Habitat and density-dependent growth of the sea urchin

Journal of Sea Research 76 (2013) 50–60
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Journal of Sea Research
journal homepage: www.elsevier.com/locate/seares
Habitat and density-dependent growth of the sea urchin Paracentrotus lividus in
Galicia (NW Spain)
Rosana Ouréns a,⁎, Luis Flores b, Luis Fernández a, Juan Freire a, 1
a
b
Grupo de Recursos Marinos y Pesquerías, Facultad de Ciencias, Universidad de A Coruña, Rúa da Fraga 10, 15008, A Coruña, Spain
Investigación de Recursos Bioacuáticos y su Ambiente, Instituto Nacional de Pesca, Letamendí 102 y La Ría, P.O. Box 09-01-15131, Guayaquil, Ecuador
a r t i c l e
i n f o
Article history:
Received 12 July 2012
Received in revised form 18 October 2012
Accepted 28 October 2012
Available online 15 November 2012
Keywords:
Growth Rings
Tanaka Function
Paracentrotus lividus
Echinoidea
Small-Scale Variability
NE Atlantic
a b s t r a c t
We studied the small-scale spatial variability in the growth of Paracentrotus lividus in two populations in Galicia
(NW Spain) by reading growth rings. A tetracycline marking experiment was carried out to verify that the rings
form annually. The growth rings were read by two independent readers in order to estimate the uncertainty
involved in assigning the age. Of the six growth models evaluated (Tanaka, von Bertalanffy, Gompertz, Richards,
logistic and Jolicoeur) the Tanaka function obtained the best fit to the data. This function predicts unlimited
growth and a maximum growth rate of 15.00 (±0.97 SE) mm·year−1 at 3.09±0.10 years old, which progressively decreases at older ages. However, habitat characteristics lead to intrapopulation variations in this general
function. Recruitment seems to occur mainly in shallow waters (≤4 m) and when the sea urchins reach 50 mm
(approximately 4 years old) they migrate to deeper areas. Sea urchins larger than 50 mm that stayed in shallow
waters grew at a rate between 0.41 and 0.43 mm·year−1 less than the sea urchins that moved to depths of 8 and
12 m. The population density also influenced the growth, and individuals older than 4 years had higher growth
rates in high-density patches than in low-density areas. This could be due to the better environmental conditions
in aggregation areas, that is, better protection against waves and predators and/or more abundant food.
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
The great commercial interest in sea urchins has arisen over recent decades and it has led to very high extraction rates. Consequently, echinoid
stocks have decreased drastically worldwide and several cases of
overexploitation and collapse have been reported (Andrew et al., 2002;
Micael et al., 2009; Williams, 2002). This situation has made it necessary
to revise the fisheries management policies that govern the exploitation
of this resource and look for new management strategies that guarantee
the sustainability of these fisheries (Rogers-Bennett et al., 2003).
To do this it is necessary to have information on both the fishing
strategy and the basic biological processes that determine the population dynamics of the resource. Growth is one of these processes, and
can be used to obtain very relevant information for fisheries management, such as the age at which individuals become part of the exploited
or reproductive biomass, or indirect estimates of the longevity and
stock productivity (Haddon, 2011; Ziegler et al., 2007).
In addition, many sedentary invertebrates, including echinoids, have
a strong and persistent spatial structure, which should be taken into
account in fisheries assessment models and management strategies
(Booth, 2000). The variation in the distribution of the species occurs at
different spatial scales, and therefore it is necessary to identify the appro⁎ Corresponding author. Tel.: +34 981 167000x2204; fax: +34 981167065.
E-mail address: [email protected] (R. Ouréns).
1
Present address: Barrabés Next, C. Serrano 16 – 1, 28001 Madrid, Spain.
1385-1101/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.seares.2012.10.011
priate scale for observing, analysing and managing the stock (Orensanz
et al., 2005, 2006). Echinoid metapopulations are formed by populations
that are connected with each other by larval dispersion (at macroscale,
according to the hierarchy proposed by Orensanz and Jamieson, 1998).
Each local population covers an area in the order of various km2 in
which the sea urchins are abundant, and therefore exploiting them is
profitable. This situation generally leads to resource management
models being implemented at the mesoscale. In turn, sea urchins are distributed irregularly in each local population (microscale) so that in certain areas the individuals form patches of varying sizes (generally from
10s to 100s m) while in the rest of the available habitat the sea
urchins are scattered or even absent (Orensanz and Jamieson, 1998).
The aggregating behaviour of echinoids has been analysed in various
studies, and has occasionally been associated with a defense mechanism by which individuals are able to defend themselves against predators and waves (Pearse and Arch, 1969; Tuya et al., 2007; Vega-Suárez
and Romero-Kutzner, 2011). Food availability also seems to be a relevant factor in the formation of aggregations, and some studies associate
patches with feeding processes (Alvarado, 2008; Unger and Lott, 1994).
As well as these more or less permanent patches, during the spawning
period sea urchins frequently group together in order to increase
fertilisation success (Levitan et al., 1992; Unger and Lott, 1994).
