1 Introduction
The Pontic shad (Alosa immaculata Bennet 1835) is the largest species of the family Clupeidae in the Black Sea. It is an anadromous fish species which inhabits Black and Azov Sea, and for spawning enters the big rivers. In Danube River for spawning migrates the individuals inhabiting the western part of Black sea (Kolarov, 1958a, Navodaru, 2001).

The Pontic shad is an economically important fish. In the period 2003–2011, the annual catch of Pontic shad in the Black Sea and the Danube has dropped averagely with 3.5 times (Ministry of Agriculture and Food). Despite it is a commercial fish species A. immaculatа is vulnerable according to IUCN and Bulgarian Red Book (http://www.iucnredlist.org/apps/redlist/details/907/0; http://e-ecodb.bas.bg/rdb/bg/vol2/Alpontic.html). The species is also included in Annex 2 and 4 of the Bulgarian Biodiversity Act and Annex 2 of the Habitats Directive 92/43ЕЕС for 15 Protected areas from the national Natura 2000 ecological net.

The sustainable exploitation of this commercial fish species requires detailed study of the biological parameters of its populations. There is an insufficiency of contemporary data about the biology of Pontic shad in Danube River. Data about the species in Bulgarian water area were published by Drenski (1923; 1931; 1951; 1958), Kolarov (1958 а, б; 1960 а, б; 1962; 1964; 1965; 1978; 1979; 1980; 1982; 1983; 1991), Prodanov and Kolarov (1983), Stoianov et al. (1963), Marinov (1966), Karapetkova and Penchev (1973), Karapetkova (1974; 1975; 1976), Pehlivanov (1999), Sivkov (2000; 2003), Karapetkova et al. (2003), Trichkova et al. (2006), Shlyakhov and Daskalov (2009), Raikova-Petrova et al. (2013) and Rozdina et al. (2013).

The aim of this article is to study the relation between the basic biological parameters in A. immaculata from the Bulgarian sector of Danube River.

2 Material and methods
Altogether 293 specimens of A. immaculata were collected in April and May 2010 and 2011 during the spawning migration of the species in Danube River. Sampling points were located in the area between the towns Lom and Vidin, with geographical coordinates as follows: Sampling point 1: 43°54'17.96"N and 22°50'27.45"E; Sampling point 2: 43°47'40.46"N and 23°4'50.41"E; Sampling point 3: 43°50'45.61"N and 23°18'44.17"E. Gill nets were used which mesh size from 32 to 88 mm and a length of 50 m.

Each specimen was measured the standard length (L) to the nearest 1 mm, the total weight (W) and the gutted weight (w) to the nearest 1 g. The age was determined by the scales at magnification of 17.5x with Projector Dokumator, Lasergeret (Carl Zeiss, Jena).

Age-length relationships were determined by linear regression, by the equation: L=a+b.t, where L is the standard length and t is the age of the fish.

The absolute individual fecundity (F) was determined by the weighing method. The relation between the fecundity and the temp of growth was studied by linear regression. The linear temp of growth was represented from the coefficient b from the equation L=a+b.S, where L is the standard length in cm and S is the scale radius, in units. To express the weight temp of growth the coefficient b from the equation W=a+b.L (L - standard length in cm and W- total weight in g) was used.

Condition factor was studied by the coefficient of Fulton: K_f=(w/L³).100 and K_f=(W/L³).100 where w is the gutted weight in g, W is the total weight in g, and L is the standard length in cm.

3 Results
3.1 Length-age relationship
It is established high relation between the fish length and the age (Table 1). During the years the coefficient b was declining (Figure 1). On Figure 2 are represented the annual fluctuations in the average length of the catches of A. immaculata, from the Bulgarian sector of the Danube River. The range of the average length was between 20.1 cm and 26.3 cm. Between 1962 and 2010 the average length varies within 23.7 cm and 26.3 cm. In 2011, there is a significant decrease in the average fish length of the catches.
 

