Northeast Fisheries Science Center Reference Document 16-07

Geomorphometric Analysis Indicates

Overlap in Body Shape between Sexes

of Black Sea Bass (Centropristis striata)

by Bradley Keigwin, Gary R Shepherd, and Mark J Wuenschel

doi:10.7289/V50Z71B9
Northeast Fisheries Science Center Reference Document 16-07

U.S. DEPARTMENT OF COMMERCE

National Oceanic and Atmospheric Administration

National Marine Fisheries Service

Northeast Fisheries Science Center

Woods Hole, Massachusetts

August 2016

Geomorphometric Analysis Indicates

Overlap in Body Shape between Sexes 

of Black Sea Bass (Centropristis striata)

by Bradley Keigwin1, Gary R Shepherd2, and Mark J Wuenschel2

1

Department of Mathematics and Statistics

Lederle Graduate Research Tower, 1623D

University of Massachusetts Amherst

710 N. Pleasant Street 

Amherst, MA 01003-9305

2

NOAA National Marine Fisheries Service

Northeast Fisheries Science Center

166 Water Street

Woods Hole, MA 02543

doi:10.7289/V50Z71B9
Northeast Fisheries Science Center Reference Documents

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This document may be cited as:

Keigwin B, Shepherd GR, Wuenschel MJ. 2016. Geomorphometric analysis indicates 

overlap in body shape between sexes of black sea bass (Centropristis striata). US Dept 

Commer, Northeast Fish Sci Cent Ref Doc. 16-07; 26 p. Available from: National Marine 

Fisheries Service, 166 Water Street, Woods Hole, MA 02543-1026, or online at http://

www.nefsc.noaa.gov/publications/
1

TABLE OF CONTENTS

Introduction ................................................................................................................................2

Methods......................................................................................................................................3

Results........................................................................................................................................5

Discussion...................................................................................................................................6

References Cited .........................................................................................................................8
2

INTRODUCTION

Black sea bass (Centropristis striata) is a protogynous hermaphrodite and member of the 

family Serranidae (Steimle et al. 1999). The species is considered a temperate reef fish (Steimle 

et al. 1999), which is distributed from the Gulf of Mexico to Maine with 3 distinct and separate 

populations partitioned at Cape Hatteras, North Carolina, and the Florida Keys (Bowen and 

Avise 1990; Roy et al. 2012; McCartney et al. 2013). Black sea bass are routinely targeted by 

commercial and recreational fisheries and are regulated primarily by quota, seasons, and 

minimum sizes (Shepherd and Terceiro 1994). 

As a protogynous hermaphrodite, black sea bass begins life as female but may switch to 

male either pre- or post- maturity (Lavenda 1949). In the male stage the phenotypic 

characteristics may differ if an individual takes on a role as a dominant male. Dominant males 

display aggressive behavior during spawning season and either control a group of females (a 

harem) or control a territory while fending off other males (a lek). The secondary sexual 

characteristics in black sea bass are dimorphic, with dominant males generally larger than 

females. Dominant males develop a nuchal hump, a prominent fat deposit on their nape that

becomes iridescent blue during mating season, as well as white highlights on their fins and face. 

In contrast, other, perhaps secondary males, look very similar to females that lack the nuchal 

hump and bright coloration. Determining the sex of fishes is generally accomplished through 

internal examination of gonad tissue, unless there are definitive external characteristics unique to 

each sex (e.g., the blue nuchal hump in black sea bass). In this study, we analyzed the shape of 

males and females to quantitatively evaluate differences between sexes. By using shape analysis, 

sexes were compared to determine the reliability of sex determination from external features.

Geomorphometrics (geometric morphometrics) is commonly used to analyze and 

characterize the physical appearance of shapes (Adams et al. 2003). The morphological 

comparisons may be shapes of interest within species or between different species or 

populations. The methods have also been used for other purposes such as facial recognition 

software or as diagnostic tools in examining medical images (Bookstein 1982). 

Geomorphometrics use landmarks to analyze shape (Bookstein 1982; Rohlf 1990). Landmarks 

are discrete locations (anatomical features) that can be identified consistently on each specimen 

but are not dynamic features; the relative location of the landmark must be constant and 

independent of size (Smith 2002). The objective of geomorphometrics is to identify landmarks 

that can be recorded in Cartesian coordinates, so the landmarks and the interlandmark distances 

can be used as a representation of shape. 