This strong spatial heterogeneity in the distribution of the species
can give rise to spatial variations in the life history traits (Hereu et al.,
2004; Molinet et al., 2012; Tomas et al., 2004). Thus, the high population
densities in the aggregation areas can lead to competition for space and
R. Ouréns et al. / Journal of Sea Research 76 (2013) 50–60
food, and reduce the growth and reproduction rates (Grosjean et al.,
1996; Tomas et al., 2005). As an alternative hypothesis, the higher quality of the habitat in the patches makes it possible to maintain, or even
increase, the growth and reproduction rates despite the higher density
(possible Allee effect; see Berec et al., 2007; Kramer et al., 2009). Similarly, depth is the environmental variable that leads to the largest differences in the distribution of the species (Agatsuma et al., 2006; Lecchini
et al., 2002). Like the previous case, this variable can indirectly affect the
life history traits because it is linked to environmental factors that influence the fitness of the individuals, such as the availability and quality of
food, exposure to waves, temperature and light (Garrabou et al., 2002;
Tuya and Duarte, 2012).
The commercial sea urchin Paracentrotus lividus is distributed all along
the Mediterranean and northeast Atlantic coasts, from Ireland to Morocco,
including the Canary Islands and the Azores Islands (Boudouresque and
Verlaque, 2007). The studies on this species show that it has very diverse
growth rates (e.g. Sellem et al., 2000; Turon et al., 1995), and numerous
experiments in culture have analysed the factors that produce this variation (Cellario and Fenaux, 1990; Fernandez and Pergent, 1998; Grosjean
et al., 1996; Spirlet et al., 2001). However, there are very few field
works that study the effect of habitat on the growth of echinoids in general (Brady and Scheibling, 2006; Ebert, 2010; Russell, 2000) and P. lividus
in particular (Gago et al., 2003; Lustres, 2001; Turon et al., 1995).
As well as the spatial variability in growth, certain methodological
factors can also contribute to the differences observed between
studies. The various methodologies employed for estimating growth
(mark-recapture, cohorts monitoring, or reading growth rings), as well
as the numerous mathematical models that have been developed for describing this process (von Bertalanffy, Gompertz, Tanaka, Richards, etc.
See Ebert, 2007; Grosjean, 2001) have generated a wide range of possible
study methods, which can lead to variations in the results obtained.
Because the growth is related to the stock productivity (Haddon,
2011), knowledge of the growth dynamics is a necessary prerequisite
for an effective management of this resource. The objective of this
study was to analyse the spatial variability in the somatic growth of
P. lividus in two populations in Galicia (NW Spain), based on individuals
between 6 and 91 mm in diameter. Although sizes close to 90 mm
have also been recorded in other Atlantic regions (Allain, 1978;
González-Irusta, 2009), their growth has never been fitted, and the current curves estimated for P. lividus were obtained with individuals less
than 75 mm in diameter (Turon et al., 1995). To fulfil the study objective, and once the method had been validated, the age of the individuals
was estimated by reading the growth rings that form in the genital
plates. We then identified the growth model that best fitted the data,
and analysed its variability within the population (at mesoscale),
evaluating the effect of depth and population density (and/or quality
of the associated habitat) on growth.
2. Methodology
2.1. Study area and sampling strategy
The sea urchins employed in the study were collected in Lira (NW
Spain, 42° 47.8′ N, 9° 8.94′ W) during 2008. This exposed location has
large extensions of rocky substrate covered by algae, mainly in the
shallow areas and during spring and summer. This habitat is suitable
for the colonization of P. lividus, which is the target species of an intense fishery (43.6 t landed in 2011 2). The sea urchins were sampled
in the Ardeleiro and Os Forcados fishing grounds, which have similar
habitats. Therefore, we considered them as replicates.
The two fishing grounds were sampled at the depths of 4, 8 and
12 m. At each depth we differentiated between high-density areas,
where large numbers of individuals aggregate forming patches (in this
2
http://www.pescadegalicia.com/.
51
study: 86.57 individuals·m −2 ± 8.04 SE), and low-density areas,
(0.65± 0.03 individuals·m−2) where sea urchins are scattered and do
not form patches.
The size of the P. lividus specimens, expressed as the maximum diameter without spines, was measured with a vernier caliper (± 0.1 mm).
Our intention was to carry out stratified sampling by size, i.e. collect 20 individuals for each 10-mm size class at each depth; however, this was not
possible due to the bathymetric segregation in the population structure
(unpublished data). Thus, the mean test diameter at 4 m was 50.3±
0.2 mm, while at 8 and 12 m increased to 63.5±0.2 and 67.3±
0.1 mm, respectively. The study was performed with a total of 358 sea
urchins with sizes between 6.3 and 91.2 mm (Appendix A).
2.1.1. Age estimation
We estimated the age of the sea urchins by reading the growth
rings that form in the genital plates. Due to the seasonal growth of
P. lividus, the trabecules that form the ossicles are deposited at different densities depending on the growth rate (Pearse and Pearse,
1975). Visually this process generates a series of rings formed by a
translucent band and an opaque band, corresponding to slow and
fast growth periods respectively. Although the rings are visible in different skeletal structures (interambulacral plates or rotulae from the
Aristotle's lantern), we chose the genital plates as they form at the
beginning of ontogeny, and therefore contain all the rings that are
deposited after metamorphosis (nucleus of the plate).
Following the methodology described by Moore (1935) and modified by Flores (2009), the plates were carefully hand-polished with
water-sandpaper of 600–1000 grits, depending on the thickness of
the plate. First the interior face was polished in order to facilitate
homogenous polishing of the external face, where the readings
were performed. This is an important process because being able to
see the rings clearly depends greatly on the polishing.
