediate value between the variation in body mass(978.3 times) and in brain mass (6.3 times; Table 1). Theincrease in mass of the spinal cord relative to body masswas investigated using the Weibull growth model andpower functions. Examining the raw data allowed us todetermine that during the post-hatching period therewas a rapid increase in the mass of the spinal cord bothabsolutely and in relation to body mass, and that thisshowed a consistent but steady increase in massthroughout the life period sampled (Fig.F5 5A). When usingthe Weibull growth model to fit the entire data theresults indicated a highly predictable relationshipbetween body mass and spinal cord mass (r2 5 0.99;AICC 5 15.14). Throughout the life period sampled, thegrowth model clearly predicted the values obtained inthe raw data, thus substantiating our use of this growthmodel (see equation provided in Fig. 5A). The growthmodel predicted that the average mass of the spinal cordat hatching for the Nile crocodile, which have a bodymass of around 80 g (Pooley and Gans, 1976), should beapproximately 0.35 g. This growth model also predictsthe upper asymptote, which is the average spinal cordmass at maturity; however, as there is no clear pointwhere the crocodile reaches maturity, we investigated

two points of interest. The Nile crocodile is thought toreach reproductive age at �150 kg in body mass, and canreach body masses up to 1,000 kg (Pooley and Gans,1976). In these two cases, the model predicted that, whenbody mass is 150 kg, spinal cord mass should be approxi-mately 41.7 g, while that at a body mass of 1,000 kg spi-nal cord mass should be approximately 88.6 g. Thus, thespinal cord is predicted to continue to increase in massthroughout life in the Nile crocodile, and follows a pre-dictable pattern of growth that slows with increasingbody mass.

As for the brain, the relationship between spinal cordmass and body mass within Nile crocodiles can also bedescribed across the entire range of masses as a singlepower function, Msc 5 0.07 3 Mbd

0.54 (SE 0.008, Puncorr 5 2.93 10268, r2 5 0.985; AICC5 15.82; Fig. 5B). As in the brain,this indicates that while growth proceeds at different ratesover the lifespan, spinal cord mass maintains a singlerelationship to body mass as both change together. Thelarger exponent of 0.54, compared to 0.256, indicates thatbody growth is accompanied by a faster increase in spinal

Fig. 1. A plot of body mass (g) against body length (cm) in the croc-odiles sampled for both parameters in the current study (Table 1). Anegative allometric relationship was observed indicating that increasesin body mass occur at a faster rate than increases in body length. Thedashed lines above and below the solid regression line represent the95% prediction intervals based on the equation derived from the data.Lbd—body length, Mbd—body mass, Puncorr—probability of the datanot being correlated.

Fig. 2. Plots of body mass (g) against liver mass (g) in the crocodilessampled for both parameters in the current study (Table 1). A: Notethe strongly statistically significant linear relationship between the twovariables. As body mass increases, the percentage of the body masstaken up by the liver slowly decreases. Thus, in younger crocodiles,more of the body is occupied by liver than in larger crocodiles.B: Strongly statistically significant single power function also describesthe relationship between the two variables. The dashed lines aboveand below the solid regression line represent the 95% prediction inter-vals based on the equation derived from the data. Mliv—liver mass,Mbd—body mass, Puncorr—probability of the data not being correlated.

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CROCODILE BRAIN GROWTH 5

cord mass than in brain mass over time. As the animalgrows, the relative mass of the spinal cord decreasesfrom 0.8% of body mass in the smallest animals to0.04% of body mass in the largest animals in oursample. Thus, although the relative size of the brain isinitially larger than the relative size of the spinal cord,

as the animals grow, the spinal cord grows to becomerelatively larger than the brain.