Figure 1 Changes in the coefficient b from the relationship between the fish length and age (L=a+b.t) during the years

Figure 2 Annual fluctuations in the average length of the catches of A. immaculata, from the Bulgarian sector of the Danube River

Table 1 Regression between the standard length and age in A. immaculata from Danube River

3.2 Relationship between the fecundity and the temp of growth
The equations representing the linear growth of two, three and four years old females are as follows: L=8.8037+0.2427S, r=0.8; L=3.0593+2.471S, r=0.77 and L=26.36+0.0148S, r=0.08.

The equation representing the weight growth for the two, three and four years old female fishes are as follows: W=19.881L–302.81, r=0.97; W=21.354L–334.96, r=0.97; W=13.629L–116.19, r=0.4.

Although no correlation was found between L-S and L-W for the 4 years old females a positive correlation was found between the fecundity and the coefficient b from the relations L-S and L-W (Figure 3 and Figure 4). The fish fecundity declines with increasing the linear and weight growth rate of the fishes. The relationship between the fecundity and the coefficient b is: F=45382–6416.6b, r =0.8.

Figure 3 Relation between the fecundity (F) and the coefficient b from the equation L=a+b.S

Figure 4 Relation between the fecundity (F) and the coefficient b from the equation W=a+b.L

3.3 Condition factor
The value of the coefficient of Fulton for the studied population, calculated using the gutted weight of the individuals is about 1. For males and females the values of K_f are respectively 1.05 and 1.07. Condition factor was studied also for each age group separately for males and females and combined. Its values for the population increase with the fish age. For males and females by age groups the values of the condition factor are above 1 or very close to 1 (Table 2).

Table 2 Condition factor and fecundity by age in A. immaculata from the Bulgarian sector of the Danube River

With increasing the age, the condition of females is decreasing and the fecundity is growing (Table 2). The correlation between the fecundity and K_f (calculated using the gutted weight) is represented with the following equation: F=234898–180246K_f, r=0.84.

4 Discussion
Decreasing the coefficient b from the relationship between the fish length and age with the years is a sign that the temp of growth of the fishes in long term is decreasing. This is also confirmed from the drop of the annual length of the catches in 2011. The main reason for the reduction of the temp of growth is the overexploitation of the stocks of the Pontic shad. The permanent removal of the biggest individuals from the fish stock of the commercial fish species leads to the size reduction of the individuals in the stock.  According to the data of the National Agency of Fisheries and Aquaculture (personal communication) the annual catches of the species in the Danube River from 2004 to 2011 have declined with 3.7 times.

Although the fecundity of A. immaculata is increasing with the fish length and weight (Raikova-Petrova et al., 2013) we have established that the fecundity declines with increasing the temp of growth. This inverse correlation is due to the faster temp of growth of the younger individuals, which however have a lower fecundity. According to Roff (1992), Saborido-Rey and Kjesbu (2005) the reproductive effort reduces the fish growth, which is the reason to decrease the fecundity.

The values of K_f greater than 1 or very close to 1 are indication for the "well-being" of the population (Fulton, 1902). In our previous study the value of K_f was calculated as 1.22 (calculations were made with the total weight of the individuals) (Rozdina et al., 2013). The received values for the condition factor for males (1.05) are the same or very close to the one for the populations studied in Marmara sea – 1.05 (Ergüden et al., 2007) and Turkish part of the Black sea – 1,02 (Samsun, 1995). The condition factor for the females and the both sexes in the Sea of Marmara (1.1 and 1.08 respectively) and the Turkish part of the Black sea (1.21 and 1.12 respectively) are higher than the received values by us. This difference is due to the spawning migration of the Pontic shad in Danube River. During the migration from the sea to the river the fish cease the feeding, spend a lot of energy to reach the spawning sites and lose weight. This inevitably reduces the fish condition. Kolarov (1965) reports significant changes in the condition of Pontic shad during its migrations in the river. The decrease in the condition of the fishes is due to the feeding termination.

The process of gonad development and eggs production requires a lot of energy. A lot of the deposited fats are utilized for egg production (Okafor et al., 2011, Oso et al., 2011). This is the reason for increasing the fish fecundity with decreasing the condition.

Authors' Contributions
DR participated in the design of the study, statistical analysis and drafted the manuscript. GR conceived of the study, participated in its design and helped with the statistical analysis and to draft the manuscript. PM and SV were involved in the laboratory samples and the primary data procession. All of the authors red and approved the final manuscript.

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