The shape coordinates can be analyzed by using several methods (Cadrin 2000), but one 

of the more common approaches is Principal Component Analysis (PCA). PCA creates linear 

combinations of orthonormal eigenvectors to describe the variance within a data set. The 

eigenvectors are the Principal Components (PC), which are linear combinations of the distances 

presented as a correlation matrix or covariance matrix. In the correlation matrix, the weight of 

each element in the matrix ranges between -1 and 1, whereas, in a covariance matrix, the values 

would not be bounded by -1 and 1. The PCs make up a vector space, and each PC axis is used to 

describe variance components. Higher weighted variables are the more important ones for a 

particular principal component. The first PC (PC1) accounts for the most variance, and the 

second (PC2) describes less, and so on. Since the PCs are orthogonal, variables that are weighted 

high in PC1 will not likely be weighted high in PC2, etc. By using PCA we can reduce the 
3

dimension of the data to determine which landmark distances account for the most variance and 

consequently could best be used to describe shape. 

METHODS

Black sea bass used for analysis were caught during the Massachusetts Division of 

Marine Fisheries survey cruises in May and June 2014. The fish were briefly frozen and then 

thawed before they were photographed, dissected, and their shape information was evaluated. 

Landmark locations were identified with dissecting pins on individual fish and positioned for 

photographs (Figure 1). Landmarks were chosen based on a similar morphometric evaluation of 

scup by Love and Chase (2009). Sea bass were photographed by using an adjustable camera 

stand with a Nikon1 digital camera positioned approximately 80cm above the fish. Total length

(mm), weight (g), maturity stage, gonad weight (g), and sex (based on macroscopic evaluation of 

the gonad) were then determined.

Interlandmark distance measurements were obtained from the digital images using the 

software tpsUtil 1.53 (Rohlf 20042

)). Each image included a ruler which was used to rescale 

image measurements from pixels to millimeters. The resulting x, y coordinates created in tpsUtil,

from 77 fish were imported into Microsoft Excel and SAS (2000). (Figure 1, Table 1). The 

distances between every landmark (n=22) combination (252 distances) were calculated with the 

equation:

disti = sqrt (( xi – xj) 2 + (yi – yj)

2

) (1)

where disti is the distance from landmark i to j measured in pixels. Distance coordinates (Table 

1, Figure 1) for each fish (disti) were converted from pixels to millimeters and standardized by 

dividing by total fish length. Total length accounted for obvious variation among fish and, since 

we are interested in the sex-specific differences in shape among fish, dividing by length removed

length as an influencing factor of shape.

Principal components can be calculated by using either a correlation matrix or a 

covariance matrix. We used the correlation matrix since the correlation matrix can give accurate 

results for 2 variables of different units. All the measurements were initially standardized to the 

mean.

Standardized disti= (disti – mean(disti)) / (standard deviation(disti)) (2)

Since the correlation matrix is symmetric and semipositive definite, we can make use of the 

Spectral Theorem and Schur’s Lemma to diagonalize the matrix with orthonormal eigenvectors

(Strang 2006). The eigenvalues are arranged from highest to lowest across the diagonal, and their 

corresponding eigenvectors are arranged accordingly. Only the highest eigenvalues that explain 

the majority of the variance in the data are important. The correlation matrix could be recreated 

by matrix multiplication of eigenpairs. The lower valued eigenpairs could be discarded, and most 

 1 All specific brand names found in this document are used for descriptive purposes only and do not constitute 

endorsement of any product, service, organization, or company.

2 available at http://life.bio.sunysb.edu/ee/rohlf/software.html
4

of the data would still be explained since the low valued eigenpairs have little influence in the 

correlation matrix. 

The standardization process using all possible landmark measurement combinations 

produced a 77 x 252 matrix. There were 22 zeroes in the data set along the diagonal, since the 

distance from landmark i to i is 0, and those zeroes were removed. Two of the 4 head bump 

landmarks were considered redundant, so distances originating from them were removed. Also 

removed were any distances originating at the tip of the pelvic fin since it was evident that 

location of the end of the fin was not constant in each photo. Removing these values resulted in 

210 possible distances from the 19 remaining landmarks.

The 210 distances were evaluated for normality by using a Shapiro-Wilk’s test (SAS Proc 

Univariate). Data should be normally distributed in order to perform PCA, since it requires linear 

relations (Zar 1974). We identified distances that have Wilk’s value <0.05, implying a departure 

from a normal distribution. Therefore a loge transformation (m_distX = log(m_distX +1)) was 

done to normalize the distance measurements. 

