Biometric Relationships for the Bivalve Mussel, Brachidontes pharaonis Populations from the North-Western Coast of Suez Gulf, Egypt

Egyptian Academic Journal of Biological Sciences is the official English language journal of the Egyptian Society of Biological Sciences, Department of Entomology, Faculty of Sciences Ain Shams University. The Journal publishes original research papers and reviews from any zoological discipline or from directly allied fields in ecology, behavioral biology, physiology, biochemistry, www.eajbs.eg.net Provided for non-commercial research and education use.  Not for reproduction, distribution or commercial use.

rocky shores when wave exposure and sedimentation conditions are optimal (Safriel et al., 1980).
This species has high fecundity, early maturity, with planktonic larvae, and its tolerance of high salinity and high temperature enable it to occupy diverse habitats across a wide geographic range.It has been reported in high-salinity lagoons, on open coasts, and in polluted waters (Radwan (2014).
It was widely reported that the geographical range of Brachidontes pharaonis includes the western Pacific Ocean, the Indian Ocean, the Red Sea (Taylor 1971;Sasekumar 1974; Barash and Danin 1986;Morton 1988), and had migrated to the Mediterranean Sea after opening Suez Canal (Sara et al., 2000(Sara et al., , 2008;;Zenetos, et al., 2005;Radwan, 2014), but the occurrence of this species in some areas is controversial (Sara et al., 2008).According to Barash and Danin (1986), Brachidontes pharaonis occurs along eastern African coasts, from the Red Sea to southern Africa, in the Indian Ocean except for the Persian subregion and Malaysia, and in the western Pacific Ocean.Sasekumar (1974) reported Brachidontes pharaonis, in Malaysia, while Arcidiacono and Di Geronimo (1976) supported the occurrence of Brachidontes pharaonis, along the western African coasts.It was reported from the Red Sea including Gulfs of Suez and Aqaba by several authors particularly Sharabati (1984), Vine (1986), Head (1987), Mastaller (1987), Mohamed (1992), Rusmore-Villaume, (2008), and Radwan (2014).
Scattered studies on distributions, ecology, interaction between adults and recruitments, age structure, as well as reproduction in addition to length weight relationships for Brachidontes pharaonis under its specific name or for its synonyms were treated in few articles in the Red Sea, Gulf of Suez as well as at Suez Canal and at eastern Mediterranean Egyptian coasts by Mohamed (1992Mohamed ( , 1997) ) and Radwan (2014).But no intensive studies were done on the biometric relationships for those populations of this species at the north-western coasts of the Gulf of Suez.Therefore, this study aims to investigate the biometric relationships of Brachidontes pharaonis collected from the intertidal and shallow subtidal zone at the north-western portion of Suez Gulf.
The habitats at these sites were characterized by rocky, sandy, sand-rock and coral reefs at Ain Sokhna, but has sandy bottom with scattered rock boulders at Adabia.The individuals of this species were collected by hand and detached from its substrates using forcipes of different sizes.Other two sites comprised Km 78 and 85   South Suez City were surveyed three times but no specimens B. pharaonis were collected.

Sampling and identification:
A total of 1103 individuals of Brachidontes pharaonis were collected from Adabia (532) and Ain Sokhna (571), at the northern-west portion of the Suez Gulf.These specimens were fixed in 10 % formalin solution and kept in plastic containers provided with information on date and site of collection and transferred for laboratory.
At the laboratory, each individual of the collected mussel was firstly cleaned from the extraneous bio-fouling organisms by scraping shell, then sorted, and examined morphologically and identified according to Sharabati (1984), andRusmore-Villaume (2008) to its specific level, depending on form, external sculpture and color of the shell.
Fig. 1: Study sites at the north-western coast of Suez Gulf.
Morphometric measurement had been recorded for each of the collected sample.Each mussel was measured with caliper veriner to the nearest 0.1mm and weighed to the nearest 0.01 mg using an electric balance (Centaurus Scale, JM, 1002).All terminology and measurements were recorded for each individual as illustrated in Fig.
( The relationship between shell lengths and total body weight was calculated and represent by the following equation: Y = a  bX (Hile, 1936, Bagenal andTesch, 1978).Where Y= body weight in mg, X = shell length in mm, a = constant and equal to the intercept of the straight line with Y axis; b = the coefficient of allometry.
The method of least squares was used and the coefficients "a" and "b" were calculated by plotting log Y (body weight) against log X (shell length) according to the following formula: Log Y = Log a  b log X (Hile, 1936 andBagenal &Tesch, 1978) Condition factor: The well-being or the relative condition factor "Kn'" was calculated for the collected individuals according the following formula: Kn = W/W` (Hile, 1936, Bagenal andTesch, 1978) Where W = observed weight, and W`= calculated weight from the lengthweight relationship.

