Length-Weight Relationship and Condition Factor of Schizothorax plagiostomus found in River Jhelum from Kashmir Valley

Length weight relationship is important in describing several biological aspects of fish species found under cultured and natural condition. Length weight relationship provides information about whether somatic growth was isometric or allometric. While condition factor provide information about the well being fish. In the present study the individuals of Schizothorax plagiostomus were collected from river Jhelum from different locations for the determination of length weight relationship and condition factor during the period of 2014–2016. Length weight relationship was computed using the equation W = aLb, which was further transformed into LogW = Loga + bLog L. Results showed that the value of b in length weight relationship of male S. plagiostomus ranged from 2.316–2.965, while in female fishes the value of b ranged from 2.01–3.66. The results clearly show allometric type of growth in male and isometric type of growth in females. The regression coefficient between males and female did not shows any significant difference, (p > 0.05) whereas significant difference (P < 0.01) could be noticed between males and between females (p < 0.01). However, condition factor (K) of S. plagiostomus fluctuates between 0.82–1.58 in male and between 0.870–1.31in female, indicating the robustness of the fish inhabiting in river Jhelum.


Introduction
Length-weight Relationship (LWR) studies of fishes is considered as an important tool for understanding of fish health status. Length-weight Relationship of fishes is also important in fisheries and fish biology as its allow the estimation of the average weight of the fish of a given length group by establishing a mathematical relation between them 6 . Length-weight Relationships have broadly been used for the conversion of growth-in-length equations to growth-in-weight for use in stock assessment models in order to estimate the stock assessment, relate the life histories of certain species and other changing aspects of fish population 2,32,48,31,51 Nile et al., 2013;. Like any other morphometric characters, the LWR can be used as a character for the differentiation of taxonomic units and the relationship changes with the various developmental events. In addition, the Length-weight Relationship indicates the degrees of stabilization of taxonomic characters in fish species and very useful in the management and exploitation of fish populations 39 . Growth of fish, usually indicated through increase in length and weight which is considered as the most appropriate characteristic to determine the population analysis at a particular time 21 . Now a days study of Length-weight Relationships (LWRs) of threatened fish species are the most important biological parameters to provide information about the growth and condition of fish species as well as entire fish community and are highly significant for management and conservation of natural populations 43,33 . Fulton's condition factor (k) is extensively used in fisheries and fish biology studies. This factor refers to the well-being of a certain species and its degree of fatness which depends on the weight of the fish 38,13 . Condition factor reflects the variations by interaction among feeding conditions, parasitic infection and physiological factors and recent physical and biological circumstances 24,5,49,28 . The study of condition assumes that heavier organisms of a given length are in better physical state, therefore, condition indices are used in fishery sciences as indicators of the length-weight-relationship of a population. Condition factor also helps to reflect the feeding conditions of the species. *Author for correspondence

Material and Method
Our study estimates LWRs of indigenous cold water species Schizothorax plagiostomus belonging to family Cyprinidae and order Cypriniformes. The samples of S. plagiostomus were collected from 2014-2016 from locations of river Jhelum of Kashmir valley with the help of fisherman. After collection, the samples were brought into wet laboratory Department of Zoology, University of Kashmir and the required measurement of length and weight were taken by using digital caliper and digital weighing balance, respectively. The total length of fish was measured to its nearest 0.01 cm and total body weight was measured to its near 0.01 g. The total length of fish was taken from the tip of snout to the extended tip of the caudal fin and the relationship was analyzed by measuring length and weight of fish specimen collected from study area. The statistical relationship between these parameters of fishes was analyzed with the help of algometric equation by Forese (2006).
W= aL b Where W = Total weight (g). L = length of fish (cm). a = Initial growth coefficient. B = Slope or the growth coefficient. The value of constants 'a' and 'b' was estimated by linear regression after logarithimic transformation of weight and length data by using formula: LogW = Loga + bLog L

Determination of Condition Factor
Condition factor is used for comparing the condition, fatness or well-being of fish, based on the assumption that heavier fish of a given length are in better condition. The coefficient of condition 'K' was calculated using 15 equation: K = W/L 3 × 100 Where, W = weight (g), L = length (cm) and 100 is a factor to bring the value of K near unity.

Results
The Length-weight Relationship of S. plagiostomus representing male, female and pooled (both sexes) are presented in Figure 1, Figure 2 and Figure 3, respectively. The equations thus derived in respect of Length-weight Relationship are as follows: Females: logW = 1.764 + 2.895 logL Males: logW = 1.690 + 2.736 logL Combined: LogW = 1.656 + 2.7145 logL In the present study increase in 'b' value in male fish showed deviation from cube law throughout the annual period as negative allometric growth was observed throughout the annual period i:e b < 3. The growth coefficient was minimum in March (2.315) and maximum was observed in July (2.965). The coefficient of determination 'r 2 ' fluctuates from 0.90 (January) to 0.990 in (June) as shown in Table 1. In case of females the value of 'b' also indicated deviation from cube law throughout annual period except, May, July and August were value of b > 3. However, this was to be attributed to the fact that during these months presence of high food availability and favorable environmental temperature, as compared to rest of months. This has led to almost ideal growth pattern of the fish. During annual period the female S. plagiostomus, shows coefficient of determination oscillates between (July) 0.901 to 0.975 in October ( Table 2). The month wise Fulton's condition factor, of male, S. plagiostomus ranged from 0.82 to1.583 and it was observed highest in the month of June followed in the month of July and December, respectively while lowest value was recorded in the month of September followed by January. Whereas in case of female, S. plagiostomus the condition factor values are in the range of 0.870-1.31 with highest condition factor was recorded in the month of June followed by July, October and lowest value was recorded in the month of April followed March and January, respectively ( Table 3). The variation of condition factor in both male and female Schizothorax plagiostomus is depicted in Figure 4.