Principal component analysis (PCA) was conducted on the 210 distance measurements

(SAS Proc Princomp; Table 2). However, a sample size of 77 fish presented a problem since 

there can only be as many principal components (in this case 210) as there are samples in the 

dataset. Principal components 77 through 210 had values of zero and were removed, as were 

distances that had low weights on each of the principal components. Higher weighted 

components correspond to a larger variance, which imply features of interest, whereas lower 

valued components correspond to noise within the data set. In addition, if distances were highly 

correlated with each other, one was removed to prevent redundancy. Reducing the data based on 

these criteria resulted in a final set of 11 distance measurements that accounted for the greatest 

degree of separation among sexes (Table 3). An alternative approach was evaluated which 

replaced some landmark combinations with ones expected to have biological significance among 

sexes, particularly head, body, and tail measurements. Final principal components were

calculated (Table 5) for each fish by using the standardized distance multiplied by each 

coefficient (eigenvalue) in each eigenvector (Table 4). For example, for each fish: 

Principal component 1 = 0.304*m_dist4 + 0.317*m_dist17 + 0.323*m_dist15 + 0.311*m_dist77 

+ 0.337*m_dist72 + 0.249*m_dist107 + 0.259*m_dist112 + 0.389*m_dist9 + 0.186*m_dist216 

- 0.377*m_dist135 + 0.187*m_dist223

with each m_dist standardized to total length prior to use.

In the PCA plots of principal component 1 vs. principal component 2 for the reduced data 

set (115 distance measurements), 2 fish were identified as outliers (Figure 2). Further 

examination of the photos showed that both fish had abnormal body shapes because of either a 

distended stomach (full of squid) or an eroded/damaged tail (Figure 3). These fish were excluded 

from further analysis, leaving a total sample size of 75 fish.

Centroid size was calculated for each fish to compare body shape among sexes. The 

photo of each fish was partitioned into 9 triangles by using 11 landmarks (Figure 4). The 

centroid position of each local triangle was calculated by adding the 3 vertex coordinates of the 

local triangle and dividing by 3. The area of each local triangle was determined by using the law 

of cosines and the area formula: area = height* (base/2). The fishes “main centroid” was 

calculated by multiplying coordinates of local centroids by its corresponding area. The main 
5

centroid position of each fish was generally slightly above the midpoint of the pectoral fin. The 

centroid size is the square root of the sum of distances from each landmark to the main centroid.

RESULTS

The number of distance measurements used in the PCA were reduced from the original 

210 distance measures, and each reduction increased separation between the clusters of males 

and females (Figures 5-10). We removed the highly correlated distances with low weight in PC1 

and PC2, but if a distance was low in PC1 but high in PC2, it was not removed. The selection

process identified 11 distance measures that had the most explanatory power. PC1 explained

46% of the total variance while PC2 explained 16% (Figure 10). The first 5 principal

components explained almost 90% of the variance as shown in a scree plot (Figure 11). However 

since the first 2 PCs only explained 62% of the variance (Table 3), this suggests that the 2 sexes 

cannot be distinguished accurately from external morphometric characteristics.

Principal component 1 (PC1) accounts for the greatest source of variation among fish

morphometric characteristics, which is generally various length measurements. Consequently the 

highest weights are related to distances 9 and 135, which are measures of fish length (Table 4;

Figure 1). Principal component 2 (PC2) appears to be influenced by head measurements; it has 

highest weights on distances 216 and 223 (Table 4; Figure 1). In the graph of PC2 vs total length, 

there is almost no correlation, implying that PC2 is not influenced by length (Figure 12).

The separate clusters of males and females (Figure 10) show that males are different from 

females based on the final suite of 11 landmark distance measurements; however, some overlap 

between the sexes is apparent (Figures 13-14). Overlapping males (i.e., males with form similar 

to females) have larger body length measurements (Figure 14b) and shorter tails than average 

males (Figure 14i). Conversely, overlapping females (i.e., females with form similar to males) 

have smaller tails than average females (Figure 14i). Additionally, the overlapping males lacked 

a noticeable nuchal hump, as seen in their low values of distance 223 (tip of operculum to head 

bump #2; Figure 14k), and may be considered secondary males. They also have larger than 

average distance 4 (mouth to start of dorsal fin; Figure 14a), distance 15 (mouth to tip of 

operculum; Figure 14c), and distance 17 (mouth to start of pelvic fin; Figure 14d) measurements, 

which imply they have longer heads than typical males; this is a characteristic of females. 