Size-frequency distribution:
The size frequency distribution for the monthly sampled individuals of B. pharaonis was estimated.The individuals of this species were measured and allocated to 2.5 mm size classes.The frequency of each size class was determined and plotted histographically according to Hartnoll and Bryant (1990).

A-General morphology:
The collected specimens of B. pharaonis were varied from 2.8 to 37.3 mm in shell length, 1.6 to 22.3 mm in shell breadth, and from 1.2 to 15.9 mm in shell width.Shell is equivalent, in equilateral, attached to substrate by stout byssus.Sculptures are numerous, with fine radial bifurcating ribs, which become coarser posteriorly.Margin is crenulated.The hinge has dysodont teeth.Shell has dark brown-black color and internally tinged violet-black.

B-Length-weight relationship:
A total of 1103 individuals of Brachidontes pharaonis were used for studying the length-weight relationships at the two sites.For Adabia, 532 specimens were varied from 3.6-33.2mmin total length, and 0.01-3.25 g in body total weight.While at Ain Sokhna, 571 specimens were collected and varied from 2.8-37.3mm in total length and 0.01-4.75gm in total body weight.
The relationships between shell length (L) and total body wet weight (W) for the whole population is considered (Table 1 and Fig pharaonis at Adabia and 2.376 with an intercept with Y axis a= 0.037 for those collected from Ain Sokhna.However, the two relations have high correlation coefficient 'r' being 0.997 and 0.993 for the two stations, respectively.These results exhibit that "b" values being clearly lower than an isometric value (b=3.0).

Seasonal variation in length weight relationships:
The length-weight relationship was also treated for the two populations in Adabia and Ain Sokhna during different seasons.All seasons have negative allometric

C-Length breadth relationship:
The present results show that, shell breadth varied from 2.3 to 17.6 mm in Adabia and between 1.6 and 22.3 mm at Ain Sokhna .

D-Length-width relationship:
The individuals of B. pharaonis were varied from 1.2 to 15.9 mm in shell width at Ain Sokhna and between 1.4 and 13.4 mm at Adabia.The length-width relationships (Fig. 5) for the two populations were calculated and represented by the following equations: Log width = -0.025+ 0.746 Log L (r = 0.998) for Adabia Log width = -0.105+ 0.853 Log L (r = 0.994) for Ain Sokhna These relations are linear and show an allometric negative regression coefficients b= 0.746 and 0.853, with an intercept of Y-axis 'a'= -0.0.025 and 0.105, with correlation coefficients 'r'=0.998and 0.994 for Adabia and Ain Sokhna, respectively.6).The overall value for "kn" varied from 0.83 to 1.22 and from 0.67 to 1.41 with an average of 1.01±0.13and 1.02±0.22for the two populations, respectively.These values denote to good well-being or fitness.However, these values were not stable between different size classes; being very high, 1.22 and 1.24 for the two stations respectively, in smaller individuals at size class 2.5 mm but decreased in the following larger size classes between 5-12.5 mm, and increased again slightly in medium-sized and larger individuals (Table 1).The values of condition factor were very close in the two stations within all seasons (Table 2).

F -Size-frequency distribution:
The size frequency distribution for the populations of B. pharaonis is represented in Fig. (7).These data show that, population of this species is stable during the period of study.The population at both sites composes of at least five size classes.It was represented by early juveniles (from 2.5 to <5.0 mm), small size (between 5.0 and <12.50 mm), medium size (from 12.50 to <17.50 mm), larger individuals (from 17.50 to <25.0 mm), and oldest individuals (>25.0 mm).The monthly fluctuations were clearly observed.The onset of juveniles was detected in most months of the year (Figs. 8 & 9).With exception only February, April, June and September at Adabia, the recruitment of juveniles was reported in all months.This leads to increasing modes of size classes from three modes during these months to at least 4 or five modes in the next month.
At Ain Sokhna (Fig. 9), the recruitments disappeared during February, March, May, June, and October, in addition to disappearance of old and adult individuals in other months particularly September and November, which may be attributed to an increasing in sea level, compared with January and May at Adabia (Fig. 8).