Brain Mass vs. Spinal Cord Mass

As expected from their individual power relationships tobody mass, brain mass and spinal cord mass in the croco-diles sampled in the current study are directly related by apower function such that Mbr increases with Msc

0.430, or,reciprocally, Msc increases with Mbr

2.296 (Fig. F66). Both partsof the CNS thus grow in parallel, but at different rates,such that for every doubling in brain mass, the mass of thespinal cord increases by 4.91 times (Fig. 6).

Spinal Cord Length In situ vs. Ex Situ

During the course of this study, we measured thelength of the spinal cord both in situ prior to removalfrom the vertebral canal, and ex situ following 24 hr in

Fig. 3. Lateral view photographs of the brain of the Nile crocodilefrom animals with different body masses, from small (upper most) tolarge (lower most). Note the slow increase in brain mass with the morerapid increase in body mass (see also Table 1). Also note the exten-sion of the olfactory tract, but the relatively constant increase in allcomponents of the brain. Scale bar 5 1 cm.

Fig. 4. A plot of body mass (g) against brain mass (g) in the croco-diles sampled for both parameters in the current study (Table 1). Thepattern of brain growth shows 2 distinct phases. In the early post-hatching period, in animals with a body mass less than 2,500 g, braingrowth is rapid. Following this period, when animals have a bodymass greater than 2,500 g brain growth appears to slow, but stillincreases consistently. Despite this, the relationship between bodyand brain mass can be described by a single power function showingthat a 10-fold increase in body mass is accompanied by an increaseof only 1.8-fold in brain mass. The dashed lines above and below thesolid regression line represent the 95% prediction intervals based onthe equation derived from the data. Mbd—body mass, Mbr—brainmass, Puncorr—probability of the data not being correlated.

Fig. 5. A plot of body mass (g) against spinal cord mass (g) in thecrocodiles sampled for both parameters in the current study (Table 1).A rapid increase in the mass of the spinal cord, both absolute and rel-ative to body mass was observed throughout the life period sampled.This relationship was highly predictable and indicated that it was likelythat the spinal cord continues to increase in mass throughout the lifeof the Nile crocodile, even after the life period sampled. The upperplot (A) represents the Weibell growth curve model, the lower plot (B)the power function relationship between the two variables. Thedashed lines above and below the solid regression line on the lowerplot represent the 95% prediction intervals based on the equationderived from the data. Mbd—body mass, Msc—spinal cord mass, Pun-

corr—probability of the data not being correlated.

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6 NGWENYA ET AL.

post-fixation. During this process we noted that the exsitu, or post-fixed, spinal cord length appeared to be sub-stantially shorter than the in situ spinal cord length. Wecompared these two parameters statistically and con-firmed our visual observation, finding that ex situ spinalcord length was always shorter than in situ spinal cordlength: fixation caused a linearly predictable shorteningof spinal cord length to, on average, 76.7% of the origi-nal in situ spinal cord length (Fig.F7 7).

Body Length vs. Spinal Cord Length, In Situand Ex Situ

Given that the length of the fixed ex situ spinal cordis linearly related to the length of the spinal cord insitu, we could use the former measurement to analyzehow the spinal cord increases in length as the bodygrows, given the lack of in situ measurements for thesmallest animals in the sample (Table 1). Although thelength of the ex situ spinal cord can be described to varylinearly with body length (at an average of 71% of bodylength; r2 5 0.98, Puncorr 5 6.37 3 10238; Fig.F8 8A), wefind that it is best described to vary as a power functionof body length of exponent 1.13 6 0.026 (r2 5 0.98,Puncorr 5 6.82 3 10243; Fig. 8B). Despite the same r2

value, the power function is the best fit because the ratiobetween spinal cord length and body length is not con-stant, as expected if the two variables were linearlyrelated, but rather increases together with body length(Spearman correlation, q 5 0.760, P< 0.0001). Spinalcord length thus increases hypermetrically with bodylength, extending for about 50% of body length in thesmallest animals but 66% of body length in the largestanimals in our sample.

