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## Models for length back-calculation in Caspian kutum, Rutilus kutum (Pisces: Cyprinidae) from the Caspian Sea | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Caspian Journal of Environmental Sciences | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

مقالات آماده انتشار، اصلاح شده برای چاپ ، انتشار آنلاین از تاریخ 10 اسفند 1396 اصل مقاله (792 K) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

نوع مقاله: Research Paper | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

نویسندگان | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

S Kouhestan Eskandari؛ MK Khalesi؛ M Khoramgah؛ S Asgari؛ N Mirzakhani | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

^{}University of Sari | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

چکیده | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

The Caspian kutum, Rutilus kutum (Kamensky 1901) specimens were sampled by purse seine in the northern Iranian coast of the Caspian Sea at four locations: Feridoonkenar Shahed, Mahmoudabad Khoram, Lariim Azadi fishing coop, and the Shiroud River in Ramsar city. “Back-calculation” is a retrospective method of estimating the characteristics of growth of fish in terms of length and rate of growth in the years preceding capture. Back-calculation of fish lengths at previous ages from scales or otoliths is a widely used approach to estimate both individual and population growth history. The back-calculated lengths of the Caspian kutum,Rutilus kutum (Kamensky 1901) were obtained using six different models, namely scale proportional hypothesis , body proportional hypothesis , Fraser Lee, nonlinear scale proportional hypothesis, nonlinear body proportional hypothesis, and the newest method, Morita Matsuishi model. The results showed that the preferred back-calculation models is Fraser Lee model for both males and females, while the nonlinear body proportional hypothesis is only for the females. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

کلیدواژهها | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Northern Iran, Back-calculation؛ Rutilus kutum | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

