Revista de Biología Tropical, ISSN: 2215-2075, Vol. 72(S1): e59016, marzo 2024 (Publicado Mar. 01, 2024)

Analyzing morphometry among extant and extinct species: A case study of

genus Agassizia (Spatangoida: Echinoidea)

Alejandra Martinez-Melo1; https://orcid.org/0000-0003-2314-689X

Carolina Martin-Cao Romero2; https://orcid.org/0000-0003-4215-8036

Cristian Moisés Galván-Villa3; https://orcid.org/0000-0003-1927-2500

Rosa Carmen Sotelo-Casas*4; https://orcid.org/0000-0002-9297-6099

1. Invertebrate Paleontology, Academy of Natural Sciences of Philadelphia, 1900 Benjamin Franklin Pkwy, 19103,

Philadelphia, Pennsylvania, United States; Martinez-Melo@drexel.edu

2. Red Mexicana de Equinodermos, Ciudad de México, México; caromcr@gmail.com

3. Laboratorio de Ecología Molecular, Microbiología y Taxonomía (LEMITAX), Departamento de Ecología, Centro

Universitario de Ciencias Biológicas y Agropecuarias, Universidad de Guadalajara, Zapopan, Jalisco, CP 45200,

México; cristian.galvan@academicos.udg.mx

4. Departamento para el Desarrollo Sustentable de Zonas Costeras (DEDSZC), Centro Universitario de la Costa Sur,

Universidad de Guadalajara, Gómez Farias 480, Centro, 48980, San Patricio-Melaque, Jalisco, Mexico e-mail: rosacar-

mensotelocasas@gmail.com (Correspondence*)

Received 04-VII-2023. Corrected 27-XII-2023. Accepted 06-I-2024.

ABSTRACT

Introduction: The genus Agassizia in Mexico is represented both in the fossil record by the species Agassizia

regia† during the Miocene of Chiapas and by the extant species Agassizia excentrica on the Atlantic coast and

Agassizia scrobiculata on the Pacific coast. Qualitative diagnosis and descriptions make it hard to distinguish

morphological boundaries between species, especially in groups with fossils and recent representatives, increas-

ing the level of complexity by having samples of disparate qualities and quantities.

Objective: We propose the use of little explored statistical methods in the comparison of paleontological and

biological populations. This methodology allowed us to resolve issues of missing values in a morphometric data

set for the genus Agassizia.

Methods: Using samples recently collected and specimens already housed in collections, we explore a routine of

recovery of missing data MICE and the numerical and graphic analyses PERMANOVA, PCA, and SIMPER to

compare morphometric parameters between these species for recognizing diagnostic characters.

Results: Our results show a morphological difference in the length of the ambulacrum II and the length and

width of the periproct and peristome structures, these being greater in A. scrobiculata, with a consistent pattern

in both population samples not previously described.

Conclusions: Quantitative morphometric comparisons can be an assertive and complementary tool to determine

distinctive differentiation characteristics in species of the same genus. Comparative morphology reviews should

be an ongoing exercise to keep taxonomic knowledge on both extinct and extant species up to date. Our research

encourage the scientific community studying fossil populations to utilize quantitative and multivariate methods

to strengthen their investigations.

Key words: Miocene, multivariate analysis, Chiapas, Colima, Mexico, MICE.

https://doi.org/10.15517/rev.biol.trop..v72iS1.59016

SUPPLEMENT

2Revista de Biología Tropical, ISSN: 2215-2075 Vol. 72(S1): e59016, marzo 2024 (Publicado Mar. 01, 2024)

INTRODUCTION

Echinoids present a rich fossil record since

the Mississippian (Early Carboniferous) (Mon-

giardino-Koch & Thompson, 2021); this is due

to the susceptibility to fossilization of their

high-magnesium calcite endoskeleton (Kroh,

2020). Currently, the extant biodiversity of

this class includes 1 000 valid species around

the world, ranging from the shore to the deep

sea and from tropical to polar waters (Kroh &

Mooi, 2019). The great fossil record of echi-

noids added to their extant diversity allows us

to propose them as models to make paleoeco-

logical and paleoenvironmental interpretations

and, at simultaneously, can help us predict what

will happen with future communities.

According to the World Register of Marine

Species (WoRMS, 2023), the genus Agassizia

Valenciennes in Agassiz & Desor, 1847 includes

15 extinct and five extant species (Kroh &

Mooi, 2022), with a stratigraphic range between

the middle Eocene to Recent (Smith & Kroh,

2011), and a distribution in North America, the

Caribbean, in West Europe (Portugal, Spain,

and France), the Middle East, and the East

Pacific. The type species is Agassizia scrobicu-

lata Valenciennes in Agassiz & Desor, 1847.