In order to see the rings more clearly the plates are usually immersed
in xylene when they are read. We replaced this carcinogenic compound
with body oil, as it has the same effect. The plates were examined under a
binocular microscope with cold light from an epiluminator.
The main reader of the samples (RO, Rosana Ouréns) did not have
experience at the start of the study in age estimation. Therefore, the
learning process began with preliminary readings (n ≈ 20) under
the guidance of an experienced reader (LF, Luis Flores). The two
readers then read the genital plates of the study independently (LF1
and RO1 readings) and the results were pooled later. This stage was
considered as part of the training phase of RO, and so the two readers
revised together the plates in which there were differences between
the two readings. After discussing the number of rings observed, the
new reading by RO was recorded (reading called RO2). Therefore,
the differences observed between RO1 and RO2 are due to the learning process, while the RO2 and LF1 readings can be used to estimate
the uncertainty of the readings. We consider that RO2 is independent
of LF1 given that when the genital plates were read a second time the
readers did not know the number of rings counted before.
We constructed a similarities matrix between the readings RO1–RO2
and RO2–LF1, and then examined the asymmetry of these matrices
using the Bowker's symmetry test (Hoenig et al., 1995). That is, we determined whether there were significant differences between the two sides
of the diagonal, which would indicate systematic differences between
readings. In addition, the presence of bias was also examined based on
the graphs given in Campana et al. (1995) and Muir et al. (2008).
To determine the accuracy of the readings we estimated the
average percentage error (APE) and the coefficient of variation (CV)
between the RO2 and LF1 independent readings according to the
following equations (Campana, 2001):
R X −X ij
j
1X
APEj ¼ 100% Xj
R i¼1
52
R. Ouréns et al. / Journal of Sea Research 76 (2013) 50–60
where Xij is the ith reading of the jth individual, Xj is the average age
estimated for the jth individual, and R is the number of times that
each plate was read. The APEj is the percentage error for the jth individual, and by determining the average of all the individuals we obtain the APE.
CVj ¼ 100% vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u
u R X −X 2
uX ij
j
t
R−1
i¼1
Xj
Similarly, the CVj is the accuracy with which the age of the jth individual was determined and CV is the average of the individual coefficient of variation.
2.2. Periodicity of growth ring formation
To be able to determine the age of individuals based on growth rings
it is necessary to know the periodicity with which they form. One of the
methods that is usually applied consists in injecting tetracycline hydrochloride into the body cavity of the individual (Gage, 1992). This antibiotic adheres to the areas of the endoskeleton where there is calcification,
and produces fluorescence under UV light. Therefore, the position of the
compound represents the size of the skeletal structure when it was
marked. If the sea urchin growth rings form annually, as established in
the literature (Sellem et al., 2000; Turon et al., 1995), it would be
expected that a complete ring would form between the position of the
antibiotic and the edge of the genital plate 1 year after the individual
had been marked.
To test this hypothesis we carried out an experiment in culture. On
10/09/2010, we collected 50 sea urchins from different size classes (5
individuals of 11–20 mm, and 9 individuals for the sizes 21–30,
31–40, 41–50, 51–60 and 61–70 mm) in the intertidal area of A Coruña
(43° 21.82′ N, 8° 20.77′ W) and transported them cold to an aquarium
in the same location. In order to reproduce the natural conditions of
the external environment as much as possible, the sea urchins were
kept in a tank in an open circuit and were fed ad libitum with algae,
mainly Laminaria spp. The photoperiod and temperature followed
their natural cycle, and the latter ranged between 13.1 and 19.0 °C
during the study period.
After a 6-day acclimation period, we injected a solution of 1% tetracycline hydrochloride (Sigma Aldrich Company) in filtered sea water
into the body cavity of the sea urchins through the peristomial membrane, at a dose of 0.1 ml per 10 g of sea urchin wet weight.
After 1 year in these conditions, we dissected the sea urchins and
processed the genital plates as described above. This time the readings
were carried out with an epifluorescence microscope, and the tetracycline showed up as a yellow fluorescent band under a DAPI filter (EX:
330–380 nm, DM: 400 nm).
2.3. Estimating growth
We selected the growth curve that best represented the relationship
between size and age estimated by RO2 for the entire population. We
then studied the effect of depth, density type and sampling site on the
estimated growth curve. All the statistical analyses were carried out
using the free software R (v2.14.1, R Development Core Team, 2012).
Many different growth models are applied to echinoids, and include
from asymptotic models (logistic model, von Bertalanffy, Gompertz,
Jolicoeur, Richards) to unlimited growth models (Tanaka) in which
the number of parameters can vary between 3 and 4. The functions
shown in Table 1 were fitted to the dataset using nonlinear least
squares, and the fit was assessed according to the Akaike information
criterion (AIC, Akaike, 1974) and the Bayesian information criterion
(BIC, Schwarz, 1978). The values resulting from the two criteria can
Table 1
Growth models fitted to the size–age data for P. lividus. L (t) represents the diameter of
the individual at time t. a, b, c and d are parameters of the models.