Compared to other females, the overlapping females have lower than average distance 4, 

distance 15, distance 17, and distance 77 (start of dorsal fin to pelvic fin; Figure 14f ) and 

distance 107 (start of anal fin to end of dorsal fin; Figure 14g) measurements, meaning that they 

are more slender and have smaller heads than average females, which are characteristics of a 

secondary male. Within the cluster of males there are many males without humps, implying that 

there are features that distinguish sex other than the presence of a nuchal hump. Several males 

that are mixed within the female cluster do not have nuchal humps, which is often a 

characteristic of secondary males that practice sneak copulation (sneakers). However, there are 

also similar shaped males within the male cluster. Several females are interspersed within the 

male cluster, which could be females prior to transitioning to males, although they were not 

categorized macroscopically as transitioning.

The centroid size measurement was not as good at reducing the influence of shape on 

PC1 as was the measurement of length as (Figures 15A-C). The centroid size does not account 

for differences in shape (circular, or varying degrees of stretched ovals that may or may not be 

aligned with the long axis). An oval aligned with the long axis would represent the centroid of a 
6

longer fish, while a more circular centroid would indicate a wider fish, but the different centroid 

shapes could have the same size (area). Thus, 2 fish with different shapes could have the same 

centroid size, limiting the explanatory power of this metric.

DISCUSSION

We expected clearly separated PC clusters by sex, but instead the PCA does not support 

the conclusion that there are a suite of morphological features that distinguish between males and 

females in all cases. The fish used for measurements were in spawning or postspawning 

condition with the exception of 3 immature females. During the spawning season males typically 

develop prominent secondary sex characteristics such as a colorful nuchal hump. Given that 

these secondary characteristics occur during the spawning season, we expected to see the 

maximum degree of separation among sexes at the time when the samples were collected. We 

did not encounter any “transitional” (females going through the process of becoming males), nor 

did we expect to because black sea bass do not transition during the spawning season when these 

samples were taken. Similar to other Serranidae, they usually change sex following the spawning 

season, in this case during the fall to winter. Similar morphometric analysis of transitional fish 

from the nonspawning period may reveal distinguishing characteristics.

Black sea bass exhibit wide variation in external appearance during the breeding season, 

with distinguishable differences between most males and females. The secondary sexual 

characteristics were most evident in males that were presumed to be “dominant,” typified by 

large a nuchal hump, long feathery tail, and dark blue coloration (with a lighter face mask). 

Females are generally lighter in color and lacked the prominent nuchal hump. However, many 

individuals of both sexes were “indistinguishable,” possessing morphometric characteristics that 

clustered with the opposite sex. It is unknown whether these morphological differences are 

indicative of different behavioral roles (i.e. dominant, subordinate, sneaker).

The complex life history of black sea bass probably contributes to the wide variation in 

morphological characteristics. Although the species is hermaphroditic, individual life histories 

vary. Some individuals change sex before maturing as a female (prematurational sex change), 

evidenced by the presence of small and young males. Some individuals never change sex, 

evidenced by large and old females in the population. Between these 2 functionally 

gonochoristic conditions, individuals may first reproduce as female for 1 or more years before 

changing sex and reproducing as male for 1 or more years. Therefore larger and older males may 

arise from different individual trajectories, with accompanying morphometric characteristics. For

example, it is reasonable to expect that the morphometric characteristics of a 5 year old male that 

transitioned at age 4 could be different from that of a 5 year old male that underwent 

prematurational sex change at age 1 and has only functioned as a male. Further complicating 

matters are the multiple roles that males can play in spawning. Though observations are limited, 

it appears that large “dominant” males with prominent secondary sexual characteristics initiate 

the majority of spawning bouts, keeping “subordinate” (or secondary) males to the periphery (J. 

Rosendale, NOAA-NEFSC, 74 Magruder Rd., Sandy Hook, NJ, pers. comm., unpublished data).

The subordinate males typically lack secondary sexual characteristics, and take on a more 

“female” appearance, consistent with a “sneaker” male strategy. The multiple paths leading to 

functional reproductive males, and multiple roles of males in the mating system, probably leads 

to variation in the appearance of males. Similar variation in female morphometrics may result if 

the transition to male is preceded by physiological changes (e.g., accumulation of fat, energy) 
7

that may alter the external shape/appearance of soon-to-transition females. Experimental studies 

have shown that black sea bass injected with hormones displayed secondary male sexual 

characteristics within 2 weeks (Benton and Berlinsky 2006). Therefore the external appearance 

and morphometric characteristics may be more labile than the production of functional gametes.