Three species of genus Agassizia have

been recorded for Mexico (Fig. 1). The extinct

Agassizia regia Israelsky, 1924†, that has been

reported from the Eocene-Oligocene of Tux-

pam Beds, Tampico Region (Israelsky, 1924),

and the Miocene of Tulijá, Chiapas (Martínez-

Melo, 2019). Two extant species, Agassizia

excentrica A. Agassiz, 1869, occurred in Yuca-

tán (Gabino-García et al., 2021), with a depth

ranging between 43–900 m, and Agassizia scro-

biculata Valenciennes, 1846 in Agassiz & Desor,

1847, has been recorded on the Pacific coast of

RESUMEN

Análisis de la morfometría entre especies existentes y extintas:

Un estudio de caso del género Agassizia (Spatangoida: Echinoidea)

Introducción: El género Agassizia en México está representado tanto en el registro fósil por la especie Agassizia

regia† del Mioceno de Chiapas, como por las especies actuales Agassizia excentrica de la costa del Atlántico y

Agassizia scrobiculata de la costa del Pacífico. Las descripciones y diagnosis cualitativas dificultan reconocer los

limites morfológicos entre especies, especialmente en grupos con representantes fósiles y recientes, e incremen-

tando el nivel de complejidad al tener muestras de cantidad y calidad desiguales.

Objetivo: Proponemos el uso de métodos estadísticos poco explorados en la comparación de poblaciones paleon-

tológicas y biológicas. Esta metodología nos permitió resolver problemas de valores faltantes en un conjunto de

datos morfométricos para el género Agassizia.

Métodos: Usando muestras recolectadas para este fin, así como provenientes de colecciones científicas, explora-

mos una rutina de recuperación de datos faltantes MICE, y los análisis numéricos y gráficos PERMANOVA, PCA

y SIMPER para comparar parámetros morfométricos entre estas especies y reconocer caracteres de diagnóstico.

Además, comparamos cuidadosamente los caracteres morfológicos descritos previamente en la literatura taxonó-

mica y la descripción ambiental del hábitat actual de A. scrobiculata.

Resultados: Nuestros resultados muestran una diferencia morfológica en la longitud del ambulacrum II y la

longitud y anchura de las estructuras del periprocto y peristoma, siendo estas mayores en A. scrobiculata, con un

patrón consistente en ambas muestras poblacionales no descrito previamente. El hábitat actual de las muestras de

A. scrobiculata en la costa del Pacífico es un sistema costero poco profundo con sedimentos arenosos y temperatu-

ras tropicales. Bahía Chamela comparte varias similitudes con la fauna y las condiciones ambientales previamente

descritas en el Mioceno de Chiapas.

Conclusiones: Las comparaciones morfométricas cuantitativas pueden ser una herramienta poderosa y comple-

mentaria para determinar caracteres distintivos de diferenciación en especies del mismo género. Las revisiones

de morfología comparativa deben ser un ejercicio continuo para mantener actualizado el conocimiento taxo-

nómico sobre las especies existentes y extintas. Nuestro trabajo busca incentivar a la comunidad científica que

trabaja con poblaciones fósiles a explorar estos y otros métodos cuantitativos y multivariados para fortalecer sus

investigaciones.

Palabras clave: Mioceno, análisis multivariado, Chiapas, Colima, México.

Revista de Biología Tropical, ISSN: 2215-2075, Vol. 72(S1): e59016, marzo 2024 (Publicado Mar. 01, 2024)

Mexico, including the eastern coast of the Baja

California Peninsula and the Gulf of California,

with a depth range from the intertidal to 62 m

(Galván-Villa et al., 2018; Maluf, 1988).

The advantage of having large samples of

both fossil and extant echinoids is that we can

apply a population approach with multivariate

statistical methods (McNamara, 1989; Solís-

Marín et al., 2013) and explore new statistical

dimensions, such as size variability in a popula-

tion, changes in growth patterns associated with

age, and changes in the allometric relationships

for body structures (e. g. Caballero-Ochoa et

al., 2021; Ciampaglio & D’Orazio, 2007).

Qualitative diagnosis and descriptions

make it hard to distinguish morphological

boundaries between species, especially in

groups with fossils and recent representatives;

the dissimilar quality and quantity of the fossil

samples increase complexity when analyzing

and comparing morphology within a group.

This study aims to propose a practical and

effective multivariate statistics routine to solve

the problems derived from comparing poor

paleontological samples with recent samples

using two species of genus Agassizia from

Mexico as a model.