Model
Logistic
Gompertz
Von
Bertalanffy
Richards
Jolicoeur
Tanaka
Equation
Lðt Þ ¼
Source
a
Grosjean (2001)
1 þ e−b⋅ðt−cÞ
−bðt−cÞ
Lðt Þ ¼ a⋅e−e
Grosjean (2001)
L(t) = a ⋅ (1 − e−b⋅(t−c))
Pauly (1981)
−d
Lðt Þ ¼ a⋅ 1 þ 1d e−b⋅ðt−cÞ
a
Lðt Þ ¼
1 þ b⋅t −c
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
Lðt Þ ¼ p1ffiffia ⋅In2⋅a⋅ðt−bÞ þ 2⋅ a2 ⋅ðt−bÞ þ a⋅c þ d
Schnute (1981)
Jolicoeur (1985)
Tanaka (1982)
vary by hundreds in magnitude, and individual values are not of interest
as they cannot be interpreted. However, it is possible to estimate
weighted values that range between 0 and 1 and whose sum is 1. The
advantage of these values is that they can be interpreted as the probability that model i is the best model in the set for the data (Burnham
and Anderson, 2002, 2004):
wi ¼
expð−0:5 ðICi −IC min ÞÞ
R
X
expð−0:5 ðICi −IC min ÞÞ
i¼1
where IC is the value of AIC or BIC, depending on the criterion that is
being used, and ICmin is the lowest AIC (or BIC) of the R models under
consideration.
As mentioned above, the size of the sea urchin varies with depth, so
that in shallow areas there are very few large individuals, while at
8 and 12 m depth juveniles are rare. Therefore, it was not possible to
carry out a single analysis to evaluate the effect of the sampling site,
depth and density type on growth.
We estimated the parameters for the growth curve selected in the
previous phase with generalized nonlinear least squares (gnls function
in the nlme package of R, Pinheiro and Bates, 2000) for the area at 4 m
depth because the range of available sizes and number of observations
was highest in this area. Independent variables included in this analysis
were the type of distribution (patches or scattered) and the sampling
area. A correction for heteroscedasticity was applied by using a variance
structure that allowed a different spread per age (varIdent function in R).
We then selected the individuals with sizes between 50 and 80 mm,
which is the size range present at the three study depths. In this case, a
linear model represented the data better than the growth models in
Table 1, given that the size range is small and corresponds to a phase
in the life-cycle in which growth is approximately constant. As there
were hardly any juveniles at 8 and 12 m, we consider that the individuals at these depths could only come from recruitments in shallow
areas, and therefore the intercept of the line was constant (given that
they would have a common growth history). Using generalized least
squares (the gls function in the nlme package) we studied the effect of
the categorical variables sampling site, depth and type of distribution
on the slope of the growth equation. The heteroscedasticity was
corrected with a variance structure that allowed a bigger spread of the
residuals at lower ages (varFixed ~1/age, in R).
For each analysis we used a backward elimination approach to select
the variables that affected the fixed structured. The minimum adequate
model was chosen by comparing the AIC and BIC, and, when models
were nested, testing the improvement in the likelihood ratio using an
X2 test.
We used graphical methods (e.g. residual diagnostic plots, the
observed trends increased with the fitted trends plots) to assess the
appropriateness of the final fitted models (Appendix B).
R. Ouréns et al. / Journal of Sea Research 76 (2013) 50–60
53
(21.8% of the cases) were attributed to the learning process. According
to Bowker's symmetry test, these differences were consistent (p =
0.02), so that RO1 overestimated ages between 2 and 8 years in relation
to RO2 (Fig. 3A). However, the RO2 and LF1 readings were concordant in
84.7% of the specimens, and there was no significant bias between them
(p = 0.06, Fig. 3B). The confidence intervals were larger in the older sea
urchins, probably due that the identification of the complete sequence
of rings is more difficult in these cases.
Furthermore, the readings RO2 and LF1 were disparate for some of
the individuals smaller than 20 mm, resulting in high CV and APE coefficients (Table 2). However, both coefficients were low in all other cases,
and the mean values for the sample were acceptable (Campana, 2001).
3.2. Growth analysis
Fig. 1. Genital plate of a 35-mm sea urchin illuminated with UV light. The fluorescent
band marks the position of the tetracycline, and is located just before the last natural ring.
3. Results
3.1. Validation of the age estimation model
The injection of tetracycline was not completely effective because
the mark was only visible in 26 of the 50 sea urchins marked, which
had sizes between 23.3 and 53.8 mm. For this size range 92.3% (IC
95% = 73.4–98.7%) of the individuals showed a complete natural
ring after the fluorescent band produced by the tetracycline (Fig. 1).
However, the remaining 7.7% showed fluorescence at the edge of
the plate. This would indicate zero growth during the study period,
perhaps due to internal damage caused by the marking process.
The age estimation was viable in practically the entire sample, although viewing and identifying the rings was more difficult in highly
porous plates (Fig. 2). The differences observed between RO1 and RO2
Both the AIC and BIC indicate that the Tanaka model is the growth
function that best fits our data set (Table 3). Furthermore, the differences between this function and the other models examined were
considerable, as shown by the high weighted AIC and BIC values
(98.9 and 94.2% probability of being the most appropriate model of
those evaluated respectively). The logistic model and the Richards
model were the models with the next best fit. The two functions are
very similar given that parameter d of the Richards function is close
to 1. However, this last function was more highly penalized due to
the estimation of an additional parameter d. Finally, the models
with the worst fit were the von Bertalanffy and Jolicoeur models.
Both obtained a maximum size that is much larger than that observed
in nature (131.5 and 139.9 mm respectively), which seems to indicate unlimited growth for the organisms.