اصل مقاله | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

The Caspian kutum,
Back-calculation of lengths from scales is a widely used approach for estimating the growth history of individual fish and characterizing the growth of fish populations (Jearld 1983; Carlander 1987; Busacker “Back-calculation” is a retrospective method of estimating fish growth characteristics in terms of length and rate of growth in the years preceding capture. Back-calculation of fish lengths at previous ages from scales or otoliths is a widely used approach to estimate both individual and population growth history (Francis 1990). Identification of variations in growth seen in different populations provides tools for identifying environmental pressures or factors that challenge the populations of species under study. Back-calculation, in conjunction with other bio-environmental study tools, is a useful method for tracking environmental challenges encountered by fish populations. Back-calculation of fish lengths has widely been used to increase the number of observations in length-at-age data or to estimate lengths at ages not included in the dataset. This procedure is based on the assumption that the growth of fish is proportional to the growth of its bony structures. A number of procedures are available for the length back-calculation (Horppila & Nyberg 1999). As a result of several possibilities at each step, back-calculation methodology has been diverse with no consistency achieved even within the same species (Horppila & Nyberg 1999). Many back-calculation formulae have been proposed (Francis 1990) and several studies evaluated which formulae are more accurate (Smedstad & Holm 1996; Horppila & Nyberg, 1999). Traditionally, back-calculation models were based on a proposal that fish grows in length as a linear relationship with the growth of fish otolith or scales (Bagenal & Tesch 1978). The relationship between a chosen structure and body length of fish may be described with various linear or non-linear equations (Francis 1990; Secor & Dean 1992). In the past decade, introduction of two variables into this seemingly linear relationship has added a certain complexity to these equations. These two factors are “growth effect” and “age effect” (Morita & Matsuishi 2001). The growth effect refers to the finding that otolith or scales in slow-growing fish are larger than those of fast-growing fish with the same size (Reznick
The radii of scales were measured using a stereomicroscope monitor using Nikon’s Act-1 software. Each scale was magnified 24.6 times, the true size on the monitor. The scales were measured using the reference in the Atc-1 software, so that the length of the radii were determined in pixels and then converted into millimeters with a ratio of (228 pixels/1mm). In the process of age determination based on the scales, identification of the first ring was relatively difficult due to the presence of false rings. Therefore, in order to obtain a proper estimation of the first year ring on the scales, a number of (n = 30) two-month-old kutums (1.0 g) were selected from the Shahid Rajaee fish farm (Mazandaran, Iran) and the scales were analyzed for this purpose. Statistical analyses including regression analysis to achieve the formulas 12, 13, and 14, t-test, paired t-test, and One-Way ANOVA were employed, respectively, to compare mean scale radii between males and females, calculated lengths, and the measured and back-calculated lengths.
The majority of back-calculation models assume that fish growth and otolith (or scale) growth are proportional. Several linear and nonlinear back-calculation models have been proposed. The most common back-calculation models are based on the following regression formulas (Morita & Matsuishi 2001):
(1) O = a + bL (2) L = c + dO (3) O = uLv or lnO = lnu + vlnL (4) L = wOk or lnL = lnw + klnO
Where O is the radius of otolith or scale, L is fish body length, and a, b, c, d, u, v, w, and k are constants obtained from regression analyses. The most commonly used back-calculation models are as the following.
5) Lt = - ab-1+ (Lt + ab-1) Ot OT-1
Which assumes that deviation of the scale radius (or that of some other hard structures) of a fish from the average value for a given size of fish is relatively the same throughout the life of a fish (Whitney & Carlander 1956).
6) Lt = [(C + dOt) (C + doT)-1] LT
Which hypothesizes that deviation of the length of a fish from the average for fish with the same size of a scale is relatively similar throughout the life of a fish (Whitney & Carlander 1956).
7) Lt = C + (LT – C) (Ot OT-1)
The linear equation of Fraser and Lee (reviewed by Fraser 1916; Lee 1920; Bagenal & Tesch 1978) is popular and widely used but has been criticized because it follows no clear hypothesis on the body scale relationship (Whitney & Carlander 1956; Francis 1990).
8) Lt = (Ot OT-1)1/v LT
9) Lt = (Ot OT-1) k LT
In the above models, L is back-calculated fish body length at age t, L is fish body length at the time of capture T, O is otolith or scale length at annulus t, O is otolith or scale length at the time of capture T, a and b are constants as in eq. 1, c and d are constants as in eq. 2, v is a constant as in eq. 3, and k is a constant as in eq. 4. As the growth of scale is a conservative process with scales increasing continuously during starvation or negative somatic growth (Secor & Dean 1992; Holmgren 1996; Barber & Jenkins 2001), it is assumed that the scale number increases with increasing in both fish body length and its age (Morita & Matsuishi 2001):
10) O = α+βL+ γ t Where O is scale’s radius, L is fish body length, t is fish age, and α, β, and γ are constants obtained from multiple regression analyses. If it is assumed that the deviation of the radius of a fish scale from the average for both fish length and age is relatively similar throughout the life span of a fish (i.e., SPH), then:
11) Lt = - α β-1 + (LT + α β-1 + γ β-1 T) Ot OT-1 - γ β-1 t
Where L is the back-calculated fish body length at age t, L is the fish body length at the time of capture T, O is the scale radius at annulus (age) t, O is the scale radius at the time of capture T, and α, β, and γ are constants as in eq. 10 (Morita & Matsuishi 2001).The aim of this study was to employ the models above for the estimation of back-calculated total length based on scale radius in the Caspian kutum. The following formulas were used for the back-calculation of fish length (BCLT): Scale proportional hypothesis [SPH (5)], body proportional hypothesis [BPH (6)], Fraser Lee (7), nonlinear scale proportional hypothesis [Nonlinear SPH (8)], nonlinear body proportional hypothesis [Nonlinear BPH (9)], and Morita Matsuishi model (11). The length back-calculations from the first to the third years of life in the captured four-year-old fish have been abbreviated as: BCLT. 1 age 4, BCLT. 2 age 4, and BCLT. 3 age 4, BCLT. This fish year class was selected because there were far greater numbers of the fish caught in this year class than other age classes.
The ages of 581 fish were determined. Weight, total length, and scale radii characteristics are shown in Table 1. Irrespective of the gender, the correlation coefficient was significant for the relationship between the total length and scale radius (p≤ 0.01, r = 0.61). To relate the fork and standard lengths, the following formula was used: The relationships between the total length and age are as in formulas for males and 13 for females:
The mean scale radii at all stages of growth were statistically larger in the females than in the males (t-test, n = 579; p ≤ 0.05). By using Fraser-Lee (7), no significant differences were obtained in three-year-old and four-year-old as well as nonlinear BPH (9), in four-year-old females only (One-Way ANOVA; females: n = 112, males: n = 263; p ≤ 0.05) between the measured mean total length of the three-year-old fish and the back-calculated mean fish length in the third year of life among the captured four-year-old males and females. Back-calculations of the mean total length in the females at one year prior to capture using Fraser Lee and nonlinear BPH yielded different results ( paired t test; females: n = 112, males: n = 263; p ≤ 0.05). The length estimates from the first through the third years of life in the captured four-year-old males and females are shown in Figs. 2 and 3, respectively.
From the six models employed to achieve a model or models suitable for length back-calculation of Caspian kutum, only models 7 and 9 were found to be appropriate for the males and females, respectively. These two models, however, are applicable for the estimation of total length at the age of 3 for the 4-year-old fish, and not at the ages of 1 and 2. In addition, the averages of calculated total length obtained through models 7 and 9 showed that they were significantly different. Table 2 shows the mean total length of
between estimates from Fraser Lee (7) and BPH (6) models at all ages were not significant (Johal Previous studies demonstrated that in e roach, The use of Fraser-Lee (seven), biological intercept and Weisberg back-calculation models for the hybrid species It is well-known that the bony structures used must be taken into account in the interpretation of results obtained from various back-calculations models.
Nevertheless, the use of dorsal fin spines of From other point of view, growth of different fish species, in addition to an increase in fish length, is associated with elevated body height and diameter with variable ratios (fatness coefficient). Accordingly, fatness coefficient as a correction factor can also be added to formulas 1 - 4, likely leading to identical application of back-calculation models for a variety of fish species. Because fatness coefficient may also be different during a year for males and females, its inclusion as a correction factor (formulas 1 - 4) would result in the use of back-calculation models in males and females.
After thanking HE, the authors is also grateful to H. Rahmani for statistical analysis. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

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