MATERIALS AND METHODS

Data collection:

Recent and fossil samples: We used fossil

specimens collected by Martínez-Melo (2019)

and housed in the Colección Nacional de

Paleontología, Instituto de Geología, Univer-

sidad Nacional Autónoma de México (IGeol,

UNAM), Mexico and recent specimens housed

in the LEMA-EQ, Echinoderms Collection,

Laboratorio de Ecología Molecular, Microbi-

ología y Taxonomía (LEMITAX), Departa-

mento de Ecología, Centro Universitario de

Ciencias Biológicas y Agropecuarias, Univer-

sidad de Guadalajara (CUCBA-UDG), Mexico.

For the fossils, we included 49 specimens

of A. regia† housed in IGeol, catalog numbers

IGM 11257 - IGM 11307, from the Tulijá

Formation at IGM-loc 3636, El Gato site, near

Palenque, northern Chiapas, Mexico (17°29’

N, 92°56’ W) (Fig. 2c). We used a total of 78

recent specimens of A. scrobiculata, housed in

Fig. 1. Distribution of the genus Agassizia Valenciennes in Agassiz & Desor, 1847 in Mexico.

4Revista de Biología Tropical, ISSN: 2215-2075 Vol. 72(S1): e59016, marzo 2024 (Publicado Mar. 01, 2024)

CUCBA-UDG; 10 specimens (LEMA EQ-583)

collected in San Andrés, Chamela Bay, Jalisco,

Mexico (19°31’32” N, 105°05’31” W) (Fig. 2a),

in December 2013, at 3 m depth; 68 speci-

mens collected in Punta Santiago, Manzanillo,

Colima, Mexico (19° 05’ 58” N, 104° 21’ 11”

W) (Fig. 2b), 12 of them collected in February

2016 (LEMA EQ-592), 23 in July 2017 (LEMA

EQ-601), and 33 in October 2021 (LEMA

EQ-047 and LEMA EQ-086), all specimens

were collected between 6 and 8 m depth.

Measurements: We followed the method

used by Martinez-Melo (2019) for measuring

recent (A. scrobiculata) and fossil (A. regia†)

specimens according to the data reported for A.

regia† (Table 5 in Martinez-Melo, 2019). Thir-

teen measurements per specimen were taken

(Fig. 3) using a manual caliper with a precision

of 0.05 mm.

Comparative analysis:

Recovery of missing measurements and dis-

card criteria for statistical evaluation: As with

other fossil samples, some of our A. regia†

specimens show structural damage in the test

that precludes us from taking whole body

measurements (Appendix 1). When working

with datasets that contain missing values, there

methods of treatment exist: 1) Discard any

samples or factors with missing values, even if

this represents a significant loss of information,

2) Explore statistical tools enable the handling

of missing values but assume a significant

reduction in the explanatory power of our

results, and 3) Use imputation techniques to

achieve a complete dataset of data, but being

aware of the potential bias associated with the

quality of the substituted values (Lin & Tsai,

2020; Stuart et al., 2009).

Fig. 2. Sampling sites localization. A) A. scrobiculata from San Andrés Island, Chamela Bay, Jalisco; B) A. scrobiculata from

Punta Santiago, Manzanillo, Colima; C) Agassizia regia† in the paleontological site s El Gato, Chiapas.

Revista de Biología Tropical, ISSN: 2215-2075, Vol. 72(S1): e59016, marzo 2024 (Publicado Mar. 01, 2024)

The Multivariate Imputation by Chained

Equations (MICE) is a statistical method widely

employed in medical research for treating com-

plex and incomplete datasets, yielding satisfac-

tory outcomes while maintaining original data’s

natural tendencies with a few signs of bias (Van

Buuren & Groothuis-Oudshoorn, 2011).

Due to A. regia† data set having 35 % miss-

ing data, we used the MICE routine to impute

the missing values. This was done to prevent

significant information loss that would result

from discarding incomplete samples (Acuña

& Rodríguez, 2004). We used the imputation

method by the predictive pairing of means

(pmm) with ten imputations and a scalar of ten

(maxit), following the criteria recommended by

Raghunathan et al. (2001). The data set’s quality

was tested graphically, using a xyplot to identify

outliers, and numerically, to ensure that the

mean difference between the observed and

imputed values for each morphometric factor

did not exceed two standard deviations (Stuart

et al., 2009).

Two samples of A. scrobiculata with miss-

ing data were discarded. This decision was

supported by the analysis of Acuña & Rodrí-

guez (2004), who discussed how imputing or

discarding values for missing data values <

5 % does not significantly affect the results.