Unlike the other models studied, the Tanaka function does not have
an upper asymptote, and assumes that the individuals have unlimited
growth throughout their life. Initially, sea urchins show exponential
growth, followed by a period of rapid growth, and finally a long period
of slow growth.
The following is the biological significance of the equation parameters (Tanaka, 1988): parameter c is related to the maximum growth
rate, which is approximately c−1/2; b corresponds to the age of maximum growth; a is a measure of the change in the growth rate, so that
a high a value implies a high change rate. Parameter d is a constant
that comes from integrating the growth rate. This parameter is sensitive
to the initial and final slope of the curve, so that low d values indicate
slow growth in the initial and final phases. Based on the curve parameters, individuals reach their maximum growth rate at 3.1 years, which is
15.0 mm·year−1. From this moment the instantaneous growth rate
slows down, and an 8-year-old individual grows at a mean rate of
3.2 mm·year−1 (Fig. 4).
3.3. Depth and density effect on the growth
Fig. 2. Outer face of a genital plate of a specimen measuring 77 mm, illuminated with
incident light. Eight natural growth rings are shown with arrows.
The analysis carried out with the individuals located at 4 m depth
(size range: 6.3–77.8 mm) was simplified in relation to the full model.
The area of origin of the sea urchins did not significantly improve the
model (p = 0.31), and therefore this variable was not included in the
final analysis. The population density did not affect the maximum
growth rate (14.48± 1.16 mm·year−1) or the age at which this was
reached (3.04 ±0.11 years). However, it did produce variations in the
a and d parameters of the Tanaka model (Table 4). Accordingly, the differences in the growth rate between the two types of distributions
occur exclusively in the smallest and largest age classes. The individuals
located in low-density areas had higher initial sizes compared to the sea
urchins located in high-density areas. However, this trend was reversed
for individuals older than 4 years because they reached a larger size in
the high-density areas (Fig. 5).
The analysis carried out with specimens of 50–80 mm indicates that
the size reached by individuals located at 4 m depth is always smaller
than in deeper areas, as a consequence of a slower growth rate
54
R. Ouréns et al. / Journal of Sea Research 76 (2013) 50–60
A
B
1
0
RO2−LF1
RO2−RO1
0
1
−1
−2
−1
−2
24
46
40
57
44
42
35
17
14
6
29
1
0 1 2 3 4 5 6 7 8 9
0
50
1
31
2
RO1
56
3
45
4
40
5
33
6
22
7
11
8
9
9
LF1
Fig. 3. Graphs for detecting bias between the readings RO1–RO2 (A) and RO2–LF1 (B). The mean difference (and its 95% confidence interval) between the two readings is shown for
each age estimated by the reading shown on the x axis. Therefore, when the readings are the same the means are located in the “agreement area” (dashed horizontal line). The
ranges in grey connect the maximum and minimum values, and the numbers on the x axis indicate the sample size.
(Table 5). However, no differences were observed between individuals
located at 8 and 12 m (p=0.70). For this size range, the growth rate
was also higher in high population density areas (p=0.03), while the
sampling site had no effect, and was thus eliminated from the final
analysis.
4. Discussion
Reading growth rings is a widely used method for age estimation in
marine organisms, although in many cases this procedure is used without testing its validity previously (Beamish and MacFarlane, 1983). Assuming a temporal pattern in the rings deposition has occasionally led
Table 2
Precision coefficients between RO2 and LF1 readings for each size class (test diameter)
in P. lividus. CV: coefficient of variation, APE: average percentage error, n: number of
observations.
Size
APE
CV
n
b10 mm
10–19.9 mm
20–29.9 mm
30–39.9 mm
40–49.9 mm
50–59.9 mm
60–69.9 mm
70–79.9 mm
80–89.9 mm
90–99.9 mm
Mean
13.04
12.20
4.17
1.97
2.12
1.04
1.28
1.90
1.57
2.63
4.15
18.45
17.25
5.89
2.79
2.99
1.47
1.81
2.69
2.22
3.72
5.87
23
41
48
42
36
44
41
41
8
2
326
to underestimating the lifespan of species, and therefore overestimating
growth rates. These results have encouraged the development of
low-conservation fisheries policies that lead to the overexploitation of
stocks (see examples in Cailliet and Andrews, 2008; Campana, 2001).
In this study we verified that growth rings in P. lividus form annually,
using a sample of 24 individuals with sizes between 23 and 54 mm.
Although the size range is small, it includes both juveniles and adults,
according to the size at sexual maturity estimated in the study
area (50% mature with 27.9 mm and 95% mature with 40.5 mm,
unpublished data). This result is very important because growth often
decreases as the sea urchin reaches sexual maturity, which can modify
the temporal pattern in the formation of growth rings (Beamish and
Chilton, 1982; Campana, 2001).
Previous studies have used reading growth rings as a method for estimating the age of P. lividus, but only two of these validated the periodicity of the ring formation. However, neither of these cases validated the
method for all size classes, and whereas Sellem et al. (2000) employed
individuals younger than 3 years old, Turon et al. (1995) carried out an
analysis for all sea urchin size classes together. Given the slow growth of
the older individuals, it would be recommendable to carry out an additional study that corroborates the validity of this method for older sea
urchins (Beamish and MacFarlane, 1983).
Validating the periodicity of ring formation allows the age to be estimated more or less accurately; that is, the estimate is close to the
individual's real age. However, the subjectivity involved in interpreting
the rings is another source of error that affects the precision of the estimate, whether accurate or not (Campana, 2001; Campana et al., 1995).