The gonadosomatic index of black sea bass decreases to very low levels in the nonspawning 

period (NEFSC 2012), as do some of the secondary sexual characteristics. It is unknown if the 

degree of separation between sexes based on morphometrics increases or decreases outside the 

spawning period.

The result of the analysis of black sea bass morphometric landmarks using Principal 

Component Analysis demonstrates that external features alone cannot be used to determine sex 

with 100% accuracy. Head shape is commonly used to identify males, but these results suggest it 

may only provide correct sex identification if the secondary characteristics (e.g. prominent 

nuchal hump and blue coloration) are present. Ultimately the most effective method to determine 

the sex of sea bass is internal macroscopic examination of the gonads.
8

REFERENCES CITED

Adams D, Rohlf JF, Slice DE. 2003. Geometric morphometrics: Ten years of progress following 

the ‘Revolution’. Italian Journal of Zoology 71:5-16. 

Benton CB, Berlinsky DL. 2006. Induced sex change in black sea bass. Journal of Fish Biology

69:1491-1503.

Bookstein FL. Foundations of morphometrics. 1982. Annual Review Ecological Systems

13:451-70.

Bowen BW, Avise JC. 1990. Genetic structure of Atlantic and Gulf of Mexico populations of sea 

bass, menhaden, and sturgeon: Influence of zoogeographic factors and life-history 

patterns. Marine Biology 107:371-381.

Cadrin SX. 2000. Advances in morphometric identification of fishery stocks. Reviews in Fish 

Biology and Fisheries 10:91-112

Lavenda N. 1949. Sexual differences and normal protogynous hermaphroditism in the Atlantic 

sea bass, Centropristes striata. Copeia 1949 (3): 185-194.

Love JW, Chase PD. 2009. Geometric morphological differences distinguish populations of scup 

in the Northwestern Atlantic Ocean. Marine and Coastal Fisheries: Dynamics, 

Management and Ecosystem Science I:22-28, 2009.

McCartney MA, Burton ML, Lima TG. 2013. Mitochondrial DNA differentiation between 

populations of black sea bass (Centropristis striata) across Cape Hatteras, North Carolina 

(USA). Journal of Biogeography 40:1386-1398.

Northeast Fisheries Science Center. 2012. 53rd Northeast Regional Stock Assessment Workshop 

(53rd SAW) Assessment Report. US Dept Commer, Northeast Fish Sci Cent Ref Doc. 

12-05; 559 p. Available from: http://nefsc.noaa.gov/publications/

Rohlf FJ. 1990. Morphometrics. Annual Review Ecological Systems 21:229-316.

Rohlf FJ. 2004. TpsDig. Department of Ecology and Evolution, State University of New York, 

Stony Brook, NY.

Roy EM, Quattro JM, GreigTW. 2012. Genetic management of black sea bass: Influence of 

biogeographic barriers on population structure. Marine Coastal Fisheries 4(1):391-402.

SAS Institute Inc. 2000. Statistical Analysis System, version 8. Cary, NC.

Shepherd GR, Terceiro M. 1994. The summer flounder, scup, and black sea bass fishery of the 

Middle Atlantic Bight and southern New England waters. NOAA Technical Report 

NMFS 122. US Department of Commerce, National Oceanic and Atmospheric 

Administration, National Marine Fisheries Service.

Smith LI. 2002. A tutorial on principal components analysis. http://nyx-www.informatik.unibremen.de/664/1/smith_tr_02.pdf
9

Steimle FW, Zetlin CA, Berrien PL, Chang S. 1999. Essential fish habitat source document: 

Black sea bass, Centropristis striata, life history and habitat characteristics. NOAA TM 

NMFS-NE-143. 50 pp.

Strang G. 2006. Linear algebra and its applications. 4th edition. Pacific Grove,CA. Thomson & 

Brooks/Cole. 

Zar JH. 1974. Biostatistical Analysis. Prentice-Hall, Inc., Englewood Cliffs, N.J. 
10

Table 1. All 252 calculated interlandmark standardized mean distances (m_dist)) were labeled with a 

number. The 11 distances used in the final Principal Component Analysis (PCA) are listed with a 

description of measurements’ location.