Caballero-Ochoa et al. (2021) suggest that dif-

ferences in sample population sizes can lead to

errors in interpreting allometric comparisons.

To prevent bias, we excluded 32 samples of A.

scrobiculata with sizes smaller than the inferior

size range of A. regia† (TL < 15.6 mm). The

statistical analysis included a total of 93 speci-

mens, 49 of A. regia† and 44 of A. scrobiculata

(Appendix 1).

Descriptive morphometry and degree of dis-

similarity between species: For the quantitative

evaluation, we combined three multivariate

statistical methods. To prove morphological

Fig. 3. Measured parameters used in the morphometric analysis of Agassizia. A) Zoom to the ambulacrum region: IL, length

of ambulacrum I; IIL, length of ambulacrum II; IW, width of ambulacrum I; IIW, width of ambulacrum II; B) Test in oral

view: PsF, distance from the peristome to the anterior margin; PsL, length of the peristome; PsW, width of the peristome; TL,

length; TW, width; C) Test in posterior view: PpW, width of the periproct; PpH, height of the periproct, PpL, length of the

periproct; and TH, height.

6Revista de Biología Tropical, ISSN: 2215-2075 Vol. 72(S1): e59016, marzo 2024 (Publicado Mar. 01, 2024)

differences between both species, we used a per-

mutational multivariable analysis of variance

(PERMANOVA) with fixed effects, constructed

using the factor species (Sp) as follows: Y= μ +

Spi + εi. Additionally, we conducted a similar-

ity percentage analysis (SIMPER) to identify

the main morphometric factors contributing

to the dissimilarity between the species. Prin-

cipal Component Analysis (PCA) was used

to prove or discard the separation between

recent and fossil samples, and to identify the

most effective set of morphometric factors that

account for this differentiation. The statistical

software used for the PERMANOVA and SIM-

PER analysis was Primer-e® v.6, while the PCA

graph was generated using CANOCO v.4.5.

All analysis used a Euclidean distance matrix

with measurement data previously transformed

using the fourth root and 10 000 permutations

to demonstrate statistical significance (Clarke

& Gorley, 2005; Ter Braak & Smilauer, 2002;

Zar, 1999).

To visually compare the morphology of

the two species, we constructed a box-and-

whisker plot with the values for each mor-

phological factor. The box-and-whisker plot

shows the minimum, maximum, and mean

values with the standard deviation for each

morphological factor.

Systematics

Class Echinoidea Leske, 1778

Order Spatangoida L. Agassiz, 1840

Family Prenasteridae Lambert, 1905

Genus Agassizia Valenciennes, 1846

Type species— Agassizia scrobiculata

Valenciennes in Agassiz & Desor, 1847: 20.

Stratigraphic range— Middle Eocene to

Recent (Smith & Kroh, 2011).

Modern distribution in Mexico— On the

Pacific coast of northern Mexico, including

the eastern coast of the Baja California Penin-

sula and the Gulf of California (Martínez-Melo

et al., 2015).

Agassizia scrobiculata Valenciennes in

Agassiz & Desor, 1846-1847: 20.

Agassizia scrobiculata Valenciennes in

Agassiz & Desor, 1846-1847: 20. Agassizia sub-

rotunda Gray, 1851: 133. Agassizia ovulum

Lütken, 1864: 134.

Type specimens— Syntypes MNHN-

IE-2013-10543 and MNHN-IE-2013-10544.

Distribution— From Baja California

Mexico to Capón, Peru; including the Gulf of

California and the Galapagos Islands (Galván-

Villa et al., 2018). The bathymetric distribu-

tion ranges from the intertidal to 62 m depth

(Maluf, 1988).

Referred specimens— 78 specimens,

LEMA EQ-047, LEMA EQ-086, LEMA EQ-583,

LEMA EQ-592, LEMA EQ-601.

Locality— San Andrés Island, Chamela

Bay, Jalisco and Punta Santiago, Manzanillo,

Colima, Mexico (Fig. 2a & 2b).

Habitat— San Andrés is a small island

of 7.15 ha, located between the Cuitzmala

River and the San Nicolás River. It is part of

a coastal archipelago within the Chamela Bay

Marine Protected Area, Jalisco, Mexico (Comis-

ión Nacional de Áreas Naturales Protegidas

[CONANP], 2008). According to CONANP

(2008) and Ríos-Jara et al. (2013), Chamela

Bay is a coastal system with a mixed rocky

and sandy substrate, ranging from 10 to 25 m

in depth. The sea surface temperature (SST)

oscillates between 20 and 30 °C, and the salin-

ity ranges from 34 to 35 during cold-dry and

warm-rainy seasons, respectively. The average

rainfall is 748 mm. The ecosystem supports a

high biodiversity, including plankton, corals

of the genera Porites, Pavona, and Pocillopora,

over one hundred species of Chondrichthyes

and bony fishes, and diverse invertebrates of the

phyla Mollusca, Arthropoda, Cnidaria, Annel-

ida, Porifera, and Echinodermata. During the

sampling work conducted in December 2013,

the sea surface temperature (SST) showed a

value of 27°C.