By comparing different readings of the same sample it is possible to
identify biases and quantify the precision of the readings. This process
Table 3
Estimated parameters of the growth models in P. lividus and their standard error in brackets. The AIC and BIC values and the weighted values are shown.
Model
Tanaka
Logistic
Richards
Gompertz
Von Bertalanffy
Jolicoeur
Parameters
a
b
c
d
3.85·10−3 (6.90·10−4)
77.53 (1.32)
73.36 (4.38)
85.96 (2.29)
139.24 (13.95)
132.67 (15.68)
3.09 (0.10)
0.65 (0.03)
0.68 (0.20)
0.38 (0.02)
0.10 (0.02)
8.68 (0.84)
4.45·10−3 (5.75·10−4)
3.05 (0.08)
2.92 (0.29)
2.38 (0.09)
−0.35 (0.10)
1.20 (0.09)
116.5 (7.04)
0.95 (0.61)
AIC
AICweights
BIC
BICweights
2409.20
2418.31
2420.28
2427.40
2472.20
2490.43
9.86·10−1
1.04·10−2
3.87·10−3
1.10·10−4
2.06·10−14
2.27·10−18
2428.76
2433.95
2439.84
2443.04
2487.85
2506.07
9.27·10−1
6.90·10−2
3.64·10−3
7.32·10−4
1.37·10−13
1.51·10−17
R. Ouréns et al. / Journal of Sea Research 76 (2013) 50–60
High density
Low density
12
70
10
60
8
50
6
40
4
30
Diameter (mm)
80
Diameter (mm)
Growth rate (mm · year−1)
80
90
Growth rate
Diameter
14
55
60
40
20
20
2
10
0
0
0
2
4
6
8
10
+0
1
2
Age (years)
provides information on the repeatability and consistency of the
interpretations.
In our case, the bias that was observed between the readings RO1 and
RO2 was attributed to the process of learning to age the sea urchins, and
therefore the readings RO1 were not used to estimate the final age. This
argument is supported by the fact that the readings RO2 and LF1 were
similar and did not show any bias. In addition, the precision coefficients
estimated for these two last readings were very similar to those found by
Flores et al. (2010) and Schuhbauer et al. (2010) for Loxechinus albus, the
only other studies on echinoids that estimated the uncertainty associated
with their interpretations.
There is no a priori criterion for determining whether a level of uncertainty is acceptable, since the accuracy depends on various factors, such
as the species and the nature of the structure as well as the reader's experience. However, Campana (2001) proposed a CV of 5% as a reference
point, and in this study we only exceeded this value in individuals under
30 mm. These results agree with those obtained by Flores et al. (2010),
who recorded lower uncertainty in ageing the smallest individuals.
Likewise, it was difficult to identify the complete sequence of rings in
the older sea urchins, which might lead to an underestimation of the age.
Nevertheless, the accuracy and precision of the readings suggest that
these potential errors are acceptable, and the consistency between the
size–age relationship obtained in this study and those described previously for this species supports this statement (Appendix C).
In most cases, P. lividus measures approximately 50 mm at 6 years of
age (Crapp and Willis, 1975; Gago et al., 2003; Haya de la Sierra, 1990;
Tomšić et al., 2010), although in some regions this size is never reached
by most of the individuals (Gago et al., 2003; Turon et al., 1995). The population in our study grows at a similar rate to other areas in the first years
of life (2–3 years); however, the individuals of intermediate ages
showed high growth rates, and reached 50 mm at approximately
4 years of age. Only Allain (1978), in a subtidal population in Brittany,
France, obtained similar growth rates, or even higher, to those in this
study. The high growth rate of both populations led to maximum sizes
Table 4
Parameters of the Tanaka growth function (a–d) and their standard errors (SE) estimated with generalized nonlinear least squares. The analysis was carried out with
P. lividus located at 4 m depth. The population density only influenced the parameters
a and d of the model.
Low density
b
c
d
Low density
4
5
6
7
8
Age (years)
Fig. 4. The Tanaka growth curve estimated for the study population, and the relationship between the instantaneous growth rate and the age of P. lividus.
a
3
Value
SE
t-value
p-value
0.003
0.004
3.040
0.005
128.587
−35.125
0.001
0.001
0.115
0.001
8.797
6.475
5.133
3.898
26.525
6.247
14.617
−5.425
b0.001
b0.001
b0.001
b0.001
b0.001
b0.001
Fig. 5. Growth curves estimated for the areas of high and low sea-urchin density at a
depth of 4 m. The grey circles represent the size–age relationship observed at a low
density, and the white circles correspond to a high density of P. lividus.
of 90 mm, while other populations did not exceed 60 or 70 mm. This
spatial variability observed in the growth of P. lividus evidences that
management measures should be site specific in accordance with the
life history parameters shown by the species in the area.
The oldest individuals identified in this work were 10 years old, similarly to those found by Turon et al. (1995) in NE Spain (10–11 years
old). The maximum age estimated with growth rings in P. lividus in
other studies (carried out in various areas, such as France, Ireland, Portugal and Tunisia) was from 7 to 8 years old (Allain, 1978; Crapp and
Willis, 1975; Gago et al., 2003; Sellem et al., 2000), and only Tomšić et
al. (2010) reported 15-year-old individuals, using the age estimation
method proposed by Pauly (1983).