Body Mass vs. Spinal Cord Length

The increase in length of the spinal cord (both in situand ex situ) relative to body mass was investigated using

both the Weibull growth model and power functions.Examining the raw data allowed us to determine thatduring the post-hatching period there was a rapidincrease in the length of the spinal cord both absolutelyand in relation to body mass, and that this showed aconsistent but steady increase in mass throughout thelife period sampled (Fig. F99). When using the Weibullgrowth model to fit the entire data the results indicateda highly predictable relationship between body mass andspinal cord length (r2 5 0.98 in situ and 0.99 ex situ,AICC in situ 5 147.10, AICC ex situ 5 205.50) see equa-tions provided in Fig. 9A). The growth model predictedthat the average length of the spinal cord at hatchingfor the Nile crocodile, which have a body mass of around80 g (Pooley and Gans, 1976), should be approximately17 cm ex situ. This growth model also predicts the upperasymptote, which is the average spinal cord length atmaturity; however, as there is no clear point where thecrocodile reaches maturity, we investigated spinal cordlength at the age of sexual and social maturity (150 kgin body mass) and maximum body mass (1,000 kg). Inthese two cases, the model predicted that the spinal cordlength when body mass is 150 kg should be approxi-mately 178 cm ex situ, while that at body mass of 1,000kg spinal cord length should be approximately 198 cm exsitu. Thus, the spinal cord appears to continue toincrease in length throughout life in the Nile crocodile,and follows a predictable pattern of growth that slowswith increasing body mass.

Ex situ spinal cord length was also found to vary overthe entire range of body sizes as a single power functionof body mass with an exponent of 0.34 6 0.005 (AICC insitu 5 148.00, AICC ex situ 5 227.86; Fig. 9B), which isindistinguishable from the exponent of 0.33 expected fora body that grew isometrically. However, as shownabove, the longitudinal growth of the spinal cord is not

Fig. 6. A plot of brain mass (g) against spinal cord mass (g) in thecrocodiles sampled for both parameters in the current study (Table 1).A single power function describes the relationship between brainmass and spinal cord mass. This indicates that the brain increases inmass at a much slower rate than the spinal cord, such that as thebrain doubles in mass, the spinal cord mass increases by 4.91 times.Mbr—brain mass, Msc—spinal cord mass, Puncorr—probability of thedata not being correlated.

Fig. 7. Plot of spinal cord length in situ against spinal cord length exsitu in the crocodiles sampled for both parameters in the current study(Table 1). Ex situ spinal cord length (following 1 day post-fixation in4% paraformaldehyde) was observed as being less than in situ spinalcord length (measured prior to the spinal cord being removed fromthe vertebral canal) in all instances. Post-fixation caused a predictableshortening of spinal cord length by 23.3%. The dashed lines aboveand below the solid regression line represent the 95% prediction inter-vals based on the equation derived from the data. Lscex—spinal cordlength ex situ, Lscin—spinal cord length in situ, Puncorr—probability ofthe data not being correlated.

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isometric, as shown by the increase of its relative lengthwith body growth. This is because, as shown above, bodymass increases hypermetrically with body length in thesecrocodiles. Thus, although spinal cord length increaseswith approximately the cubic root of body mass in croco-diles, it increases faster than body length does.

Body Mass, Brain Mass, and Spinal Cord Massvs. Ocular volume

We find that, like the brain and spinal cord, the eyealso appears to grow continuously during the life periodof the crocodiles sampled in the current study (Table 1).In order to investigate how the volume of the eye relatedto the other parameters measured, we analyzed ocularvolume in relation to body mass, brain mass, and spinalcord mass (Fig.F10 10). When comparing ocular volumewith body mass, it was clear that a Weibull growthcurve described the relationship most appropriately

(r2 5 0.96, AICC 5 2134.50; Fig. 10A). As with brain andspinal cord mass, the ocular volume increased more rap-idly in the earlier phases of life, up to body masses ofaround 30 kg, but after that a more steady increase inocular volume was observed. The growth curve predicts,from the sampled data and analysis, that the ocular vol-ume increases throughout the entire life span of thecrocodile.