Distance Number Measurement

 m_dist4 Mouth to Start of Dorsal Fin

 m_dist 9 Mouth to End of Lateral Line

 m_dist 15 Mouth to Tip of Operculum

 m_dist 17 Mouth to Start of Pelvic Fin

 m_dist 72 Start of Dorsal Fin to Start of Anal Fin

 m_dist 77 Start of Dorsal Fin to Pelvic Fin

 m_dist 107 Start of Anal Fin to End of Dorsal Fin

 m_dist 112 Start of Pelvic Fin to End of Dorsal Fin

 m_dist 135 End of Lateral Line to End of Tail

 m_dist 216 Start of Lateral Line to Head Bump #3

 m_dist 223 Tip of Operculum to Head Bump #2

Table 2. First Principal Component Analysis (PCA) output using 210 distances from 77 fish. Principal 

Component (PC) numbers, corresponding eigenvalues, amount of variance contributed by each PC, 

and cumulative percent of variance. 

Percent Total 

PC number Eigenvalue Variance Percent

1 80.438 38.30% 38.30%

2 29.692 14.14% 52.44%

3 19.478 9.28% 61.72%

4 14.701 7.00% 68.72%

5 10.759 5.12% 73.84%

6 8.429 4.01% 77.86%

7 5.681 2.71% 80.56%

8 5.218 2.48% 83.05%

9 5.079 2.42% 85.46%

10 3.943 1.88% 87.34%

11 3.818 1.82% 89.16%

12 3.503 1.67% 90.83%

13 2.583 1.23% 92.06%

14 2.404 1.14% 93.20%

15 2.024 0.96% 94.17%

16 1.932 0.92% 95.09%

17 1.517 0.72% 95.81%

18 1.210 0.58% 96.39%

19 1.079 0.51% 96.90%
11

Table 3. Final Principal Component Analysis (PCA) output using the 11 chosen distances described in

Table 1. 

Table 4. Summary of weights for the first 2 Principal Components (Prin1 and Prin2) for each of the final 

distances (see Table 1 for description of each numbered distance). The highest weighted distances are 

highlighted.

Percent Total 

PC number Eigenvalue Variance Percent

1 5.110 46.45% 46.45%

2 1.756 15.97% 62.42%

3 1.383 12.58% 74.99%

4 0.854 7.76% 82.75%

5 0.668 6.07% 88.83%

Prin1 Prin2

m_dist 4 0.304 -0.245

m_dist17 0.317 -0.167

m_dist15 0.323 -0.259

m_dist77 0.311 0.293

m_dist72 0.337 0.102

m_dist107 0.249 0.034

m_dist112 0.259 0.150

m_dist9 0.389 -0.221

m_dist216 0.186 0.523

m_dist135 -0.377 0.223

m_dist223 0.187 0.594
12

Table 5. Summary of the first 2 Principal Component values (Prin1 and Prin2) for each of the 75 

observed fish (obs). 1 = male, 2 = female

Obs Prin1 Prin2 sex

1 -2.094 0.978 1

2 1.046 -0.302 2

3 -1.189 0.271 1

4 0.058 -1.793 2

5 2.515 0.006 2

6 -3.030 0.498 1

7 -1.188 -0.399 2

8 4.273 2.672 1

9 0.576 1.873 2

10 1.194 0.089 2

11 -0.278 0.127 2

12 1.134 -3.557 2

13 0.639 -0.655 2

14 1.307 -2.350 2

15 -2.584 -2.459 2

16 2.707 0.013 2

17 2.480 0.603 2

18 0.942 -1.303 2

19 1.076 -0.948 2

20 0.849 0.347 2

21 2.982 1.376 2

22 2.066 -0.309 2

23 2.032 -1.291 2

24 -1.911 -1.502 2

25 1.081 -0.941 2

26 0.791 0.499 2

27 1.924 -1.174 2

28 1.796 0.694 2

29 1.946 1.348 1

30 -1.197 0.063 2

31 1.703 -0.114 2

32 -0.871 -1.088 1

33 -3.400 -0.526 1

34 -2.832 -1.806 2

35 -4.350 0.470 1

36 -2.158 1.223 1

37 -0.209 -0.716 1

38 -0.686 0.559 1

39 -2.637 -1.611 1

40 -1.169 2.609 1
13

Table 5, continued. Summary of the first 2 Principal Component values (Prin1 and Prin2) for each of the 

75 observed fish (obs). 1 = male, 2 = female.