DISCUSSION
In biological studies, the allometric relationships reflect growth patterns in several aquatic animals and may describe rates of wide range of metabolic processes and can use for description the relationships between increments in lengths associated with an increase in weight (Bagenal and Tesch, 1978).In nature, some individuals of the same age or lengths show different weights and the difference could be due to the physiological conditions and to the environmental factors (Seed, 1968;Winberg, 1971;Lee, 1986;Gasper et al., 2002).
The present results revealed that, the two populations of Brachidontes pharaonis at Adabia and Ain Sokhna being stable during this study, with shell lengths varied from 2.8 to 37.3 mm at Ain Sokhna and from 3.6 to 33.2mm at Adabia.However, the individuals of this species attained larger sizes at Ain Sokhna than those reported at Adabia.This may be attributed to occurrence of wide and extensive areas of rocky substrates and reef flats at Ain Sokhna which accommodate suitable sites for escaping from hazard conditions particularly effects of temperature, salinity, radiations and predation at the upper littoral zones, in addition to providing vast spaces between individuals at reef flats.On contrast, at Adabia, the individuals of this species are aggregated on rock boulders at the upper intertidal zones which are completely exposed during low tide during summer.
The obtained results also exhibited better environmental conditions reflected by increasing shell size compared with other world localities.At both sites, the maximum shell length reached above 33 mm at Adabia and 37 mm at Ain Sokhna, which agree well with that reported by Sara et al. (2008) for the same species, where larger individuals were varied from 30-36 mm during spring and summer, represents 5 and 6.3 % of the total populations at Sicily (Mediterranean Sea), and with Zenetos, et al., (2005), for those collected from the Indo-Pacific regions which increased into 40 mm but larger than those specimens of the same species collected from different localities including Suez Gulf, Suez Canal, Bardwil, and Marsa Alam by Radwan (2014) with shell sizes from 5 -30 mm.But in contrast to that recorded from Hong Kong by Morton (1988), and from India (Rajagopal et al., 2003), which reached about 20 mm and 22 mm in maximum length, respectively.Also, decreasing shell length was clearly recorded along the Red Sea and the eastern Mediterranean.Along the Red Sea coasts, Gilboa (1976) mentioned that the mean shell length decreased to about 18 mm maximum at the northern limits of the Gulf of Aqaba, as well as from Suez Gulf at Suez (Mohammed, 1992(Mohammed, , 1997)).The remarkable decreasing in shell length may be attributed to effect of unfavorable environmental conditions, or high predation.
In the biometric relationships studies, the constant "b", or what is also known as the coefficient of allometry or coefficient of regression expresses the rate of change of the relative animal body shape during the growth process (Laxmilatha, 2008).The length-weight relationship for the whole population of B. pharaonis showed regression coefficients b=2.376 at Ain Sokhna compared with 2.112 at Adabia.These coefficients are allometric, but showed slightly heavier individuals at Ain Sokhna.These values are clearly lower than an isometric regression (b=3) for the two populations but are very similar to that recoded by Wilbur andOwen (1964), andSara et al. (2008) for the same species from Mediterranean Sea.Sara et al. (2008) recoded that the allometric values are varied from the minimum (2.0) during winter to 2.6 and 2.7 during summer and autumn, respectively.They also were higher (2.4 ) in submerged during summer and autumn than those emerged (2.2) , but lower than that recorded by Radwan (2014) for those collected from Lake Timash (Suez Canal), Gulf of Suez, Marsa Alam (Red Sea), Bardawil Lagoon, and Port Said (Mediterranean Sea) which varied from 2. 38, 2.76,2.78, 2.97, and 2.71, respectively.On the other hand seasonal variations in slopes of the two populations at Adabia and Ain Sokhna stations were significant.The maximum regression coefficient (b) was 2.22 obtained during winter and increased to 2.59 during summer for the two stations respectively.However, it decreased to lowest value during autumn being 2.004 and 2.303 for the two populations respectively.From previous results it is evident that the population of Ain Sokhna is different from that at Adabia.This may be due to the immersed population of Adabia all year around, so they exposed to low temperatures which limited their physiological activity which are in agreement well with Bayne (1976) and Sara et al. (2000).For confirmation, Sara et al. (2000) observed a decrease in the physiological activity of B. pharaonis which corresponded to low winter temperatures.But the population of Ain Sokhna was partially exposed to air and slightly higher temperature due to nature of it′s habitat.
The relationships between shell length and shell breadth as well as shell length and shell width for B. pharaonis showed linear relations between these variables.This indicates to broader and wider shell for this species at both sites.However, the individuals of this species have wider and broader shells at Ain Sokhna which indicates to presence of vast and available habitats which agree with those reported on other bivalve species such as the green mussel (Thejasvi et al., 2014).The value of regression coefficient "b" is allometric and has 0.663 and 0.740 for breadth -length relationship at Adabia and Ain Sokhna , respectively, increased slightly to 0.746 and 0.853 for length-width relationships at the same sites, respectively.
The relative condition factor (kn) showed an isometric growth and good wellbeing of this species all over the year without any significant seasonal variations.The two populations of B. pharaonis showed the same pattern of Kn within its size class being 1.22 and 1.24 at first recorded size class (5mm) which decreased to less 1 during small size classes from 5mm to 15mm, then increased again at the following classes and averaged 1.01 ±0.13 and 1.02±0.22for Adabia and Ain Sokhna, respectively.This may be predicting that its maturation occurs in this size interval which consumes more energy.These results are in well agreement with Radwan (2014).
The size frequency distribution for B. pharaonis populations at Adabia and Ain Sokhna show that, this species was stable during the period of study.The population at both sites composes of at least five size classes.It was represented by early juveniles (from 2.5 to <5.0 mm), small side (from 5.0 to <12.50 mm), medium size (from 12.50 to <17.50 mm), larger individuals (between 17.50 and < 25.0 mm), and oldest individuals (>25.0 mm).
The monthly fluctuations were clearly observed and showed recruitment of juveniles in most months of the year with exception only February, April, June and September at Adabia, February, March, May, June, and October, in addition to disappearance of old and adult individuals in other months particularly September and November at Ain Sokhna.This events lead to increasing modes of size classes from three modes during these months to at least 4 or five modes in next month.
2) and taken according to Rusmore-Villaume (2008), and comprised mainly the following: a) Shell length (L): It taken as the maximum distance between the anterior and posterior margins of the shell.b) Shell breadth (B): It represents the maximum distance from hinge to ventral margin.c) Shell width (W): It represents by the maximum distance between outer edges of the two valves.Biometric relationships: Length-weight relationship:

Fig. 3 :
Fig. 3: Observed and calculated weight for the whole population of B. pharaonis from Adabia and Ain Sokhna.
The relation between shell length (L) and shell breadth for the two populations is considered, and represented in Fig. (4) and by the following equation: Log Breadth = 0.170 + 0.663 Log L (r = 0.997) Adabia Log Breadth = 0.082 + 0.740 Log L (r = 0.997) Ain Sokhna This relation is linear and shows an allometric negative regression coefficient b= 0. 663 and 0.740 with an intercept of Y-axis 'a'= 0. 0.170 and 0.082 for Adabia and Ain Sokhna respectively, with high correlation coefficient 'r'= 0.997 for both stations.

Fig. 4 :
Fig. 4: Length-breadth relationship for the whole population of B. pharaonis from Adabia and Ain Sokhna.

Fig. 5 :
Fig. 5: Length-width relationship for the whole population of B. pharaonis from Adabia and Ain Sokhna.E-Condition factor:Results of relative condition factor 'Kn' for the two populations of B. pharaonis from Adabia and Ain Sokhna are given in Tables (1&2) and represented in

Fig. 6 :
Fig. 6: Relative condition factor (Kn) for the whole population of B. pharaonis from Adabia and Ain Sokhna.

Fig. 7 :
Fig. 7: Size frequency distribution for the whole populations of B. pharaonis from Adabia and Ain Sokhna.

Table 1 :
coefficients, being slightly higher in summer at Adabia and reached the highest value during winter at Ain Sokhna.These relations are represented by the following equations: The length-weight relationship and condition factor for B. pharaonis from Adabia and Ain Sokhna.

Table 2 :
Seasonal variation of condition factor for B. pharaonis in Adabia and Ain Sokhna.