Simultaneously, ocular volume can also be described toincrease as a power function of body mass with an expo-nent of 0.37 (r2 5 0.95, Puncorr 5 2.05 3 10244,AICC 5 2125.08; Fig. 10B), thus faster than brain mass(0.26, see above), but more slowly than spinal cord mass(0.60, see above). Indeed, when compared directly, ocularvolume was found to increase as a power function of brainmass of exponent 1.18 (r2 5 0.93, Puncorr 5 1.34 3 10236;

Fig. 8. Plot of body length (cm) against ex situ spinal cord length(cm) in the crocodiles sampled for both parameters in the currentstudy (Table 1). A: A strongly statistically significant linear relationshipexists between the length of the body and the length of the spinalcord (ex situ measurements) such that for every 10 cm increase inbody length, there is a 7.11 cm increase in the spinal cord ex situ.B: A strongly statistically significant single power function alsodescribes the relationship between the two variables. The dashedlines above and below the solid regression line represent the 95%prediction intervals based on the equation derived from the data.Lbd—body length, Lscex—spinal cord length ex situ, Puncorr—probabilityof the data not being correlated.

Fig. 9. Plots of body mass (g) against spinal cord length (cm) in thecrocodiles sampled for both parameters in the current study (Table 1),plot A being the Weibull growth curve and plot B representing thepower functions. Both in situ and ex situ measurements of the spinalcord indicated that a highly predictable relationship exists betweenthe length of the spinal cord and body mass. The relationship sug-gests that while the length of the spinal cord continues to increasethroughout the life of the Nile crocodile, even after the life periodsampled, the increase in length does slow down with increases inbody mass, but throughout can be described as a single power func-tion. The dashed lines above and below the solid regression line in thelower plot represent the 95% prediction intervals based on the equa-tion derived from the data. Mbd—body mass, Lscex—spinal cord lengthex situ, Lscin—spinal cord length in situ, Puncorr—probability of the datanot being correlated.

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Fig. 10C) and as a power function of spinal cord massof exponent 0.65 (r2 5 0.93, Puncorr 5 2.35 3 10243;Fig. 10D).

DISCUSSION

Here we find that body growth in the crocodile isaccompanied by growth of all portions of the CNS exam-ined (brain, spinal cord and eye), although at differentrates: in mass or volume, the spinal cord is the fastestgrowing structure, followed by the eye and the brain. Incomparison, the liver was found to grow more rapidlythan all CNS structures, although still not linearly withbody mass. Although each structure grows at a differentrate, these rates are coordinated across structures, suchthat the mass of each part of the CNS varies as a powerfunction of the others. Should these relationships bemaintained throughout the full extent of life in the croc-odile, our analyses indicate how the different parts ofthe CNS are likely to continue growing.

The Brain, Spinal Cord, and Eye of the NileCrocodile Grow Throughout Life

The results of the current study indicate that the pat-tern of brain growth in the Nile crocodile does notresemble that seen in mammals. For example, in thehuman the brain grows during the period of life leadingup to �18 years of age, after which any further growthis not clearly evident (e.g., Count, 1947; Dobbing andSands, 1973; Burn et al., 1975; Vrba, 1998; Leigh, 2001;Rice, 2002; Vinicius, 2005). In contrast to this, the brainof the Nile crocodile was observed to grow in a mannerdescribed by a power function indicating that growthwill continue throughout life. As the Nile crocodile canreach a body mass of up to 1,000 kg, we can estimatethat the largest brain that could be recorded for anextant Nile crocodile would have a mass of approxi-mately 15.8 g. This extrapolation of the data must beviewed with caution, as it is entirely possible that theremay be a change in the growth pattern of the brainabove 90 kg body mass as the Nile crocodile only reaches