Obs Prin1 Prin2 sex

41 -1.795 -0.896 1

42 -2.408 0.204 1

43 -1.110 1.347 1

44 -0.465 1.503 1

45 -3.110 -0.531 1

46 -4.874 -0.274 1

47 -2.770 1.059 1

48 -2.509 2.270 1

49 -0.197 -0.652 2

50 2.455 2.365 2

51 -2.712 1.801 1

52 -3.850 1.462 1

53 -1.104 -1.576 1

54 2.684 0.616 2

55 0.965 -0.011 1

56 -1.149 -0.208 1

57 -0.278 1.889 1

58 -1.450 -0.699 2

59 -1.146 -0.708 2

60 0.527 0.626 2

61 2.791 1.599 2

62 1.444 0.272 2

63 -0.376 -1.447 2

64 -0.979 -1.910 2

65 3.086 -0.797 2

66 4.393 0.276 2

67 -3.046 -0.793 1

68 1.511 0.365 2

69 4.129 0.503 2

70 2.930 0.252 2

71 2.067 0.465 2

72 -1.509 1.543 1

73 3.596 -3.390 2

74 -3.678 2.088 1

75 2.607 -0.090 2
14

Figure 1. Locations for the 11 selected (of 252 calculated) interlandmark distances (lines) from the 19 landmarks (circles) used in the final 

analysis. See Table 1 for a description of each distance (labeled by number).
15

Figure 2. Biplot of the first 2 Principal Components (PC1 and PC2) by sex (■ females; ● males) for 

reduced data set of 115 distances. Irregular fish from Figure 3 are red squares outlined in black. 

-15

-10

-5

0

5

10

15

20

-20 -10 0 10 20 30 PC2

PC1
16

A.

B.

Figure 3. Fish removed from data set because of deformed shapes. The tail of fish A was stunted and in 

bad condition, influencing distance measurements. Fish B had a distended stomach from large squid 

which created irregular shape measurements.
17

Figure 4. Black sea bass (Centropristis striata) separated into 9 local triangles by using 11 landmarks 

for calculating centroid size (CS).

Figure 5. Biplot of the first 2 Principal Components (PC1 and PC2) by sex (■ females; ● males) for full 

data set of 210 distances. Irregular fish from Figure 3 are red squares outlined in black.

-15

-10

-5

0

5

10

15

-20 -10 0 10 20 30 40 PC2

PC1
18

Figure 6. Biplot of the first 2 Principal Components (PC1 and PC2) by sex (■ females; ● males) for 

reduced data set of 115 distances. Irregular fish from Figure 3 are red highlighted ( ).

Figure 7. Biplot of the first 2 Principal Components (PC1 and PC2) by sex (■ females; ● males) with 

irregular fish removed after data set further reduced to 35 distances.

-15

-10

-5

0

5

10

15

20

-20 -10 0 10 20 30 PC2

PC1

-8

-6

-4

-2

0

2

4

6

8

-10 -5 0 5 10 PC2

PC1
19

Figure 8. Biplot of the first 2 Principal Components (PC1 and PC2) by sex (■ females; ● males) of 20 

distance measurement data set. 

Figure 9. Biplot of the first 2 Principal Components (PC1 and PC2) by sex (■ females; ● males) for 11 

distance measurements.

-5

-4

-3

-2

-1

0

1

2

3

4

5

-8 -6 -4 -2 0 2 4 6 PC2

PC1

-6

-5

-4

-3

-2

-1

0

1

2

3

4

-6 -4 -2 0 2 4 6 PC2

PC1
20

Figure 10. Biplot of the first 2 Principal Components (PC1 and PC2) by sex (■ females; ● males;

males mixing with females) using the final 11 distances from Table 1.

Figure 11. Scree plot of % variance explained per Principal Component from final Principal Component 

Analysis.

-4

-3

-2

-1

0

1

2

3

-6 -4 -2 0 2 4 6 PC2

PC1

0

0.1

0.2

0.3

0.4

0.5

1 2 3 4 5 6 7 8 9 10 11

% of Variance Explained

Principal Component Number
21

Figure 12. Relationship between total fish length (mm) and Principal Component 2 (PC2) showing little 

correlation with length.

y = 0.006x - 1.982

R2 = 0.130

-4

-3

-2

-1

0

1

2

3

0 100 200 300 400 500 600

PC2

Length (mm)
22

Figure 13. Frequency distribution of Principal Component 1 (PC1) and Principal Component 2 (PC 2) by 

sex based on final 11 landmark distances. 

0

2

4

6

8

10

12

14

-5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3

Frequency

PC2

males

females

0

1

2

3

4

5

6

7

8

-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

Frequency

PC1

males

females
23

Figure 14. Variation in morphometric distances in relation to sex. For each morphometric length, the 

relative distance was calculated standardized (to length) differences as the observed – mean across all 

sex classes.
24

Figure 15. Principal Component 1(PC1), Principal Component 2 (PC2), and total length vs. centroid size. 