Discussion
The Length Weight Relationship of fish has significant importance in studying the growth, gonadal development, general well being of fish population and for comparing life history of fishes 24,38,40 . Fisheries management and research often requires the use of biometric relationships in order to transform data collecting from the field into appropriate indices 37 . Studies on the Length Weight Relation of fishes constitutes an important tool in fishery biology and helps to understand whether variations from the expected weight for the known groups are the indicators of fatness, wellbeing and gonadal development in relation to the environment 4,24,50 .I n the present study, the 'b' value was found higher in females as compared to males. The highest 'b' value in females of S. plagiostomus implies that the females gain weight at a faster rate in relation to its length. The b value of males indicates negative allometric, which indicates that, the increase in length is not in accordance with increase in weight. Similar results were observed by Dar et al. (2012) in Schizopyge esocinus. Le Cren (1951) had reported that females are heavier than males of the same length probably because of difference in fatness and gonadal development. The slope value of regression line less than '3' has been reported in Tortor (Malhotra, 1982), Labeo dero (Malhotra and Chauhan, 1984), Labeo dyocheilus (Malhotra, 1985), Cyprinus communis and Ctenopharyngodon idella (Dhanze and Dhanze. 1997) and Rasbora daniconius (Sunil, 2000). According to Ruz Campos, 2010, the b value ranged from a minimum of 2.863 for reef fin spot (Paraclinus integripinnis) to 3.404 for the fluffy sculpin (Oligocottus snyderi). All the earlier reports are in compliance with the present study in which the b value was very close to isometric value of 3 and this indicates that S. plagiostomus in the present study showed an isometric growth. Also it is well known that the functional regression b value represents the body form and is directly related to the weight affected by ecological factors habitat, area, seasonal effects, degree stomach fullness, gonad maturity, sex, health, preservation techniques and differences in the observed length ranges of the captured specimens 29,17,18 (Ricker, 1973. Several workers reported positive allometric growth in freshwater fish; notable among them are 20,34,23,9,19,45,30,42,35 in Cirrhina mrigala, Catla catla, Labeo bata, Labeo rohita, Pristolepis fasciata, Pangasius pangsius, Pseudorasbora parva and Macrognathus aculeatus respectively. The greater value of 'b' mainly depends on shape and fatness of individuals of fish. Isometric growth was also reported by (Haniffa et al., 2006;Serajuddin et al., 2013;Kashyap et al., 2015) in Channa punctatus collected from lentic and lotic water bodies. According to to Copp et al. (2013), the isometric body growth of Barbatula barbatula changes to allometric type when it reaches a certain standard length in order to become an adult. This indicates that body growth type sometimes changes accordingly to their physiology needs. Allen, (1938) have reported that the cube law is applicable only for those species which maintain the form and specific gravity throughout their life, but the shape and the form of fish may change with time, so the Length-weight relationship of most of fish species may deviate the cube law. The value of 'b' reported by Bhat et al. (2010) for S. labiatus differs from the present study, which is possibly due to several factors such as habitat, number of specimens examined and length ranges and length types used. Qadri and Mir (1980) reported the value of 'b' as 2.4487 for S. plagiostomus from the peripheral water bodies of Dal Lake, where as 7 have reported the 'b' value of S. plagiostomus (2.928) for the same fish from Jammu water bodies. Our results are in conformity with the earlier reports of Bhagat and Sunder (1983); Qadri and Mir (1980); Bhat (2010). In general it has been observed that the 'b' values reported of snow trout species from this part of the world are within the range of 2.5 to 3.5 which are considered as normal 'b' value as reported by 14 . The b values observed in this study were significantly below 3 which mean that the S. plagiostomus in river Jhelum exhibited negative allometric growth pattern except few months in case of females. Finally, the Length-weight relationships and condition factor presented here will provide useful information for fisheries management and fish population dynamic studies. Therefore, the results of the present study can serve as baseline data for these species and for comparisons with future studies.

Acknowledgements
The author is grateful to the Head, Department of Zoology, University of Kashmir, Hazratbal, Srinagar, India for providing the laboratory facilities and gratefully acknowledge the finincal support from the Department of Biotechnology (DBT), Govt of India, New Delhi on Fish Nutrition and Diet development program. Thanks are also due to Mr. Mufti Buhran, University Chief Executive Engineer for helping the construction of new Feed Technology Laboratory (Wet-Lab.) in the Department of Zoology.