Fig. 10. Plots of ocular volume (mL) against body mass (g), brainmass (g) and spinal cord mass (g) in the crocodiles sampled for theseparameters in the current study (Table 1). The relationship betweenincreases in ocular volume and increases in body mass was analyzedusing the Weibull growth curve (A) and a power function (B). An initialphase of rapid increase of ocular volume (observed in animals with amass less than 30 kg), is followed by a second phase showing a moresteady increase in ocular volume (observed in animals with a massgreater than 30 kg). This relationship can be described as a single

power function. A power function was observed to describe the rela-tionship between ocular volume and brain mass, such that as thebrain mass doubles, the ocular volume increases 2.27 times (C). Therelationship between ocular volume and spinal cord mass was alsodescribed by a single power function, but unlike the brain, the spinalcord increased in mass at a rate faster than the increase in ocular vol-ume (D). Mbd—body mass, Mbr—brain mass, Msc—spinal cord mass,Puncorr—probability of the data not being correlated, Veye—ocularvolume.

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sexual and social maturity when body mass has reached�150 kg (Pooley and Gans, 1976; Ferguson, 1985). It istherefore possible that the power function providedherein describes brain growth up to �150 kg, but thatbrain growth may slow or become static after this point(but see analysis below related to fossil Crocodyliforms).

Two novel findings in the current study indicate thatnot only does the brain continue to grow throughout thelife period sampled, but both the spinal cord (mass andlength) and eye (ocular volume) appear to continuouslygrow. Our analysis showed that the mass and length ofthe spinal cord followed a sigmoidal growth pattern inrelation to body mass. This indicates that there is anearly period of relative rapid growth, up to �4–5 kg, fol-lowed by a much longer period of steadily slowinggrowth, indicating that the spinal cord will continue togrow throughout the life of the crocodile, but that as theanimals become larger, the rate of growth slows accord-ingly. Interestingly, the relationship between spinal cordand body masses can also be described as a power func-tion. Power functions are biologically interesting becausethey describe scale–invariant relationships, that is rela-tionships between parameters that are maintained evenas the parameters changes, such as during body growth.The power functions of body mass with positive expo-nents found here for spinal cord, brain, and eye size(mass or volume) as well as between the three CNS vari-ables indicate that there are fixed relationships betweenthese four variables as the crocodile body continues togrow post-hatching.

It was to be expected, but had not yet been demon-strated, that the continuous growth of the body requiresa continuous growth of the spinal cord and brain, allow-ing for neural control/sensation/regulation of the enlarg-ing somatic elements (Jerison, 1973). Here we find thatthe brain and spinal cord do become larger with continu-ous growth in crocodiles. However, the enlargement ofthese two CNS structures occurs not only at differentrates (with faster growth of the spinal cord than thebrain), but also very slowly, with body mass variationraised to exponents of 0.59 (spinal cord) and 0.26 (brain),such that their relative sizes decrease continuously andby a factor of as much as 150 times for the brain, and 20times for the spinal cord. In contrast, the liver, which isexpected to grow linearly with body mass (e.g., Franzet al., 2009), was found to grow much more rapidly(although sublinearly) with body mass variation raisedto an exponent of 0.82.

The smaller exponents describing spinal cord andbrain allometry than liver allometry indicate that, whilelarger bodies might indeed require larger neural process-ing power, this increases at a rate far below the growthof body mass, and below the growth of another organwhose function is related to body volume. These findingsstrongly suggest that the demand for more neural proc-essing power increases only very slowly with increasingbody mass, although a definitive answer awaits deter-mining how numbers of neurons in the crocodile spinalcord and brain vary with continuous body growth.