Low R2 values show that centroid size is not a good measurement.

R2 = 0.007

0.0

0.5

1.0

1.5

2.0

2.5

-6 -4 -2 0 2 4 6

Centroid Size

PC1

R2 = 0.003

0.0

0.5

1.0

1.5

2.0

2.5

-4 -3 -2 -1 0 1 2 3

Centroid Size

PC2

R2 = 0.23

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500 600

Centroid Size

Total Length (mm)
25

Appendix Table 1. Correlation matrix for the 11 selected mean distances (m_dist)) used in the final Principal Component Analysis. Distances 

are labeled by number; see Table 1 for description of the distances measured.

m_dist4 m_dist17 m_dist15 m_dist77 m_dist72 m_dist107 m_dist112 m_dist9 m_dist216 m_dist135m_dist223

m_dist4 1 0.441 0.718 0.427 0.378 0.293 0.198 0.617 0.079 -0.553 0.149

m_dist17 0.441 1 0.748 0.340 0.405 0.507 0.113 0.576 0.346 -0.575 0.127

m_dist15 0.718 0.748 1 0.257 0.361 0.289 0.130 0.649 0.248 -0.607 0.190

m_dist77 0.427 0.340 0.257 1 0.688 0.440 0.611 0.421 0.340 -0.388 0.464

m_dist72 0.378 0.405 0.361 0.688 1 0.322 0.557 0.631 0.222 -0.631 0.335

m_dist107 0.293 0.507 0.289 0.440 0.322 1 0.243 0.395 0.262 -0.371 0.155

m_dist112 0.198 0.113 0.130 0.611 0.557 0.243 1 0.563 0.117 -0.533 0.258

m_dist9 0.617 0.576 0.649 0.421 0.631 0.395 0.563 1 0.174 -0.985 0.155

m_dist216 0.079 0.346 0.248 0.340 0.222 0.262 0.117 0.174 1 -0.165 0.780

m_dist135 -0.553 -0.575 -0.607 -0.388 -0.631 -0.371 -0.533 -0.985 -0.165 1 -0.137

m_dist223 0.149 0.127 0.190 0.464 0.335 0.155 0.258 0.155 0.780 -0.137 1
26

Appendix Table 2. Eigenvectors (i.e., Principal Components [Prin] 1-11) of the correlation matrix between the 11 mean distances (m_dist). 

(Distances are labeled by number; see Table 1 for a description of each distance measurement). Each Prini is an eigenvector.

Prin1 Prin2 Prin3 Prin4 Prin5 Prin6 Prin7 Prin8 Prin9 Prin10 Prin11

m_dist4 0.3036 -0.2454 0.1362 -0.2342 0.6320 -0.3299 -0.1352 -0.1843 0.2114 0.4066 -0.0600

m_dist17 0.3170 -0.1668 0.3774 0.2512 -0.1786 0.4348 0.3691 -0.1317 -0.2180 0.4929 0.0349

m_dist15 0.3225 -0.2592 0.3772 -0.2187 0.1121 0.0683 0.3013 0.4831 0.1324 -0.5261 -0.0548

m_dist77 0.3115 0.2933 -0.2465 0.1772 0.4765 0.2013 0.2067 -0.4014 -0.3007 -0.4034 0.0121

m_dist72 0.3372 0.1016 -0.2960 -0.0255 0.0452 0.6094 -0.4644 0.2634 0.3437 0.1055 0.0071

m_dist107 0.2488 0.0338 0.1015 0.8205 0.0222 -0.3648 -0.2215 0.2522 0.0622 -0.0522 -0.0233

m_dist112 0.2595 0.1500 -0.5583 -0.0378 -0.1471 -0.2557 0.5866 0.2110 0.2502 0.2350 -0.0602

m_dist9 0.3894 -0.2208 -0.1220 -0.1491 -0.2970 -0.1986 -0.1688 -0.1518 -0.1339 -0.1142 0.7432

m_dist216 0.1862 0.5226 0.3986 -0.0801 -0.2659 -0.0815 0.0124 -0.3929 0.5316 -0.1095 -0.0195

m_dist135 -0.3772 0.2232 0.1287 0.1423 0.3805 0.1313 0.2342 0.2129 0.2475 0.1133 0.6594

m_dist223 0.1865 0.5942 0.1900 -0.2803 0.0333 -0.1540 -0.1405 0.3923 -0.5034 0.2128 0.0161
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