Sotelo-Casas et al. (2019) reported an SST

range of 21.3 and 31.8 °C for Punta Santiago,

Manzanillo bays. The authors described the

locality as a coastal system with a mixed sandy

and rocky substrate, and a seasonal influx

of runoff sediments from Juluapan’s Lagoon.

Revista de Biología Tropical, ISSN: 2215-2075, Vol. 72(S1): e59016, marzo 2024 (Publicado Mar. 01, 2024)

During our sampling work in Punta Santia-

go, we recorded the following environmental

parameters: SST of 30.2 °C, dissolved oxygen

concentration of 24.7 %, salinity of 33 ppt, and

organic matter content in the sediments of 0.86

%. Additionally, granulometric characteriza-

tion revealed a predominance of medium sand

(Table 1).

Description (Tapia-Ramírez, 2012) —Test

slightly oval, posterior side truncate, anterior

side slightly wider than the posterior region.

Apical system ethmolytic, with four gonopores.

Anterior ambulacra long, reaching the ambi-

tus. Posterior ambulacra petaloid, short and

wide. The single anterior ambulacrum without

pores, slightly sunken and elongated, reaches

the frontal ambitus. Periproct on the posterior

side, oval, wider than long. Peristome reniform

with prominent labrum. Plastron wide, cov-

ered by small tubercles, wider on the posterior

region. Peripetal fasciole forming obtuse angles

between the ambulacra, except at the front

ambulacrum, where it joins the latero-anal

fasciole, which forms a “v” below the periproct.

Test with abundant tubercles, being more evi-

dent on the anterior region.

Agassizia regia Israelsky, 1924

Agassizia clevei Cotteau, 1875 pl. 7, Figs 1a, 1b.

Agassizia regia Israelsky, 1924, p. 142.

Type specimens— Holotype CAS-IG 363

from Eocene-Oligocene, Tuxpam Beds, Tam-

pico Region, Mexico.

Geographical and time record— Report-

ed from the Eocene-Oligocene, Tuxpam Beds,

Tampico Region, Mexico (Israelsky, 1924).

Referred specimens— 49 specimens, IGM

11257 through IGM 11307.

Locality and age—Specimens discussed

herein were collected from the Tulijá Formation

at IGM-loc 3636, El Gato site, near Palenque,

northern Chiapas, Mexico (Fig. 2c).

Habitat— The Tulijá Formation is a cal-

careous sequence of strata clays ranging from

30 to 150 cm in thickness. It is exposed along

the Tulijá River and extenders to Palenque. The

formation contains high abundance of inverte-

brate fossils, including foraminifera, ostracods,

gastropods, ostreid, bivalves, echinoderms, cor-

als, portunid crabs, tubes of polychaete worms,

and sponges, which are so numerous that they

form embedded coquinas. The fossil assem-

blage also includes vertebrate remains, such as

shark, ray, and teleostean fish teeth, fish scales,

pycnodonts, serranids, percomorphs, and other

fish bones, as well as sirenid bones. These

extensive fossil records suggest that during

the early Miocene, the Tulijá Formation sedi-

ments were deposited in a marine environment

near the shore, under shallow and high-energy

conditions that may have included transgres-

sive and regressive episodes along the inner

platform and/or coastal lagoons (Alvarado-

Ortega et al., 2018; Martínez-Ortiz et al., 2017;

Meneses-Rocha, 2001; Riquelme et al., 2012;

Velasquillo-García, 2011).

Table 1

Grain size distribution of sediment in Punta Santiago, Manzanillo, Colima.

Diameter (phi) Percentage (%) Size class

Coarse texture -2 4.86 Very coarse sand

-1 28.816 Coarse sand

0 40.411 Medium sand

1 17.511 Fine sand

2 7.422 Very fine sand

3 0.977 Very coarse silt

Fine texture 4 0.001 Very fine sand

5 0 Very coarse silt

6 0.001 Coarse silt

7 0 Medium silt

8 0.001 Fine silt

9 0 Very fine silt

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Description— Small (length 16-27 mm)

almost spherical test (width 13-23 mm and

height 13-20 mm), more rounded anteriorly

than posteriorly, slightly flat near the periproct.