In spite of this, the finding of a significant but slowincrease in brain and spinal cord mass with growingbody mass within a single species is consistent with pre-vious findings that the number of all neurons in the spi-nal cord varies with body mass raised to a smallexponent of 0.360 across primate species (Burish et al.,

2010), and that the number of motor neurons in thefacial nucleus increases slowly with body mass raised toa small exponent of 0.184 across marsupials (Watsonet al., 2012) and 0.127 across primates (Sherwood, 2005).Since motor neurons are an important fraction of all spi-nal cord neurons, these findings across mammalian spe-cies suggest that a similarly small increase in numbersof neurons might suffice to control the increasing muscu-lar mass of continuously growing crocodiles. Moreintriguing, however, is the slower increase in brain massthan in spinal cord mass with body growth across theseanimals. Although we don’t yet know how the gain inCNS mass relates to changes in numbers of neurons,this raises the interesting possibility that the crocodilebrain gains neurons even more slowly than the spinalcord throughout life, suggesting that while directly body-related functions do scale as crocodiles grow, cognition-related functions may lag behind.

Continuous neurogenesis has been well established inreptiles (e.g., Kaslin et al., 2008), which lends support tothe supposition that the increase in mass of CNS struc-tures does result from the addition of neurons, as wellas of other cells, to these structures as body mass grows.There is, however, the possibility that the growth of theCNS structures accompanying body growth occurs solelythrough the increase in average cell size, as axons anddendrites become more elongated and possibly the cellsoma increases in size. These possibilities are currentlybeing investigated by determining how the cellular com-position of CNS structures varies with continuousgrowth in the current sample of Nile crocodiles.

We find that the eye also exhibits continuous growthin the crocodile. This is a sensory structure whose size isnot a priori expected to scale as the result of a demandimposed by larger body mass; the fact that it doesincrease in volume suggests that body structures, includ-ing the brain and spinal cord, might increase in massdue to systemic regulation in the absence of any imposi-tion of more neuronal processing power by a larger body.Still, the fact that the eye grows continuously through-out life has interesting implications for the visual acuityof the crocodile. A larger eye, due to the larger axialdiameter, usually indicates an increase in visual acuity(if the density of ganglion cells of the retina remainsconstant). It will be of interest to understand whetherthe observed eye growth in the crocodile does lead to anincrease in visual acuity in the crocodile by mappingpeak ganglion cell densities in the retinas and determin-ing visual acuity at different stages of crocodile growth.

Is the Growth of the Nile Crocodile BrainRepresentative of All Crocodilians?

The data provided herein are species specific, but arethese patterns of growth representative of the Crocodili-ans as a whole? In order to test this, we plotted the datafrom previous studies (C. siamensis, Chentanez et al.,1983; A. mississippiensis, Crile and Quiring, 1940; Cai-man crocodilus, Gans, 1980) together with the data pro-vided in the current study (Fig. F1111). The outcome of thiscomparison is that the data for all four species doappear, for the most part, to be superposed, and thus thepresent data for the Nile crocodile seem to accuratelypredict the data derived from the other species. Interest-ingly, Crile and Quiring (1940) obtained data from three

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alligators that had body masses larger than the Nilecrocodiles sampled in the current study (109, 173, and205 kg). In these three cases the reported brain masseswere 8.4, 11.2, and 14.08 g, respectively. Using thepower function derived with our data on the Nile croco-dile, the predicted brain mass for these three alligatorswould be 8.96, 10.09, and 10.53 g. The good matchessuggest that the body–brain relationships are fairly sim-ilar across species, and that the Nile crocodile is likelyto be representative of Crocodilians. Alternatively, thelarger difference between predicted and actual brainmass for the largest alligator might result from a changein growth-regulating mechanisms past a certain bodymass, or may also result from differences in collection ofbrain tissue, especially in determining the caudal end ofthe brain (which for the Nile crocodiles we used the fora-men magnum as the indicator of the end of the brain).