There are many different functions for modelling growth, but the
von Bertalanffy model is the most commonly used in fisheries because
it describes the growth pattern of many species satisfactorily. Using
the von Bertalanffy equation it is possible to easily obtain other biological parameters of the population, such as the mortality or recruitment rates. In addition, specialized software has been developed for
fisheries assessments that estimates the parameters of this growth
curve directly by introducing the size frequency distribution of the
population (e.g. FISAT II, MULTIFAN CL). All this has led to the widespread use of the von Bertalanffy equation, which in many cases is
applied without previously verifying whether it is appropriate for the
study population (e.g. Allain, 1978; Gage, 1992; Tomšić et al., 2010).
The objective comparison of the models evaluated in this study
shows that the Tanaka model best fits our data. Although this model
has never been used (or evaluated) in P. lividus, it has been used for
other echinoids, such as Anthocidaris crassispina (Lau et al., 2011),
Strongylocentrotus franciscanus (Ebert and Russell, 1993; Shelton et
al., 2006; Zhang et al., 2008), and Strongylocentrotus droebachiensis
(Russell, 2000; Russell et al., 1998).
The model predicts an increase in the growth rate until 3.1 years,
and then a steady decrease towards older ages, so that 10-year-old
Table 5
Generalized linear least squares between the diameter and the age of the sea urchins
with sizes between 50 and 80 mm. The effects of density and depth on the slope are
also shown.
Intercept
Slope
Low density
8m
12 m
Value
SE
t-value
p-value
41.692
3.901
−0.305
0.433
0.405
2.045
0.367
0.135
0.167
0.166
20.387
10.623
−2.265
2.595
2.447
b0.001
b0.001
0.025
0.010
0.015
56
R. Ouréns et al. / Journal of Sea Research 76 (2013) 50–60
sea urchins do not exceed a growth rate of 2.3 mm·year −1. The inflexion point in the curve coincides approximately with the size of
sexual maturity of the species in the study area (unpublished data),
which reflects the great energetic investment into reproduction
made by adult individuals at the expense of somatic growth.
However, this general growth function can be affected by the environmental and demographic conditions to which the sea urchins are
subjected. Thus, individuals older than 4 years located in patches
reach larger sizes than sea urchins located in scattered distributions.
The advantages of living in patches, such as being protected from predators and waves (Pearse and Arch, 1969; Tuya et al., 2007; Vega-Suárez
and Romero-Kutzner, 2011), and being located in areas of high food
availability (Alvarado, 2008; Unger and Lott, 1994), generate an ideal
micro-habitat for the development of the species. Therefore, these individuals have a better physiological state than the sea urchins living in
scattered distributions. This hypothesis would also explain the larger
gonad sizes of P. lividus in high population density areas (unpublished
data).
In other echinoid species a negative effect of population density on
somatic growth has been detected as a response to competition between
individuals for space and food (Lau et al., 2011; Levitan, 1988). However,
these studies are not comparable to ours because they assume that the
environmental conditions are similar in areas of high- and low-density
and the carrying capacity is the same in the two habitats. Thus, Lau et
al. (2011) estimated the density without differentiating between the
two types of sea urchin distributions, and therefore the density is a
mean of the area, that does not necessarily reflect the real density in
which the individuals live. Likewise, Levitan (1988) carried out an
experiment in a controlled environment to study the growth of sea urchins in three size classes (15–20, 30–35, 45–50 mm in diameter) and
in three different population densities (12, 24, 48 individuals·m −2)
while keeping the rest of the environmental conditions constant.
Levitan (1988) therefore analysed the specific effect of the density on
growth without taking into account the particular environmental
characteristics generated by the sea urchin patches. Moreover, the experiment lasted for 2 months, and the growth of 50-mm individuals in this
time period can be less than the errors involved in measuring them.
The environmental variables associated with depth are responsible
for the increase in the growth rate in deeper areas. Although there is
often less food available in these areas (Keats et al., 1984; Tuya and
Duarte, 2012), growth can be favoured by the calmer hydrodynamic
conditions, which do not require high energy expenditure for
maintaining and repairing the test (Ebert, 1982). In addition, we
observed that the individuals located at 4 m depth developed larger
gonads than those in the deeper areas (unpublished data), which contributes to reducing the energy available for somatic growth.
Our results are similar to those obtained by Turon et al. (1995), who
detected higher growth in habitats characterised by abundant food and
low wave exposure. The energy invested in reproduction also followed
the reverse pattern in this case, and gonad production was higher in a
changing habitat subjected to strong wave action. Larsson (1968) and
Nichols (1982) also observed a direct relationship between depth and
the diameter of Echinus esculentus, while Brady and Scheibling (2006)
reported an inverse relationship between these two variables for S.
droebachiensis. It should be mentioned, however, that the bathymetric
range considered in this last study was different to ours, and their
shallowest sampling site coincided with our deepest areas (8–10 m).
The spatial variability that shows the growth of P. lividus on the
fishing grounds should be taken into account in the management of
the fishery. In view of the results, P. lividus does not reach legal commercial size in Galicia (55 mm diameter) up to 4 or 5 years old. This
age coincides with that estimated by Lustres (2001) for subtidal
populations of Galicia and is below the age of commercialization for
intertidal populations (Lustres, 2001). In addition, the highest concentration of juveniles is located in shallow waters, and the protection of these nursery habitats may be a useful regulation.