Apex slightly posterior, at the apical system,

which has four genital pores. Anterior ambu-

lacrum (III) non-petaloid, in slight furrow,

with no visible pores. Ambulacra petaloid, II

and IV divergent at 120°, petals almost reach-

ing the ambitus; anterior series of pore pairs

atrophied, the posterior row with conspicu-

ous pairs of elongated pores. Anterior paired

petals depressed, posterior petals short, more

depressed than anterior pair, width about one-

third the length. Petals I and V 2/3 the length of

the anterior pair of petals, lacking interporifer-

ous zones. Periproct high on the posterior the

test, horizontally ovate. Peripetalous fasciole

unindented in the interporiferous area, extends

below the anterior petals; latero-anal fasciole

extends from below the periproct upward to

point of juncture with peripetalous fasciole,

then downward anteriorly to below ambitus in

anterior ambulacrum. Oral surface more swol-

len at the interambulacral 5. Plastron strongly

elevated, ornamented with closely spaced scaly

tubercles. Peristome reniform, extremely ante-

rior, at 17 % of the length, labiate posteriorly.

Size and morphological references for

the Agassizia genus: The average measure-

ments and the minimum and maximum range

of sizes were included in Appendix 2. Agassizia

scrobiculata had a smaller average size than A.

regia†. Thirty-three samples of A. scrobiculats

were smaller than the smallest specimen of

A. regia†. Fig. 4 showed a visual comparison

between fossil species A. regia† and recent spe-

cies A. scrobiculata.

Morphometric analysis on genus Agas-

sizia: The Multivariate Imputation by Chained

Equations (MICE) generated 209 imputed val-

ues for A. regia†. The xyplot does not indicate

the presence of outliers (Fig. 5), and only

4.8 % (n = 10) of the imputed values differed

Fig. 4. A morphological comparison between fossil species A. regia† (A: test in apical view, B: test in oral view) and recent

species A. scrobiculata (C: test in apical view, D: test in oral view).

Revista de Biología Tropical, ISSN: 2215-2075, Vol. 72(S1): e59016, marzo 2024 (Publicado Mar. 01, 2024)

Fig. 5. The xyplot shows the values of the morphometric measurements for A. regia†. The blue circles represent the original

values, and the pink circles represent the imputed data: TL, length; TW, width; TH, height; IL, length of ambulacrum I; IW,

width of ambulacrum I; IIL, length of ambulacrum II; IIW, width of ambulacrum II; PsW, width of the peristome; PsL, length

of the peristome; PsF, distance from the peristome to the anterior margin; PpW, width of the periproct; PpL, length of the

periproct; and PpH, height of the periproct.

Table 2

The average dissimilarity between morphometric factors

was computed by the SIMPER test for A. regia† and A.

scrobiculata.

Species Contribution % Cumulative contribution %

PsF 13.17 13.17

PsL 12.22 25.39

IIL 10.66 36.05

PpL 8.62 44.67

TL 7.73 52.40

from the mean of the observed values by more

than two standard deviations. Therefore, we

deemed the quality of the imputed data ade-

quate for analysis.

The PERMANOVA test revealed signifi-

cant differences between morphometric values

of A. regia† and A. scrobiculata (Peudo-F =

6.9196, P = 0.0003). The SIMPER test (cut-off

of 50 %) identified PsF, PsL, IIL, PpL, and TL as

the morphological values that most contributed

to the differences between species (Table 2).

The box-and-whisker plot shows that, on

average, the samples of the A. regia† species

samples were larger in size. Specifically, they

had higher values for TL, TW, TH, IL, IW, IIW,

PpW, and PpH (Fig. 6). Conversely, A. scrobicu-

lata had the larger sizes for IIL, PsW, PsL, PsF,

and PpL.

The Principal Component Analysis (PCA)

indicated a clear separation between the popu-

lations of A. regia† and A. scrobiculata (Fig. 7).

The maximum body size (TL, TH, TW) did

not consistently differentiate between the two

species. However, the measurements associated

with the length (PsL, PsF) and width (PsW)

of the peristome, and the length (PpL) of the

periproct, as well as the length of the ambula-

crum II (IIL) were significantly shorter in the

A. regia† samples.

It is evident that the morphometric charac-

ters of the peristome (PsL, PsF, and PsW), and

the length of the periproct (PpL) were larger

in A. scrobiculata samples (Fig. 6). Despite A.

scrobiculata having smaller specimens on aver-

age, the peristome and periproct of A. regia†

is proportionally larger. The morphological

difference is evident in the arrangement of the

10 Revista de Biología Tropical, ISSN: 2215-2075 Vol. 72(S1): e59016, marzo 2024 (Publicado Mar. 01, 2024)

samples in the PCA plot (Fig. 7), where the

samples with smaller peristome and periproct

(A. regia†) are distinct from the species with the

larger oral and anal structures (A. scrobiculata)

through a vertical gradient.