If the equations derived from the current study areindeed representative of the Crocodilians, they may beused to predict such features as brain mass for fossilspecies. If we take as an example a very large Crocodyli-form, Aegisuchus witmeri, which has an estimated bodylength of 15 m and endocranial volume of 40 cm3 (Holli-day and Gardner, 2012). Based on our analysis of therelationship between body mass to body length in theNile crocodile we would predict that A. witmeri shouldhave a body mass of approximately 35,757 kg. Thiswould then lead to a predicted brain mass of 39.48 gbased on the power function describing the relationshipbetween body and brain mass in the Nile crocodile. Thisis very close to the actual endocranial volume of 40 cm3

reported for A. witmeri based on CT scanning (Hollidayand Gardner, 2012). Given that endocranial volumealways slightly overestimates brain volume (and thusbrain mass), and given the inter-individual variabilityinherent in the brain mass of any species, it appearsthat our analyses and the subsequent predictions do

accurately predict brain mass across Crocodyliforms,even though they vary tremendously in body size.

Future Studies

The current study has raised several questions thatare of interest for future study. As the brain appears togrow continuously throughout life, it is of interest toknow if the increases in brain mass are matched byincreases in neuronal number, or whether the increasedbrain mass is made up of non-neural cells, or both, orthe result of increases in average cell size without anyaddition of new cells. Moreover, if neurons are beingadded, it is of interest to determine where in the brainthese are being added—are these potential additionalneurons being added to regions of the brain involved insensory processing and motor control, or are they alsobeing added to those parts of the brain involved in cogni-tive processes? Studies of communication signals associ-ated with courtship and reproduction indicate thatlarger alligators exhibit a greater behavioral plasticitythan smaller alligators (Vliet, 1989). Perhaps addition ofneurons throughout life may underlie this potentiallygreater behavioral flexibility. In addition, are the contin-uous increases in spinal cord mass and ocular volumerepresented by increased neuronal numbers? Is there anincrease in sensory input from the skin and retina to thebrain in larger crocodiles? By not only determiningmasses and volumes of structures, but by detailing num-bers of neurons and regions where additional neuronsare being/may be added, future research will lead to astronger understanding of the neuronal demandsimposed by body growth; an understanding of the proc-esses underlying the continuously growing CNS of thecrocodile; and, ultimately, the relationship between bodygrowth and Crocodyliform behavior.

ACKNOWLEDGEMENTS

The authors would like to express their sincere gratitudeto Mr. Albert Pretorius and his team at Thaba KwenaCrocodile Farm for all their enthusiastic assistance withthis project and their expert help with the handling ofthe crocodiles.

LITERATURE CITED

Brisbin IL. 1989. Growth curve analyses and their applications tothe conservation and captive management of crocodilians. In:King FW, editor. Proceedings of the Ninth Working Meeting ofthe Crocodile Specialist Group. Gland, Switzerland: SSCHUSN.

Burish MJ, Peebles JK, Bladwin MK, Tavares L, Kaas JH,Herculano-Houzel S. 2010. Cellular scaling rules for primate spi-nal cords. Brain Behav Evol 76:45–59.

Burn J, Birkbeck JA, Roberts DF. 1975. Early fetal brain growth.Hum Biol 47:511–522.

Chabreck RH, Joanen T. 1979. Growth rates of American alligatorsin Louisiana. Herpetologica 35:51–57.

Chentanez T, Huggins SE, Chentanez V. 1983. Allometric relation-ships for the Siamese crocodile, Crocodylus siamensis. J Sci SocThailand 9:5–26.

Count EW. 1947. Brain and body weight in man: their antecedentsin growth and evolution. Ann NY Acad Sci 46:993–1122.

Crile G, Quiring DP. 1940. A record of body weight and certainorgan and gland weights of 3690 animals. Ohio J Sci 40:219–259.

Dobbing J, Sands J. 1973. Quantitative growth and development ofhuman brain. Arch Dis Childhood 48:757–767.