Acknowledgements
This work was funded by the Ministerio Español de Educación y
Ciencia and by the European Regional Development Fund (ERDF). The
authors are grateful for the collaboration with the institutes Aquarium
Finisterrae de A Coruña, who kept the sea urchins involved in the
age-validation experiment in their installations for 1 year; the
Departamento de Biología Celular of the Universidad de A Coruña, for
the use of their epifluorescence microscope; and the Instituto Nacional
de Pesca in Guayaquil (Ecuador), who provided an area for carrying out
growth ring readings. We also appreciate the willingness shown by the
fishermen who collected the samples in Lira and Porto do Son, and the
cooperation of the other members of the Universidad de A Coruña research group in processing the samples. Rosana Ouréns would personally like to thank the Consellería de Economía e Industria of the Xunta
de Galicia for their contribution in funding the research stay in Ecuador,
and the Baños family for their hospitality during this stay.
Appendix A. Number of P. lividus specimens that had their age
determined, by size class (test diameter), depth and type of
distribution (HD: high density, LD: low density)
4m
Size
b10 mm
10–19.9 mm
20–29.9 mm
30–39.9 mm
40–49.9 mm
50–59.9 mm
60–69.9 mm
70–79.9 mm
80–89.9 mm
90–99.9 mm
Total
8m
HD
12 m
HD
LD
LD
18
23
21
22
14
16
7
8
2
16
22
13
11
13
16
2
2
13
16
6
13
8
2
129
95
34
31
1
2
HD
LD
1
2
2
1
14
12
2
1
31
2
11
13
9
1
38
Appendix B. Graphic assessment of the adequacy of the final fitted
models (Figs. B1–B9)
Model 1. Nonlinear least squares model between the diameter and
the age of the Paracentrotus lividus for the entire population.
Fig. B1. Raw residuals vs. fitted values plot.
R. Ouréns et al. / Journal of Sea Research 76 (2013) 50–60
57
0
-10
-20
Sample Quantiles
10
Quantiles of standard normal
3
2
1
0
-1
-2
-3
-3
-2
-1
0
1
2
3
-2
Theoretical Quantiles
-1
0
Fig. B2. Residuals Q–Q plot with the Q–Q line.
2
2
1
0
1
0
-1
-1
-2
80
-2
100
Residuals
120
2
Fig. B5. Residuals normal Q–Q plot with the Q–Q line.
60
High
Low
ardeleiro
Density
os forcados
Location
-20
-10
0
10
20
1
0
-1
-2
0
20
Residuals
2
40
Frequency
1
Standardized residuals
Raw residuals
0
2
4
6
8
Age
Fig. B3. Histogram of raw residuals.
Fig. B6. Standardized residuals versus the fitted values of the variables.
Model 3. Generalized linear least squares model between the diameter and the age of the sea urchins with sizes between 50 and 80 mm.
0
-1
0
-2
-1
-2
Residuals
1
Residuals
1
2
2
Model 2. Generalized nonlinear least squares model between the
diameter and the age of the sea urchins. The analysis was carried
out with Paracentrotus lividus located at 4 m depth.
10
20
30
40
50
60
70
Fitted values
Fig. B4. Standardized residuals vs. fitted values plot.
55
60
65
70
Fitted values
Fig. B7. Standardized residuals vs. fitted values plot.
75
R. Ouréns et al. / Journal of Sea Research 76 (2013) 50–60
1
0
-2
-1
0
-2
0
1
2
1
-1
2
Residuals
-1
High
Low
4
8
Density
2
-2
12
Depth
2
Quantiles of standard normal
3
2
58
1
-2
-2
Fig. B8. Residuals normal Q–Q plot with the Q–Q line.
0
2
-1
1
1
0
0
-1
Standardized residuals
-1
-2
Residuals
-3
ardeleiro
os forcados
3
4
5
Location
6
7
8
Age
Fig. B9. Standardized residuals versus the fitted values of the variables.
Appendix C. Field studies of Paracentrotus lividus growth. The study region, size range of the sea urchins analysed, the growth model
fitted and the maximum age observed are shown. The mean diameter (mm) of the sea urchins for each age (1–11 years) predicted by
the growth model is also indicated. When the growth was not mathematically modelled, the size–age relationship obtained from the
raw data is indicated
Reference
Region
Size class
Growth model
Sellem et al., 2000
González-Irusta, 2009
Fenaux et al., 1987
Allain, 1978
Allain, 1978
Gago et al., 2003
Gago et al., 2003
Crapp and Willis, 1975
Crapp and Willis, 1975
Crapp and Willis, 1975
Turon et al., 1995
Turon et al., 1995
Haya de la Sierra, 1990
Lustres, 2001
Lustres, 2001
Azzolina, 1988
Tomšić et al., 2010
This study
Tunisia
N Spain
S France
N France
N France
Portugal
Portugal
Ireland
Ireland
Ireland
NE Spain
NE Spain
N Spain
NW Spain
NW Spain
S France
Croatia
NW Spain
23–62
2–52
5–58
55–92
8–62
40–65
30–50
5–53
7–46
7–56
8–75
10–52
5–55
42–58
49–66
11–57
10–65
6–91
Von Bertalanffy
Seasonal von Bertalanffy
Logistic
Von Bertalanffy
Gompertz
Gompertz
Logistic
Von Bertalanffy
Von Bertalanffy
Tanaka
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