When comparing the length of ambulacra

I and II, it was observed that individuals of A.

regia† have a smaller ambulacrum I (IL of A.

regia† < IL of A. scrobiculata). Conversely, in

ambulacrum II the relationship is inverted (IIL

of A. regia† > IIL of A. scrobiculata; Fig. 6 and

Fig. 7). This morphological difference appears

to be related to a variation in the position of the

Fig. 7. Principal Component Analysis (PCA) plots of morphological factors for Agassizia; black squares represent the samples

of Agassizia regia†, and gray circles represent the samples of A. scrobiculata: TL, length; TW, width; TH, height; IL, length of

ambulacrum I; IW, width of ambulacrum I; IIL, length of ambulacrum II; IIW, width of ambulacrum II; PsW, width of the

peristome; PsL, length of the peristome; PsF, distance from the peristome to the anterior margin; PpW, width of the periproct;

PpL, length of the periproct; PpH, height of the periproct.

Fig. 6. Box-and-whisker plot for the morphological factors. The plot shows the mean, standard deviation, and outliers for

each factor. Dark gray represents the values of A. regia† and light gray values of A. scrobiculata: TL, length; TW, width; TH,

height; IL, length of ambulacrum I; IW, width of ambulacrum I; IIL, length of ambulacrum II; IIW, width of ambulacrum

II; PsW, width of the peristome; PsL, length of the peristome; PsF, distance from the peristome to the anterior margin; PpW,

width of the periproct; PpL, length of the periproct; and PpH, height of the periproct.

Revista de Biología Tropical, ISSN: 2215-2075, Vol. 72(S1): e59016, marzo 2024 (Publicado Mar. 01, 2024)

apical system in each species, with A. scrobicu-

lata having a more anterior position (Fig. 4).

DISCUSSION

The representation of irregular sea urchins

in the fossil record tends to be higher than that

of regular echinoids (Greenstein, 1993). This is

attributed mainly to the ecology developed by

both forms and taphonomic processes related

to their preservation (Greenstein, 1993; Kier,

1977; Mancosu & Nebelsick, 2019; Nebelsick,

1996; Smith, 1984). In general, irregular echi-

noids feed on organic matter deposited in sedi-

ments, so they remain primarily buried in soft

substrates (Nebelsick, 1996), while regular sea

urchins are mainly herbivorous organisms that

inhabit rocky substrates (Steneck, 2020). The

significant representation of irregular echinoids

in the fossil record makes it possible to have

population samples of some species, as is the

case of A. regia† in our study. Population data-

sets open the possibility of implementing new

quantitative comparisons using multivariate

statistical methods.

An obstacle to using multivariate statistics

on fossil data is the loss of anatomical struc-

tures during the fossilization process and the

consequent loss of measurements in the data

sets (Clarke & Gorley, 2005; Stuart et al., 2009;

Zar, 1999). The use of the multivariate statis-

tical method in the descriptive taxonomy of

echinoderms is not new. During the last two

decades, their use has increased since they are

helpful tools to solve taxonomic determina-

tions that classical and genetic methods can-

not resolve alone. For example, Coppard &

Campbell (2006) applied multivariate statistics

to explore morphological differences within the

genera Diadema and Echinothrix, and Deli et al.

(2019) used these tools to compare populations

of Arbacia lixula along the African Mediter-

ranean coast. Multivariate statistics have also

been used in morphological analyses with other

fossil groups (Lefebvre et al., 2006), and in

irregular echinoids (Stara et al., 2023), however

performing the MICE routine to recover miss-

ing values from damaged specimens is a novel

and a complementary alternative. In our study,

data recovery using the MICE routine allowed

us to work with multivariate statistical tests that

do not admit missing data, and avoided the loss

of information associated to discard of incom-

plete data series.

The PERMANOVA analysis confirmed the

morphometric differences between A. regia†

and A. scrobiculata. The box-and-whisker plot

(Fig. 6) showed that morphological factors

related to the total size of the test (TL, TH,

TW), as well as the width of ambulacra (IW,

IIW), the width (PpW), and the height (PpH)

of the periproct, and the length of ambula-

crum I (IL), being higher in A. regia†. These

differences show that despite a priori discard-

ing A. scrobiculata samples with sizes smaller

than the lower range of A. regia† (TL < 15.6

mm), on average A. scrobiculata specimens are

smaller. However, in the PCA plot, we show

that these differences between both species are

insufficient to recognize two groups through a

size gradient.