Fig. 11. Plot of brain mass (g) and body mass (g) with the data fromSiamese crocodile (Chentanez et al., 1983), alligator (Crile and Quiring,1940) and caiman crocodile (Gans, 1980) superimposed on the regres-sion line and 95% prediction interval established in the current studyfrom the Nile crocodile. The comparison shows that the data obtainedfrom other species of Crocodilians fits reasonably well into the rela-tionship observed in the Nile crocodile. This suggests that the dataand equations derived from the Nile crocodile do appear to be accu-rate predictors of brain mass across crocodilian species, at least dur-ing the period of life sampled in the current study.

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CROCODILE BRAIN GROWTH 11

Ferguson MWJ. 1985. Reproductive biology and embryology of theCrocodilians. In: Gans C, Billet F, Maderson PFA, editors. Biologyof the reptilia. Vol. 14: Development A. New York: Wiley. p 329–491.

Franz R, Hummel J, Kienzle E, Kolle P, Gunga HC, Clauss M.2009. Allometry of visceral organs in living amniotes and itsimplications for sauropod dinosaurs. Proc R Soc B 276:1731–1736.

Gans C. 1980. Allometric changes in the skull and brian of Caimancrocodilus. J Herpetol 14:297–301.

Herculano-Houzel S. 2011. Brains matter, bodies maybe not: thecase for examining neuron numbers irrespective of body size. AnnNY Acad Sci 1225:191–199.

Holliday CM, Gardner NM. 2012. A new Esuchian Crocodyliformwith novel cranial integument and its signficance for the originand evolution of the Crocodylia. PLoS One 7:e30471.

Horgan GW, Stubbs J. 2003. Predicting basal metabolic rate in theobese is difficult. Eur J Clin Nutr 57:335–340.AQ1

Hyams DG. 2010. CurveExpert software, http://www.curveexpert.net, 2010.AQ2

Jerison H. 1973. Evolution of the brain and intelligence. New York:Academic Press.

Kaslin J, Ganz J, Brand M. 2008. Proliferation, neurogenesis andregeneration in the non-mammalian vertebrate brain. PhilosTrans R Soc Lond B Biol Sci 363:101–122.

Katkowsky DA. 1990. Handbook of nonlinear regression models.New York: Marcel Dekken Inc.

Leigh SR. 2001. Evolution of human growth. Evol Anthropol 10:223–236.

Manger PR, Pillay P, Maseko BC, Bhagwandin A, Gravett N,Moon D, Jillani NE, Hemingway J. 2009. Acquisition of the brainof the African elephant (Loxodonta africana): perfusion-fixationand dissection. J Neurosci Methods 179:16–21.

Pooley AC, Gans C. 1976. The Nile crocodile. Sci Am 234:114–124.Rice SH. 2002. The role of heterochrony in primate brain evolution.

In: Minugh-Purvis N, McNamara KJ, editors. Human evolutionthrough developmental change. Baltimore: The Johns HopkinsUniversity Press. p 154–170.

Sherwood CC. 2005. Comparative anatomy of the facial motornucleus in mammals, with an analysis of neuron numbers in pri-mates. Anat Rec 287:1067–1079.

Sokal RR, Rohlf FJ. 1995. Biometry: the principles and practice of statis-tics in biological research. 3rd ed. New York: W. H. Freeman and Co.

Vinicius L. 2005. Human encephalization and developmental tim-ing. J Hum Evol 49:762–776.

Vliet KA. 1989. Social displays of the American alligator (Alligatormississippiensis). Am Zool 29:1019–1031.

Vrba ES. 1998. Multiphasic growth models and the evolution of pro-longed growth exemplified by human brain evolution. J TheorBiol 190:227–239.

Watson C, Provis J, Herculano-Houzel S. 2012. What determinesmotor neuron number? Slow scaling of facial motor neuron num-bers with body mass in marsupials and primates. Anat Rec 295:1683–1691.

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