During the process of statistical analysis,

the smaller average size for A. scrobiculata was

evident. This is because more small samples

were collected in the field, in contrast with sam-

ples with major size in the fossil record of A.

regia†. Both species presented a similar range

of maximum size (Appendix 2). Further studies

would be necessary to explain the absence of

small-sized A. regia† in the fossil record.

According to the SIMPER analysis, the dif-

ferences between the length of the peristome

(PsF & PsL), the length of the ambulacrum II

(IIL), and the length of the periproct (PpL)

are those that contribute the most to explain-

ing the dissimilarity between species (Table 2).

The results of these three multivariate tools are

consistent, so we can conclude that the differ-

ences in the size of the periproct and peristome,

as well as in the length of the ambulacra and

the position of the apical system, can be used

as diagnostic criteria to distinguish these two

species within the genus. An extensive and

comparative review with population samples of

all species would be necessary to know if these

12 Revista de Biología Tropical, ISSN: 2215-2075 Vol. 72(S1): e59016, marzo 2024 (Publicado Mar. 01, 2024)

diagnostic characters can be extended to all

members of the genus Agassizia.

Previous descriptions for the genus Agassiz-

ia (Valenciennes in Agassiz & Desor, 1847), A.

regia† (Israelsky, 1924; Martínez-Melo, 2019),

and A. scrobiculata (Gray, 1851; Mortensen,

1951; Lütken, 1864; Tapia-Ramírez, 2012) show

how these morphometric differences had not

been identified as a descriptive character. This

omission seems to be due precisely to the fact

that traditional taxonomy does not always con-

template the quantitative comparison of the

specimens, nor are statistical methods explored

to evaluate the differences between the possible

diagnostic characters. By recognizing the mor-

phometric differences between these two spe-

cies from qualitative and multivariate analysis,

we tested the effectiveness and the relevance of

incorporating this type of technique in future

descriptive methodologies.

The qualitative descriptions of the species

in taxonomic reports are always necessary; nev-

ertheless, those could be non-resolutive when

identifying diagnostic characters for species

within a genus. Applying multivariate analysis

to morphometric data provides an objective

and complementary way to revise diagnostic

characters, supporting descriptive information

with numeric data. Proposing a routine to

impute missing data and perform multivariate

analysis offers several benefits. The absence of

data caused by poorly preserved fossil speci-

mens does not distort the natural patterns of

real data. Additionally, it allows for working

with populations instead of just individual

specimens and reinforces the recognition of

morphological patterns. Currently, taxonomists

and systematists have started to integrate novel

types of analysis to solve complex classification

problems (e.g., Dos Santos-Alitto et al., 2019;

Humara-Gil et al., 2022; Nethupul et al., 2022),

mainly including macro and micromorphol-

ogy and DNA sequences. As recovering DNA

information from fossil records is practically

impossible, analyzing qualitative and quantita-

tive morphological information can offer a new

data dimension for integrative taxonomy.

Ethical statement: the authors declare that

they all agree with this publication and made

significant contributions; that there is no con-

flict of interest of any kind; and that we fol-

lowed all pertinent ethical and legal procedures

and requirements. All financial sources are fully

and clearly stated in the acknowledgments sec-

tion. A signed document has been filed in the

journal archives.

See supplementary material

a20v72s1-MS1 • a20v72s1-MS2

ACKNOWLEDGEMENTS

This work is supported by Proyecto INAH

“Estudio arqueológico y paleontológico de

los fósiles marinos que proceden del sitio de

Palenque, Chiapas”; UNAM DGAPA-PAPIIT

Project IN 207314 and IN209017 “Vertebra-

dos Marinos del Mesozoico and Cenozoico de

México”; Project P3E 2021, Universidad de Gua-

dalajara. R.C.S.C. thanks the National Council

of Humanities, Science and Technologies for

the postdoctoral fellowship CONAHCYT I.D.

291281. We thank Jesus Alvarado Ortega, Insti-

tuto de Geología, UNAM, for supporting this

project throughout. Lorena Altamirano Curiel,

Regional Center for Fisheries Research, Man-

zanillo (CRIP-INAPESCA) for performing the

texture analysis of sediments. Jared Alvizo, Ana

Rodríguez, Diego Araiza, and Paula Ortega for

their support during the underwater collec-

tions. To Mariana Figueroa for taking pictures

of A. scrobiculata. We thank to the editors and

anonymous reviewers for their helpful com-

ments on earlier versions of the manuscript.

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